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231.601 547.354 229.979 545.821 229.979 545.422 c
229.979 545.26 230.2 545.276 230.318 545.276 c
231.055 545.319 l
231.055 546.131 230.952 546.618 231.97 546.618 c
233.135 546.618 233.548 545.953 233.43 544.346 c
230.17 542.871 l
f
238.902 542.399 m
238.902 541.189 238.961 541.072 240.377 540.909 c
240.377 540.688 l
236.689 540.688 l
236.689 540.909 l
237.707 541.072 237.751 541.248 237.766 542.399 c
237.766 545.217 l
237.766 545.836 237.781 546.028 237.043 546.559 c
237.043 546.706 l
238.798 547.354 l
238.961 547.296 l
238.902 545.556 l
238.931 545.556 l
239.256 546.337 240.082 547.354 241.011 547.354 c
241.424 547.354 241.763 547.09 241.763 546.677 c
241.763 546.278 241.335 545.91 240.996 545.747 c
240.745 545.939 240.377 546.263 240.052 546.234 c
238.798 546.116 238.902 544.11 238.902 543.889 c
238.902 542.399 l
f
246.763 545.556 m
246.438 545.497 l
246.232 546.175 245.907 547.001 245.066 547.001 c
244.462 547.001 244.093 546.559 244.093 545.969 c
244.093 544.449 247.146 544.494 247.146 542.591 c
247.146 541.278 245.892 540.541 244.698 540.541 c
244.049 540.541 243.415 540.718 242.898 541.086 c
242.78 542.724 l
243.12 542.783 l
243.326 541.883 243.828 540.924 244.875 540.924 c
245.553 540.924 246.011 541.426 246.011 542.089 c
246.011 543.771 242.958 543.431 242.958 545.541 c
242.958 546.691 244.034 547.354 245.081 547.354 c
245.656 547.354 246.246 547.192 246.718 546.868 c
246.763 545.556 l
f
254.521 543.83 m
254.521 542.561 253.857 540.865 252.367 540.865 c
250.774 540.865 250.007 542.65 250.007 544.021 c
250.007 545.379 250.656 547.03 252.249 547.03 c
253.857 547.03 254.521 545.187 254.521 543.83 c
h
255.892 543.977 m
255.892 546.057 254.284 547.354 252.279 547.354 c
250.302 547.354 248.636 545.953 248.636 543.918 c
248.636 541.824 250.243 540.541 252.264 540.541 c
254.211 540.541 255.892 541.971 255.892 543.977 c
f
258.267 545.217 m
258.267 545.836 258.281 546.028 257.544 546.559 c
257.544 546.706 l
259.299 547.354 l
259.461 547.296 l
259.343 546.219 l
260.184 546.839 260.995 547.354 261.939 547.354 c
263.709 547.354 263.798 545.895 263.798 545.025 c
263.798 542.399 l
263.798 541.189 263.857 541.072 264.948 540.909 c
264.948 540.688 l
261.511 540.688 l
261.511 540.909 l
262.603 541.072 262.647 541.248 262.662 542.399 c
262.662 544.096 l
262.662 545.128 262.706 546.588 260.907 546.588 c
260.302 546.588 259.889 546.396 259.402 545.953 c
259.402 542.399 l
259.402 541.189 259.461 541.072 260.553 540.909 c
260.553 540.688 l
257.116 540.688 l
257.116 540.909 l
258.208 541.072 258.252 541.248 258.267 542.399 c
258.267 545.217 l
f
0.35 g
246.873 577.654 m
246.734 579.462 l
243.165 573.622 240.616 566.857 239.274 560.138 c
237.882 566.857 235.334 573.622 231.767 579.462 c
231.627 577.654 l
234.825 572.141 237.697 565.606 239.274 558.98 c
240.848 565.606 243.722 572.141 246.873 577.654 c
f
253.036 575.987 m
246.363 570.379 243.953 565.746 239.272 557.821 c
234.593 565.746 232.183 570.379 225.464 575.987 c
225.696 574.364 l
232.924 568.479 235.426 562.919 239.272 557.266 c
243.072 562.919 245.574 568.479 252.85 574.364 c
253.036 575.987 l
f
258.109 570.936 m
250.046 567.785 244.717 562.132 239.249 556.061 c
233.781 562.132 228.407 567.785 220.39 570.936 c
220.805 569.592 l
229.982 565.513 234.153 560.741 239.249 555.596 c
244.3 560.741 248.471 565.513 257.646 569.592 c
258.109 570.936 l
f
261.632 564.911 m
252.224 563.614 245.413 559.119 239.25 554.346 c
233.041 559.119 226.274 563.614 216.868 564.911 c
217.285 563.753 l
227.433 562.826 234.153 557.311 239.25 553.883 c
244.3 557.311 251.066 562.826 261.216 563.753 c
261.632 564.911 l
f
263.578 558.794 m
254.124 558.423 246.107 556.106 239.249 552.585 c
232.345 556.106 224.329 558.423 214.922 558.794 c
215.292 557.636 l
225.441 557.868 234.523 554.346 239.249 552.121 c
243.929 554.346 253.012 557.868 263.16 557.636 c
263.578 558.794 l
f
263.832 550.698 m
263.832 552.121 l
221.796 552.121 l
223.618 551.676 223.96 550.698 v
263.832 550.698 l
f
0.8 0.4 0 0 k
215.37 534.655 m
215.37 533.743 215.33 533.435 216.409 533.354 c
216.409 533.167 l
213.6 533.167 l
213.6 533.354 l
214.398 533.488 214.485 533.442 214.485 534.655 c
214.485 536.438 l
214.485 537.444 214.425 537.424 213.6 537.538 c
213.6 537.725 l
215.685 537.725 l
216.315 537.725 217.663 537.725 217.663 536.532 c
217.663 535.513 216.624 535.232 215.806 535.07 c
215.759 535.265 l
216.315 535.412 216.657 535.761 216.657 536.358 c
216.657 537.129 216.114 537.457 215.37 537.457 c
215.37 534.655 l
f
222 537.725 m
224.092 537.725 l
224.092 537.538 l
223.449 537.37 223.449 537.269 223.395 536.15 c
223.348 535.144 l
223.328 534.615 223.314 534.011 222.926 533.609 c
222.53 533.193 221.92 533.052 221.363 533.052 c
220.84 533.052 220.21 533.187 219.815 533.542 c
219.346 533.964 219.412 534.615 219.412 535.178 c
219.412 536.237 l
219.412 537.45 219.326 537.404 218.528 537.538 c
218.528 537.725 l
221.182 537.725 l
221.182 537.538 l
220.257 537.457 220.297 537.148 220.297 536.237 c
220.297 535.299 l
220.297 534.909 220.277 534.38 220.492 534.044 c
220.76 533.636 221.303 533.475 221.772 533.475 c
222.879 533.475 223.046 534.28 223.019 535.111 c
222.973 536.733 l
222.953 537.45 222.631 537.41 222 537.538 c
222 537.725 l
f
226.7 535.714 m
226.7 537.457 l
227.317 537.457 227.886 537.363 227.886 536.619 c
227.886 535.962 227.39 535.714 226.8 535.714 c
226.7 535.714 l
h
226.7 535.459 m
227.484 535.52 228.195 535.057 228.195 534.293 c
228.195 533.777 227.84 533.428 227.323 533.428 c
226.673 533.428 226.7 533.951 226.7 534.44 c
226.7 535.459 l
h
227.149 533.167 m
227.987 533.167 229.201 533.267 229.201 534.38 c
229.201 535.178 228.463 535.566 227.786 535.707 c
227.786 535.721 l
228.282 535.841 228.892 536.11 228.892 536.713 c
228.892 537.725 227.719 537.725 226.955 537.725 c
224.93 537.725 l
224.93 537.538 l
225.802 537.457 225.788 537.343 225.815 536.438 c
225.815 534.655 l
225.815 533.442 225.728 533.488 224.93 533.354 c
224.93 533.167 l
227.149 533.167 l
f
234.141 533.167 m
230.125 533.167 l
230.125 533.354 l
230.923 533.488 231.011 533.442 231.011 534.655 c
231.011 536.237 l
231.011 537.45 230.923 537.404 230.125 537.538 c
230.125 537.725 l
232.781 537.725 l
232.781 537.538 l
231.855 537.457 231.896 537.148 231.896 536.237 c
231.896 533.77 l
231.896 533.548 231.795 533.468 232.506 533.468 c
233.652 533.468 233.914 533.898 234.45 534.822 c
234.637 534.749 l
234.141 533.167 l
f
236.977 534.655 m
236.977 533.442 237.064 533.488 237.862 533.354 c
237.862 533.167 l
235.207 533.167 l
235.207 533.354 l
236.005 533.488 236.092 533.442 236.092 534.655 c
236.092 536.237 l
236.092 537.45 236.005 537.404 235.207 537.538 c
235.207 537.725 l
237.862 537.725 l
237.862 537.538 l
237.064 537.404 236.977 537.45 236.977 536.237 c
236.977 534.655 l
f
241.838 536.371 m
241.636 536.371 l
241.509 536.921 241.348 537.531 240.658 537.531 c
240.249 537.531 239.974 537.229 239.974 536.834 c
239.974 535.747 242.18 535.822 242.18 534.42 c
242.18 533.455 241.254 533.052 240.396 533.052 c
239.92 533.052 239.451 533.18 239.035 533.394 c
238.814 534.722 l
239.022 534.762 l
239.243 534.105 239.732 533.361 240.524 533.361 c
240.966 533.361 241.295 533.65 241.295 534.085 c
241.295 535.218 239.089 535.124 239.089 536.452 c
239.089 537.343 239.94 537.84 240.758 537.84 c
241.16 537.84 241.556 537.738 241.898 537.538 c
241.838 536.371 l
f
244.834 534.655 m
244.834 533.743 244.794 533.435 245.719 533.354 c
245.719 533.167 l
243.064 533.167 l
243.064 533.354 l
243.862 533.488 243.949 533.442 243.949 534.655 c
243.949 536.237 l
243.949 537.45 243.862 537.404 243.064 537.538 c
243.064 537.725 l
245.719 537.725 l
245.719 537.538 l
244.794 537.457 244.834 537.148 244.834 536.237 c
244.834 535.768 l
247.275 535.768 l
247.275 536.237 l
247.275 537.148 247.315 537.457 246.39 537.538 c
246.39 537.725 l
249.044 537.725 l
249.044 537.538 l
248.247 537.404 248.159 537.45 248.159 536.237 c
248.159 534.655 l
248.159 533.442 248.247 533.488 249.044 533.354 c
249.044 533.167 l
246.39 533.167 l
246.39 533.354 l
247.315 533.435 247.275 533.743 247.275 534.655 c
247.275 535.366 l
244.834 535.366 l
244.834 534.655 l
f
251.625 534.655 m
251.625 533.442 251.713 533.488 252.51 533.354 c
252.51 533.167 l
249.855 533.167 l
249.855 533.354 l
250.653 533.488 250.74 533.442 250.74 534.655 c
250.74 536.237 l
250.74 537.45 250.653 537.404 249.855 537.538 c
249.855 537.725 l
252.51 537.725 l
252.51 537.538 l
251.713 537.404 251.625 537.45 251.625 536.237 c
251.625 534.655 l
f
254.099 536.217 m
254.099 536.908 254.079 537.39 253.228 537.538 c
253.228 537.725 l
254.769 537.725 l
255.614 536.626 256.781 535.513 257.746 534.386 c
257.76 534.4 l
257.719 536.532 l
257.706 537.33 257.505 537.43 256.714 537.538 c
256.714 537.725 l
258.752 537.725 l
258.752 537.538 l
258.162 537.484 258.128 537.202 258.128 536.11 c
258.128 533.126 l
257.826 532.979 l
257.17 533.783 255.574 535.392 254.468 536.586 c
254.448 535.835 254.481 535.131 254.508 534.4 c
254.535 533.575 254.682 533.521 255.474 533.354 c
255.474 533.167 l
253.274 533.167 l
253.274 533.354 l
253.764 533.448 254.099 533.421 254.099 534.326 c
254.099 536.217 l
f
264.262 533.69 m
264.624 533.69 l
264.624 533.535 l
263.914 533.24 263.143 533.052 262.372 533.052 c
260.984 533.052 259.724 533.924 259.724 535.372 c
259.724 536.988 261.138 537.84 262.593 537.84 c
263.19 537.84 263.746 537.698 264.303 537.484 c
264.303 536.204 l
264.102 536.204 l
263.901 537.002 263.358 537.531 262.479 537.531 c
261.407 537.531 260.81 536.599 260.81 535.614 c
260.81 534.38 261.614 533.361 262.881 533.361 c
263.358 533.361 263.337 533.475 263.378 533.756 c
263.378 534.105 l
263.378 534.976 263.331 535.037 262.405 535.164 c
262.405 535.352 l
264.772 535.352 l
264.772 535.164 l
264.316 535.051 264.262 534.97 264.262 534.501 c
264.262 533.69 l
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 0.0278 Tw 8 0 0 8 153.7769 78.6124 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
55.99 134.65 368.51 -42.93 re
f*
Q Q 
q
55.99 134.65 368.51 -42.93 re
W* n
0 0.2 1 0 k
/GS6 gs
247.77 96.049 m
271.149 100.598 290.039 111.555 289.962 120.524 c
289.887 129.492 270.875 133.075 247.496 128.527 c
224.119 123.979 205.228 113.022 205.303 104.052 c
205.379 95.086 224.393 91.502 247.77 96.049 c
f
Q 
/CS4 cs 1  scn
0 0 0 0 K
3 w 4 M 0 j 0 J []0 d 
/GS7 gs
213.806 123.465 m
223.07 123.465 l
225.925 123.465 226.776 122.373 226.776 119.638 c
226.776 115.567 225.439 115.233 221.672 115.233 c
213.806 115.233 l
213.806 123.465 l
211.345 125.532 l
211.345 105.269 l
213.806 105.269 l
213.806 113.198 l
223.161 113.198 l
224.831 113.198 226.806 113.258 228.052 114.535 c
229.206 115.719 229.328 118.18 229.328 119.76 c
229.328 124.226 227.626 125.532 223.312 125.532 c
211.345 125.532 l
213.806 123.465 l
h
B
231.814 109.309 m
231.814 107.214 233.424 107.032 235.156 107.001 c
237.647 106.94 l
239.165 106.94 241.626 106.94 243.085 107.335 c
244.178 107.638 244.817 108.368 244.817 109.523 c
244.817 110.374 244.421 111.164 243.632 111.527 c
242.75 111.922 241.08 112.014 239.621 112.014 c
238.892 112.014 238.224 111.984 237.738 111.984 c
236.341 111.984 234.275 111.984 232.968 111.497 c
231.996 111.133 231.814 110.252 231.814 109.309 c
229.536 109.309 l
229.536 112.378 230.508 113.442 233.576 113.714 c
234.943 113.866 236.341 113.866 237.708 113.866 c
239.044 113.866 240.381 113.836 241.717 113.745 c
243.206 113.624 243.935 113.35 244.817 112.166 c
244.817 113.684 l
244.817 114.93 244.755 116.479 243.663 117.208 c
242.72 117.845 240.108 117.876 238.588 117.876 c
237.222 117.876 235.825 117.876 234.457 117.694 c
232.908 117.482 232.483 116.723 232.483 115.264 c
230.174 115.264 l
230.174 118.423 231.51 119.303 234.488 119.578 c
235.581 119.7 236.705 119.76 237.799 119.76 c
239.834 119.76 241.992 119.76 243.966 119.244 c
246.579 118.544 246.943 116.54 246.943 114.171 c
246.943 105.269 l
244.817 105.269 l
244.817 106.94 l
244.057 105.634 242.963 105.269 241.536 105.147 c
240.229 105.055 238.922 105.055 237.617 105.055 c
235.763 105.055 l
232.696 105.055 229.536 105.391 229.536 109.309 c
231.814 109.309 l
h
B
266.352 110.374 m
266.26 105.998 263.526 105.239 259.668 105.117 c
258.878 105.087 258.088 105.087 257.299 105.087 c
251.769 105.087 248.368 105.876 248.368 112.286 c
248.368 113.774 248.399 115.841 249.188 117.117 c
250.646 119.456 253.532 119.791 256.053 119.791 c
256.509 119.791 256.934 119.76 257.329 119.76 c
261.369 119.669 266.138 120.003 266.138 114.565 c
263.921 114.565 l
263.891 115.719 263.618 116.692 262.524 117.269 c
261.43 117.845 259.09 117.876 257.694 117.876 c
257.329 117.876 l
255.931 117.876 253.897 117.876 252.589 117.36 c
251.83 117.025 251.223 116.419 250.98 115.598 c
250.646 114.535 250.646 113.35 250.646 112.255 c
250.646 109.917 250.828 107.7 253.653 107.274 c
255.111 107.032 256.569 106.97 258.028 106.97 c
259.243 106.97 260.518 107.001 261.704 107.274 c
263.406 107.669 264.074 108.703 264.134 110.374 c
266.352 110.374 l
h
B
279.931 119.547 m
283.515 119.547 l
273.004 112.834 l
284.488 105.269 l
280.963 105.269 l
270.969 112.014 l
269.693 112.014 l
269.693 105.269 l
267.566 105.269 l
267.566 125.714 l
269.693 125.714 l
269.693 113.836 l
270.969 113.836 l
279.931 119.547 l
h
B
298.903 115.567 m
298.751 117.269 298.295 117.544 296.564 117.755 c
295.165 117.876 293.739 117.876 292.371 117.876 c
291.035 117.876 289.698 117.845 288.392 117.664 c
287.116 117.482 286.023 117.117 286.023 115.719 c
286.023 113.866 287.116 113.592 288.726 113.592 c
292.403 113.503 l
296.382 113.503 l
299.481 113.503 301.576 112.864 301.576 109.371 c
301.576 105.147 298.691 105.36 295.44 105.117 c
294.104 105.087 292.796 105.055 291.46 105.055 c
289.911 105.055 288.027 105.087 286.661 105.36 c
284.23 105.876 283.562 107.153 283.562 109.462 c
283.562 109.674 283.592 109.886 283.592 110.099 c
285.748 110.099 l
285.779 109.977 285.779 109.856 285.779 109.765 c
285.779 107.73 286.599 107.245 288.514 107.062 c
289.758 107.001 291.004 106.94 292.25 106.94 c
293.891 106.94 295.532 106.94 297.141 107.123 c
298.477 107.304 299.297 107.669 299.297 109.036 c
299.297 111.194 298.205 111.649 296.168 111.649 c
292.311 111.679 l
288.635 111.679 l
285.809 111.679 283.745 112.196 283.745 115.476 c
283.745 118.454 285.657 119.395 288.331 119.578 c
289.667 119.669 291.035 119.76 292.371 119.76 c
293.891 119.76 295.44 119.76 296.958 119.608 c
299.875 119.395 300.908 118.454 301.03 115.567 c
298.903 115.567 l
h
B
193.004 114.079 m
193.065 115.113 193.157 116.296 194.006 117.025 c
195.192 118.028 197.561 118.089 199.292 118.089 c
200.963 118.089 l
202.604 118.089 204.822 117.998 205.885 116.995 c
206.736 116.235 206.796 115.113 206.827 114.079 c
193.004 114.079 l
192.944 112.255 l
209.014 112.255 l
209.014 112.5 209.044 112.743 209.044 112.985 c
209.044 119.7 205.703 119.73 200.082 119.972 c
199.626 119.972 199.141 120.003 198.624 120.003 c
192.852 120.003 190.817 118.575 190.817 112.59 c
190.817 105.269 194.979 105.269 200.903 105.269 c
209.044 105.269 l
209.044 107.153 l
200.022 107.153 l
198.685 107.153 197.257 107.153 195.952 107.425 c
193.278 107.973 193.004 109.917 192.944 112.255 c
193.004 114.079 l
h
B
1 0.8 0 0.2 k
213.806 123.465 m
223.07 123.465 l
225.925 123.465 226.776 122.373 226.776 119.638 c
226.776 115.567 225.439 115.233 221.672 115.233 c
213.806 115.233 l
213.806 123.465 l
211.345 125.532 l
211.345 105.269 l
213.806 105.269 l
213.806 113.198 l
223.161 113.198 l
224.831 113.198 226.806 113.258 228.052 114.535 c
229.206 115.719 229.328 118.18 229.328 119.76 c
229.328 124.226 227.626 125.532 223.312 125.532 c
211.345 125.532 l
213.806 123.465 l
f
231.814 109.309 m
231.814 107.214 233.424 107.032 235.156 107.001 c
237.647 106.94 l
239.165 106.94 241.626 106.94 243.085 107.335 c
244.178 107.638 244.817 108.368 244.817 109.523 c
244.817 110.374 244.421 111.164 243.632 111.527 c
242.75 111.922 241.08 112.014 239.621 112.014 c
238.892 112.014 238.224 111.984 237.738 111.984 c
236.341 111.984 234.275 111.984 232.968 111.497 c
231.996 111.133 231.814 110.252 231.814 109.309 c
229.536 109.309 l
229.536 112.378 230.508 113.442 233.576 113.714 c
234.943 113.866 236.341 113.866 237.708 113.866 c
239.044 113.866 240.381 113.836 241.717 113.745 c
243.206 113.624 243.935 113.35 244.817 112.166 c
244.817 113.684 l
244.817 114.93 244.755 116.479 243.663 117.208 c
242.72 117.845 240.108 117.876 238.588 117.876 c
237.222 117.876 235.825 117.876 234.457 117.694 c
232.908 117.482 232.483 116.723 232.483 115.264 c
230.174 115.264 l
230.174 118.423 231.51 119.303 234.488 119.578 c
235.581 119.7 236.705 119.76 237.799 119.76 c
239.834 119.76 241.992 119.76 243.966 119.244 c
246.579 118.544 246.943 116.54 246.943 114.171 c
246.943 105.269 l
244.817 105.269 l
244.817 106.94 l
244.057 105.634 242.963 105.269 241.536 105.147 c
240.229 105.055 238.922 105.055 237.617 105.055 c
235.763 105.055 l
232.696 105.055 229.536 105.391 229.536 109.309 c
231.814 109.309 l
f
266.352 110.374 m
266.26 105.998 263.526 105.239 259.668 105.117 c
258.878 105.087 258.088 105.087 257.299 105.087 c
251.769 105.087 248.368 105.876 248.368 112.286 c
248.368 113.774 248.399 115.841 249.188 117.117 c
250.646 119.456 253.532 119.791 256.053 119.791 c
256.509 119.791 256.934 119.76 257.329 119.76 c
261.369 119.669 266.138 120.003 266.138 114.565 c
263.921 114.565 l
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233.386 430.778 l
233.386 430.09 l
231.376 430.09 l
231.376 428.079 l
230.688 428.079 l
230.688 430.09 l
228.677 430.09 l
228.677 430.778 l
f
0.188 0.137 0.063 0.008 k
176.135 424.49 m
177.445 424.49 178.516 425.561 178.516 426.871 c
178.516 434.014 l
178.516 435.324 177.445 436.395 176.135 436.395 c
163.039 436.395 l
161.73 436.395 160.658 435.324 160.658 434.014 c
160.658 426.871 l
160.658 425.561 161.73 424.49 163.039 424.49 c
176.135 424.49 l
h
B
176.5 425.665 m
176.993 425.665 177.392 426.065 177.392 426.558 c
B
162.692 435.378 m
162.199 435.378 161.8 434.978 161.8 434.485 c
S
0 g
169.297 430.31 m
167.815 432.259 l
168.838 432.259 l
169.852 430.778 l
170.849 432.259 l
171.81 432.259 l
170.381 430.31 l
172.074 428.079 l
171.051 428.079 l
169.817 429.834 l
168.582 428.079 l
167.603 428.079 l
169.297 430.31 l
f
0.188 0.137 0.063 0.008 k
298.592 424.49 m
299.902 424.49 300.973 425.561 300.973 426.871 c
300.973 434.014 l
300.973 435.324 299.902 436.395 298.592 436.395 c
285.496 436.395 l
284.186 436.395 283.115 435.324 283.115 434.014 c
283.115 426.871 l
283.115 425.561 284.186 424.49 285.496 424.49 c
298.592 424.49 l
h
B
298.956 425.665 m
299.449 425.665 299.849 426.065 299.849 426.558 c
S
285.149 435.378 m
284.656 435.378 284.256 434.978 284.256 434.485 c
B
0 g
289.811 431.424 4.709 -0.688 re
289.811 430.039 4.709 -0.688 re
f
0.188 0.137 0.063 0.008 k
196.545 424.49 m
197.854 424.49 198.926 425.561 198.926 426.871 c
198.926 434.014 l
198.926 435.324 197.854 436.396 196.545 436.396 c
183.449 436.396 l
182.139 436.396 181.068 435.324 181.068 434.014 c
181.068 426.871 l
181.068 425.561 182.139 424.49 183.449 424.49 c
196.545 424.49 l
h
B
196.909 425.665 m
197.402 425.665 197.802 426.065 197.802 426.558 c
S
183.102 435.378 m
182.609 435.378 182.209 434.978 182.209 434.485 c
B
0 g
190.371 433.954 m
189.613 432.764 189.243 431.794 189.243 430.374 c
189.243 429.086 189.622 427.843 190.371 426.811 c
189.842 426.459 l
189.031 427.561 188.555 428.928 188.555 430.374 c
188.555 431.723 189.004 433.134 189.842 434.289 c
190.371 433.954 l
f
0.188 0.137 0.063 0.008 k
278.183 424.49 m
279.492 424.49 280.564 425.561 280.564 426.871 c
280.564 434.014 l
280.564 435.324 279.492 436.396 278.183 436.396 c
265.087 436.396 l
263.777 436.396 262.706 435.324 262.706 434.014 c
262.706 426.871 l
262.706 425.561 263.777 424.49 265.087 424.49 c
278.183 424.49 l
h
B
278.547 425.665 m
279.04 425.665 279.44 426.065 279.44 426.558 c
B
264.74 435.378 m
264.246 435.378 263.847 434.978 263.847 434.485 c
S
0 g
271.388 426.741 m
272.146 427.932 272.516 428.902 272.516 430.321 c
272.516 431.609 272.137 432.852 271.388 433.884 c
271.917 434.237 l
272.728 433.134 273.204 431.767 273.204 430.321 c
273.204 428.972 272.754 427.561 271.917 426.406 c
271.388 426.741 l
f
Q Q Q 
q
134.65 404.54 207.14 -16.71 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.125 0.067 0.051 0.004 k
0 G
0.3 w 4 M 0 j 0 J []0 d 
/GS10 gs
278.103 389.65 m
279.412 389.65 280.484 390.721 280.484 392.031 c
280.484 399.174 l
280.484 400.484 279.412 401.555 278.103 401.555 c
265.007 401.555 l
263.697 401.555 262.626 400.484 262.626 399.174 c
262.626 392.031 l
262.626 390.721 263.697 389.65 265.007 389.65 c
278.103 389.65 l
h
B
278.467 390.825 m
278.96 390.825 279.36 391.225 279.36 391.718 c
264.66 400.538 m
264.166 400.538 263.767 400.138 263.767 399.645 c
S
0 g
270.666 393.973 m
270.869 393.374 271.151 393.083 271.813 393.083 c
272.465 393.083 273.021 393.541 273.021 394.212 c
273.021 395.252 272.06 395.376 271.266 395.376 c
271.266 396.116 l
272.554 396.116 272.862 396.478 272.862 397.095 c
272.862 397.756 272.412 398.109 271.813 398.109 c
271.354 398.109 270.957 397.818 270.772 397.386 c
269.908 397.677 l
270.234 398.471 270.966 398.85 271.795 398.85 c
272.818 398.85 273.708 398.303 273.708 397.148 c
273.708 396.496 273.277 395.922 272.641 395.737 c
272.641 395.719 l
273.426 395.587 273.867 394.917 273.867 394.15 c
273.867 392.951 272.888 392.342 271.786 392.342 c
270.834 392.342 270.058 392.756 269.776 393.7 c
270.666 393.973 l
f
0.125 0.067 0.051 0.004 k
216.874 389.65 m
218.184 389.65 219.255 390.721 219.255 392.031 c
219.255 399.174 l
219.255 400.484 218.184 401.555 216.874 401.555 c
203.779 401.555 l
202.469 401.555 201.397 400.484 201.397 399.174 c
201.397 392.031 l
201.397 390.721 202.469 389.65 203.779 389.65 c
216.874 389.65 l
h
B
217.238 390.825 m
217.731 390.825 218.131 391.225 218.131 391.718 c
203.431 400.538 m
202.938 400.538 202.538 400.138 202.538 399.645 c
S
0 g
212.39 397.979 m
209.859 397.979 l
209.832 396.418 l
210.009 396.498 210.467 396.55 210.67 396.55 c
211.843 396.55 212.61 395.704 212.61 394.487 c
212.61 393.244 211.631 392.424 210.415 392.424 c
209.568 392.424 208.827 392.873 208.536 393.685 c
209.391 393.975 l
209.612 393.402 209.991 393.164 210.547 393.164 c
211.217 393.164 211.764 393.649 211.764 394.443 c
211.764 395.351 211.146 395.81 210.256 395.81 c
209.938 395.81 209.391 395.695 208.968 395.484 c
209.039 398.773 l
212.39 398.773 l
212.39 397.979 l
f
0.125 0.067 0.051 0.004 k
176.055 389.65 m
177.365 389.65 178.436 390.721 178.436 392.031 c
178.436 399.174 l
178.436 400.484 177.365 401.555 176.055 401.555 c
162.959 401.555 l
161.65 401.555 160.578 400.484 160.578 399.174 c
160.578 392.031 l
160.578 390.721 161.65 389.65 162.959 389.65 c
176.055 389.65 l
h
B
176.42 390.825 m
176.913 390.825 177.312 391.225 177.312 391.718 c
162.612 400.538 m
162.119 400.538 161.72 400.138 161.72 399.645 c
S
0 g
167.431 394.419 m
167.431 395.195 167.942 395.759 168.621 395.944 c
168.621 395.971 l
168.154 396.094 167.643 396.561 167.643 397.426 c
167.643 398.369 168.489 398.978 169.468 398.978 c
170.447 398.978 171.293 398.369 171.293 397.426 c
171.293 396.561 170.782 396.094 170.314 395.971 c
170.314 395.944 l
170.994 395.759 171.505 395.195 171.505 394.419 c
171.505 393.237 170.605 392.523 169.468 392.523 c
168.33 392.523 167.431 393.237 167.431 394.419 c
h
169.468 396.315 m
170.121 396.315 170.447 396.791 170.447 397.302 c
170.447 397.875 170.05 398.29 169.468 398.29 c
168.93 398.29 168.489 397.884 168.489 397.302 c
168.489 396.817 168.842 396.315 169.468 396.315 c
h
170.658 394.419 m
170.658 395.177 170.129 395.565 169.468 395.574 c
168.78 395.565 168.277 395.08 168.277 394.419 c
168.277 393.687 168.824 393.264 169.468 393.264 c
170.173 393.264 170.658 393.74 170.658 394.419 c
f
0.188 0.137 0.063 0.008 k
196.465 389.65 m
197.774 389.65 198.846 390.721 198.846 392.031 c
198.846 399.174 l
198.846 400.484 197.774 401.555 196.465 401.555 c
183.369 401.555 l
182.059 401.555 180.988 400.484 180.988 399.174 c
180.988 392.031 l
180.988 390.721 182.059 389.65 183.369 389.65 c
196.465 389.65 l
h
B
196.829 390.825 m
197.322 390.825 197.722 391.225 197.722 391.718 c
183.022 400.538 m
182.529 400.538 182.129 400.138 182.129 399.645 c
S
0 g
187.737 396.447 4.409 -0.688 re
f
0.188 0.137 0.063 0.008 k
257.693 389.65 m
259.003 389.65 260.074 390.721 260.074 392.031 c
260.074 399.174 l
260.074 400.484 259.003 401.555 257.693 401.555 c
244.597 401.555 l
243.288 401.555 242.216 400.484 242.216 399.174 c
242.216 392.031 l
242.216 390.721 243.288 389.65 244.597 389.65 c
257.693 389.65 l
h
B
258.057 390.825 m
258.551 390.825 258.95 391.225 258.95 391.718 c
244.25 400.538 m
243.757 400.538 243.357 400.138 243.357 399.645 c
S
0 g
250.854 395.47 m
249.373 397.419 l
250.396 397.419 l
251.41 395.938 l
252.406 397.419 l
253.368 397.419 l
251.939 395.47 l
253.632 393.239 l
252.609 393.239 l
251.375 394.994 l
250.14 393.239 l
249.161 393.239 l
250.854 395.47 l
f
0.188 0.137 0.063 0.008 k
298.512 389.65 m
299.822 389.65 300.893 390.721 300.893 392.031 c
300.893 399.174 l
300.893 400.484 299.822 401.555 298.512 401.555 c
285.416 401.555 l
284.106 401.555 283.035 400.484 283.035 399.174 c
283.035 392.031 l
283.035 390.721 284.106 389.65 285.416 389.65 c
298.512 389.65 l
h
B
298.876 390.825 m
299.369 390.825 299.769 391.225 299.769 391.718 c
285.069 400.538 m
284.576 400.538 284.176 400.138 284.176 399.645 c
S
0 g
289.731 396.584 4.709 -0.688 re
289.731 395.199 4.709 -0.688 re
f
0.188 0.137 0.063 0.008 k
155.646 389.65 m
156.956 389.65 158.027 390.721 158.027 392.031 c
158.027 399.174 l
158.027 400.484 156.956 401.555 155.646 401.555 c
142.55 401.555 l
141.241 401.555 140.169 400.484 140.169 399.174 c
140.169 392.031 l
140.169 390.721 141.241 389.65 142.55 389.65 c
155.646 389.65 l
h
B
156.01 390.825 m
156.503 390.825 156.903 391.225 156.903 391.718 c
142.203 400.538 m
141.71 400.538 141.31 400.138 141.31 399.645 c
S
0 g
149.472 399.114 m
148.714 397.924 148.344 396.953 148.344 395.534 c
148.344 394.246 148.723 393.003 149.472 391.971 c
148.943 391.619 l
148.132 392.721 147.656 394.088 147.656 395.534 c
147.656 396.883 148.105 398.294 148.943 399.449 c
149.472 399.114 l
f
0.188 0.137 0.063 0.008 k
237.284 389.65 m
238.593 389.65 239.665 390.721 239.665 392.031 c
239.665 399.174 l
239.665 400.484 238.593 401.555 237.284 401.555 c
224.188 401.555 l
222.878 401.555 221.807 400.484 221.807 399.174 c
221.807 392.031 l
221.807 390.721 222.878 389.65 224.188 389.65 c
237.284 389.65 l
h
B
237.648 390.825 m
238.141 390.825 238.541 391.225 238.541 391.718 c
223.841 400.538 m
223.348 400.538 222.948 400.138 222.948 399.645 c
S
0 g
230.489 391.901 m
231.247 393.092 231.618 394.062 231.618 395.481 c
231.618 396.769 231.238 398.012 230.489 399.044 c
231.018 399.397 l
231.829 398.294 232.305 396.927 232.305 395.481 c
232.305 394.132 231.856 392.721 231.018 391.566 c
230.489 391.901 l
f
Q Q Q 
q
67.48 314.13 319.45 -39.02 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.125 0.067 0.051 0.004 k
0 G
0.3 w 4 M 0 j 0 J []0 d 
/GS11 gs
322.632 300.583 m
323.941 300.583 325.013 301.654 325.013 302.964 c
325.013 310.107 l
325.013 311.416 323.941 312.488 322.632 312.488 c
309.536 312.488 l
308.226 312.488 307.154 311.416 307.154 310.107 c
307.154 302.964 l
307.154 301.654 308.226 300.583 309.536 300.583 c
322.632 300.583 l
h
B
322.996 301.757 m
323.489 301.757 323.889 302.157 323.889 302.65 c
B
309.189 311.47 m
308.695 311.47 308.296 311.07 308.296 310.577 c
S
0 g
314.501 304.174 m
317.005 306.661 l
317.349 306.996 317.693 307.428 317.693 307.94 c
317.693 308.557 317.208 308.936 316.617 308.936 c
316.009 308.936 315.586 308.566 315.48 307.975 c
314.562 308.054 l
314.73 309.156 315.55 309.677 316.626 309.677 c
317.702 309.677 318.593 309.095 318.593 307.948 c
318.593 307.128 318.063 306.537 317.508 305.999 c
315.453 304.015 l
318.593 304.015 l
318.593 303.275 l
314.501 303.275 l
314.501 304.174 l
f
0.125 0.067 0.051 0.004 k
220.584 282.97 m
221.894 282.97 222.965 284.041 222.965 285.351 c
222.965 292.494 l
222.965 293.804 221.894 294.875 220.584 294.875 c
207.489 294.875 l
206.179 294.875 205.107 293.804 205.107 292.494 c
205.107 285.351 l
205.107 284.041 206.179 282.97 207.489 282.97 c
220.584 282.97 l
h
B
220.948 284.145 m
221.441 284.145 221.841 284.544 221.841 285.038 c
S
207.141 293.858 m
206.648 293.858 206.248 293.458 206.248 292.965 c
B
0 g
212.454 286.562 m
214.958 289.048 l
215.302 289.383 215.646 289.815 215.646 290.327 c
215.646 290.944 215.161 291.324 214.57 291.324 c
213.962 291.324 213.538 290.953 213.433 290.362 c
212.515 290.442 l
212.683 291.544 213.503 292.064 214.579 292.064 c
215.655 292.064 216.545 291.482 216.545 290.336 c
216.545 289.516 216.016 288.925 215.461 288.387 c
213.406 286.403 l
216.545 286.403 l
216.545 285.662 l
212.454 285.662 l
212.454 286.562 l
f
0.125 0.067 0.051 0.004 k
281.813 282.97 m
283.122 282.97 284.194 284.041 284.194 285.351 c
284.194 292.494 l
284.194 293.804 283.122 294.875 281.813 294.875 c
268.717 294.875 l
267.407 294.875 266.336 293.804 266.336 292.494 c
266.336 285.351 l
266.336 284.041 267.407 282.97 268.717 282.97 c
281.813 282.97 l
h
B
282.177 284.145 m
282.67 284.145 283.07 284.544 283.07 285.038 c
268.37 293.858 m
267.876 293.858 267.477 293.458 267.477 292.965 c
S
0 g
274.376 287.293 m
274.579 286.694 274.861 286.403 275.523 286.403 c
276.175 286.403 276.731 286.861 276.731 287.531 c
276.731 288.572 275.77 288.696 274.976 288.696 c
274.976 289.436 l
276.264 289.436 276.572 289.798 276.572 290.415 c
276.572 291.076 276.122 291.429 275.523 291.429 c
275.064 291.429 274.667 291.138 274.482 290.706 c
273.618 290.997 l
273.944 291.791 274.676 292.17 275.505 292.17 c
276.528 292.17 277.418 291.623 277.418 290.468 c
277.418 289.815 276.987 289.242 276.351 289.057 c
276.351 289.04 l
277.136 288.907 277.577 288.237 277.577 287.47 c
277.577 286.27 276.598 285.662 275.496 285.662 c
274.544 285.662 273.768 286.076 273.486 287.02 c
274.376 287.293 l
f
0.125 0.067 0.051 0.004 k
343.041 300.583 m
344.351 300.583 345.422 301.654 345.422 302.964 c
345.422 310.107 l
345.422 311.416 344.351 312.488 343.041 312.488 c
329.945 312.488 l
328.636 312.488 327.564 311.416 327.564 310.107 c
327.564 302.964 l
327.564 301.654 328.636 300.583 329.945 300.583 c
343.041 300.583 l
h
B
343.405 301.757 m
343.898 301.757 344.298 302.157 344.298 302.65 c
S
329.598 311.47 m
329.105 311.47 328.705 311.07 328.705 310.577 c
B
0 g
335.605 304.906 m
335.807 304.306 336.089 304.015 336.751 304.015 c
337.404 304.015 337.959 304.474 337.959 305.144 c
337.959 306.185 336.998 306.308 336.204 306.308 c
336.204 307.049 l
337.492 307.049 337.8 307.41 337.8 308.027 c
337.8 308.689 337.351 309.042 336.751 309.042 c
336.293 309.042 335.896 308.751 335.71 308.319 c
334.846 308.61 l
335.172 309.403 335.904 309.782 336.733 309.782 c
337.756 309.782 338.647 309.236 338.647 308.08 c
338.647 307.428 338.215 306.855 337.58 306.669 c
337.58 306.652 l
338.365 306.52 338.806 305.849 338.806 305.082 c
338.806 303.883 337.827 303.275 336.725 303.275 c
335.772 303.275 334.996 303.689 334.714 304.633 c
335.605 304.906 l
f
0.125 0.067 0.051 0.004 k
179.765 300.583 m
181.075 300.583 182.146 301.654 182.146 302.964 c
182.146 310.107 l
182.146 311.416 181.075 312.488 179.765 312.488 c
166.669 312.488 l
165.36 312.488 164.288 311.416 164.288 310.107 c
164.288 302.964 l
164.288 301.654 165.36 300.583 166.669 300.583 c
179.765 300.583 l
h
B
180.13 301.757 m
180.623 301.757 181.022 302.157 181.022 302.65 c
166.322 311.47 m
165.829 311.47 165.43 311.07 165.43 310.577 c
S
0 g
172.329 304.906 m
172.532 304.306 172.814 304.015 173.475 304.015 c
174.128 304.015 174.683 304.474 174.683 305.144 c
174.683 306.185 173.722 306.308 172.929 306.308 c
172.929 307.049 l
174.216 307.049 174.525 307.41 174.525 308.027 c
174.525 308.689 174.075 309.042 173.475 309.042 c
173.017 309.042 172.62 308.751 172.435 308.319 c
171.571 308.61 l
171.897 309.403 172.629 309.782 173.458 309.782 c
174.481 309.782 175.371 309.236 175.371 308.08 c
175.371 307.428 174.939 306.855 174.304 306.669 c
174.304 306.652 l
175.089 306.52 175.53 305.849 175.53 305.082 c
175.53 303.883 174.551 303.275 173.449 303.275 c
172.497 303.275 171.721 303.689 171.438 304.633 c
172.329 304.906 l
f
0.125 0.067 0.051 0.004 k
281.813 300.583 m
283.122 300.583 284.194 301.654 284.194 302.964 c
284.194 310.107 l
284.194 311.416 283.122 312.488 281.813 312.488 c
268.717 312.488 l
267.407 312.488 266.336 311.416 266.336 310.107 c
266.336 302.964 l
266.336 301.654 267.407 300.583 268.717 300.583 c
281.813 300.583 l
h
B
282.177 301.757 m
282.67 301.757 283.07 302.157 283.07 302.65 c
268.37 311.47 m
267.876 311.47 267.477 311.07 267.477 310.577 c
S
0 g
275.243 304.831 m
272.58 304.831 l
272.58 305.695 l
275.066 309.699 l
276.089 309.699 l
276.089 305.572 l
276.971 305.572 l
276.971 304.831 l
276.089 304.831 l
276.089 303.455 l
275.243 303.455 l
275.243 304.831 l
h
275.243 308.693 m
275.225 308.693 l
273.32 305.572 l
275.243 305.572 l
275.243 308.693 l
f
0.125 0.067 0.051 0.004 k
240.994 282.97 m
242.303 282.97 243.375 284.041 243.375 285.351 c
243.375 292.494 l
243.375 293.804 242.303 294.875 240.994 294.875 c
227.898 294.875 l
226.588 294.875 225.517 293.804 225.517 292.494 c
225.517 285.351 l
225.517 284.041 226.588 282.97 227.898 282.97 c
240.994 282.97 l
h
B
241.358 284.145 m
241.851 284.145 242.251 284.544 242.251 285.038 c
227.551 293.858 m
227.058 293.858 226.658 293.458 226.658 292.965 c
S
0 g
236.509 291.299 m
233.978 291.299 l
233.952 289.738 l
234.128 289.818 234.587 289.87 234.79 289.87 c
235.962 289.87 236.73 289.024 236.73 287.807 c
236.73 286.564 235.751 285.744 234.534 285.744 c
233.687 285.744 232.947 286.193 232.656 287.005 c
233.511 287.296 l
233.731 286.722 234.111 286.484 234.666 286.484 c
235.336 286.484 235.883 286.969 235.883 287.763 c
235.883 288.671 235.266 289.13 234.375 289.13 c
234.058 289.13 233.511 289.015 233.088 288.803 c
233.158 292.093 l
236.509 292.093 l
236.509 291.299 l
f
0.125 0.067 0.051 0.004 k
322.632 282.97 m
323.941 282.97 325.013 284.041 325.013 285.351 c
325.013 292.494 l
325.013 293.804 323.941 294.875 322.632 294.875 c
309.536 294.875 l
308.226 294.875 307.154 293.804 307.154 292.494 c
307.154 285.351 l
307.154 284.041 308.226 282.97 309.536 282.97 c
322.632 282.97 l
h
B
322.996 284.145 m
323.489 284.145 323.889 284.544 323.889 285.038 c
B
309.189 293.858 m
308.695 293.858 308.296 293.458 308.296 292.965 c
S
0 g
315.555 289.776 m
315.59 289.776 l
315.793 289.873 316.022 289.917 316.278 289.917 c
317.177 289.917 318.209 289.308 318.209 287.941 c
318.209 286.566 317.239 285.843 316.066 285.843 c
314.893 285.843 313.923 286.636 313.923 287.853 c
313.923 288.621 314.17 289.097 314.549 289.696 c
316.128 292.192 l
317.124 292.192 l
315.555 289.776 l
h
316.066 286.584 m
316.842 286.584 317.362 287.121 317.362 287.88 c
317.362 288.638 316.842 289.176 316.066 289.176 c
315.29 289.176 314.77 288.638 314.77 287.88 c
314.77 287.121 315.29 286.584 316.066 286.584 c
f
0.125 0.067 0.051 0.004 k
240.994 300.583 m
242.303 300.583 243.375 301.654 243.375 302.964 c
243.375 310.107 l
243.375 311.416 242.303 312.488 240.994 312.488 c
227.898 312.488 l
226.588 312.488 225.517 311.416 225.517 310.107 c
225.517 302.964 l
225.517 301.654 226.588 300.583 227.898 300.583 c
240.994 300.583 l
h
B
241.358 301.757 m
241.851 301.757 242.251 302.157 242.251 302.65 c
227.551 311.47 m
227.058 311.47 226.658 311.07 226.658 310.577 c
S
0 g
233.917 307.388 m
233.952 307.388 l
234.155 307.485 234.384 307.529 234.64 307.529 c
235.539 307.529 236.571 306.921 236.571 305.554 c
236.571 304.178 235.601 303.455 234.428 303.455 c
233.255 303.455 232.285 304.249 232.285 305.466 c
232.285 306.233 232.532 306.709 232.911 307.309 c
234.49 309.805 l
235.486 309.805 l
233.917 307.388 l
h
234.428 304.196 m
235.204 304.196 235.725 304.734 235.725 305.492 c
235.725 306.251 235.204 306.788 234.428 306.788 c
233.652 306.788 233.132 306.251 233.132 305.492 c
233.132 304.734 233.652 304.196 234.428 304.196 c
f
0.125 0.067 0.051 0.004 k
179.765 282.97 m
181.075 282.97 182.146 284.041 182.146 285.351 c
182.146 292.494 l
182.146 293.804 181.075 294.875 179.765 294.875 c
166.669 294.875 l
165.36 294.875 164.288 293.804 164.288 292.494 c
164.288 285.351 l
164.288 284.041 165.36 282.97 166.669 282.97 c
179.765 282.97 l
h
B
180.13 284.145 m
180.623 284.145 181.022 284.544 181.022 285.038 c
166.323 293.858 m
165.829 293.858 165.43 293.458 165.43 292.965 c
S
0 g
174.452 291.345 m
171.436 291.345 l
171.436 292.086 l
175.36 292.086 l
175.36 291.363 l
172.874 285.843 l
171.921 285.843 l
174.452 291.345 l
f
0.125 0.067 0.051 0.004 k
343.041 282.97 m
344.351 282.97 345.422 284.041 345.422 285.351 c
345.422 292.494 l
345.422 293.804 344.351 294.875 343.041 294.875 c
329.945 294.875 l
328.636 294.875 327.564 293.804 327.564 292.494 c
327.564 285.351 l
327.564 284.041 328.636 282.97 329.945 282.97 c
343.041 282.97 l
h
B
343.405 284.145 m
343.898 284.145 344.298 284.544 344.298 285.038 c
S
329.598 293.858 m
329.105 293.858 328.705 293.458 328.705 292.965 c
B
0 g
334.416 287.739 m
334.416 288.515 334.928 289.079 335.607 289.264 c
335.607 289.291 l
335.139 289.414 334.628 289.882 334.628 290.746 c
334.628 291.689 335.475 292.298 336.453 292.298 c
337.432 292.298 338.279 291.689 338.279 290.746 c
338.279 289.882 337.767 289.414 337.3 289.291 c
337.3 289.264 l
337.979 289.079 338.49 288.515 338.49 287.739 c
338.49 286.557 337.591 285.843 336.453 285.843 c
335.316 285.843 334.416 286.557 334.416 287.739 c
h
336.453 289.635 m
337.106 289.635 337.432 290.111 337.432 290.622 c
337.432 291.195 337.036 291.61 336.453 291.61 c
335.915 291.61 335.475 291.204 335.475 290.622 c
335.475 290.137 335.827 289.635 336.453 289.635 c
h
337.644 287.739 m
337.644 288.497 337.115 288.885 336.453 288.894 c
335.766 288.885 335.263 288.4 335.263 287.739 c
335.263 287.007 335.81 286.584 336.453 286.584 c
337.159 286.584 337.644 287.06 337.644 287.739 c
f
0.125 0.067 0.051 0.004 k
220.584 300.583 m
221.894 300.583 222.965 301.654 222.965 302.964 c
222.965 310.107 l
222.965 311.416 221.894 312.488 220.584 312.488 c
207.489 312.488 l
206.179 312.488 205.107 311.416 205.107 310.107 c
205.107 302.964 l
205.107 301.654 206.179 300.583 207.489 300.583 c
220.584 300.583 l
h
B
220.948 301.757 m
221.441 301.757 221.841 302.157 221.841 302.65 c
S
207.141 311.47 m
206.648 311.47 206.248 311.07 206.248 310.577 c
B
0 g
211.96 305.351 m
211.96 306.127 212.471 306.691 213.15 306.877 c
213.15 306.903 l
212.683 307.027 212.171 307.494 212.171 308.358 c
212.171 309.302 213.018 309.91 213.997 309.91 c
214.976 309.91 215.822 309.302 215.822 308.358 c
215.822 307.494 215.311 307.027 214.843 306.903 c
214.843 306.877 l
215.522 306.691 216.034 306.127 216.034 305.351 c
216.034 304.17 215.134 303.455 213.997 303.455 c
212.859 303.455 211.96 304.17 211.96 305.351 c
h
213.997 307.247 m
214.649 307.247 214.976 307.723 214.976 308.235 c
214.976 308.808 214.579 309.222 213.997 309.222 c
213.459 309.222 213.018 308.817 213.018 308.235 c
213.018 307.75 213.371 307.247 213.997 307.247 c
h
215.187 305.351 m
215.187 306.11 214.658 306.498 213.997 306.506 c
213.309 306.498 212.806 306.013 212.806 305.351 c
212.806 304.619 213.353 304.196 213.997 304.196 c
214.702 304.196 215.187 304.672 215.187 305.351 c
f
0.188 0.137 0.063 0.008 k
261.403 300.583 m
262.713 300.583 263.784 301.654 263.784 302.964 c
263.784 310.107 l
263.784 311.416 262.713 312.488 261.403 312.488 c
248.307 312.488 l
246.998 312.488 245.926 311.416 245.926 310.107 c
245.926 302.964 l
245.926 301.654 246.998 300.583 248.307 300.583 c
261.403 300.583 l
h
B
261.767 301.757 m
262.26 301.757 262.66 302.157 262.66 302.65 c
B
247.96 311.47 m
247.467 311.47 247.067 311.07 247.067 310.577 c
S
0 g
252.675 307.38 4.409 -0.688 re
f
0.188 0.137 0.063 0.008 k
383.86 300.583 m
385.17 300.583 386.241 301.654 386.241 302.964 c
386.241 310.107 l
386.241 311.416 385.17 312.488 383.86 312.488 c
370.764 312.488 l
369.454 312.488 368.383 311.416 368.383 310.107 c
368.383 302.964 l
368.383 301.654 369.454 300.583 370.764 300.583 c
383.86 300.583 l
h
B
384.224 301.757 m
384.717 301.757 385.117 302.157 385.117 302.65 c
S
370.417 311.47 m
369.924 311.47 369.524 311.07 369.524 310.577 c
B
0 g
375.215 306.815 4.709 -0.688 re
377.57 308.535 m
377.887 308.535 378.152 308.27 378.152 307.953 c
378.152 307.635 377.887 307.371 377.57 307.371 c
377.253 307.371 376.988 307.635 376.988 307.953 c
376.988 308.27 377.253 308.535 377.57 308.535 c
h
377.57 305.572 m
377.887 305.572 378.152 305.307 378.152 304.99 c
378.152 304.672 377.887 304.408 377.57 304.408 c
377.253 304.408 376.988 304.672 376.988 304.99 c
376.988 305.307 377.253 305.572 377.57 305.572 c
f
0.188 0.137 0.063 0.008 k
261.403 282.97 m
262.713 282.97 263.784 284.041 263.784 285.351 c
263.784 292.494 l
263.784 293.804 262.713 294.875 261.403 294.875 c
248.307 294.875 l
246.998 294.875 245.926 293.804 245.926 292.494 c
245.926 285.351 l
245.926 284.041 246.998 282.97 248.307 282.97 c
261.403 282.97 l
h
B
261.767 284.145 m
262.26 284.145 262.66 284.544 262.66 285.038 c
B
247.96 293.858 m
247.467 293.858 247.067 293.458 247.067 292.965 c
S
0 g
254.564 288.79 m
253.083 290.739 l
254.106 290.739 l
255.12 289.258 l
256.116 290.739 l
257.078 290.739 l
255.649 288.79 l
257.342 286.559 l
256.319 286.559 l
255.085 288.314 l
253.85 286.559 l
252.871 286.559 l
254.564 288.79 l
f
0.188 0.137 0.063 0.008 k
383.86 282.97 m
385.17 282.97 386.241 284.041 386.241 285.351 c
386.241 292.494 l
386.241 293.804 385.17 294.875 383.86 294.875 c
370.764 294.875 l
369.454 294.875 368.383 293.804 368.383 292.494 c
368.383 285.351 l
368.383 284.041 369.454 282.97 370.764 282.97 c
383.86 282.97 l
h
B
384.224 284.145 m
384.717 284.145 385.117 284.544 385.117 285.038 c
S
370.417 293.858 m
369.924 293.858 369.524 293.458 369.524 292.965 c
B
0 g
375.079 289.904 4.709 -0.688 re
375.079 288.519 4.709 -0.688 re
f
0.188 0.137 0.063 0.008 k
200.175 282.97 m
201.484 282.97 202.556 284.041 202.556 285.351 c
202.556 292.495 l
202.556 293.804 201.484 294.875 200.175 294.875 c
187.079 294.875 l
185.769 294.875 184.698 293.804 184.698 292.495 c
184.698 285.351 l
184.698 284.041 185.769 282.97 187.079 282.97 c
200.175 282.97 l
h
B
200.539 284.145 m
201.032 284.145 201.432 284.544 201.432 285.038 c
B
186.732 293.858 m
186.239 293.858 185.839 293.458 185.839 292.965 c
S
0 g
193.347 289.577 m
193.664 289.577 193.929 289.313 193.929 288.996 c
193.929 288.678 193.664 288.413 193.347 288.413 c
193.029 288.413 192.765 288.678 192.765 288.996 c
192.765 289.313 193.029 289.577 193.347 289.577 c
f
0.188 0.137 0.063 0.008 k
200.175 300.583 m
201.484 300.583 202.556 301.654 202.556 302.964 c
202.556 310.107 l
202.556 311.416 201.484 312.488 200.175 312.488 c
187.079 312.488 l
185.769 312.488 184.698 311.416 184.698 310.107 c
184.698 302.964 l
184.698 301.654 185.769 300.583 187.079 300.583 c
200.175 300.583 l
h
B
200.539 301.757 m
201.032 301.757 201.432 302.157 201.432 302.65 c
B
186.732 311.47 m
186.239 311.47 185.839 311.07 185.839 310.577 c
S
0 g
193.347 307.19 m
193.664 307.19 193.929 306.926 193.929 306.608 c
193.929 306.291 193.664 306.026 193.347 306.026 c
193.029 306.026 192.765 306.291 192.765 306.608 c
192.765 306.926 193.029 307.19 193.347 307.19 c
f
0.188 0.137 0.063 0.008 k
302.222 300.583 m
303.532 300.583 304.603 301.654 304.603 302.964 c
304.603 310.107 l
304.603 311.416 303.532 312.488 302.222 312.488 c
289.126 312.488 l
287.816 312.488 286.745 311.416 286.745 310.107 c
286.745 302.964 l
286.745 301.654 287.816 300.583 289.126 300.583 c
302.222 300.583 l
h
B
302.586 301.757 m
303.079 301.757 303.479 302.157 303.479 302.65 c
B
288.779 311.47 m
288.286 311.47 287.886 311.07 287.886 310.577 c
S
0 g
295.394 307.19 m
295.712 307.19 295.976 306.926 295.976 306.608 c
295.976 306.291 295.712 306.026 295.394 306.026 c
295.077 306.026 294.812 306.291 294.812 306.608 c
294.812 306.926 295.077 307.19 295.394 307.19 c
f
0.188 0.137 0.063 0.008 k
302.222 282.97 m
303.532 282.97 304.603 284.041 304.603 285.351 c
304.603 292.495 l
304.603 293.804 303.532 294.875 302.222 294.875 c
289.126 294.875 l
287.816 294.875 286.745 293.804 286.745 292.495 c
286.745 285.351 l
286.745 284.041 287.816 282.97 289.126 282.97 c
302.222 282.97 l
h
B
302.586 284.145 m
303.079 284.145 303.479 284.544 303.479 285.038 c
B
288.779 293.858 m
288.286 293.858 287.886 293.458 287.886 292.965 c
S
0 g
295.394 289.577 m
295.712 289.577 295.976 289.313 295.976 288.996 c
295.976 288.678 295.712 288.413 295.394 288.413 c
295.077 288.413 294.812 288.678 294.812 288.996 c
294.812 289.313 295.077 289.577 295.394 289.577 c
f
0.188 0.137 0.063 0.008 k
159.356 300.583 m
160.666 300.583 161.737 301.654 161.737 302.964 c
161.737 310.107 l
161.737 311.416 160.666 312.488 159.356 312.488 c
146.26 312.488 l
144.951 312.488 143.879 311.416 143.879 310.107 c
143.879 302.964 l
143.879 301.654 144.951 300.583 146.26 300.583 c
159.356 300.583 l
h
B
159.72 301.757 m
160.213 301.757 160.613 302.157 160.613 302.65 c
S
145.913 311.47 m
145.42 311.47 145.02 311.07 145.02 310.577 c
B
0 g
153.182 310.047 m
152.424 308.856 152.054 307.886 152.054 306.466 c
152.054 305.179 152.433 303.935 153.182 302.904 c
152.653 302.551 l
151.842 303.653 151.366 305.02 151.366 306.466 c
151.366 307.815 151.815 309.226 152.653 310.382 c
153.182 310.047 l
f
0.188 0.137 0.063 0.008 k
159.356 282.97 m
160.666 282.97 161.737 284.041 161.737 285.351 c
161.737 292.495 l
161.737 293.804 160.666 294.875 159.356 294.875 c
146.26 294.875 l
144.951 294.875 143.879 293.804 143.879 292.495 c
143.879 285.351 l
143.879 284.041 144.951 282.97 146.26 282.97 c
159.356 282.97 l
h
B
159.72 284.145 m
160.213 284.145 160.613 284.544 160.613 285.038 c
S
145.913 293.858 m
145.42 293.858 145.02 293.458 145.02 292.965 c
B
0 g
153.182 292.434 m
152.424 291.244 152.054 290.274 152.054 288.854 c
152.054 287.566 152.433 286.323 153.182 285.291 c
152.653 284.939 l
151.842 286.041 151.366 287.407 151.366 288.854 c
151.366 290.203 151.815 291.614 152.653 292.769 c
153.182 292.434 l
f
0.188 0.137 0.063 0.008 k
363.45 300.583 m
364.76 300.583 365.832 301.654 365.832 302.964 c
365.832 310.107 l
365.832 311.416 364.76 312.488 363.45 312.488 c
350.354 312.488 l
349.045 312.488 347.974 311.416 347.974 310.107 c
347.974 302.964 l
347.974 301.654 349.045 300.583 350.354 300.583 c
363.45 300.583 l
h
B
363.815 301.757 m
364.308 301.757 364.707 302.157 364.707 302.65 c
B
350.008 311.47 m
349.514 311.47 349.115 311.07 349.115 310.577 c
S
0 g
356.656 302.834 m
357.414 304.024 357.784 304.994 357.784 306.414 c
357.784 307.701 357.405 308.945 356.656 309.976 c
357.185 310.329 l
357.996 309.227 358.472 307.86 358.472 306.414 c
358.472 305.065 358.022 303.654 357.185 302.499 c
356.656 302.834 l
f
0.188 0.137 0.063 0.008 k
363.45 282.97 m
364.76 282.97 365.832 284.041 365.832 285.351 c
365.832 292.495 l
365.832 293.804 364.76 294.875 363.45 294.875 c
350.354 294.875 l
349.045 294.875 347.974 293.804 347.974 292.495 c
347.974 285.351 l
347.974 284.041 349.045 282.97 350.354 282.97 c
363.45 282.97 l
h
B
363.815 284.145 m
364.308 284.145 364.707 284.544 364.707 285.038 c
B
350.008 293.858 m
349.514 293.858 349.115 293.458 349.115 292.965 c
S
0 g
356.656 285.221 m
357.414 286.412 357.784 287.381 357.784 288.801 c
357.784 290.089 357.405 291.332 356.656 292.364 c
357.185 292.717 l
357.996 291.614 358.472 290.247 358.472 288.801 c
358.472 287.452 358.022 286.041 357.185 284.886 c
356.656 285.221 l
f
Q Q Q 
q
66.68 211.13 338.67 -72.89 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.3 w 4 M 0 j 0 J []0 d 
/GS12 gs
319.219 190.246 m
320.528 190.246 321.6 191.317 321.6 192.627 c
321.6 199.77 l
321.6 201.08 320.528 202.151 319.219 202.151 c
306.123 202.151 l
304.813 202.151 303.742 201.08 303.742 199.77 c
303.742 192.627 l
303.742 191.317 304.813 190.246 306.123 190.246 c
319.219 190.246 l
h
B
290.31 160.89 m
291.62 160.89 292.692 161.962 292.692 163.271 c
292.692 170.415 l
292.692 171.724 291.62 172.796 290.31 172.796 c
277.214 172.796 l
275.905 172.796 274.834 171.724 274.834 170.415 c
274.834 163.271 l
274.834 161.962 275.905 160.89 277.214 160.89 c
290.31 160.89 l
h
B
290.675 162.065 m
291.168 162.065 291.567 162.465 291.567 162.958 c
S
276.868 171.778 m
276.374 171.778 275.975 171.378 275.975 170.885 c
B
0 g
280.298 170.084 m
281.559 170.084 l
283.543 165.357 l
283.578 165.357 l
285.545 170.084 l
286.806 170.084 l
286.806 163.84 l
285.959 163.84 l
285.959 168.972 l
285.942 168.972 l
283.834 163.84 l
283.27 163.84 l
281.162 168.972 l
281.144 168.972 l
281.144 163.84 l
280.298 163.84 l
280.298 170.084 l
f
0.188 0.137 0.063 0.008 k
310.72 143.277 m
312.03 143.277 313.101 144.349 313.101 145.659 c
313.101 152.802 l
313.101 154.111 312.03 155.183 310.72 155.183 c
297.624 155.183 l
296.314 155.183 295.243 154.111 295.243 152.802 c
295.243 145.659 l
295.243 144.349 296.314 143.277 297.624 143.277 c
310.72 143.277 l
h
B
311.084 144.453 m
311.577 144.453 311.977 144.852 311.977 145.345 c
297.277 154.165 m
296.784 154.165 296.384 153.765 296.384 153.272 c
S
0 g
298.268 152.394 m
299.529 152.394 l
301.513 147.667 l
301.548 147.667 l
303.515 152.394 l
304.776 152.394 l
304.776 146.15 l
303.929 146.15 l
303.929 151.283 l
303.911 151.283 l
301.804 146.15 l
301.24 146.15 l
299.132 151.283 l
299.114 151.283 l
299.114 146.15 l
298.268 146.15 l
298.268 152.394 l
f
306.318 152.394 m
308.514 152.394 l
310.11 152.394 310.516 151.433 310.516 150.648 c
310.516 149.854 309.925 149.105 308.982 148.999 c
310.754 146.15 l
309.696 146.15 l
308.109 148.902 l
307.165 148.902 l
307.165 146.15 l
306.318 146.15 l
306.318 152.394 l
h
307.165 149.642 m
308.276 149.642 l
308.946 149.642 309.616 149.801 309.616 150.648 c
309.616 151.494 308.946 151.653 308.276 151.653 c
307.165 151.653 l
307.165 149.642 l
f
307.475 198.767 m
308.736 198.767 l
310.72 194.04 l
310.755 194.04 l
312.722 198.767 l
313.983 198.767 l
313.983 192.523 l
313.136 192.523 l
313.136 197.655 l
313.119 197.655 l
311.011 192.523 l
310.446 192.523 l
308.339 197.655 l
308.321 197.655 l
308.321 192.523 l
307.475 192.523 l
307.475 198.767 l
f
319.583 191.421 m
320.076 191.421 320.476 191.82 320.476 192.314 c
305.776 201.134 m
305.283 201.134 304.883 200.734 304.883 200.241 c
S
315.015 199.541 0.423 -3.122 re
f
316.24 199.541 m
316.796 199.541 l
318.515 196.975 l
318.524 196.975 l
318.524 199.541 l
318.948 199.541 l
318.948 196.419 l
318.41 196.419 l
316.672 198.985 l
316.664 198.985 l
316.664 196.419 l
316.24 196.419 l
316.24 199.541 l
f
0.125 0.067 0.051 0.004 k
229.082 143.277 m
230.392 143.277 231.463 144.349 231.463 145.659 c
231.463 152.802 l
231.463 154.111 230.392 155.183 229.082 155.183 c
215.986 155.183 l
214.676 155.183 213.605 154.111 213.605 152.802 c
213.605 145.659 l
213.605 144.349 214.676 143.277 215.986 143.277 c
229.082 143.277 l
h
B
229.446 144.452 m
229.939 144.452 230.339 144.852 230.339 145.345 c
B
215.639 154.165 m
215.146 154.165 214.746 153.765 214.746 153.272 c
S
0 g
220.951 146.869 m
223.456 149.356 l
223.8 149.691 224.144 150.123 224.144 150.634 c
224.144 151.252 223.659 151.631 223.068 151.631 c
222.459 151.631 222.036 151.261 221.93 150.67 c
221.013 150.749 l
221.181 151.851 222.001 152.372 223.076 152.372 c
224.153 152.372 225.043 151.79 225.043 150.643 c
225.043 149.823 224.514 149.232 223.959 148.694 c
221.904 146.71 l
225.043 146.71 l
225.043 145.97 l
220.951 145.97 l
220.951 146.869 l
f
0.125 0.067 0.051 0.004 k
127.035 160.89 m
128.344 160.89 129.416 161.962 129.416 163.271 c
129.416 170.414 l
129.416 171.724 128.344 172.796 127.035 172.796 c
113.939 172.796 l
112.629 172.796 111.558 171.724 111.558 170.414 c
111.558 163.271 l
111.558 161.962 112.629 160.89 113.939 160.89 c
127.035 160.89 l
h
B
127.399 162.065 m
127.892 162.065 128.292 162.465 128.292 162.958 c
B
113.592 171.778 m
113.099 171.778 112.699 171.378 112.699 170.885 c
S
0 g
118.904 164.482 m
121.409 166.968 l
121.753 167.303 122.096 167.735 122.096 168.247 c
122.096 168.864 121.611 169.244 121.021 169.244 c
120.412 169.244 119.989 168.873 119.883 168.282 c
118.966 168.362 l
119.134 169.464 119.954 169.984 121.029 169.984 c
122.105 169.984 122.996 169.402 122.996 168.256 c
122.996 167.436 122.467 166.845 121.911 166.307 c
119.857 164.323 l
122.996 164.323 l
122.996 163.582 l
118.904 163.582 l
118.904 164.482 l
f
0.125 0.067 0.051 0.004 k
188.263 160.89 m
189.573 160.89 190.644 161.962 190.644 163.271 c
190.644 170.414 l
190.644 171.724 189.573 172.796 188.263 172.796 c
175.167 172.796 l
173.858 172.796 172.786 171.724 172.786 170.414 c
172.786 163.271 l
172.786 161.962 173.858 160.89 175.167 160.89 c
188.263 160.89 l
h
B
188.627 162.065 m
189.121 162.065 189.52 162.465 189.52 162.958 c
B
174.82 171.778 m
174.327 171.778 173.927 171.378 173.927 170.885 c
S
0 g
180.827 165.213 m
181.03 164.614 181.312 164.323 181.973 164.323 c
182.626 164.323 183.181 164.781 183.181 165.452 c
183.181 166.492 182.22 166.616 181.427 166.616 c
181.427 167.356 l
182.714 167.356 183.023 167.718 183.023 168.335 c
183.023 168.997 182.573 169.349 181.973 169.349 c
181.515 169.349 181.118 169.058 180.933 168.626 c
180.068 168.917 l
180.395 169.711 181.127 170.09 181.956 170.09 c
182.978 170.09 183.869 169.543 183.869 168.388 c
183.869 167.735 183.437 167.162 182.802 166.977 c
182.802 166.96 l
183.587 166.827 184.028 166.157 184.028 165.39 c
184.028 164.19 183.049 163.582 181.947 163.582 c
180.994 163.582 180.218 163.996 179.936 164.94 c
180.827 165.213 l
f
0.125 0.067 0.051 0.004 k
249.492 143.277 m
250.801 143.277 251.873 144.349 251.873 145.659 c
251.873 152.802 l
251.873 154.111 250.801 155.183 249.492 155.183 c
236.396 155.183 l
235.086 155.183 234.014 154.111 234.014 152.802 c
234.014 145.659 l
234.014 144.349 235.086 143.277 236.396 143.277 c
249.492 143.277 l
h
B
249.856 144.452 m
250.349 144.452 250.749 144.852 250.749 145.345 c
S
236.049 154.165 m
235.555 154.165 235.156 153.765 235.156 153.272 c
B
0 g
242.055 147.601 m
242.258 147.001 242.54 146.71 243.202 146.71 c
243.854 146.71 244.41 147.169 244.41 147.839 c
244.41 148.88 243.448 149.003 242.655 149.003 c
242.655 149.744 l
243.942 149.744 244.251 150.105 244.251 150.723 c
244.251 151.384 243.801 151.737 243.202 151.737 c
242.743 151.737 242.346 151.446 242.161 151.014 c
241.297 151.304 l
241.623 152.098 242.355 152.478 243.184 152.478 c
244.207 152.478 245.097 151.931 245.097 150.775 c
245.097 150.123 244.665 149.55 244.03 149.364 c
244.03 149.347 l
244.815 149.215 245.256 148.544 245.256 147.777 c
245.256 146.578 244.277 145.97 243.175 145.97 c
242.223 145.97 241.447 146.384 241.165 147.327 c
242.055 147.601 l
f
0.125 0.067 0.051 0.004 k
86.216 143.277 m
87.526 143.277 88.597 144.349 88.597 145.659 c
88.597 152.802 l
88.597 154.111 87.526 155.183 86.216 155.183 c
73.12 155.183 l
71.81 155.183 70.739 154.111 70.739 152.802 c
70.739 145.659 l
70.739 144.349 71.81 143.277 73.12 143.277 c
86.216 143.277 l
h
B
86.58 144.452 m
87.073 144.452 87.473 144.852 87.473 145.345 c
S
72.773 154.165 m
72.28 154.165 71.88 153.765 71.88 153.272 c
B
0 g
78.78 147.601 m
78.982 147.001 79.265 146.71 79.926 146.71 c
80.579 146.71 81.134 147.169 81.134 147.839 c
81.134 148.88 80.173 149.003 79.379 149.003 c
79.379 149.744 l
80.667 149.744 80.975 150.105 80.975 150.723 c
80.975 151.384 80.525 151.737 79.926 151.737 c
79.467 151.737 79.071 151.446 78.885 151.014 c
78.021 151.304 l
78.348 152.098 79.079 152.478 79.908 152.478 c
80.931 152.478 81.822 151.931 81.822 150.775 c
81.822 150.123 81.39 149.55 80.755 149.364 c
80.755 149.347 l
81.54 149.215 81.981 148.544 81.981 147.777 c
81.981 146.578 81.002 145.97 79.899 145.97 c
78.947 145.97 78.171 146.384 77.889 147.327 c
78.78 147.601 l
f
0.125 0.067 0.051 0.004 k
188.263 143.277 m
189.573 143.277 190.644 144.349 190.644 145.659 c
190.644 152.802 l
190.644 154.111 189.573 155.183 188.263 155.183 c
175.167 155.183 l
173.858 155.183 172.786 154.111 172.786 152.802 c
172.786 145.659 l
172.786 144.349 173.858 143.277 175.167 143.277 c
188.263 143.277 l
h
B
188.627 144.452 m
189.121 144.452 189.52 144.852 189.52 145.345 c
B
174.82 154.165 m
174.327 154.165 173.927 153.765 173.927 153.272 c
S
0 g
181.693 147.526 m
179.03 147.526 l
179.03 148.39 l
181.517 152.394 l
182.54 152.394 l
182.54 148.267 l
183.422 148.267 l
183.422 147.526 l
182.54 147.526 l
182.54 146.15 l
181.693 146.15 l
181.693 147.526 l
h
181.693 151.388 m
181.676 151.388 l
179.771 148.267 l
181.693 148.267 l
181.693 151.388 l
f
0.125 0.067 0.051 0.004 k
147.444 160.89 m
148.754 160.89 149.826 161.962 149.826 163.271 c
149.826 170.414 l
149.826 171.724 148.754 172.796 147.444 172.796 c
134.349 172.796 l
133.039 172.796 131.967 171.724 131.967 170.414 c
131.967 163.271 l
131.967 161.962 133.039 160.89 134.349 160.89 c
147.444 160.89 l
h
B
147.808 162.065 m
148.301 162.065 148.701 162.465 148.701 162.958 c
S
134.001 171.778 m
133.508 171.778 133.108 171.378 133.108 170.885 c
B
0 g
142.96 169.219 m
140.429 169.219 l
140.402 167.658 l
140.579 167.738 141.037 167.79 141.24 167.79 c
142.413 167.79 143.18 166.944 143.18 165.727 c
143.18 164.484 142.201 163.663 140.985 163.663 c
140.138 163.663 139.397 164.113 139.106 164.925 c
139.962 165.216 l
140.182 164.642 140.561 164.404 141.117 164.404 c
141.787 164.404 142.334 164.889 142.334 165.683 c
142.334 166.591 141.716 167.05 140.826 167.05 c
140.508 167.05 139.962 166.935 139.538 166.723 c
139.609 170.013 l
142.96 170.013 l
142.96 169.219 l
f
0.125 0.067 0.051 0.004 k
229.082 160.89 m
230.392 160.89 231.463 161.962 231.463 163.271 c
231.463 170.414 l
231.463 171.724 230.392 172.796 229.082 172.796 c
215.986 172.796 l
214.676 172.796 213.605 171.724 213.605 170.414 c
213.605 163.271 l
213.605 161.962 214.676 160.89 215.986 160.89 c
229.082 160.89 l
h
B
229.446 162.065 m
229.939 162.065 230.339 162.465 230.339 162.958 c
B
215.639 171.778 m
215.146 171.778 214.746 171.378 214.746 170.885 c
S
0 g
222.005 167.696 m
222.041 167.696 l
222.243 167.793 222.473 167.837 222.728 167.837 c
223.628 167.837 224.659 167.228 224.659 165.861 c
224.659 164.486 223.69 163.763 222.517 163.763 c
221.344 163.763 220.374 164.556 220.374 165.773 c
220.374 166.541 220.621 167.017 221 167.616 c
222.578 170.112 l
223.575 170.112 l
222.005 167.696 l
h
222.517 164.504 m
223.293 164.504 223.813 165.041 223.813 165.8 c
223.813 166.558 223.293 167.096 222.517 167.096 c
221.741 167.096 221.221 166.558 221.221 165.8 c
221.221 165.041 221.741 164.504 222.517 164.504 c
f
0.125 0.067 0.051 0.004 k
147.444 143.277 m
148.754 143.277 149.826 144.349 149.826 145.659 c
149.826 152.802 l
149.826 154.111 148.754 155.183 147.444 155.183 c
134.349 155.183 l
133.039 155.183 131.967 154.111 131.967 152.802 c
131.967 145.659 l
131.967 144.349 133.039 143.277 134.349 143.277 c
147.444 143.277 l
h
B
147.808 144.452 m
148.301 144.452 148.701 144.852 148.701 145.345 c
S
134.001 154.165 m
133.508 154.165 133.108 153.765 133.108 153.272 c
B
0 g
140.367 150.083 m
140.403 150.083 l
140.605 150.18 140.835 150.224 141.091 150.224 c
141.99 150.224 143.022 149.616 143.022 148.249 c
143.022 146.873 142.052 146.15 140.879 146.15 c
139.706 146.15 138.736 146.944 138.736 148.161 c
138.736 148.928 138.983 149.404 139.362 150.004 c
140.941 152.499 l
141.937 152.499 l
140.367 150.083 l
h
140.879 146.891 m
141.655 146.891 142.175 147.429 142.175 148.187 c
142.175 148.946 141.655 149.484 140.879 149.484 c
140.103 149.484 139.583 148.946 139.583 148.187 c
139.583 147.429 140.103 146.891 140.879 146.891 c
f
0.125 0.067 0.051 0.004 k
86.216 160.89 m
87.526 160.89 88.597 161.962 88.597 163.271 c
88.597 170.414 l
88.597 171.724 87.526 172.796 86.216 172.796 c
73.12 172.796 l
71.811 172.796 70.739 171.724 70.739 170.414 c
70.739 163.271 l
70.739 161.962 71.811 160.89 73.12 160.89 c
86.216 160.89 l
h
B
86.58 162.065 m
87.073 162.065 87.473 162.465 87.473 162.958 c
S
72.773 171.778 m
72.28 171.778 71.88 171.378 71.88 170.885 c
B
0 g
80.903 169.265 m
77.887 169.265 l
77.887 170.006 l
81.811 170.006 l
81.811 169.283 l
79.324 163.763 l
78.372 163.763 l
80.903 169.265 l
f
0.125 0.067 0.051 0.004 k
249.492 160.89 m
250.801 160.89 251.873 161.962 251.873 163.271 c
251.873 170.414 l
251.873 171.724 250.801 172.796 249.492 172.796 c
236.396 172.796 l
235.086 172.796 234.014 171.724 234.014 170.414 c
234.014 163.271 l
234.014 161.962 235.086 160.89 236.396 160.89 c
249.492 160.89 l
h
B
249.856 162.065 m
250.349 162.065 250.749 162.465 250.749 162.958 c
S
236.049 171.778 m
235.555 171.778 235.156 171.378 235.156 170.885 c
B
0 g
240.867 165.659 m
240.867 166.435 241.379 166.999 242.057 167.184 c
242.057 167.211 l
241.59 167.334 241.079 167.802 241.079 168.666 c
241.079 169.609 241.925 170.218 242.904 170.218 c
243.883 170.218 244.729 169.609 244.729 168.666 c
244.729 167.802 244.218 167.334 243.751 167.211 c
243.751 167.184 l
244.429 166.999 244.941 166.435 244.941 165.659 c
244.941 164.477 244.042 163.763 242.904 163.763 c
241.766 163.763 240.867 164.477 240.867 165.659 c
h
242.904 167.555 m
243.557 167.555 243.883 168.031 243.883 168.542 c
243.883 169.116 243.486 169.53 242.904 169.53 c
242.366 169.53 241.925 169.124 241.925 168.542 c
241.925 168.057 242.278 167.555 242.904 167.555 c
h
244.095 165.659 m
244.095 166.417 243.566 166.805 242.904 166.814 c
242.216 166.805 241.714 166.32 241.714 165.659 c
241.714 164.927 242.26 164.504 242.904 164.504 c
243.609 164.504 244.095 164.98 244.095 165.659 c
f
0.125 0.067 0.051 0.004 k
127.035 143.277 m
128.344 143.277 129.416 144.349 129.416 145.659 c
129.416 152.802 l
129.416 154.111 128.344 155.183 127.035 155.183 c
113.939 155.183 l
112.629 155.183 111.558 154.111 111.558 152.802 c
111.558 145.659 l
111.558 144.349 112.629 143.277 113.939 143.277 c
127.035 143.277 l
h
B
127.399 144.452 m
127.892 144.452 128.292 144.852 128.292 145.345 c
B
113.592 154.165 m
113.099 154.165 112.699 153.765 112.699 153.272 c
S
0 g
118.41 148.046 m
118.41 148.822 118.922 149.387 119.601 149.572 c
119.601 149.598 l
119.134 149.722 118.622 150.189 118.622 151.053 c
118.622 151.997 119.468 152.605 120.447 152.605 c
121.426 152.605 122.273 151.997 122.273 151.053 c
122.273 150.189 121.761 149.722 121.294 149.598 c
121.294 149.572 l
121.973 149.387 122.484 148.822 122.484 148.046 c
122.484 146.865 121.585 146.15 120.447 146.15 c
119.31 146.15 118.41 146.865 118.41 148.046 c
h
120.447 149.942 m
121.1 149.942 121.426 150.418 121.426 150.93 c
121.426 151.503 121.029 151.917 120.447 151.917 c
119.91 151.917 119.468 151.512 119.468 150.93 c
119.468 150.445 119.821 149.942 120.447 149.942 c
h
121.638 148.046 m
121.638 148.805 121.109 149.192 120.447 149.202 c
119.76 149.192 119.257 148.708 119.257 148.046 c
119.257 147.314 119.804 146.891 120.447 146.891 c
121.153 146.891 121.638 147.367 121.638 148.046 c
f
0.188 0.137 0.063 0.008 k
167.854 143.277 m
169.163 143.277 170.235 144.349 170.235 145.659 c
170.235 152.802 l
170.235 154.111 169.163 155.183 167.854 155.183 c
154.758 155.183 l
153.448 155.183 152.377 154.111 152.377 152.802 c
152.377 145.659 l
152.377 144.349 153.448 143.277 154.758 143.277 c
167.854 143.277 l
h
B
168.218 144.453 m
168.711 144.453 169.111 144.852 169.111 145.345 c
B
154.411 154.165 m
153.918 154.165 153.518 153.765 153.518 153.272 c
S
0 g
159.125 150.075 4.409 -0.688 re
f
0.188 0.137 0.063 0.008 k
290.31 143.277 m
291.62 143.277 292.692 144.349 292.692 145.659 c
292.692 152.802 l
292.692 154.111 291.62 155.183 290.31 155.183 c
277.214 155.183 l
275.905 155.183 274.834 154.111 274.834 152.802 c
274.834 145.659 l
274.834 144.349 275.905 143.277 277.214 143.277 c
290.31 143.277 l
h
B
290.675 144.453 m
291.168 144.453 291.567 144.852 291.567 145.345 c
S
276.868 154.165 m
276.374 154.165 275.975 153.765 275.975 153.272 c
B
0 g
281.666 149.51 4.709 -0.688 re
284.02 151.23 m
284.338 151.23 284.603 150.965 284.603 150.648 c
284.603 150.33 284.338 150.066 284.02 150.066 c
283.703 150.066 283.439 150.33 283.439 150.648 c
283.439 150.965 283.703 151.23 284.02 151.23 c
h
284.02 148.267 m
284.338 148.267 284.603 148.002 284.603 147.685 c
284.603 147.367 284.338 147.103 284.02 147.103 c
283.703 147.103 283.439 147.367 283.439 147.685 c
283.439 148.002 283.703 148.267 284.02 148.267 c
f
0.188 0.137 0.063 0.008 k
167.854 160.89 m
169.163 160.89 170.235 161.962 170.235 163.271 c
170.235 170.414 l
170.235 171.724 169.163 172.796 167.854 172.796 c
154.758 172.796 l
153.448 172.796 152.377 171.724 152.377 170.414 c
152.377 163.271 l
152.377 161.962 153.448 160.89 154.758 160.89 c
167.854 160.89 l
h
B
168.218 162.065 m
168.711 162.065 169.111 162.465 169.111 162.958 c
B
154.411 171.778 m
153.918 171.778 153.518 171.378 153.518 170.885 c
S
0 g
161.015 166.71 m
159.534 168.659 l
160.556 168.659 l
161.571 167.178 l
162.567 168.659 l
163.528 168.659 l
162.1 166.71 l
163.793 164.479 l
162.77 164.479 l
161.535 166.234 l
160.301 164.479 l
159.322 164.479 l
161.015 166.71 l
f
0.188 0.137 0.063 0.008 k
269.901 160.89 m
271.211 160.89 272.282 161.962 272.282 163.271 c
272.282 170.414 l
272.282 171.724 271.211 172.796 269.901 172.796 c
256.805 172.796 l
255.496 172.796 254.424 171.724 254.424 170.414 c
254.424 163.271 l
254.424 161.962 255.496 160.89 256.805 160.89 c
269.901 160.89 l
h
B
270.265 162.065 m
270.758 162.065 271.158 162.465 271.158 162.958 c
B
256.458 171.778 m
255.965 171.778 255.565 171.378 255.565 170.885 c
S
0 g
261.12 167.824 4.709 -0.688 re
261.12 166.439 4.709 -0.688 re
f
0.188 0.137 0.063 0.008 k
331.129 143.277 m
332.439 143.277 333.51 144.349 333.51 145.659 c
333.51 152.802 l
333.51 154.111 332.439 155.183 331.129 155.183 c
318.034 155.183 l
316.724 155.183 315.652 154.111 315.652 152.802 c
315.652 145.659 l
315.652 144.349 316.724 143.277 318.034 143.277 c
331.129 143.277 l
h
B
331.493 144.453 m
331.986 144.453 332.386 144.852 332.386 145.345 c
S
317.686 154.165 m
317.193 154.165 316.794 153.765 316.794 153.272 c
B
0 g
322.348 150.211 4.709 -0.688 re
322.348 148.827 4.709 -0.688 re
f
0.188 0.137 0.063 0.008 k
269.901 143.277 m
271.211 143.277 272.282 144.349 272.282 145.659 c
272.282 152.802 l
272.282 154.111 271.211 155.183 269.901 155.183 c
256.805 155.183 l
255.496 155.183 254.424 154.111 254.424 152.802 c
254.424 145.659 l
254.424 144.349 255.496 143.277 256.805 143.277 c
269.901 143.277 l
h
B
270.265 144.453 m
270.758 144.453 271.158 144.852 271.158 145.345 c
B
256.458 154.165 m
255.965 154.165 255.565 153.765 255.565 153.272 c
S
0 g
261.12 150.211 4.709 -0.688 re
261.12 148.827 4.709 -0.688 re
f
0.188 0.137 0.063 0.008 k
106.625 160.89 m
107.935 160.89 109.006 161.962 109.006 163.271 c
109.006 170.415 l
109.006 171.724 107.935 172.796 106.625 172.796 c
93.529 172.796 l
92.22 172.796 91.148 171.724 91.148 170.415 c
91.148 163.271 l
91.148 161.962 92.22 160.89 93.529 160.89 c
106.625 160.89 l
h
B
106.99 162.065 m
107.483 162.065 107.882 162.465 107.882 162.958 c
B
93.183 171.778 m
92.689 171.778 92.29 171.378 92.29 170.885 c
S
0 g
99.798 167.497 m
100.115 167.497 100.379 167.233 100.379 166.916 c
100.379 166.598 100.115 166.334 99.798 166.334 c
99.48 166.334 99.215 166.598 99.215 166.916 c
99.215 167.233 99.48 167.497 99.798 167.497 c
f
0.188 0.137 0.063 0.008 k
106.625 143.277 m
107.935 143.277 109.006 144.349 109.006 145.659 c
109.006 152.802 l
109.006 154.111 107.935 155.183 106.625 155.183 c
93.529 155.183 l
92.22 155.183 91.148 154.111 91.148 152.802 c
91.148 145.659 l
91.148 144.349 92.22 143.277 93.529 143.277 c
106.625 143.277 l
h
B
106.99 144.453 m
107.483 144.453 107.882 144.852 107.882 145.345 c
B
93.183 154.165 m
92.689 154.165 92.29 153.765 92.29 153.272 c
S
0 g
99.798 149.885 m
100.115 149.885 100.379 149.621 100.379 149.303 c
100.379 148.986 100.115 148.721 99.798 148.721 c
99.48 148.721 99.215 148.986 99.215 149.303 c
99.215 149.621 99.48 149.885 99.798 149.885 c
f
0.188 0.137 0.063 0.008 k
208.673 143.277 m
209.982 143.277 211.054 144.349 211.054 145.659 c
211.054 152.802 l
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B
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B
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B
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B
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h
B
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B
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B
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B
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B
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B
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B
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B
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B
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B
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h
B
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B
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B
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B
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B
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h
B
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B
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B
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B
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B
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0 Tc 0 Tw 6.3 0 0 6.3 337.8122 301.0297 Tm
(5)Tj
9 0 0 9 341.3144 297.4298 Tm
(?)Tj
-0.0002 Tc 0.0278 Tw -30.3315 -1.9633 Td
[(3)-1334(A squar)18(e has an ar)18(ea of 81 cm)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 207.9474 283.3604 Tm
(2)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 211.4496 279.7606 Tm
(. What is the length of each side?)Tj
-15.9021 -1.9633 Td
[(4)-1334(A cube has a volume of 64 cm)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 208.2923 265.6911 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 211.7945 262.0912 Tm
(. What is the length of each side?)Tj
-0.0002 Tc -15.9404 -1.9633 Td
[(5)-1334(y = 3x)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 110.5095 248.0219 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 116.7623 244.422 Tm
(+ 4x)Tj
0 Tc 0 Tw 6.3 0 0 6.3 134.8454 248.0219 Tm
(2)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 141.0981 244.422 Tm
(+ 2x. Calculate the value of y when x = 2)Tj
/T1_4 1 Tf
0 Tc 0 Tw 18.4446 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0001 Tc 0.2779 0 Td
(974)Tj
11.9532 Tw -26.8078 -1.9633 Td
[(6)-1334(Calculate 7)-1334(Calculate )11925(4)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 6.3 0 0 6.3 294.8244 230.3527 Tm
(\320)Tj
/T1_3 1 Tf
0.4998 0 Td
(2)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 8 0 0 8 51.3228 206.2487 Tm
(Answers)Tj
ET
0 0 0 0 k
52.32 203.43 357.64 -138.24 re
f*
Q Q 
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
164.095 68.59 m
165.213 68.59 166.128 69.504 166.128 70.622 c
166.128 76.717 l
166.128 77.835 165.213 78.75 164.095 78.75 c
152.92 78.75 l
151.802 78.75 150.888 77.835 150.888 76.717 c
150.888 70.622 l
150.888 69.504 151.802 68.59 152.92 68.59 c
164.095 68.59 l
h
B
0.125 0.067 0.051 0.004 k
254.551 128.953 m
255.668 128.953 256.583 129.867 256.583 130.984 c
256.583 137.08 l
256.583 138.198 255.668 139.112 254.551 139.112 c
243.375 139.112 l
242.258 139.112 241.343 138.198 241.343 137.08 c
241.343 130.984 l
241.343 129.867 242.258 128.953 243.375 128.953 c
254.551 128.953 l
h
B
254.861 129.955 m
255.282 129.955 255.623 130.296 255.623 130.717 c
243.079 138.244 m
242.658 138.244 242.317 137.903 242.317 137.482 c
S
0 g
247.612 132.017 m
249.75 134.14 l
250.043 134.425 250.337 134.794 250.337 135.231 c
250.337 135.757 249.922 136.081 249.418 136.081 c
248.899 136.081 248.538 135.765 248.447 135.261 c
247.665 135.328 l
247.808 136.269 248.508 136.713 249.426 136.713 c
250.344 136.713 251.104 136.217 251.104 135.238 c
251.104 134.538 250.652 134.034 250.178 133.575 c
248.425 131.882 l
251.104 131.882 l
251.104 131.25 l
247.612 131.25 l
247.612 132.017 l
f
0.125 0.067 0.051 0.004 k
337.996 113.432 m
339.113 113.432 340.027 114.347 340.027 115.464 c
340.027 121.56 l
340.027 122.678 339.113 123.592 337.996 123.592 c
326.82 123.592 l
325.703 123.592 324.789 122.678 324.789 121.56 c
324.789 115.464 l
324.789 114.347 325.703 113.432 326.82 113.432 c
337.996 113.432 l
h
B
338.306 114.435 m
338.727 114.435 339.068 114.776 339.068 115.197 c
326.524 122.723 m
326.104 122.723 325.762 122.382 325.762 121.961 c
S
0 g
331.057 116.497 m
333.194 118.619 l
333.488 118.905 333.781 119.274 333.781 119.71 c
333.781 120.237 333.367 120.561 332.863 120.561 c
332.344 120.561 331.983 120.245 331.893 119.74 c
331.11 119.808 l
331.253 120.749 331.953 121.193 332.871 121.193 c
333.789 121.193 334.549 120.696 334.549 119.718 c
334.549 119.018 334.098 118.514 333.624 118.055 c
331.87 116.362 l
334.549 116.362 l
334.549 115.73 l
331.057 115.73 l
331.057 116.497 l
f
0.125 0.067 0.051 0.004 k
250.723 113.422 m
251.84 113.422 252.755 114.336 252.755 115.454 c
252.755 121.549 l
252.755 122.667 251.84 123.581 250.723 123.581 c
239.547 123.581 l
238.43 123.581 237.516 122.667 237.516 121.549 c
237.516 115.454 l
237.516 114.336 238.43 113.422 239.547 113.422 c
250.723 113.422 l
h
B
251.033 114.424 m
251.454 114.424 251.795 114.765 251.795 115.186 c
239.251 122.713 m
238.831 122.713 238.489 122.372 238.489 121.951 c
S
0 g
245.117 117.047 m
242.844 117.047 l
242.844 117.785 l
244.966 121.201 l
245.839 121.201 l
245.839 117.679 l
246.591 117.679 l
246.591 117.047 l
245.839 117.047 l
245.839 115.873 l
245.117 115.873 l
245.117 117.047 l
h
245.117 120.343 m
245.102 120.343 l
243.476 117.679 l
245.117 117.679 l
245.117 120.343 l
f
0.125 0.067 0.051 0.004 k
164.983 143.788 m
166.101 143.788 167.015 144.702 167.015 145.819 c
167.015 151.915 l
167.015 153.033 166.101 153.947 164.983 153.947 c
153.808 153.947 l
152.69 153.947 151.776 153.033 151.776 151.915 c
151.776 145.819 l
151.776 144.702 152.69 143.788 153.808 143.788 c
164.983 143.788 l
h
B
165.294 144.79 m
165.715 144.79 166.056 145.131 166.056 145.552 c
S
153.512 153.079 m
153.091 153.079 152.75 152.737 152.75 152.317 c
B
0 g
159.377 147.413 m
157.105 147.413 l
157.105 148.15 l
159.227 151.567 l
160.099 151.567 l
160.099 148.045 l
160.852 148.045 l
160.852 147.413 l
160.099 147.413 l
160.099 146.239 l
159.377 146.239 l
159.377 147.413 l
h
159.377 150.709 m
159.362 150.709 l
157.736 148.045 l
159.377 148.045 l
159.377 150.709 l
f
0.125 0.067 0.051 0.004 k
324.997 128.931 m
326.114 128.931 327.029 129.846 327.029 130.963 c
327.029 137.059 l
327.029 138.176 326.114 139.091 324.997 139.091 c
313.821 139.091 l
312.704 139.091 311.79 138.176 311.79 137.059 c
311.79 130.963 l
311.79 129.846 312.704 128.931 313.821 128.931 c
324.997 128.931 l
h
B
325.308 129.934 m
325.729 129.934 326.069 130.275 326.069 130.696 c
313.526 138.222 m
313.105 138.222 312.764 137.881 312.764 137.46 c
S
0 g
319.391 132.557 m
317.118 132.557 l
317.118 133.294 l
319.24 136.711 l
320.113 136.711 l
320.113 133.189 l
320.865 133.189 l
320.865 132.557 l
320.113 132.557 l
320.113 131.383 l
319.391 131.383 l
319.391 132.557 l
h
319.391 135.853 m
319.376 135.853 l
317.75 133.189 l
319.391 133.189 l
319.391 135.853 l
f
0.125 0.067 0.051 0.004 k
146.892 174.359 m
148.01 174.359 148.924 175.273 148.924 176.39 c
148.924 182.486 l
148.924 183.604 148.01 184.518 146.892 184.518 c
135.717 184.518 l
134.6 184.518 133.685 183.604 133.685 182.486 c
133.685 176.39 l
133.685 175.273 134.6 174.359 135.717 174.359 c
146.892 174.359 l
h
B
147.203 175.361 m
147.624 175.361 147.965 175.702 147.965 176.123 c
S
135.421 183.65 m
135 183.65 134.659 183.308 134.659 182.888 c
B
0 g
141.286 177.984 m
139.014 177.984 l
139.014 178.721 l
141.135 182.138 l
142.008 182.138 l
142.008 178.616 l
142.761 178.616 l
142.761 177.984 l
142.008 177.984 l
142.008 176.81 l
141.286 176.81 l
141.286 177.984 l
h
141.286 181.28 m
141.271 181.28 l
139.646 178.616 l
141.286 178.616 l
141.286 181.28 l
f
0.125 0.067 0.051 0.004 k
199.797 188.684 m
200.914 188.684 201.829 189.598 201.829 190.716 c
201.829 196.812 l
201.829 197.929 200.914 198.844 199.797 198.844 c
188.622 198.844 l
187.504 198.844 186.589 197.929 186.589 196.812 c
186.589 190.716 l
186.589 189.598 187.504 188.684 188.622 188.684 c
199.797 188.684 l
h
B
200.107 189.687 m
200.528 189.687 200.87 190.028 200.87 190.449 c
188.325 197.975 m
187.904 197.975 187.564 197.634 187.564 197.213 c
S
0 g
195.97 195.792 m
193.81 195.792 l
193.788 194.46 l
193.938 194.528 194.33 194.573 194.502 194.573 c
195.503 194.573 196.158 193.85 196.158 192.812 c
196.158 191.751 195.323 191.051 194.284 191.051 c
193.562 191.051 192.93 191.435 192.682 192.127 c
193.411 192.375 l
193.6 191.886 193.923 191.683 194.397 191.683 c
194.969 191.683 195.436 192.097 195.436 192.774 c
195.436 193.549 194.909 193.941 194.149 193.941 c
193.878 193.941 193.411 193.843 193.05 193.662 c
193.11 196.469 l
195.97 196.469 l
195.97 195.792 l
f
0.125 0.067 0.051 0.004 k
182.858 174.369 m
183.975 174.369 184.89 175.284 184.89 176.401 c
184.89 182.497 l
184.89 183.614 183.975 184.529 182.858 184.529 c
171.683 184.529 l
170.565 184.529 169.65 183.614 169.65 182.497 c
169.65 176.401 l
169.65 175.284 170.565 174.369 171.683 174.369 c
182.858 174.369 l
h
B
183.168 175.372 m
183.589 175.372 183.931 175.713 183.931 176.134 c
S
0.188 0.137 0.063 0.008 k
171.386 183.66 m
170.966 183.66 170.625 183.319 170.625 182.898 c
B
0 g
179.031 181.477 m
176.871 181.477 l
176.849 180.145 l
176.999 180.213 177.391 180.258 177.564 180.258 c
178.564 180.258 179.219 179.535 179.219 178.497 c
179.219 177.436 178.384 176.736 177.345 176.736 c
176.623 176.736 175.991 177.12 175.743 177.812 c
176.473 178.061 l
176.661 177.571 176.984 177.368 177.459 177.368 c
178.03 177.368 178.497 177.782 178.497 178.459 c
178.497 179.234 177.97 179.626 177.21 179.626 c
176.939 179.626 176.473 179.528 176.111 179.347 c
176.171 182.154 l
179.031 182.154 l
179.031 181.477 l
f
0.125 0.067 0.051 0.004 k
147.21 143.8 m
148.327 143.8 149.241 144.714 149.241 145.832 c
149.241 151.928 l
149.241 153.045 148.327 153.959 147.21 153.959 c
136.034 153.959 l
134.917 153.959 134.002 153.045 134.002 151.928 c
134.002 145.832 l
134.002 144.714 134.917 143.8 136.034 143.8 c
147.21 143.8 l
h
B
147.52 144.802 m
147.941 144.802 148.282 145.144 148.282 145.565 c
S
135.738 153.091 m
135.317 153.091 134.976 152.75 134.976 152.329 c
B
0 g
141.171 149.608 m
141.201 149.608 l
141.374 149.69 141.569 149.728 141.788 149.728 c
142.555 149.728 143.436 149.209 143.436 148.042 c
143.436 146.869 142.608 146.251 141.607 146.251 c
140.606 146.251 139.778 146.929 139.778 147.967 c
139.778 148.622 139.989 149.028 140.313 149.54 c
141.66 151.67 l
142.51 151.67 l
141.171 149.608 l
h
141.607 146.884 m
142.269 146.884 142.713 147.343 142.713 147.99 c
142.713 148.637 142.269 149.096 141.607 149.096 c
140.945 149.096 140.501 148.637 140.501 147.99 c
140.501 147.343 140.945 146.884 141.607 146.884 c
f
0.125 0.067 0.051 0.004 k
307.527 128.953 m
308.645 128.953 309.559 129.867 309.559 130.984 c
309.559 137.08 l
309.559 138.198 308.645 139.112 307.527 139.112 c
296.352 139.112 l
295.234 139.112 294.32 138.198 294.32 137.08 c
294.32 130.984 l
294.32 129.867 295.234 128.953 296.352 128.953 c
307.527 128.953 l
h
B
307.838 129.955 m
308.258 129.955 308.6 130.296 308.6 130.717 c
296.056 138.244 m
295.635 138.244 295.293 137.903 295.293 137.482 c
S
0 g
302.993 136.1 m
300.419 136.1 l
300.419 136.732 l
303.768 136.732 l
303.768 136.115 l
301.646 131.404 l
300.833 131.404 l
302.993 136.1 l
f
0.125 0.067 0.051 0.004 k
146.906 188.673 m
148.023 188.673 148.938 189.588 148.938 190.705 c
148.938 196.801 l
148.938 197.919 148.023 198.833 146.906 198.833 c
135.73 198.833 l
134.613 198.833 133.698 197.919 133.698 196.801 c
133.698 190.705 l
133.698 189.588 134.613 188.673 135.73 188.673 c
146.906 188.673 l
h
B
147.216 189.676 m
147.637 189.676 147.978 190.017 147.978 190.438 c
S
135.434 197.965 m
135.013 197.965 134.672 197.623 134.672 197.202 c
B
0 g
139.546 192.743 m
139.546 193.405 139.982 193.887 140.562 194.045 c
140.562 194.067 l
140.163 194.173 139.727 194.571 139.727 195.309 c
139.727 196.114 140.449 196.633 141.284 196.633 c
142.119 196.633 142.842 196.114 142.842 195.309 c
142.842 194.571 142.405 194.173 142.006 194.067 c
142.006 194.045 l
142.586 193.887 143.022 193.405 143.022 192.743 c
143.022 191.734 142.255 191.125 141.284 191.125 c
140.314 191.125 139.546 191.734 139.546 192.743 c
h
141.284 194.361 m
141.841 194.361 142.119 194.767 142.119 195.204 c
142.119 195.693 141.781 196.046 141.284 196.046 c
140.825 196.046 140.449 195.7 140.449 195.204 c
140.449 194.79 140.75 194.361 141.284 194.361 c
h
142.3 192.743 m
142.3 193.39 141.849 193.721 141.284 193.729 c
140.697 193.721 140.268 193.307 140.268 192.743 c
140.268 192.118 140.735 191.757 141.284 191.757 c
141.886 191.757 142.3 192.163 142.3 192.743 c
f
0.125 0.067 0.051 0.004 k
147.193 158.596 m
148.311 158.596 149.225 159.51 149.225 160.628 c
149.225 166.723 l
149.225 167.841 148.311 168.755 147.193 168.755 c
136.018 168.755 l
134.9 168.755 133.986 167.841 133.986 166.723 c
133.986 160.628 l
133.986 159.51 134.9 158.596 136.018 158.596 c
147.193 158.596 l
h
B
147.504 159.598 m
147.925 159.598 148.266 159.94 148.266 160.36 c
S
135.722 167.887 m
135.301 167.887 134.96 167.546 134.96 167.125 c
B
0 g
139.834 162.665 m
139.834 163.327 140.27 163.809 140.85 163.967 c
140.85 163.989 l
140.451 164.095 140.014 164.494 140.014 165.231 c
140.014 166.036 140.737 166.556 141.572 166.556 c
142.407 166.556 143.129 166.036 143.129 165.231 c
143.129 164.494 142.693 164.095 142.294 163.989 c
142.294 163.967 l
142.874 163.809 143.31 163.327 143.31 162.665 c
143.31 161.657 142.543 161.047 141.572 161.047 c
140.601 161.047 139.834 161.657 139.834 162.665 c
h
141.572 164.283 m
142.129 164.283 142.407 164.689 142.407 165.126 c
142.407 165.615 142.068 165.969 141.572 165.969 c
141.113 165.969 140.737 165.622 140.737 165.126 c
140.737 164.712 141.038 164.283 141.572 164.283 c
h
142.588 162.665 m
142.588 163.312 142.136 163.643 141.572 163.651 c
140.985 163.643 140.556 163.23 140.556 162.665 c
140.556 162.04 141.022 161.679 141.572 161.679 c
142.174 161.679 142.588 162.086 142.588 162.665 c
f
0.125 0.067 0.051 0.004 k
164.964 158.596 m
166.082 158.596 166.996 159.51 166.996 160.628 c
166.996 166.723 l
166.996 167.841 166.082 168.755 164.964 168.755 c
153.789 168.755 l
152.671 168.755 151.757 167.841 151.757 166.723 c
151.757 160.628 l
151.757 159.51 152.671 158.596 153.789 158.596 c
164.964 158.596 l
h
B
165.275 159.598 m
165.696 159.598 166.037 159.94 166.037 160.36 c
S
153.493 167.887 m
153.072 167.887 152.731 167.546 152.731 167.125 c
B
0.188 0.137 0.063 0.008 k
233.298 113.424 m
234.416 113.424 235.331 114.338 235.331 115.455 c
235.331 121.551 l
235.331 122.669 234.416 123.583 233.298 123.583 c
222.123 123.583 l
221.006 123.583 220.091 122.669 220.091 121.551 c
220.091 115.455 l
220.091 114.338 221.006 113.424 222.123 113.424 c
233.298 113.424 l
h
B
233.61 114.426 m
234.03 114.426 234.371 114.767 234.371 115.188 c
221.827 122.714 m
221.406 122.714 221.065 122.373 221.065 121.952 c
S
0 g
225.886 118.789 m
227.602 118.789 l
227.602 120.505 l
228.189 120.505 l
228.189 118.789 l
229.904 118.789 l
229.904 118.202 l
228.189 118.202 l
228.189 116.487 l
227.602 116.487 l
227.602 118.202 l
225.886 118.202 l
225.886 118.789 l
f
0.188 0.137 0.063 0.008 k
320.596 113.424 m
321.713 113.424 322.627 114.338 322.627 115.455 c
322.627 121.551 l
322.627 122.669 321.713 123.583 320.596 123.583 c
309.42 123.583 l
308.303 123.583 307.388 122.669 307.388 121.551 c
307.388 115.455 l
307.388 114.338 308.303 113.424 309.42 113.424 c
320.596 113.424 l
h
B
320.906 114.426 m
321.327 114.426 321.668 114.767 321.668 115.188 c
309.124 122.714 m
308.703 122.714 308.362 122.373 308.362 121.952 c
S
0 g
313.183 118.789 m
314.899 118.789 l
314.899 120.505 l
315.486 120.505 l
315.486 118.789 l
317.201 118.789 l
317.201 118.202 l
315.486 118.202 l
315.486 116.487 l
314.899 116.487 l
314.899 118.202 l
313.183 118.202 l
313.183 118.789 l
f
0.188 0.137 0.063 0.008 k
182.397 188.673 m
183.514 188.673 184.429 189.588 184.429 190.705 c
184.429 196.801 l
184.429 197.919 183.514 198.833 182.397 198.833 c
171.221 198.833 l
170.104 198.833 169.189 197.919 169.189 196.801 c
169.189 190.705 l
169.189 189.588 170.104 188.673 171.221 188.673 c
182.397 188.673 l
h
B
182.707 189.676 m
183.128 189.676 183.469 190.017 183.469 190.438 c
S
170.925 197.965 m
170.504 197.965 170.163 197.623 170.163 197.202 c
B
0 g
174.984 194.039 m
176.7 194.039 l
176.7 195.755 l
177.287 195.755 l
177.287 194.039 l
179.002 194.039 l
179.002 193.452 l
177.287 193.452 l
177.287 191.736 l
176.7 191.736 l
176.7 193.452 l
174.984 193.452 l
174.984 194.039 l
f
0.125 0.067 0.051 0.004 k
146.481 113.424 m
147.599 113.424 148.513 114.338 148.513 115.455 c
148.513 121.551 l
148.513 122.669 147.599 123.583 146.481 123.583 c
135.306 123.583 l
134.189 123.583 133.274 122.669 133.274 121.551 c
133.274 115.455 l
133.274 114.338 134.189 113.424 135.306 113.424 c
146.481 113.424 l
h
B
146.792 114.426 m
147.213 114.426 147.554 114.767 147.554 115.188 c
135.01 122.714 m
134.589 122.714 134.248 122.373 134.248 121.952 c
S
0 g
140.135 117.113 m
140.309 116.601 140.549 116.353 141.114 116.353 c
141.67 116.353 142.145 116.744 142.145 117.316 c
142.145 118.204 141.324 118.309 140.647 118.309 c
140.647 118.942 l
141.746 118.942 142.009 119.25 142.009 119.777 c
142.009 120.341 141.626 120.642 141.114 120.642 c
140.723 120.642 140.384 120.394 140.226 120.025 c
139.488 120.273 l
139.767 120.951 140.391 121.274 141.099 121.274 c
141.972 121.274 142.731 120.808 142.731 119.822 c
142.731 119.265 142.363 118.776 141.821 118.618 c
141.821 118.603 l
142.491 118.49 142.867 117.918 142.867 117.263 c
142.867 116.24 142.032 115.721 141.091 115.721 c
140.278 115.721 139.616 116.074 139.376 116.88 c
140.135 117.113 l
f
0.125 0.067 0.051 0.004 k
215.858 113.424 m
216.976 113.424 217.89 114.338 217.89 115.455 c
217.89 121.551 l
217.89 122.669 216.976 123.583 215.858 123.583 c
204.683 123.583 l
203.565 123.583 202.651 122.669 202.651 121.551 c
202.651 115.455 l
202.651 114.338 203.565 113.424 204.683 113.424 c
215.858 113.424 l
h
B
216.169 114.426 m
216.589 114.426 216.931 114.767 216.931 115.188 c
204.387 122.714 m
203.966 122.714 203.625 122.373 203.625 121.952 c
S
0 g
209.512 117.113 m
209.686 116.601 209.926 116.353 210.491 116.353 c
211.047 116.353 211.522 116.744 211.522 117.316 c
211.522 118.204 210.701 118.309 210.024 118.309 c
210.024 118.942 l
211.123 118.942 211.386 119.25 211.386 119.777 c
211.386 120.341 211.002 120.642 210.491 120.642 c
210.099 120.642 209.761 120.394 209.603 120.025 c
208.865 120.273 l
209.144 120.951 209.768 121.274 210.476 121.274 c
211.348 121.274 212.109 120.808 212.109 119.822 c
212.109 119.265 211.74 118.776 211.198 118.618 c
211.198 118.603 l
211.868 118.49 212.244 117.918 212.244 117.263 c
212.244 116.24 211.409 115.721 210.468 115.721 c
209.655 115.721 208.993 116.074 208.752 116.88 c
209.512 117.113 l
f
0.188 0.137 0.063 0.008 k
163.897 113.424 m
165.015 113.424 165.929 114.338 165.929 115.455 c
165.929 121.551 l
165.929 122.669 165.015 123.583 163.897 123.583 c
152.722 123.583 l
151.605 123.583 150.69 122.669 150.69 121.551 c
150.69 115.455 l
150.69 114.338 151.605 113.424 152.722 113.424 c
163.897 113.424 l
h
B
164.208 114.426 m
164.629 114.426 164.97 114.767 164.97 115.188 c
152.426 122.714 m
152.005 122.714 151.664 122.373 151.664 121.952 c
S
0 g
158.062 118.39 m
156.797 120.053 l
157.671 120.053 l
158.536 118.789 l
159.386 120.053 l
160.207 120.053 l
158.987 118.39 l
160.432 116.487 l
159.559 116.487 l
158.506 117.984 l
157.452 116.487 l
156.617 116.487 l
158.062 118.39 l
f
0.188 0.137 0.063 0.008 k
268.347 113.424 m
269.464 113.424 270.378 114.338 270.378 115.455 c
270.378 121.551 l
270.378 122.669 269.464 123.583 268.347 123.583 c
257.171 123.583 l
256.054 123.583 255.14 122.669 255.14 121.551 c
255.14 115.455 l
255.14 114.338 256.054 113.424 257.171 113.424 c
268.347 113.424 l
h
B
268.657 114.426 m
269.078 114.426 269.419 114.767 269.419 115.188 c
256.875 122.714 m
256.455 122.714 256.113 122.373 256.113 121.952 c
S
0 g
262.511 118.39 m
261.247 120.053 l
262.12 120.053 l
262.985 118.789 l
263.835 120.053 l
264.655 120.053 l
263.437 118.39 l
264.881 116.487 l
264.008 116.487 l
262.955 117.984 l
261.901 116.487 l
261.066 116.487 l
262.511 118.39 l
f
0.188 0.137 0.063 0.008 k
355.132 113.424 m
356.25 113.424 357.164 114.338 357.164 115.455 c
357.164 121.551 l
357.164 122.669 356.25 123.583 355.132 123.583 c
343.957 123.583 l
342.839 123.583 341.924 122.669 341.924 121.551 c
341.924 115.455 l
341.924 114.338 342.839 113.424 343.957 113.424 c
355.132 113.424 l
h
B
355.442 114.426 m
355.863 114.426 356.204 114.767 356.204 115.188 c
343.66 122.714 m
343.239 122.714 342.898 122.373 342.898 121.952 c
S
0 g
349.296 118.39 m
348.032 120.053 l
348.904 120.053 l
349.77 118.789 l
350.62 120.053 l
351.44 120.053 l
350.222 118.39 l
351.666 116.487 l
350.793 116.487 l
349.74 117.984 l
348.687 116.487 l
347.851 116.487 l
349.296 118.39 l
f
0.188 0.137 0.063 0.008 k
389.741 113.424 m
390.858 113.424 391.773 114.338 391.773 115.455 c
391.773 121.551 l
391.773 122.669 390.858 123.583 389.741 123.583 c
378.565 123.583 l
377.447 123.583 376.533 122.669 376.533 121.551 c
376.533 115.455 l
376.533 114.338 377.447 113.424 378.565 113.424 c
389.741 113.424 l
h
B
390.051 114.426 m
390.472 114.426 390.813 114.767 390.813 115.188 c
S
378.269 122.714 m
377.848 122.714 377.507 122.373 377.507 121.952 c
B
0 g
382.247 119.34 4.019 -0.587 re
382.247 118.159 4.019 -0.587 re
f
0.188 0.137 0.063 0.008 k
234.987 188.673 m
236.105 188.673 237.019 189.588 237.019 190.705 c
237.019 196.801 l
237.019 197.919 236.105 198.833 234.987 198.833 c
223.812 198.833 l
222.694 198.833 221.779 197.919 221.779 196.801 c
221.779 190.705 l
221.779 189.588 222.694 188.673 223.812 188.673 c
234.987 188.673 l
h
B
235.297 189.676 m
235.718 189.676 236.06 190.017 236.06 190.438 c
S
223.515 197.965 m
223.094 197.965 222.753 197.623 222.753 197.202 c
B
0 g
227.493 194.591 4.019 -0.587 re
227.493 193.409 4.019 -0.587 re
f
0.188 0.137 0.063 0.008 k
200.533 174.359 m
201.65 174.359 202.565 175.273 202.565 176.39 c
202.565 182.486 l
202.565 183.604 201.65 184.518 200.533 184.518 c
189.357 184.518 l
188.24 184.518 187.326 183.604 187.326 182.486 c
187.326 176.39 l
187.326 175.273 188.24 174.359 189.357 174.359 c
200.533 174.359 l
h
B
200.844 175.361 m
201.265 175.361 201.605 175.702 201.605 176.123 c
189.062 183.65 m
188.641 183.65 188.299 183.308 188.299 182.888 c
S
0 g
193.04 180.275 4.019 -0.587 re
193.04 179.094 4.019 -0.587 re
f
0.188 0.137 0.063 0.008 k
271.951 128.942 m
273.068 128.942 273.982 129.856 273.982 130.974 c
273.982 137.069 l
273.982 138.187 273.068 139.101 271.951 139.101 c
260.775 139.101 l
259.658 139.101 258.743 138.187 258.743 137.069 c
258.743 130.974 l
258.743 129.856 259.658 128.942 260.775 128.942 c
271.951 128.942 l
h
B
272.261 129.944 m
272.682 129.944 273.023 130.286 273.023 130.706 c
260.479 138.233 m
260.059 138.233 259.717 137.892 259.717 137.471 c
S
0 g
266.124 134.58 m
266.395 134.58 266.621 134.355 266.621 134.084 c
266.621 133.813 266.395 133.587 266.124 133.587 c
265.853 133.587 265.627 133.813 265.627 134.084 c
265.627 134.355 265.853 134.58 266.124 134.58 c
f
0.125 0.067 0.051 0.004 k
289.871 128.942 m
290.988 128.942 291.903 129.856 291.903 130.974 c
291.903 137.069 l
291.903 138.187 290.988 139.101 289.871 139.101 c
278.695 139.101 l
277.578 139.101 276.664 138.187 276.664 137.069 c
276.664 130.974 l
276.664 129.856 277.578 128.942 278.695 128.942 c
289.871 128.942 l
h
B
290.182 129.944 m
290.603 129.944 290.943 130.286 290.943 130.706 c
278.399 138.233 m
277.979 138.233 277.638 137.892 277.638 137.471 c
S
0.188 0.137 0.063 0.008 k
342.16 128.953 m
343.277 128.953 344.192 129.867 344.192 130.984 c
344.192 137.08 l
344.192 138.198 343.277 139.112 342.16 139.112 c
330.984 139.112 l
329.867 139.112 328.953 138.198 328.953 137.08 c
328.953 130.984 l
328.953 129.867 329.867 128.953 330.984 128.953 c
342.16 128.953 l
h
B
342.471 129.955 m
342.892 129.955 343.232 130.296 343.232 130.717 c
330.689 138.244 m
330.268 138.244 329.926 137.903 329.926 137.482 c
S
0 g
333.616 136.798 m
334.692 136.798 l
336.385 132.764 l
336.415 132.764 l
338.093 136.798 l
339.169 136.798 l
339.169 131.47 l
338.447 131.47 l
338.447 135.85 l
338.432 135.85 l
336.633 131.47 l
336.152 131.47 l
334.353 135.85 l
334.338 135.85 l
334.338 131.47 l
333.616 131.47 l
333.616 136.798 l
f
0.188 0.137 0.063 0.008 k
181.13 113.411 m
182.248 113.411 183.162 114.325 183.162 115.443 c
183.162 121.539 l
183.162 122.656 182.248 123.571 181.13 123.571 c
169.955 123.571 l
168.837 123.571 167.923 122.656 167.923 121.539 c
167.923 115.443 l
167.923 114.325 168.837 113.411 169.955 113.411 c
181.13 113.411 l
h
B
181.441 114.414 m
181.862 114.414 182.203 114.755 182.203 115.175 c
S
169.659 122.702 m
169.238 122.702 168.897 122.361 168.897 121.94 c
B
0 g
170.504 121.19 m
171.581 121.19 l
173.274 117.157 l
173.304 117.157 l
174.982 121.19 l
176.058 121.19 l
176.058 115.863 l
175.335 115.863 l
175.335 120.242 l
175.32 120.242 l
173.522 115.863 l
173.041 115.863 l
171.242 120.242 l
171.227 120.242 l
171.227 115.863 l
170.504 115.863 l
170.504 121.19 l
f
177.375 121.19 m
179.248 121.19 l
180.61 121.19 180.957 120.37 180.957 119.7 c
180.957 119.023 180.452 118.384 179.647 118.293 c
181.16 115.863 l
180.256 115.863 l
178.902 118.21 l
178.097 118.21 l
178.097 115.863 l
177.375 115.863 l
177.375 121.19 l
h
178.097 118.842 m
179.045 118.842 l
179.617 118.842 180.189 118.978 180.189 119.7 c
180.189 120.423 179.617 120.558 179.045 120.558 c
178.097 120.558 l
178.097 118.842 l
f
0.188 0.137 0.063 0.008 k
285.58 113.411 m
286.697 113.411 287.611 114.325 287.611 115.443 c
287.611 121.539 l
287.611 122.656 286.697 123.571 285.58 123.571 c
274.404 123.571 l
273.287 123.571 272.372 122.656 272.372 121.539 c
272.372 115.443 l
272.372 114.325 273.287 113.411 274.404 113.411 c
285.58 113.411 l
h
B
285.89 114.414 m
286.311 114.414 286.652 114.755 286.652 115.175 c
S
274.108 122.702 m
273.688 122.702 273.346 122.361 273.346 121.94 c
B
0 g
274.954 121.19 m
276.03 121.19 l
277.723 117.157 l
277.753 117.157 l
279.431 121.19 l
280.507 121.19 l
280.507 115.863 l
279.785 115.863 l
279.785 120.242 l
279.77 120.242 l
277.971 115.863 l
277.49 115.863 l
275.691 120.242 l
275.676 120.242 l
275.676 115.863 l
274.954 115.863 l
274.954 121.19 l
f
281.824 121.19 m
283.697 121.19 l
285.06 121.19 285.405 120.37 285.405 119.7 c
285.405 119.023 284.901 118.384 284.096 118.293 c
285.609 115.863 l
284.706 115.863 l
283.351 118.21 l
282.546 118.21 l
282.546 115.863 l
281.824 115.863 l
281.824 121.19 l
h
282.546 118.842 m
283.494 118.842 l
284.066 118.842 284.638 118.978 284.638 119.7 c
284.638 120.423 284.066 120.558 283.494 120.558 c
282.546 120.558 l
282.546 118.842 l
f
0.188 0.137 0.063 0.008 k
372.108 113.411 m
373.226 113.411 374.141 114.325 374.141 115.443 c
374.141 121.539 l
374.141 122.656 373.226 123.571 372.108 123.571 c
360.933 123.571 l
359.815 123.571 358.901 122.656 358.901 121.539 c
358.901 115.443 l
358.901 114.325 359.815 113.411 360.933 113.411 c
372.108 113.411 l
h
B
372.419 114.414 m
372.84 114.414 373.181 114.755 373.181 115.175 c
S
360.637 122.702 m
360.216 122.702 359.875 122.361 359.875 121.94 c
B
0 g
361.483 121.19 m
362.559 121.19 l
364.252 117.157 l
364.282 117.157 l
365.96 121.19 l
367.036 121.19 l
367.036 115.863 l
366.314 115.863 l
366.314 120.242 l
366.299 120.242 l
364.5 115.863 l
364.019 115.863 l
362.22 120.242 l
362.205 120.242 l
362.205 115.863 l
361.483 115.863 l
361.483 121.19 l
f
368.353 121.19 m
370.227 121.19 l
371.588 121.19 371.935 120.37 371.935 119.7 c
371.935 119.023 371.43 118.384 370.625 118.293 c
372.138 115.863 l
371.234 115.863 l
369.88 118.21 l
369.075 118.21 l
369.075 115.863 l
368.353 115.863 l
368.353 121.19 l
h
369.075 118.842 m
370.023 118.842 l
370.595 118.842 371.167 118.978 371.167 119.7 c
371.167 120.423 370.595 120.558 370.023 120.558 c
369.075 120.558 l
369.075 118.842 l
f
0.188 0.137 0.063 0.008 k
164.83 188.671 m
165.947 188.671 166.862 189.586 166.862 190.703 c
166.862 196.799 l
166.862 197.916 165.947 198.831 164.83 198.831 c
153.654 198.831 l
152.537 198.831 151.623 197.916 151.623 196.799 c
151.623 190.703 l
151.623 189.586 152.537 188.671 153.654 188.671 c
164.83 188.671 l
h
B
165.141 189.674 m
165.562 189.674 165.902 190.015 165.902 190.436 c
S
153.358 197.962 m
152.938 197.962 152.596 197.621 152.596 197.2 c
B
0 g
157.814 193.638 m
156.55 195.301 l
157.423 195.301 l
158.288 194.037 l
159.139 195.301 l
159.959 195.301 l
158.74 193.638 l
160.185 191.734 l
159.312 191.734 l
158.258 193.232 l
157.205 191.734 l
156.37 191.734 l
157.814 193.638 l
f
BT
/T1_5 1 Tf
3.072 0 0 3.072 161.1388 195.1567 Tm
(\002)Tj
ET
0.188 0.137 0.063 0.008 k
217.417 188.671 m
218.535 188.671 219.449 189.586 219.449 190.703 c
219.449 196.799 l
219.449 197.916 218.535 198.831 217.417 198.831 c
206.242 198.831 l
205.124 198.831 204.21 197.916 204.21 196.799 c
204.21 190.703 l
204.21 189.586 205.124 188.671 206.242 188.671 c
217.417 188.671 l
h
B
217.728 189.674 m
218.148 189.674 218.49 190.015 218.49 190.436 c
205.946 197.962 m
205.525 197.962 205.184 197.621 205.184 197.2 c
S
0 g
210.401 193.638 m
209.137 195.301 l
210.01 195.301 l
210.876 194.037 l
211.726 195.301 l
212.546 195.301 l
211.327 193.638 l
212.772 191.734 l
211.899 191.734 l
210.846 193.232 l
209.792 191.734 l
208.957 191.734 l
210.401 193.638 l
f
BT
/T1_5 1 Tf
3.072 0 0 3.072 213.7257 195.1567 Tm
(\002)Tj
/T1_3 1 Tf
7 0 0 7 81.42 192.09 Tm
(Calculator keys)Tj
26.7857 -0.0714 Td
(Answer 89)Tj
-28.5 0.0714 Td
(1)Tj
1.7143 -2.1429 Td
(Calculator keys)Tj
26.7857 -0.1667 Td
(Answer 1024)Tj
-28.5 0.1667 Td
(2)Tj
1.7143 -12.9286 Td
(Calculator keys)Tj
26.7857 -0.0714 Td
(Answer 2)Tj
-28.5 0.0714 Td
(6)Tj
1.7143 -2.1429 Td
(Calculator keys)Tj
26.7857 -0.1666 Td
(Answer 0)Tj
/T1_4 1 Tf
4.1121 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(0625)Tj
-32.8901 0.1666 Td
(7)Tj
1.7143 12.9286 Td
(Calculator keys)Tj
26.7857 -0.1905 Td
(Answer 9 cm)Tj
-28.5 0.1905 Td
(3)Tj
1.7143 -2.2857 Td
(Calculator keys)Tj
-0.0714 -4.1905 Td
(Calculator keys)Tj
7.6686 -2.1586 Td
(Answer 120.24)Tj
19.1885 6.4205 Td
(Answer 4 cm)Tj
-28.5 -0.0714 Td
(4)Tj
1.7143 -2.1429 Td
(First put 2.974 into memory.        Calculator keys)Tj
-1.7143 0 Td
(5)Tj
ET
0.188 0.137 0.063 0.008 k
164.873 174.111 m
165.99 174.111 166.904 175.025 166.904 176.143 c
166.904 182.239 l
166.904 183.356 165.99 184.27 164.873 184.27 c
153.697 184.27 l
152.58 184.27 151.665 183.356 151.665 182.239 c
151.665 176.143 l
151.665 175.025 152.58 174.111 153.697 174.111 c
164.873 174.111 l
h
B
165.183 175.114 m
165.604 175.114 165.945 175.455 165.945 175.876 c
S
153.401 183.402 m
152.98 183.402 152.639 183.061 152.639 182.64 c
B
0 g
159.037 179.078 m
157.772 180.741 l
158.646 180.741 l
159.511 179.477 l
160.361 180.741 l
161.181 180.741 l
159.962 179.078 l
161.407 177.174 l
160.534 177.174 l
159.48 178.671 l
158.427 177.174 l
157.592 177.174 l
159.037 179.078 l
f
BT
/T1_5 1 Tf
3.072 0 0 3.072 162.3609 180.7672 Tm
(\003)Tj
/T1_0 1 Tf
7.6799 0 0 7.6799 156.7677 160.9745 Tm
(1)Tj
ET
0.188 0.137 0.063 0.008 k
182.884 158.596 m
184.002 158.596 184.917 159.51 184.917 160.628 c
184.917 166.723 l
184.917 167.841 184.002 168.755 182.884 168.755 c
171.709 168.755 l
170.591 168.755 169.677 167.841 169.677 166.723 c
169.677 160.628 l
169.677 159.51 170.591 158.596 171.709 158.596 c
182.884 158.596 l
h
B
183.195 159.598 m
183.616 159.598 183.957 159.94 183.957 160.36 c
S
171.413 167.887 m
170.992 167.887 170.651 167.546 170.651 167.125 c
B
182.884 143.777 m
184.002 143.777 184.917 144.691 184.917 145.809 c
184.917 151.904 l
184.917 153.022 184.002 153.936 182.884 153.936 c
171.709 153.936 l
170.591 153.936 169.677 153.022 169.677 151.904 c
169.677 145.809 l
169.677 144.691 170.591 143.777 171.709 143.777 c
182.884 143.777 l
h
B
183.195 144.779 m
183.616 144.779 183.957 145.121 183.957 145.541 c
S
171.413 153.068 m
170.992 153.068 170.651 152.727 170.651 152.306 c
B
0 g
BT
/T1_3 1 Tf
3.5839 0 0 3.5839 174.5596 149.9743 Tm
(3)Tj
/T1_0 1 Tf
7.6799 0 0 7.6799 281.5806 131.246 Tm
(9)Tj
ET
0.125 0.067 0.051 0.004 k
146.095 83.59 m
147.213 83.59 148.128 84.504 148.128 85.622 c
148.128 91.717 l
148.128 92.835 147.213 93.75 146.095 93.75 c
134.92 93.75 l
133.802 93.75 132.888 92.835 132.888 91.717 c
132.888 85.622 l
132.888 84.504 133.802 83.59 134.92 83.59 c
146.095 83.59 l
h
B
146.406 84.592 m
146.827 84.592 147.168 84.934 147.168 85.355 c
134.624 92.881 m
134.203 92.881 133.862 92.54 133.862 92.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 137.8053 85.8942 Tm
(1)Tj
ET
0.125 0.067 0.051 0.004 k
164.095 83.59 m
165.213 83.59 166.128 84.504 166.128 85.622 c
166.128 91.717 l
166.128 92.835 165.213 93.75 164.095 93.75 c
152.92 93.75 l
151.802 93.75 150.888 92.835 150.888 91.717 c
150.888 85.622 l
150.888 84.504 151.802 83.59 152.92 83.59 c
164.095 83.59 l
h
B
164.406 84.592 m
164.827 84.592 165.168 84.934 165.168 85.355 c
152.624 92.881 m
152.203 92.881 151.862 92.54 151.862 92.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 155.8053 85.8942 Tm
(6)Tj
ET
0.188 0.137 0.063 0.008 k
182.095 83.59 m
183.213 83.59 184.127 84.504 184.127 85.622 c
184.127 91.717 l
184.127 92.835 183.213 93.75 182.095 93.75 c
170.92 93.75 l
169.802 93.75 168.888 92.835 168.888 91.717 c
168.888 85.622 l
168.888 84.504 169.802 83.59 170.92 83.59 c
182.095 83.59 l
h
B
182.406 84.592 m
182.827 84.592 183.168 84.934 183.168 85.355 c
170.624 92.881 m
170.203 92.881 169.862 92.54 169.862 92.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 173.8053 85.8942 Tm
(x)Tj
3 0 0 3 179.045 90.715 Tm
(1)Tj
0 -0.8333 TD
(y)Tj
-6 -4.3333 Td
(y)Tj
ET
0.125 0.067 0.051 0.004 k
200.095 83.59 m
201.213 83.59 202.127 84.504 202.127 85.622 c
202.127 91.717 l
202.127 92.835 201.213 93.75 200.095 93.75 c
188.92 93.75 l
187.802 93.75 186.888 92.835 186.888 91.717 c
186.888 85.622 l
186.888 84.504 187.802 83.59 188.92 83.59 c
200.095 83.59 l
h
B
200.406 84.592 m
200.827 84.592 201.168 84.934 201.168 85.355 c
188.624 92.881 m
188.203 92.881 187.862 92.54 187.862 92.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 191.8053 85.8942 Tm
(4)Tj
ET
0.188 0.137 0.063 0.008 k
218.095 83.59 m
219.213 83.59 220.127 84.504 220.127 85.622 c
220.127 91.717 l
220.127 92.835 219.213 93.75 218.095 93.75 c
206.92 93.75 l
205.802 93.75 204.888 92.835 204.888 91.717 c
204.888 85.622 l
204.888 84.504 205.802 83.59 206.92 83.59 c
218.095 83.59 l
h
B
218.406 84.592 m
218.827 84.592 219.168 84.934 219.168 85.355 c
206.624 92.881 m
206.203 92.881 205.862 92.54 205.862 92.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 209.8053 85.8942 Tm
(=)Tj
ET
0.125 0.067 0.051 0.004 k
146.095 68.59 m
147.213 68.59 148.128 69.504 148.128 70.622 c
148.128 76.717 l
148.128 77.835 147.213 78.75 146.095 78.75 c
134.92 78.75 l
133.802 78.75 132.888 77.835 132.888 76.717 c
132.888 70.622 l
132.888 69.504 133.802 68.59 134.92 68.59 c
146.095 68.59 l
h
B
146.406 69.592 m
146.827 69.592 147.168 69.934 147.168 70.355 c
134.624 77.881 m
134.203 77.881 133.862 77.54 133.862 77.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 137.8053 70.8942 Tm
(4)Tj
ET
164.406 69.592 m
164.827 69.592 165.168 69.934 165.168 70.355 c
152.624 77.881 m
152.203 77.881 151.862 77.54 151.862 77.119 c
S
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 155.8053 70.8942 Tm
(x)Tj
ET
0.125 0.067 0.051 0.004 k
182.095 68.59 m
183.213 68.59 184.127 69.504 184.127 70.622 c
184.127 76.717 l
184.127 77.835 183.213 78.75 182.095 78.75 c
170.92 78.75 l
169.802 78.75 168.888 77.835 168.888 76.717 c
168.888 70.622 l
168.888 69.504 169.802 68.59 170.92 68.59 c
182.095 68.59 l
h
B
182.406 69.592 m
182.827 69.592 183.168 69.934 183.168 70.355 c
170.624 77.881 m
170.203 77.881 169.862 77.54 169.862 77.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 173.8053 70.8942 Tm
(2)Tj
ET
0.188 0.137 0.063 0.008 k
200.095 68.59 m
201.213 68.59 202.127 69.504 202.127 70.622 c
202.127 76.717 l
202.127 77.835 201.213 78.75 200.095 78.75 c
188.92 78.75 l
187.802 78.75 186.888 77.835 186.888 76.717 c
186.888 70.622 l
186.888 69.504 187.802 68.59 188.92 68.59 c
200.095 68.59 l
h
B
200.406 69.592 m
200.827 69.592 201.168 69.934 201.168 70.355 c
188.624 77.881 m
188.203 77.881 187.862 77.54 187.862 77.119 c
S
0 g
BT
/T1_0 1 Tf
5 0 0 5 190.67 73.34 Tm
(+)Tj
/T1_6 1 Tf
0.925 -0.7 Td
(\320)Tj
ET
0.188 0.137 0.063 0.008 k
218.095 68.59 m
219.213 68.59 220.127 69.504 220.127 70.622 c
220.127 76.717 l
220.127 77.835 219.213 78.75 218.095 78.75 c
206.92 78.75 l
205.802 78.75 204.888 77.835 204.888 76.717 c
204.888 70.622 l
204.888 69.504 205.802 68.59 206.92 68.59 c
218.095 68.59 l
h
B
218.406 69.592 m
218.827 69.592 219.168 69.934 219.168 70.355 c
206.624 77.881 m
206.203 77.881 205.862 77.54 205.862 77.119 c
S
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 209.8053 70.8942 Tm
(=)Tj
ET
0.188 0.137 0.063 0.008 k
198.324 113.494 m
199.441 113.494 200.355 114.408 200.355 115.526 c
200.355 121.622 l
200.355 122.739 199.441 123.653 198.324 123.653 c
187.148 123.653 l
186.031 123.653 185.116 122.739 185.116 121.622 c
185.116 115.526 l
185.116 114.408 186.031 113.494 187.148 113.494 c
198.324 113.494 l
h
B
198.634 114.497 m
199.055 114.497 199.396 114.838 199.396 115.258 c
186.852 122.785 m
186.431 122.785 186.09 122.444 186.09 122.023 c
S
0 g
192.488 118.461 m
191.224 120.124 l
192.096 120.124 l
192.962 118.859 l
193.812 120.124 l
194.632 120.124 l
193.413 118.461 l
194.858 116.557 l
193.985 116.557 l
192.932 118.054 l
191.878 116.557 l
191.043 116.557 l
192.488 118.461 l
f
BT
/T1_5 1 Tf
3.072 0 0 3.072 195.8121 120.1501 Tm
(\003)Tj
ET
0.188 0.137 0.063 0.008 k
302.773 113.494 m
303.89 113.494 304.805 114.408 304.805 115.526 c
304.805 121.622 l
304.805 122.739 303.89 123.653 302.773 123.653 c
291.598 123.653 l
290.48 123.653 289.565 122.739 289.565 121.622 c
289.565 115.526 l
289.565 114.408 290.48 113.494 291.598 113.494 c
302.773 113.494 l
h
B
303.084 114.497 m
303.505 114.497 303.845 114.838 303.845 115.258 c
291.301 122.785 m
290.88 122.785 290.539 122.444 290.539 122.023 c
S
0 g
296.937 118.461 m
295.673 120.124 l
296.545 120.124 l
297.411 118.859 l
298.261 120.124 l
299.082 120.124 l
297.862 118.461 l
299.307 116.557 l
298.435 116.557 l
297.381 118.054 l
296.327 116.557 l
295.492 116.557 l
296.937 118.461 l
f
BT
/T1_5 1 Tf
3.072 0 0 3.072 300.2613 120.1501 Tm
(\002)Tj
ET
178.67 90.09 m
181.045 90.09 l
B
191.92 70.59 m
197.545 76.215 l
S
178.969 166.865 m
176.892 160.753 l
176.894 160.759 176.895 160.765 176.895 160.772 c
176.895 160.765 176.894 160.759 176.892 160.752 c
176.867 160.68 176.799 160.632 176.723 160.632 c
176.646 160.632 176.578 160.681 176.554 160.753 c
175.595 163.635 l
174.631 163.089 l
174.662 163.03 l
174.805 163.118 175.206 163.362 y
175.252 163.39 175.308 163.396 175.359 163.378 c
175.41 163.359 175.449 163.319 175.467 163.268 c
176.58 160.012 l
176.807 160.012 l
179.138 166.865 l
178.969 166.865 l
f
178.344 152.052 m
176.267 145.94 l
176.269 145.946 176.27 145.952 176.27 145.959 c
176.27 145.952 176.269 145.946 176.267 145.94 c
176.242 145.867 176.174 145.819 176.098 145.819 c
176.021 145.819 175.953 145.868 175.929 145.941 c
174.97 148.822 l
174.006 148.276 l
174.037 148.218 l
174.18 148.305 174.581 148.55 y
174.627 148.578 174.683 148.584 174.734 148.565 c
174.785 148.547 174.824 148.507 174.842 148.455 c
175.955 145.199 l
176.182 145.199 l
178.513 152.052 l
178.344 152.052 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
/GS6 gs
61.09 392.21 346.96 -20.61 re
f*
Q Q 
0.188 0.137 0.075 0.008 k
0.4 w 
179.843 375.117 m
181.24 375.117 182.383 376.259 182.383 377.656 c
182.383 385.276 l
182.383 386.673 181.24 387.816 179.843 387.816 c
165.874 387.816 l
164.477 387.816 163.334 386.673 163.334 385.276 c
163.334 377.656 l
163.334 376.259 164.477 375.117 165.874 375.117 c
179.843 375.117 l
h
B
180.231 376.37 m
180.757 376.37 181.184 376.796 181.184 377.322 c
165.504 386.73 m
164.978 386.73 164.551 386.304 164.551 385.778 c
S
0 g
169.163 384.923 m
170.508 384.923 l
172.624 379.881 l
172.662 379.881 l
174.759 384.923 l
176.104 384.923 l
176.104 378.263 l
175.202 378.263 l
175.202 383.738 l
175.182 383.738 l
172.934 378.263 l
172.332 378.263 l
170.084 383.738 l
170.066 383.738 l
170.066 378.263 l
169.163 378.263 l
169.163 384.923 l
f
0.188 0.137 0.075 0.008 k
271.427 375.557 m
272.824 375.557 273.966 376.699 273.966 378.097 c
273.966 385.716 l
273.966 387.113 272.824 388.256 271.427 388.256 c
257.458 388.256 l
256.061 388.256 254.918 387.113 254.918 385.716 c
254.918 378.097 l
254.918 376.699 256.061 375.557 257.458 375.557 c
271.427 375.557 l
h
B
271.815 376.81 m
272.341 376.81 272.767 377.236 272.767 377.762 c
257.088 387.17 m
256.561 387.17 256.135 386.744 256.135 386.218 c
S
0 g
258.144 385.281 m
259.49 385.281 l
261.606 380.239 l
261.643 380.239 l
263.741 385.281 l
265.086 385.281 l
265.086 378.621 l
264.183 378.621 l
264.183 384.095 l
264.165 384.095 l
261.916 378.621 l
261.314 378.621 l
259.066 384.095 l
259.047 384.095 l
259.047 378.621 l
258.144 378.621 l
258.144 385.281 l
f
266.732 385.281 m
269.074 385.281 l
270.777 385.281 271.209 384.255 271.209 383.418 c
271.209 382.572 270.579 381.772 269.572 381.659 c
271.463 378.621 l
270.334 378.621 l
268.641 381.556 l
267.635 381.556 l
267.635 378.621 l
266.732 378.621 l
266.732 385.281 l
h
267.635 382.346 m
268.82 382.346 l
269.535 382.346 270.25 382.515 270.25 383.418 c
270.25 384.321 269.535 384.49 268.82 384.49 c
267.635 384.49 l
267.635 382.346 l
f
BT
/T1_3 1 Tf
7.2 0 0 7.2 93.1594 379.17 Tm
(Most calculators use:)Tj
12.9259 0.0593 Td
(to put into memory.)Tj
12.9075 0.0592 Td
(is used to recall what is in memory.)Tj
ET
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
/GS7 gs
52.54 536.29 364.07 -125.97 re
f*
Q Q 
0.125 0.071 0.055 0.004 k
210.489 413.177 m
211.886 413.177 213.028 414.32 213.028 415.717 c
213.028 423.336 l
213.028 424.733 211.886 425.876 210.489 425.876 c
196.52 425.876 l
195.123 425.876 193.98 424.733 193.98 423.336 c
193.98 415.717 l
193.98 414.32 195.123 413.177 196.52 413.177 c
210.489 413.177 l
h
B
210.877 414.43 m
211.403 414.43 211.829 414.856 211.829 415.382 c
B
232.299 413.19 m
233.696 413.19 234.839 414.333 234.839 415.73 c
234.839 423.349 l
234.839 424.746 233.696 425.889 232.299 425.889 c
218.33 425.889 l
216.933 425.889 215.79 424.746 215.79 423.349 c
215.79 415.73 l
215.79 414.333 216.933 413.19 218.33 413.19 c
232.299 413.19 l
h
B
232.688 414.443 m
233.213 414.443 233.64 414.87 233.64 415.395 c
B
276.19 413.19 m
277.587 413.19 278.73 414.333 278.73 415.73 c
278.73 423.349 l
278.73 424.746 277.587 425.889 276.19 425.889 c
262.221 425.889 l
260.824 425.889 259.681 424.746 259.681 423.349 c
259.681 415.73 l
259.681 414.333 260.824 413.19 262.221 413.19 c
276.19 413.19 l
h
B
0.188 0.137 0.075 0.008 k
154.109 463.296 m
155.506 463.296 156.649 464.439 156.649 465.836 c
156.649 473.456 l
156.649 474.853 155.506 475.995 154.109 475.995 c
140.14 475.995 l
138.743 475.995 137.6 474.853 137.6 473.456 c
137.6 465.836 l
137.6 464.439 138.743 463.296 140.14 463.296 c
154.109 463.296 l
h
B
139.77 474.91 m
139.244 474.91 138.818 474.483 138.818 473.957 c
B
154.109 446.336 m
155.506 446.336 156.649 447.479 156.649 448.876 c
156.649 456.495 l
156.649 457.892 155.506 459.035 154.109 459.035 c
140.14 459.035 l
138.743 459.035 137.6 457.892 137.6 456.495 c
137.6 448.876 l
137.6 447.479 138.743 446.336 140.14 446.336 c
154.109 446.336 l
h
B
139.77 457.95 m
139.244 457.95 138.818 457.523 138.818 456.997 c
B
154.109 429.376 m
155.506 429.376 156.649 430.519 156.649 431.916 c
156.649 439.535 l
156.649 440.932 155.506 442.075 154.109 442.075 c
140.14 442.075 l
138.743 442.075 137.6 440.932 137.6 439.535 c
137.6 431.916 l
137.6 430.519 138.743 429.376 140.14 429.376 c
154.109 429.376 l
h
B
139.77 440.99 m
139.244 440.99 138.818 440.563 138.818 440.037 c
B
238.589 480.98 m
239.986 480.98 241.129 482.123 241.129 483.52 c
241.129 491.139 l
241.129 492.536 239.986 493.679 238.589 493.679 c
224.62 493.679 l
223.223 493.679 222.08 492.536 222.08 491.139 c
222.08 483.52 l
222.08 482.123 223.223 480.98 224.62 480.98 c
238.589 480.98 l
h
B
282.211 481.006 m
283.607 481.006 284.75 482.149 284.75 483.546 c
284.75 491.166 l
284.75 492.563 283.607 493.706 282.211 493.706 c
268.241 493.706 l
266.845 493.706 265.702 492.563 265.702 491.166 c
265.702 483.546 l
265.702 482.149 266.845 481.006 268.241 481.006 c
282.211 481.006 l
h
B
304.459 481.006 m
305.856 481.006 306.999 482.149 306.999 483.546 c
306.999 491.166 l
306.999 492.563 305.856 493.706 304.459 493.706 c
290.49 493.706 l
289.093 493.706 287.95 492.563 287.95 491.166 c
287.95 483.546 l
287.95 482.149 289.093 481.006 290.49 481.006 c
304.459 481.006 l
h
B
0.125 0.071 0.055 0.004 k
216.779 480.967 m
218.176 480.967 219.319 482.11 219.319 483.506 c
219.319 491.126 l
219.319 492.523 218.176 493.666 216.779 493.666 c
202.81 493.666 l
201.413 493.666 200.27 492.523 200.27 491.126 c
200.27 483.506 l
200.27 482.11 201.413 480.967 202.81 480.967 c
216.779 480.967 l
h
B
202.44 492.58 m
201.914 492.58 201.488 492.154 201.488 491.628 c
B
260.4 480.993 m
261.797 480.993 262.94 482.136 262.94 483.533 c
262.94 491.153 l
262.94 492.549 261.797 493.692 260.4 493.692 c
246.431 493.692 l
245.034 493.692 243.891 492.549 243.891 491.153 c
243.891 483.533 l
243.891 482.136 245.034 480.993 246.431 480.993 c
260.4 480.993 l
h
B
0.188 0.137 0.075 0.008 k
154.109 516.02 m
155.506 516.02 156.649 517.163 156.649 518.56 c
156.649 526.179 l
156.649 527.576 155.506 528.719 154.109 528.719 c
140.14 528.719 l
138.743 528.719 137.6 527.576 137.6 526.179 c
137.6 518.56 l
137.6 517.163 138.743 516.02 140.14 516.02 c
154.109 516.02 l
h
B
154.498 517.273 m
155.023 517.273 155.45 517.7 155.45 518.226 c
139.77 527.634 m
139.244 527.634 138.818 527.207 138.818 526.681 c
S
0 g
146.814 522.229 m
145.234 524.307 l
146.325 524.307 l
147.407 522.727 l
148.47 524.307 l
149.495 524.307 l
147.972 522.229 l
149.777 519.849 l
148.686 519.849 l
147.37 521.721 l
146.053 519.849 l
145.009 519.849 l
146.814 522.229 l
f
0.188 0.137 0.075 0.008 k
154.109 497.46 m
155.506 497.46 156.649 498.603 156.649 500 c
156.649 507.619 l
156.649 509.017 155.506 510.159 154.109 510.159 c
140.14 510.159 l
138.743 510.159 137.6 509.017 137.6 507.619 c
137.6 500 l
137.6 498.603 138.743 497.46 140.14 497.46 c
154.109 497.46 l
h
B
154.498 498.713 m
155.023 498.713 155.45 499.14 155.45 499.666 c
S
139.77 509.074 m
139.244 509.074 138.818 508.647 138.818 508.121 c
B
0 g
146.814 503.669 m
145.234 505.747 l
146.325 505.747 l
147.407 504.167 l
148.47 505.747 l
149.495 505.747 l
147.972 503.669 l
149.777 501.288 l
148.686 501.288 l
147.37 503.16 l
146.053 501.288 l
145.009 501.288 l
146.814 503.669 l
f
BT
/T1_0 1 Tf
3.84 0 0 3.84 150.9699 524.1268 Tm
(2)Tj
-1.5556 -18.1779 Td
(3)Tj
1.5556 13.4002 Td
(y)Tj
22 -4.3473 Td
(y)Tj
/T1_3 1 Tf
7.2 0 0 7.2 162.9164 520.7135 Tm
(This is used to square a number, eg 8)Tj
4.8 0 0 4.8 283.4611 524.3419 Tm
(2)Tj
7.2 0 0 7.2 286.1295 520.7135 Tm
( = 64)Tj
-26.5056 0 Td
(Square key)Tj
0 -2.6074 TD
(Power key)Tj
0 -4.7153 TD
(Square root)Tj
0 -2.3556 TD
(Cube root)Tj
T*
[(Root key)-5180(or)]TJ
ET
154.498 464.549 m
155.023 464.549 155.45 464.976 155.45 465.502 c
S
BT
/T1_3 1 Tf
7.2 0 0 7.2 162.9164 467.9896 Tm
(This is used to calculate the square root of a number, eg    36 = 6)Tj
ET
154.498 447.589 m
155.023 447.589 155.45 448.016 155.45 448.542 c
S
BT
/T1_3 1 Tf
7.2 0 0 7.2 162.9164 451.0295 Tm
(This is used to calculate the cube root of a number, eg   )Tj
4.8 0 0 4.8 344.1258 454.2295 Tm
(3)Tj
7.2 0 0 7.2 346.7942 451.0295 Tm
(  125 = 5)Tj
-21.0348 -2.3556 Td
(This is used to calculate the root of a number, eg   )Tj
4.8 0 0 4.8 358.6759 437.2693 Tm
(5)Tj
7.2 0 0 7.2 361.3443 434.0693 Tm
(  32 = 2)Tj
-27.9446 9.4265 Td
(or)Tj
-3.0815 -2.3259 Td
(Calculator keys:)Tj
25.2795 -0.0463 Td
(Answer 0)Tj
/T1_4 1 Tf
4.1118 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(125)Tj
ET
0.188 0.137 0.075 0.008 k
298.31 413.19 m
299.707 413.19 300.85 414.333 300.85 415.73 c
300.85 423.349 l
300.85 424.746 299.707 425.889 298.31 425.889 c
284.341 425.889 l
282.944 425.889 281.801 424.746 281.801 423.349 c
281.801 415.73 l
281.801 414.333 282.944 413.19 284.341 413.19 c
298.31 413.19 l
h
B
298.698 414.443 m
299.224 414.443 299.651 414.87 299.651 415.395 c
283.971 424.804 m
283.445 424.804 283.018 424.377 283.018 423.851 c
S
0 g
288.943 420.586 5.023 -0.734 re
288.943 419.109 5.023 -0.734 re
f
0.188 0.137 0.075 0.008 k
254.11 413.203 m
255.507 413.203 256.65 414.346 256.65 415.743 c
256.65 423.363 l
256.65 424.76 255.507 425.903 254.11 425.903 c
240.141 425.903 l
238.744 425.903 237.601 424.76 237.601 423.363 c
237.601 415.743 l
237.601 414.346 238.744 413.203 240.141 413.203 c
254.11 413.203 l
h
B
254.498 414.456 m
255.024 414.456 255.45 414.883 255.45 415.409 c
239.77 424.817 m
239.245 424.817 238.818 424.39 238.818 423.864 c
S
0 g
246.815 419.412 m
245.234 421.49 l
246.326 421.49 l
247.407 419.91 l
248.47 421.49 l
249.496 421.49 l
247.972 419.412 l
249.778 417.032 l
248.687 417.032 l
247.37 418.904 l
246.053 417.032 l
245.009 417.032 l
246.815 419.412 l
f
BT
/T1_0 1 Tf
3.84 0 0 3.84 250.9703 421.5232 Tm
(1)Tj
0 -0.8333 TD
(y)Tj
ET
196.149 424.79 m
195.623 424.79 195.197 424.364 195.197 423.838 c
S
202.556 417.788 m
202.773 417.149 203.074 416.838 203.779 416.838 c
204.475 416.838 205.068 417.328 205.068 418.042 c
205.068 419.152 204.043 419.284 203.196 419.284 c
203.196 420.074 l
204.57 420.074 204.898 420.46 204.898 421.118 c
204.898 421.824 204.419 422.2 203.779 422.2 c
203.29 422.2 202.867 421.889 202.669 421.428 c
201.747 421.739 l
202.096 422.585 202.876 422.99 203.761 422.99 c
204.852 422.99 205.802 422.407 205.802 421.174 c
205.802 420.478 205.341 419.867 204.663 419.669 c
204.663 419.651 l
205.501 419.51 205.971 418.795 205.971 417.976 c
205.971 416.697 204.927 416.048 203.751 416.048 c
202.735 416.048 201.907 416.49 201.606 417.497 c
202.556 417.788 l
f
BT
/T1_3 1 Tf
7.2 0 0 7.2 137.9562 417.7365 Tm
[(Calculator keys:)-16448(Answer 2)]TJ
8.0001 11.6949 Td
(This is used to calculate powers, eg  2)Tj
/T1_4 1 Tf
4.8 0 0 4.8 317.4261 505.5684 Tm
(\320)Tj
/T1_3 1 Tf
0.4999 0 Td
(3)Tj
7.2 0 0 7.2 322.494 505.5684 Tm
( )Tj
ET
0.188 0.137 0.075 0.008 k
187.389 497.46 m
188.786 497.46 189.929 498.603 189.929 500 c
189.929 507.619 l
189.929 509.017 188.786 510.159 187.389 510.159 c
173.42 510.159 l
172.023 510.159 170.88 509.017 170.88 507.619 c
170.88 500 l
170.88 498.603 172.023 497.46 173.42 497.46 c
187.389 497.46 l
h
B
187.778 498.713 m
188.304 498.713 188.73 499.14 188.73 499.666 c
S
173.05 509.074 m
172.524 509.074 172.098 508.647 172.098 508.121 c
B
0 g
BT
/T1_0 1 Tf
3.84 0 0 3.84 184.4633 506.2068 Tm
(x)Tj
8.96 0 0 8.96 178.1164 500.9803 Tm
(y)Tj
ET
351.077 474.033 m
348.837 467.444 l
348.839 467.45 348.841 467.457 348.841 467.464 c
348.841 467.457 348.839 467.45 348.837 467.443 c
348.811 467.365 348.737 467.313 348.655 467.313 c
348.572 467.313 348.499 467.366 348.473 467.444 c
347.439 470.551 l
346.4 469.962 l
346.434 469.899 l
346.588 469.994 347.019 470.257 y
347.069 470.288 347.129 470.294 347.185 470.274 c
347.24 470.254 347.282 470.211 347.301 470.155 c
348.501 466.645 l
348.746 466.645 l
351.259 474.033 l
351.077 474.033 l
f
349.957 455.953 m
347.717 449.363 l
347.72 449.37 347.721 449.377 347.721 449.384 c
347.721 449.377 347.72 449.37 347.717 449.363 c
347.691 449.285 347.617 449.233 347.535 449.233 c
347.452 449.233 347.379 449.286 347.353 449.365 c
346.319 452.471 l
345.28 451.882 l
345.314 451.819 l
345.468 451.914 345.899 452.177 y
345.949 452.208 346.009 452.213 346.064 452.194 c
346.12 452.174 346.162 452.131 346.181 452.075 c
347.38 448.565 l
347.626 448.565 l
350.139 455.953 l
349.957 455.953 l
f
363.984 439.313 m
361.744 432.723 l
361.746 432.73 361.747 432.737 361.747 432.744 c
361.747 432.737 361.746 432.73 361.744 432.723 c
361.717 432.645 361.644 432.593 361.562 432.593 c
361.479 432.594 361.406 432.646 361.38 432.724 c
360.345 435.831 l
359.307 435.242 l
359.34 435.179 l
359.495 435.274 359.926 435.537 y
359.976 435.567 360.036 435.574 360.091 435.554 c
360.146 435.534 360.189 435.49 360.208 435.435 c
361.407 431.925 l
361.653 431.925 l
364.166 439.313 l
363.984 439.313 l
f
149.989 438.58 m
147.75 431.99 l
147.752 431.997 147.754 432.004 147.754 432.01 c
147.754 432.003 147.752 431.997 147.75 431.99 c
147.723 431.912 147.65 431.86 147.568 431.86 c
147.485 431.86 147.412 431.913 147.386 431.991 c
146.352 435.097 l
145.313 434.509 l
145.346 434.446 l
145.501 434.54 145.932 434.804 y
145.982 434.834 146.042 434.84 146.097 434.821 c
146.152 434.801 146.195 434.757 146.214 434.702 c
147.413 431.192 l
147.659 431.192 l
150.172 438.58 l
149.989 438.58 l
f
149.989 455.78 m
147.75 449.19 l
147.752 449.197 147.754 449.204 147.754 449.21 c
147.754 449.203 147.752 449.197 147.75 449.19 c
147.723 449.112 147.65 449.06 147.568 449.06 c
147.485 449.06 147.412 449.113 147.386 449.191 c
146.352 452.297 l
145.313 451.709 l
145.346 451.646 l
145.501 451.74 145.932 452.004 y
145.982 452.034 146.042 452.04 146.097 452.021 c
146.152 452.001 146.195 451.957 146.214 451.902 c
147.413 448.392 l
147.659 448.392 l
150.172 455.78 l
149.989 455.78 l
f
148.789 473.38 m
146.55 466.79 l
146.552 466.797 146.553 466.804 146.553 466.81 c
146.553 466.803 146.552 466.797 146.55 466.79 c
146.523 466.712 146.45 466.66 146.368 466.66 c
146.285 466.66 146.212 466.713 146.186 466.791 c
145.152 469.897 l
144.113 469.309 l
144.146 469.246 l
144.301 469.34 144.732 469.604 y
144.782 469.634 144.842 469.64 144.897 469.621 c
144.952 469.601 144.995 469.557 145.014 469.502 c
146.213 465.992 l
146.459 465.992 l
148.972 473.38 l
148.789 473.38 l
f
BT
/T1_0 1 Tf
3.84 0 0 3.84 144.9965 437.3635 Tm
(x)Tj
ET
154.498 430.629 m
155.023 430.629 155.45 431.056 155.45 431.581 c
S
BT
/T1_0 1 Tf
9.5999 0 0 9.5999 222.2647 416.0573 Tm
(2)Tj
ET
217.96 424.803 m
217.434 424.803 217.007 424.377 217.007 423.851 c
S
BT
/T1_0 1 Tf
9.5999 0 0 9.5999 206.7448 483.8342 Tm
(2)Tj
ET
217.168 482.22 m
217.693 482.22 218.12 482.646 218.12 483.172 c
S
BT
/T1_0 1 Tf
9.5999 0 0 9.5999 228.8194 483.8475 Tm
(x)Tj
ET
238.978 482.233 m
239.504 482.233 239.93 482.66 239.93 483.186 c
224.25 492.594 m
223.724 492.594 223.298 492.167 223.298 491.641 c
S
BT
/T1_0 1 Tf
9.5999 0 0 9.5999 250.3655 483.8608 Tm
(3)Tj
ET
260.788 482.246 m
261.314 482.246 261.741 482.673 261.741 483.199 c
246.061 492.607 m
245.535 492.607 245.109 492.18 245.109 491.655 c
S
BT
/T1_0 1 Tf
7.04 0 0 7.04 270.546 486.8467 Tm
(+)Tj
/T1_6 1 Tf
0.6739 -0.5909 Td
(\320)Tj
ET
282.599 482.26 m
283.125 482.26 283.551 482.686 283.551 483.212 c
267.872 492.62 m
267.345 492.62 266.919 492.194 266.919 491.668 c
S
BT
/T1_0 1 Tf
9.5999 0 0 9.5999 294.0697 483.874 Tm
(=)Tj
ET
304.848 482.26 m
305.374 482.26 305.8 482.686 305.8 483.212 c
290.12 492.62 m
289.594 492.62 289.168 492.194 289.168 491.668 c
S
BT
/T1_0 1 Tf
9.5999 0 0 9.5999 266.1553 416.0573 Tm
(5)Tj
ET
276.578 414.443 m
277.104 414.443 277.53 414.87 277.53 415.395 c
261.85 424.803 m
261.325 424.803 260.898 424.377 260.898 423.851 c
253.65 420.909 m
250.45 420.909 l
S
0.188 0.137 0.075 0.008 k
188.517 429.376 m
189.914 429.376 191.057 430.519 191.057 431.916 c
191.057 439.535 l
191.057 440.932 189.914 442.075 188.517 442.075 c
174.548 442.075 l
173.151 442.075 172.008 440.932 172.008 439.535 c
172.008 431.916 l
172.008 430.519 173.151 429.376 174.548 429.376 c
188.517 429.376 l
h
B
188.905 430.629 m
189.431 430.629 189.857 431.056 189.857 431.581 c
174.177 440.99 m
173.652 440.99 173.225 440.563 173.225 440.037 c
S
0 g
181.222 435.584 m
179.641 437.663 l
180.733 437.663 l
181.814 436.083 l
182.877 437.663 l
183.903 437.663 l
182.379 435.584 l
184.185 433.205 l
183.094 433.205 l
181.777 435.076 l
180.46 433.205 l
179.416 433.205 l
181.222 435.584 l
f
BT
/T1_0 1 Tf
3.84 0 0 3.84 185.377 437.6959 Tm
(1)Tj
T*
(y)Tj
ET
188.057 437.082 m
184.857 437.082 l
279.29 490.367 m
272.41 483.487 l
S
BT
/T1_3 1 Tf
6 0 0 6 126.47 224.894 Tm
(4)Tj
9 0 0 9 129.8062 220.894 Tm
(  16)Tj
ET
133.262 227.449 m
130.462 219.211 l
130.465 219.22 130.467 219.228 130.467 219.237 c
130.467 219.228 130.465 219.22 130.462 219.211 c
130.429 219.114 130.338 219.048 130.235 219.049 c
130.131 219.049 130.04 219.115 130.007 219.213 c
128.714 223.096 l
127.416 222.36 l
127.458 222.282 l
127.651 222.399 128.19 222.728 y
128.252 222.767 128.327 222.774 128.397 222.749 c
128.466 222.725 128.518 222.67 128.542 222.601 c
130.042 218.214 l
130.348 218.214 l
133.49 227.449 l
133.262 227.449 l
f
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/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
49.61 42.05 368.5 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
8 0 0 8 50.6063 35.0006 Tm
(4)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 265.7926 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
49.61 593.39 368.5 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0295 Tw 14 0 0 14 186.2217 581.8038 Tm
[(Standar)18(d for)-18(m)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0278 Tw 10 0 0 10 50.6063 604.6697 Tm
(Calculator skills)Tj
/T1_3 1 Tf
-0.0002 Tc 9 0 0 9 67.6142 555.7249 Tm
[(Standar)18(d for)-18(m is used to write very lar)18(ge and very small numbers.)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 50.6063 356.3549 Tm
(Questions)Tj
0 0 0 1 k
/T1_3 1 Tf
0.0278 Tw 9 0 0 9 67.6142 341.5202 Tm
[(1)-1334(W)18(rite 8.4 x 10)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 141.1937 345.1203 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 147.4465 341.5202 Tm
[(as an or)18(dinary number)92(.)]TJ
-0.0001 Tc -8.8703 -1.9633 Td
[(2)-1334(W)18(rite 3)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 5.1368 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(24 x 10)Tj
/T1_4 1 Tf
0 Tc 0 Tw 6.3 0 0 6.3 146.1969 327.4509 Tm
(\320)Tj
/T1_3 1 Tf
0.4998 0 Td
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 155.5996 323.8509 Tm
[(as an or)18(dinary )]TJ
0 Tw -7.8864 -1.3333 Td
[(number)92(.)]TJ
0.0278 Tw -1.8898 -1.9632 Td
[(3)-1334(W)18(rite 3820 in standar)18(d for)-18(m.)]TJ
-0.0001 Tc 0 -1.9632 TD
[(4)-1334(W)18(rite 0)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 5.1367 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
[(00236 in standar)18(d for)-18(m.)]TJ
1.3338 Tc 0 Tw -5.4146 -1.9632 Td
(57)Tj
/T1_4 1 Tf
0 Tc 2.4456 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(3 x 10)Tj
0 Tc 0 Tw 6.3 0 0 6.3 116.9737 262.4431 Tm
(8)Tj
/T1_4 1 Tf
9 0 0 9 123.2264 258.8432 Tm
(\326)Tj
/T1_3 1 Tf
0.9714 0 Td
(6)Tj
/T1_4 1 Tf
0.5559 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(4 x 10)Tj
/T1_4 1 Tf
0 Tc 0 Tw 6.3 0 0 6.3 164.3206 262.4431 Tm
(\320)Tj
/T1_3 1 Tf
0.4998 0 Td
(7)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 8 0 0 8 50.6063 238.3392 Tm
(Answers)Tj
ET
Q Q 
q
55.26 235.52 357.2 -175.92 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.059 0.024 0.482 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS4 gs
227.64 61.32 177.5 26 re
B
0.125 0.071 0.055 0.004 k
156.548 95.119 m
157.665 95.119 158.579 96.034 158.579 97.151 c
158.579 103.247 l
158.579 104.364 157.665 105.279 156.548 105.279 c
145.372 105.279 l
144.255 105.279 143.341 104.364 143.341 103.247 c
143.341 97.151 l
143.341 96.034 144.255 95.119 145.372 95.119 c
156.548 95.119 l
h
B
156.859 96.122 m
157.28 96.122 157.62 96.463 157.62 96.884 c
B
145.076 104.41 m
144.656 104.41 144.314 104.07 144.314 103.649 c
B
174.459 95.119 m
175.576 95.119 176.491 96.034 176.491 97.151 c
176.491 103.247 l
176.491 104.364 175.576 105.279 174.459 105.279 c
163.284 105.279 l
162.166 105.279 161.251 104.364 161.251 103.247 c
161.251 97.151 l
161.251 96.034 162.166 95.119 163.284 95.119 c
174.459 95.119 l
h
B
174.769 96.122 m
175.19 96.122 175.531 96.463 175.531 96.884 c
B
162.987 104.41 m
162.566 104.41 162.225 104.07 162.225 103.649 c
B
0.188 0.137 0.075 0.008 k
260.245 95.119 m
261.363 95.119 262.277 96.034 262.277 97.151 c
262.277 103.247 l
262.277 104.364 261.363 105.279 260.245 105.279 c
249.069 105.279 l
247.951 105.279 247.037 104.364 247.037 103.247 c
247.037 97.151 l
247.037 96.034 247.951 95.119 249.069 95.119 c
260.245 95.119 l
h
B
260.555 96.122 m
260.976 96.122 261.317 96.463 261.317 96.884 c
B
248.773 104.41 m
248.352 104.41 248.011 104.07 248.011 103.649 c
B
138.637 95.119 m
139.755 95.119 140.669 96.034 140.669 97.151 c
140.669 103.247 l
140.669 104.364 139.755 105.279 138.637 105.279 c
127.462 105.279 l
126.344 105.279 125.43 104.364 125.43 103.247 c
125.43 97.151 l
125.43 96.034 126.344 95.119 127.462 95.119 c
138.637 95.119 l
h
B
138.948 96.122 m
139.368 96.122 139.71 96.463 139.71 96.884 c
B
127.165 104.41 m
126.745 104.41 126.404 104.07 126.404 103.649 c
B
117.226 122.82 m
118.344 122.82 119.258 123.734 119.258 124.852 c
119.258 130.947 l
119.258 132.065 118.344 132.979 117.226 132.979 c
106.051 132.979 l
104.933 132.979 104.019 132.065 104.019 130.947 c
104.019 124.852 l
104.019 123.734 104.933 122.82 106.051 122.82 c
117.226 122.82 l
h
B
117.537 123.822 m
117.957 123.822 118.299 124.164 118.299 124.585 c
B
105.755 132.111 m
105.334 132.111 104.992 131.77 104.992 131.349 c
B
153.048 122.82 m
154.165 122.82 155.08 123.734 155.08 124.852 c
155.08 130.947 l
155.08 132.065 154.165 132.979 153.048 132.979 c
141.872 132.979 l
140.755 132.979 139.84 132.065 139.84 130.947 c
139.84 124.852 l
139.84 123.734 140.755 122.82 141.872 122.82 c
153.048 122.82 l
h
B
153.358 123.822 m
153.779 123.822 154.12 124.164 154.12 124.585 c
B
141.576 132.111 m
141.156 132.111 140.814 131.77 140.814 131.349 c
B
188.869 122.82 m
189.987 122.82 190.901 123.734 190.901 124.852 c
190.901 130.947 l
190.901 132.065 189.987 132.979 188.869 132.979 c
177.694 132.979 l
176.576 132.979 175.662 132.065 175.662 130.947 c
175.662 124.852 l
175.662 123.734 176.576 122.82 177.694 122.82 c
188.869 122.82 l
h
B
189.18 123.822 m
189.601 123.822 189.942 124.164 189.942 124.585 c
B
177.398 132.111 m
176.977 132.111 176.636 131.77 176.636 131.349 c
B
224.691 122.82 m
225.808 122.82 226.722 123.734 226.722 124.852 c
226.722 130.947 l
226.722 132.065 225.808 132.979 224.691 132.979 c
213.515 132.979 l
212.398 132.979 211.484 132.065 211.484 130.947 c
211.484 124.852 l
211.484 123.734 212.398 122.82 213.515 122.82 c
224.691 122.82 l
h
B
225.001 123.822 m
225.422 123.822 225.764 124.164 225.764 124.585 c
B
213.219 132.111 m
212.799 132.111 212.457 131.77 212.457 131.349 c
B
260.513 122.82 m
261.63 122.82 262.544 123.734 262.544 124.852 c
262.544 130.947 l
262.544 132.065 261.63 132.979 260.513 132.979 c
249.337 132.979 l
248.22 132.979 247.305 132.065 247.305 130.947 c
247.305 124.852 l
247.305 123.734 248.22 122.82 249.337 122.82 c
260.513 122.82 l
h
B
260.823 123.822 m
261.244 123.822 261.585 124.164 261.585 124.585 c
B
249.041 132.111 m
248.62 132.111 248.279 131.77 248.279 131.349 c
B
296.334 122.82 m
297.452 122.82 298.366 123.734 298.366 124.852 c
298.366 130.947 l
298.366 132.065 297.452 132.979 296.334 132.979 c
285.159 132.979 l
284.041 132.979 283.127 132.065 283.127 130.947 c
283.127 124.852 l
283.127 123.734 284.041 122.82 285.159 122.82 c
296.334 122.82 l
h
B
296.645 123.822 m
297.065 123.822 297.407 124.164 297.407 124.585 c
B
284.863 132.111 m
284.442 132.111 284.1 131.77 284.1 131.349 c
B
314.245 122.82 m
315.363 122.82 316.277 123.734 316.277 124.852 c
316.277 130.947 l
316.277 132.065 315.363 132.979 314.245 132.979 c
303.069 132.979 l
301.952 132.979 301.038 132.065 301.038 130.947 c
301.038 124.852 l
301.038 123.734 301.952 122.82 303.069 122.82 c
314.245 122.82 l
h
B
314.555 123.822 m
314.976 123.822 315.317 124.164 315.317 124.585 c
B
302.773 132.111 m
302.352 132.111 302.011 131.77 302.011 131.349 c
B
0.125 0.071 0.055 0.004 k
99.315 122.82 m
100.433 122.82 101.347 123.734 101.347 124.852 c
101.347 130.947 l
101.347 132.065 100.433 132.979 99.315 132.979 c
88.14 132.979 l
87.022 132.979 86.108 132.065 86.108 130.947 c
86.108 124.852 l
86.108 123.734 87.022 122.82 88.14 122.82 c
99.315 122.82 l
h
B
99.626 123.822 m
100.047 123.822 100.388 124.164 100.388 124.585 c
B
87.844 132.111 m
87.423 132.111 87.082 131.77 87.082 131.349 c
B
135.137 122.82 m
136.254 122.82 137.169 123.734 137.169 124.852 c
137.169 130.947 l
137.169 132.065 136.254 132.979 135.137 132.979 c
123.962 132.979 l
122.844 132.979 121.93 132.065 121.93 130.947 c
121.93 124.852 l
121.93 123.734 122.844 122.82 123.962 122.82 c
135.137 122.82 l
h
B
135.448 123.822 m
135.868 123.822 136.209 124.164 136.209 124.585 c
B
123.665 132.111 m
123.245 132.111 122.904 131.77 122.904 131.349 c
B
170.958 122.82 m
172.076 122.82 172.99 123.734 172.99 124.852 c
172.99 130.947 l
172.99 132.065 172.076 132.979 170.958 132.979 c
159.783 132.979 l
158.665 132.979 157.751 132.065 157.751 130.947 c
157.751 124.852 l
157.751 123.734 158.665 122.82 159.783 122.82 c
170.958 122.82 l
h
B
171.269 123.822 m
171.69 123.822 172.031 124.164 172.031 124.585 c
B
159.487 132.111 m
159.066 132.111 158.725 131.77 158.725 131.349 c
B
206.78 122.82 m
207.898 122.82 208.812 123.734 208.812 124.852 c
208.812 130.947 l
208.812 132.065 207.898 132.979 206.78 132.979 c
195.605 132.979 l
194.487 132.979 193.573 132.065 193.573 130.947 c
193.573 124.852 l
193.573 123.734 194.487 122.82 195.605 122.82 c
206.78 122.82 l
h
B
207.091 123.822 m
207.512 123.822 207.852 124.164 207.852 124.585 c
B
195.309 132.111 m
194.888 132.111 194.547 131.77 194.547 131.349 c
B
242.601 122.82 m
243.719 122.82 244.633 123.734 244.633 124.852 c
244.633 130.947 l
244.633 132.065 243.719 132.979 242.601 132.979 c
231.426 132.979 l
230.308 132.979 229.394 132.065 229.394 130.947 c
229.394 124.852 l
229.394 123.734 230.308 122.82 231.426 122.82 c
242.601 122.82 l
h
B
242.912 123.822 m
243.333 123.822 243.674 124.164 243.674 124.585 c
B
231.13 132.111 m
230.709 132.111 230.368 131.77 230.368 131.349 c
B
278.423 122.82 m
279.541 122.82 280.455 123.734 280.455 124.852 c
280.455 130.947 l
280.455 132.065 279.541 132.979 278.423 132.979 c
267.248 132.979 l
266.13 132.979 265.216 132.065 265.216 130.947 c
265.216 124.852 l
265.216 123.734 266.13 122.82 267.248 122.82 c
278.423 122.82 l
h
B
278.734 123.822 m
279.155 123.822 279.496 124.164 279.496 124.585 c
B
266.951 132.111 m
266.531 132.111 266.19 131.77 266.19 131.349 c
B
0 g
BT
/T1_3 1 Tf
8 0 0 8 85.64 156.3201 Tm
(0)Tj
/T1_4 1 Tf
0.756 0 Td
(\341)Tj
/T1_3 1 Tf
0.2 Tc 0.478 0 Td
(00236)Tj
-1.1715 8.4792 Td
(84)Tj
0.7 g
1.512 0 Td
(00)Tj
0 g
1.512 0 Td
( = 8400)Tj
0.7 g
16.601 0 Td
(00)Tj
0 g
1.512 0 Td
(324  = 0)Tj
/T1_4 1 Tf
0 Tc 5.3239 0 Td
(\341)Tj
/T1_3 1 Tf
0.2 Tc 0.478 0 Td
(0324)Tj
ET
0.172 0.914 0.792 0.047 K
260.641 231.277 m
260.641 232.921 259.308 234.254 257.663 234.254 c
256.019 234.254 254.686 232.921 254.686 231.277 c
109.394 195.52 m
109.394 197.164 108.061 198.497 106.417 198.497 c
104.773 198.497 103.44 197.164 103.44 195.52 c
254.686 231.277 m
254.686 232.921 253.353 234.254 251.708 234.254 c
250.064 234.254 248.731 232.921 248.731 231.277 c
S
0.172 0.914 0.792 0.047 k
249.056 230.529 m
249.214 231.052 249.36 231.392 249.528 231.812 c
247.931 231.812 l
248.002 231.662 248.245 231.052 248.403 230.529 c
248.573 229.968 248.688 229.46 248.729 229.131 c
248.771 229.46 248.887 229.968 249.056 230.529 c
f
103.44 195.52 m
103.44 197.164 102.107 198.497 100.463 198.497 c
98.818 198.497 97.485 197.164 97.485 195.52 c
97.485 195.52 m
97.485 197.164 96.152 198.497 94.508 198.497 c
92.864 198.497 91.531 197.164 91.531 195.52 c
S
91.855 194.772 m
92.014 195.295 92.159 195.636 92.327 196.055 c
90.73 196.055 l
90.802 195.905 91.045 195.295 91.202 194.772 c
91.372 194.212 91.488 193.703 91.529 193.374 c
91.57 193.703 91.686 194.212 91.855 194.772 c
f
98.056 230.201 m
98.056 231.845 99.389 233.178 101.033 233.178 c
102.678 233.178 104.011 231.845 104.011 230.201 c
92.101 230.201 m
92.101 231.845 93.434 233.178 95.079 233.178 c
96.723 233.178 98.056 231.845 98.056 230.201 c
104.011 230.201 m
104.011 231.845 105.343 233.178 106.988 233.178 c
108.632 233.178 109.965 231.845 109.965 230.201 c
S
109.641 229.453 m
109.482 229.977 109.337 230.317 109.168 230.737 c
110.766 230.737 l
110.694 230.587 110.451 229.977 110.293 229.453 c
110.124 228.893 110.008 228.385 109.967 228.055 c
109.925 228.385 109.809 228.893 109.641 229.453 c
f
101.055 163.568 m
101.055 165.212 102.388 166.545 104.033 166.545 c
105.677 166.545 107.01 165.212 107.01 163.568 c
95.101 163.568 m
95.101 165.212 96.434 166.545 98.078 166.545 c
99.723 166.545 101.055 165.212 101.055 163.568 c
107.01 163.568 m
107.01 165.212 108.343 166.545 109.987 166.545 c
111.631 166.545 112.964 165.212 112.964 163.568 c
S
112.639 162.82 m
112.482 163.343 112.336 163.684 112.167 164.104 c
113.764 164.104 l
113.693 163.953 113.451 163.343 113.292 162.82 c
113.123 162.26 113.007 161.752 112.966 161.422 c
112.925 161.752 112.809 162.26 112.639 162.82 c
f
0 g
BT
/T1_0 1 Tf
0 Tc 7.6799 0 0 7.6799 91.2877 125.1139 Tm
(7)Tj
/T1_5 1 Tf
2.4802 0 Td
(\341)Tj
/T1_0 1 Tf
2.1842 0 Td
(3)Tj
6.4 0 0 6.4 141.191 125.1139 Tm
(EXP)Tj
7.6799 0 0 7.6799 162.9308 125.1139 Tm
(8)Tj
/T1_6 1 Tf
2.3537 0 Td
(\003)Tj
/T1_0 1 Tf
2.3106 0 Td
(6)Tj
/T1_5 1 Tf
2.4801 0 Td
(\341)Tj
/T1_0 1 Tf
2.1842 0 Td
(4)Tj
6.4 0 0 6.4 248.6559 125.1139 Tm
(EXP)Tj
1.7402 Tc 7.6799 0 0 7.6799 148.5201 97.4134 Tm
(10)Tj
0 Tc 6.4 0 0 6.4 248.3883 97.4134 Tm
(EXP)Tj
7.6799 0 0 7.6799 270.3956 125.1139 Tm
(7)Tj
5.6 0 0 5.6 286.3621 127.8728 Tm
(+)Tj
/T1_5 1 Tf
0.9669 -0.6429 Td
(\320)Tj
/T1_0 1 Tf
7.6799 0 0 7.6799 305.9333 125.1139 Tm
(=)Tj
ET
0 G
293.227 130.623 m
288.577 124.923 l
S
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 130.8207 97.4134 Tm
(x)Tj
/T1_3 1 Tf
0.2 Tc 8 0 0 8 86.14 187.8201 Tm
(3820)Tj
0 Tc 7 0 0 7 86.14 207.3201 Tm
(Note: In standard form the decimal point is always after the first whole\
 number.)Tj
4.5428 -2.6858 Td
(The decimal point has moved 3 places to the left.)Tj
1.7428 -4.6 Td
(The decimal point has moved 3 places to the right.)Tj
-6.3142 2.9571 Td
(We write the number in standard form as 3)Tj
/T1_4 1 Tf
19.0893 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(82 x 10)Tj
5 0 0 5 244.3456 180.0198 Tm
(3)Tj
7 0 0 7 86.6395 145.3201 Tm
(We write the number in standard form as 2)Tj
/T1_4 1 Tf
19.0893 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(36 x 10)Tj
/T1_4 1 Tf
5 0 0 5 245.0453 148.3201 Tm
(\320)Tj
/T1_3 1 Tf
0.5001 0 Td
(3)Tj
7 0 0 7 327.4261 125.3229 Tm
(Answer 1)Tj
/T1_4 1 Tf
4.1121 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(140625 x 10)Tj
0.0001 Tc 5 0 0 5 396.5593 128.3229 Tm
(15)Tj
0 Tc 7 0 0 7 233.9261 76.323 Tm
(Another common error is to write 1)Tj
/T1_4 1 Tf
15.6813 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(140625)Tj
0.0001 Tc 5 0 0 5 368.9935 79.323 Tm
(15)Tj
0 Tc 7 0 0 7 374.5541 76.323 Tm
(. )Tj
-20.0897 -1.4286 Td
(This will lose marks. You must write 1)Tj
/T1_4 1 Tf
16.5153 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(140625 x 10)Tj
0.0001 Tc 5 0 0 5 389.8818 69.3229 Tm
(15 )Tj
/T1_0 1 Tf
0 Tc 7 0 0 7 86.5692 109.3201 Tm
(Common error:)Tj
/T1_3 1 Tf
0 -1.5714 TD
(Do not put                               into your calculator.          \
  does this.)Tj
21.8124 Tc -2.5725 17.9762 Td
(12)Tj
0 Tc 0 -2.4762 TD
(3)Tj
0 -7.2143 TD
(4)Tj
-0.2031 -4.3571 Td
(5)Tj
ET
155.64 108.82 m
155.64 115.32 l
S
155.127 116.501 m
154.878 115.675 154.648 115.137 154.382 114.474 c
156.904 114.474 l
156.791 114.711 156.408 115.675 156.158 116.501 c
155.891 117.386 155.708 118.188 155.643 118.708 c
155.578 118.188 155.395 117.386 155.127 116.501 c
f
369.14 87.32 m
369.14 116.82 l
S
368.627 118.001 m
368.378 117.175 368.148 116.637 367.882 115.974 c
370.404 115.974 l
370.291 116.211 369.908 117.175 369.658 118.001 c
369.391 118.886 369.208 119.688 369.143 120.208 c
369.078 119.688 368.895 118.886 368.627 118.001 c
f
Q Q Q 
q
49.61 546.6 368.5 -285.6 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.039 0.02 0.486 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
248.26 290.87 165.688 144.667 re
B
0.188 0.141 0.039 0.004 k
361.748 339.95 m
363.145 339.95 364.288 341.093 364.288 342.49 c
364.288 350.109 l
364.288 351.507 363.145 352.649 361.748 352.649 c
347.779 352.649 l
346.382 352.649 345.239 351.507 345.239 350.109 c
345.239 342.49 l
345.239 341.093 346.382 339.95 347.779 339.95 c
361.748 339.95 l
h
B
362.137 341.204 m
362.662 341.204 363.089 341.63 363.089 342.156 c
B
347.408 351.564 m
346.883 351.564 346.456 351.137 346.456 350.611 c
B
406.686 339.95 m
408.083 339.95 409.226 341.093 409.226 342.49 c
409.226 350.109 l
409.226 351.507 408.083 352.649 406.686 352.649 c
392.717 352.649 l
391.32 352.649 390.177 351.507 390.177 350.109 c
390.177 342.49 l
390.177 341.093 391.32 339.95 392.717 339.95 c
406.686 339.95 l
h
B
407.075 341.204 m
407.6 341.204 408.027 341.63 408.027 342.156 c
B
392.347 351.564 m
391.82 351.564 391.394 351.137 391.394 350.611 c
B
0.129 0.063 0.035 0.004 k
271.871 339.95 m
273.268 339.95 274.411 341.093 274.411 342.49 c
274.411 350.109 l
274.411 351.507 273.268 352.649 271.871 352.649 c
257.903 352.649 l
256.505 352.649 255.362 351.507 255.362 350.109 c
255.362 342.49 l
255.362 341.093 256.505 339.95 257.903 339.95 c
271.871 339.95 l
h
B
272.26 341.204 m
272.786 341.204 273.212 341.63 273.212 342.156 c
B
257.532 351.564 m
257.006 351.564 256.58 351.137 256.58 350.611 c
B
0.188 0.141 0.039 0.004 k
294.341 339.95 m
295.737 339.95 296.881 341.093 296.881 342.49 c
296.881 350.109 l
296.881 351.507 295.737 352.649 294.341 352.649 c
280.371 352.649 l
278.974 352.649 277.832 351.507 277.832 350.109 c
277.832 342.49 l
277.832 341.093 278.974 339.95 280.371 339.95 c
294.341 339.95 l
h
B
294.729 341.204 m
295.255 341.204 295.681 341.63 295.681 342.156 c
B
280.001 351.564 m
279.475 351.564 279.049 351.137 279.049 350.611 c
B
0.129 0.063 0.035 0.004 k
316.81 339.95 m
318.207 339.95 319.349 341.093 319.349 342.49 c
319.349 350.109 l
319.349 351.507 318.207 352.649 316.81 352.649 c
302.841 352.649 l
301.444 352.649 300.301 351.507 300.301 350.109 c
300.301 342.49 l
300.301 341.093 301.444 339.95 302.841 339.95 c
316.81 339.95 l
h
B
317.198 341.204 m
317.724 341.204 318.151 341.63 318.151 342.156 c
B
302.47 351.564 m
301.945 351.564 301.518 351.137 301.518 350.611 c
B
339.279 339.95 m
340.676 339.95 341.819 341.093 341.819 342.49 c
341.819 350.109 l
341.819 351.507 340.676 352.649 339.279 352.649 c
325.31 352.649 l
323.912 352.649 322.77 351.507 322.77 350.109 c
322.77 342.49 l
322.77 341.093 323.912 339.95 325.31 339.95 c
339.279 339.95 l
h
B
339.667 341.204 m
340.193 341.204 340.619 341.63 340.619 342.156 c
B
324.94 351.564 m
324.413 351.564 323.987 351.137 323.987 350.611 c
B
384.217 339.95 m
385.614 339.95 386.757 341.093 386.757 342.49 c
386.757 350.109 l
386.757 351.507 385.614 352.649 384.217 352.649 c
370.248 352.649 l
368.851 352.649 367.708 351.507 367.708 350.109 c
367.708 342.49 l
367.708 341.093 368.851 339.95 370.248 339.95 c
384.217 339.95 l
h
B
384.605 341.204 m
385.132 341.204 385.558 341.63 385.558 342.156 c
B
369.878 351.564 m
369.352 351.564 368.925 351.137 368.925 350.611 c
B
0.188 0.141 0.039 0.004 k
361.748 358.109 m
363.145 358.109 364.288 359.252 364.288 360.649 c
364.288 368.269 l
364.288 369.666 363.145 370.809 361.748 370.809 c
347.779 370.809 l
346.382 370.809 345.239 369.666 345.239 368.269 c
345.239 360.649 l
345.239 359.252 346.382 358.109 347.779 358.109 c
361.748 358.109 l
h
B
362.137 359.363 m
362.662 359.363 363.089 359.789 363.089 360.315 c
B
347.408 369.723 m
346.883 369.723 346.456 369.297 346.456 368.771 c
B
384.217 358.109 m
385.614 358.109 386.757 359.252 386.757 360.649 c
386.757 368.269 l
386.757 369.666 385.614 370.809 384.217 370.809 c
370.248 370.809 l
368.851 370.809 367.708 369.666 367.708 368.269 c
367.708 360.649 l
367.708 359.252 368.851 358.109 370.248 358.109 c
384.217 358.109 l
h
B
384.605 359.363 m
385.132 359.363 385.558 359.789 385.558 360.315 c
B
369.878 369.723 m
369.352 369.723 368.925 369.297 368.925 368.771 c
B
406.686 358.109 m
408.083 358.109 409.226 359.252 409.226 360.649 c
409.226 368.269 l
409.226 369.666 408.083 370.809 406.686 370.809 c
392.717 370.809 l
391.32 370.809 390.177 369.666 390.177 368.269 c
390.177 360.649 l
390.177 359.252 391.32 358.109 392.717 358.109 c
406.686 358.109 l
h
B
407.075 359.363 m
407.6 359.363 408.027 359.789 408.027 360.315 c
B
392.347 369.723 m
391.82 369.723 391.394 369.297 391.394 368.771 c
B
0.129 0.063 0.035 0.004 k
271.871 358.109 m
273.268 358.109 274.411 359.252 274.411 360.649 c
274.411 368.269 l
274.411 369.666 273.268 370.809 271.871 370.809 c
257.903 370.809 l
256.505 370.809 255.362 369.666 255.362 368.269 c
255.362 360.649 l
255.362 359.252 256.505 358.109 257.903 358.109 c
271.871 358.109 l
h
B
272.26 359.363 m
272.786 359.363 273.212 359.789 273.212 360.315 c
B
257.532 369.723 m
257.006 369.723 256.58 369.297 256.58 368.771 c
B
0.188 0.141 0.039 0.004 k
294.341 358.109 m
295.737 358.109 296.881 359.252 296.881 360.649 c
296.881 368.269 l
296.881 369.666 295.737 370.809 294.341 370.809 c
280.371 370.809 l
278.974 370.809 277.832 369.666 277.832 368.269 c
277.832 360.649 l
277.832 359.252 278.974 358.109 280.371 358.109 c
294.341 358.109 l
h
B
294.729 359.363 m
295.255 359.363 295.681 359.789 295.681 360.315 c
B
280.001 369.723 m
279.475 369.723 279.049 369.297 279.049 368.771 c
B
0.129 0.063 0.035 0.004 k
316.81 358.109 m
318.207 358.109 319.349 359.252 319.349 360.649 c
319.349 368.269 l
319.349 369.666 318.207 370.809 316.81 370.809 c
302.841 370.809 l
301.444 370.809 300.301 369.666 300.301 368.269 c
300.301 360.649 l
300.301 359.252 301.444 358.109 302.841 358.109 c
316.81 358.109 l
h
B
317.198 359.363 m
317.724 359.363 318.151 359.789 318.151 360.315 c
B
302.47 369.723 m
301.945 369.723 301.518 369.297 301.518 368.771 c
B
339.279 358.109 m
340.676 358.109 341.819 359.252 341.819 360.649 c
341.819 368.269 l
341.819 369.666 340.676 370.809 339.279 370.809 c
325.31 370.809 l
323.912 370.809 322.77 369.666 322.77 368.269 c
322.77 360.649 l
322.77 359.252 323.912 358.109 325.31 358.109 c
339.279 358.109 l
h
B
339.667 359.363 m
340.193 359.363 340.619 359.789 340.619 360.315 c
B
324.94 369.723 m
324.413 369.723 323.987 369.297 323.987 368.771 c
B
0.188 0.141 0.039 0.004 k
306.76 414.204 m
308.157 414.204 309.3 415.346 309.3 416.743 c
309.3 424.363 l
309.3 425.76 308.157 426.903 306.76 426.903 c
292.791 426.903 l
291.394 426.903 290.251 425.76 290.251 424.363 c
290.251 416.743 l
290.251 415.346 291.394 414.204 292.791 414.204 c
306.76 414.204 l
h
B
307.148 415.456 m
307.674 415.456 308.101 415.883 308.101 416.409 c
B
292.421 425.817 m
291.895 425.817 291.468 425.391 291.468 424.865 c
B
342.76 414.204 m
344.157 414.204 345.3 415.346 345.3 416.743 c
345.3 424.363 l
345.3 425.76 344.157 426.903 342.76 426.903 c
328.791 426.903 l
327.394 426.903 326.251 425.76 326.251 424.363 c
326.251 416.743 l
326.251 415.346 327.394 414.204 328.791 414.204 c
342.76 414.204 l
h
B
343.148 415.456 m
343.674 415.456 344.101 415.883 344.101 416.409 c
B
328.421 425.817 m
327.895 425.817 327.468 425.391 327.468 424.865 c
B
0.039 0.02 0.486 0 k
248.26 472.849 167.667 68.708 re
B
0 g
BT
/T1_3 1 Tf
9 0 0 9 255.76 417.2035 Tm
(Use the           or           key)Tj
10 0 0 10 77.26 526.8895 Tm
(5)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(36 x 10)Tj
6 0 0 6 118.2175 532.8895 Tm
(4)Tj
0.2 Tc 10 0 0 10 77.26 477.2036 Tm
(536)Tj
0.7 g
2.2679 0 Td
(00)Tj
0 g
1.5119 0 Td
(    =  53 600)Tj
0 Tc 7 0 0 7 104.2248 509.5692 Tm
(Means move the decimal point)Tj
0 -1.1429 TD
(4 places to the right)Tj
10 0 0 10 77.26 441.9575 Tm
(8)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(31 x 10)Tj
/T1_4 1 Tf
6 0 0 6 118.2175 447.9575 Tm
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
(3)Tj
0.7 g
0.2 Tc 10 0 0 10 77.26 396.8828 Tm
(000)Tj
0 g
2.2679 0 Td
(831  = 0)Tj
/T1_4 1 Tf
0 Tc 5.3238 0 Td
(\341)Tj
/T1_3 1 Tf
0.2 Tc 0.478 0 Td
(00831)Tj
0 Tc 7 0 0 7 104.2248 424.8701 Tm
(Means move the decimal point)Tj
T*
(3 places to the left)Tj
ET
0.172 0.89 0.796 0.047 K
98.771 405.204 m
98.771 407.259 97.105 408.925 95.049 408.925 c
92.994 408.925 91.328 407.259 91.328 405.204 c
106.214 405.204 m
106.214 407.259 104.548 408.925 102.492 408.925 c
100.437 408.925 98.771 407.259 98.771 405.204 c
91.328 405.204 m
91.328 407.259 89.661 408.925 87.606 408.925 c
85.551 408.925 83.885 407.259 83.885 405.204 c
S
0.172 0.89 0.796 0.047 k
84.29 404.268 m
84.488 404.923 84.67 405.348 84.881 405.873 c
82.884 405.873 l
82.973 405.685 83.277 404.923 83.474 404.268 c
83.686 403.568 83.831 402.933 83.883 402.521 c
83.934 402.933 84.079 403.568 84.29 404.268 c
f
99.214 484.925 m
99.214 486.98 100.88 488.647 102.935 488.647 c
104.991 488.647 106.657 486.98 106.657 484.925 c
91.771 484.925 m
91.771 486.98 93.437 488.647 95.492 488.647 c
97.548 488.647 99.214 486.98 99.214 484.925 c
84.328 484.925 m
84.328 486.98 85.994 488.647 88.049 488.647 c
90.105 488.647 91.771 486.98 91.771 484.925 c
106.657 484.925 m
106.657 486.98 108.323 488.647 110.379 488.647 c
112.434 488.647 114.1 486.98 114.1 484.925 c
S
113.695 483.99 m
113.497 484.645 113.315 485.07 113.104 485.595 c
115.101 485.595 l
115.011 485.407 114.708 484.645 114.51 483.99 c
114.299 483.29 114.154 482.655 114.102 482.243 c
114.05 482.655 113.906 483.29 113.695 483.99 c
f
0 g
BT
/T1_0 1 Tf
8 0 0 8 291.9392 417.0707 Tm
(EXP)Tj
9.5999 0 0 9.5999 261.8374 360.9769 Tm
(3)Tj
/T1_5 1 Tf
2.4885 0 Td
(\341)Tj
/T1_0 1 Tf
1.7485 Tc 2.1926 0 Td
(82)Tj
0 Tc 8 0 0 8 346.927 360.9769 Tm
(EXP)Tj
9.5999 0 0 9.5999 374.1827 360.9769 Tm
(4)Tj
2.3681 0.1042 Td
(x)Tj
-14.0708 -1.9958 Td
(4)Tj
/T1_5 1 Tf
2.4885 0 Td
(\341)Tj
/T1_0 1 Tf
1.7485 Tc 2.1926 0 Td
(26)Tj
0 Tc 8 0 0 8 346.927 342.8178 Tm
(EXP)Tj
1.7116 Tc 9.5999 0 0 9.5999 374.1827 342.8178 Tm
(6=)Tj
0 Tc 8 0 0 8 330.6792 417.0707 Tm
(EE)Tj
/T1_3 1 Tf
9 0 0 9 255.76 396.3701 Tm
(Example 3)Tj
/T1_4 1 Tf
4.6868 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(82 x 10)Tj
6 0 0 6 329.8 400.3701 Tm
(4)Tj
9 0 0 9 333.1362 396.3701 Tm
( x 4)Tj
/T1_4 1 Tf
1.5939 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(26 x 10)Tj
6 0 0 6 379.3403 400.3701 Tm
(6)Tj
9 0 0 9 252.4265 529.0365 Tm
(In standard form a number is written in)Tj
0 -1.3333 TD
(the form:)Tj
T*
(a x 10)Tj
7 0 0 7 276.4465 508.0365 Tm
(n)Tj
9 0 0 9 252.4265 493.0365 Tm
(Where a is a number between 1 and 10)Tj
T*
(and n is an appropriate power of 10)Tj
0.3704 -11.3148 Td
(Calculator keys:)Tj
0 -5.963 TD
(The calculator display shows)Tj
0 -1.3333 TD
(1)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(62732)Tj
6 0 0 6 288.2847 317.5366 Tm
( 11)Tj
9 0 0 9 255.76 301.5365 Tm
(This means 1)Tj
/T1_4 1 Tf
5.8168 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(62732 x 10)Tj
6 0 0 6 354.981 305.5365 Tm
(11)Tj
/T1_0 1 Tf
10 0 0 10 247.9265 456.0365 Tm
(Using a calculator with numbers in)Tj
0 -1.2 TD
(standard form)Tj
ET
0 G
0.51 w 
123.26 535.537 m
143.26 535.537 l
143.26 521.536 l
S
143.782 520.332 m
144.037 521.175 144.272 521.724 144.543 522.4 c
141.971 522.4 l
142.086 522.158 142.477 521.175 142.731 520.332 c
143.004 519.43 143.191 518.611 143.257 518.081 c
143.324 518.611 143.51 519.43 143.782 520.332 c
f
127.643 450.34 m
147.643 450.34 l
147.643 436.34 l
S
148.166 435.136 m
148.421 435.979 148.655 436.527 148.927 437.204 c
146.354 437.204 l
146.469 436.961 146.86 435.979 147.115 435.136 c
147.387 434.233 147.574 433.415 147.64 432.884 c
147.707 433.415 147.893 434.233 148.166 435.136 c
f
Q Q Q 
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/RelativeColorimetric ri
/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS1 cs 1  scn
58.66 306.25 359.92 -56.19 re
f*
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
58.66 306.25 359.92 -56.19 re
S
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
8 0 0 8 413.0924 35.0006 Tm
(5)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 560.68 368.51 -22.67 re
f*
/CS3 cs 1  scn
BT
/T1_0 1 Tf
0.0296 Tw 14 0 0 14 149.2667 549.1018 Tm
[(Per)18(centages and fractions)]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 528.8405 Tm
[(Y)92(ou have to be able to work out per)18(centages. Shops often have sales with 20% of)18(f. If)]TJ
0 -1.3333 TD
[(you cannot do per)18(centages you cannot work out the sale price.)]TJ
/CS4 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 51.3228 400.2002 Tm
(Examples)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0001 Tc 0.0277 Tw 9 0 0 9 68.3307 385.3657 Tm
[(1)-1332(A man ear)-18(ns \24312 000 per annum. He r)18(eceives a 4% incr)18(ease each year)92(. How much)]TJ
1.888 -1.3333 Td
[(does he ear)-18(n after five years?)]TJ
0.0017 -1.9633 Td
(Method: 12 000 x 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 8.8549 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(04 x 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.7608 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(04 x 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.7608 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(04 x 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.7608 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(04 x 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.7608 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(04 = \24314 599)Tj
/T1_3 1 Tf
0 Tc 0 Tw 6.0298 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(83)Tj
0.0277 Tw -27.5953 -1.3333 Td
(A shortcut is: 12 000 x 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 10.8881 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(04)Tj
0 Tc 6.3 0 0 6.3 195.8386 347.2962 Tm
(5)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 202.0914 343.6963 Tm
(= \24314 599.83)Tj
-14.8623 -1.9633 Td
[(2)-1334(A television costs \243200 + 17)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 14.5827 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
[(5% V)55(A)68(T)111(. What is the total cost?)]TJ
-0.0001 Tc -12.9708 -1.3333 Td
(200 x 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.3167 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(175 = \243235)Tj
/T1_0 1 Tf
0.0296 Tw -5.4843 -2.5932 Td
(This is a common examination question:)Tj
/T1_2 1 Tf
-0.0224 Tc 0.0278 Tw -0.0009 -1.6483 Td
(A television costs \243235 including 17)Tj
/T1_3 1 Tf
0 Tc 0 Tw 15.318 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0224 Tc 0.0278 Tw 0.2556 0 Td
[(5% V)55(A)68(T)111(. Calculate the cost befor)18(e V)55(A)68(T was added.)]TJ
-0.0001 Tc -15.5728 -1.9633 Td
(\243235 is 117)Tj
/T1_3 1 Tf
0 Tc 0 Tw 5.1681 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
[(5%. W)18(e need to find 100%. It is example 2 r)18(eversed. 235 )]TJ
/T1_3 1 Tf
0 Tc 0 Tw 25.9103 0 Td
(\326)Tj
/T1_2 1 Tf
0.9714 0 Td
(1)Tj
/T1_3 1 Tf
0.5559 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(175 = \243200)Tj
/CS4 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 51.3228 234.8459 Tm
(Questions)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 9 0 0 9 68.3307 220.0113 Tm
[(1)-1332(A car is bought for \24315 000. It depr)18(eciates by 9% each year)92(. How much is it worth)]TJ
-0.0002 Tc 1.888 -1.3333 Td
[(after thr)18(ee years? \(Give your answer to the near)18(est \243.\))]TJ
-1.888 -1.9633 Td
[(2)-1334(Decr)18(ease 48 by )]TJ
0 Tc 0 Tw 6.3 0 0 6.3 150.774 193.942 Tm
(1)Tj
9 0 0 9 154.2762 190.3421 Tm
(/)Tj
6.3 0 0 6.3 157.6051 188.542 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 249.748 190.3421 Tm
[(3)-1397(Find 8% of 20)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
0 Tw 8 0 0 8 51.3228 169.8381 Tm
(Answers )Tj
0 0 0 1 k
/T1_2 1 Tf
0 Tc 7 0 0 7 68.3307 157.8382 Tm
(1)Tj
-0.0002 Tc 0.0278 Tw 0 -12.405 TD
[(2)-1064(Decr)18(ease by )]TJ
0 Tc 0 Tw 4.9 0 0 4.9 120.6415 73.8035 Tm
(1)Tj
7 0 0 7 123.3655 71.0034 Tm
(/)Tj
4.9 0 0 4.9 125.9546 69.6035 Tm
(3)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 130.8178 71.0034 Tm
(means multiply by \(1 )Tj
/T1_3 1 Tf
0 Tc 0 Tw 9.5913 0 Td
(\320)Tj
/T1_2 1 Tf
0.4999 0 Td
( )Tj
4.9 0 0 4.9 203.5967 73.8035 Tm
(1)Tj
7 0 0 7 206.3206 71.0034 Tm
(/)Tj
4.9 0 0 4.9 208.9097 69.6035 Tm
(3)Tj
-0.0003 Tc 0.0278 Tw 7 0 0 7 211.6336 71.0034 Tm
(\) = )Tj
0 Tc 0 Tw 4.9 0 0 4.9 222.391 73.8035 Tm
(1)Tj
7 0 0 7 225.115 71.0034 Tm
(/)Tj
4.9 0 0 4.9 227.7041 69.6035 Tm
(3)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 249.748 71.0034 Tm
(48 x )Tj
0 Tc 0 Tw 4.9 0 0 4.9 265.1828 73.8035 Tm
(2)Tj
7 0 0 7 267.9068 71.0034 Tm
(/)Tj
4.9 0 0 4.9 270.4959 69.6035 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 275.3591 71.0034 Tm
(= 32)Tj
-0.0001 Tc -29.5755 -1.7143 Td
[(3)-1064(Find 8% means multiply by 0)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 14.6082 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 3.62 Tw 0.2779 0 Td
(08 0)Tj
/T1_3 1 Tf
0 Tc 0 Tw 5.5655 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0277 Tw 0.2779 0 Td
(08 x 20 = 1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 5.1496 0 Td
(\341)Tj
/T1_2 1 Tf
0.2779 0 Td
(6)Tj
ET
Q Q 
q
183.46 65.63 21 -6.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.4 w 4 M 0 j 0 J []0 d 
/GS4 gs
180.62 61.76 m
197.42 61.76 l
S
0 g
198.365 62.17 m
197.704 62.37 197.274 62.554 196.743 62.767 c
196.743 60.749 l
196.933 60.839 197.704 61.146 198.365 61.346 c
199.073 61.559 199.714 61.705 200.131 61.758 c
199.714 61.81 199.073 61.956 198.365 62.17 c
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS1 cs 1  scn
89.93 508.29 289.29 -87.34 re
f*
0 0 0 1 k
BT
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 9 0 0 9 108.1914 495.1124 Tm
[(T)111(o find 6%, multiply by 0)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 11.154 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(06)Tj
0.0278 Tw -11.4319 -1.4261 Td
[(T)111(o calculate a 6% incr)18(ease, multiply by 1)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 18.1545 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(06 \(ie 1 + 0)Tj
/T1_3 1 Tf
0 Tc 0 Tw 5.1676 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(06\))Tj
0.0278 Tw -23.8778 -1.4261 Td
[(T)111(o calculate a 12% decr)18(ease, multiply by 0)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 19.0814 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(88 \(ie 1 )Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.6402 0 Td
(\320)Tj
/T1_2 1 Tf
0.0277 Tc 0.4999 0 Td
( 0)Tj
/T1_3 1 Tf
0 Tc 0.8615 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(12\))Tj
0.0278 Tw -24.6388 -1.4261 Td
[(T)111(o calculate )]TJ
0 Tc 0 Tw 6.3 0 0 6.3 158.5211 460.2084 Tm
(2)Tj
9 0 0 9 162.0233 456.6085 Tm
(/)Tj
6.3 0 0 6.3 165.3522 454.8084 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 168.8544 456.6085 Tm
(, multiply by )Tj
0 Tc 0 Tw 6.3 0 0 6.3 221.4117 460.2084 Tm
(2)Tj
9 0 0 9 224.9139 456.6085 Tm
(/)Tj
6.3 0 0 6.3 228.2428 454.8084 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 108.1914 443.7739 Tm
[(T)111(o calculate a )]TJ
0 Tc 0 Tw 6.3 0 0 6.3 165.9409 447.3737 Tm
(2)Tj
9 0 0 9 169.4431 443.7739 Tm
(/)Tj
6.3 0 0 6.3 172.7719 441.9738 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 179.0247 443.7739 Tm
[(incr)18(ease, multiply by 1)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 269.4189 447.3737 Tm
(2)Tj
9 0 0 9 272.9211 443.7739 Tm
(/)Tj
-0.0003 Tc 6.3 0 0 6.3 276.25 441.9738 Tm
(3 )Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 284.4281 443.7739 Tm
(\(ie 1 + )Tj
0 Tc 0 Tw 6.3 0 0 6.3 313.1759 447.3737 Tm
(2)Tj
9 0 0 9 316.6781 443.7739 Tm
(/)Tj
6.3 0 0 6.3 320.007 441.9738 Tm
(3)Tj
9 0 0 9 323.5092 443.7739 Tm
(\))Tj
-0.0001 Tc 0.0278 Tw -23.9242 -1.4261 Td
[(T)111(o calculate a )]TJ
0 Tc 0 Tw 6.3 0 0 6.3 165.9409 434.5391 Tm
(2)Tj
9 0 0 9 169.4431 430.9391 Tm
(/)Tj
6.3 0 0 6.3 172.7719 429.1393 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 179.0247 430.9391 Tm
[(decr)18(ease, multiply by )]TJ
0 Tc 0 Tw 6.3 0 0 6.3 267.7534 434.5391 Tm
(1)Tj
9 0 0 9 271.2556 430.9391 Tm
(/)Tj
-0.0003 Tc 6.3 0 0 6.3 274.5845 429.1393 Tm
(3 )Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 282.7626 430.9391 Tm
(\(ie 1 )Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.2228 0 Td
(\320)Tj
/T1_2 1 Tf
0.4999 0 Td
( )Tj
6.3 0 0 6.3 310.0184 434.5391 Tm
(2)Tj
9 0 0 9 313.5206 430.9391 Tm
(/)Tj
6.3 0 0 6.3 316.8495 429.1393 Tm
(3)Tj
9 0 0 9 320.3517 430.9391 Tm
(\))Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
89.93 508.29 289.29 -87.34 re
S
Q Q 
q
73 163.94 331.93 -86.66 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS5 gs
BT
/T1_2 1 Tf
7 0 0 7 76.8335 157.5466 Tm
(15 000      x      0)Tj
/T1_3 1 Tf
7.4321 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(91      x      0)Tj
/T1_3 1 Tf
5.4861 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(91      x      0)Tj
/T1_3 1 Tf
5.4861 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(91      =     \24311 304)Tj
-13.739 -3.8571 Td
(to find the )Tj
-0.019 -1.2143 Td
(value after )Tj
0.536 -1.2143 Td
(one year)Tj
5.3878 2.4286 Td
(to find the )Tj
-0.019 -1.2143 Td
(value after )Tj
0.352 -1.2143 Td
(two years)Tj
5.5241 2.4286 Td
(to find the )Tj
-0.019 -1.2143 Td
(value after )Tj
0.0095 -1.2143 Td
(three years)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
131.75 140.88 m
131.75 146.714 l
S
131.237 147.894 m
130.988 147.068 130.758 146.53 130.492 145.867 c
133.014 145.867 l
132.901 146.105 132.518 147.068 132.268 147.894 c
132.001 148.779 131.818 149.581 131.753 150.102 c
131.688 149.581 131.505 148.779 131.237 147.894 c
f
172.5 140.88 m
172.5 146.714 l
S
171.987 147.894 m
171.738 147.068 171.508 146.53 171.242 145.867 c
173.764 145.867 l
173.651 146.105 173.268 147.068 173.018 147.894 c
172.751 148.779 172.568 149.581 172.503 150.102 c
172.438 149.581 172.255 148.779 171.987 147.894 c
f
213 140.88 m
213 146.714 l
S
212.487 147.894 m
212.238 147.068 212.008 146.53 211.742 145.867 c
214.264 145.867 l
214.151 146.105 213.768 147.068 213.518 147.894 c
213.251 148.779 213.068 149.581 213.003 150.102 c
212.938 149.581 212.755 148.779 212.487 147.894 c
f
BT
/T1_2 1 Tf
7 0 0 7 76.8335 98.8801 Tm
[(The calculation can be shortened)-2058(15 000 x \(0)]TJ
/T1_3 1 Tf
21.7692 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(91\))Tj
5 0 0 5 240.7683 101.8801 Tm
(3)Tj
7 0 0 7 77.5 87.3801 Tm
(Calculator keys:)Tj
/T1_0 1 Tf
3 0 0 3 318.5879 90.7141 Tm
(y)Tj
ET
0.188 0.137 0.075 0.008 k
321.638 84.089 m
322.756 84.089 323.67 85.004 323.67 86.121 c
323.67 92.216 l
323.67 93.334 322.756 94.249 321.638 94.249 c
310.463 94.249 l
309.345 94.249 308.431 93.334 308.431 92.216 c
308.431 86.121 l
308.431 85.004 309.345 84.089 310.463 84.089 c
321.638 84.089 l
h
B
321.949 85.092 m
322.37 85.092 322.711 85.433 322.711 85.854 c
B
310.167 93.38 m
309.746 93.38 309.405 93.039 309.405 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 313.3481 86.3933 Tm
(x)Tj
ET
0.125 0.071 0.055 0.004 k
146.638 84.089 m
147.755 84.089 148.67 85.004 148.67 86.121 c
148.67 92.216 l
148.67 93.334 147.755 94.249 146.638 94.249 c
135.463 94.249 l
134.345 94.249 133.431 93.334 133.431 92.216 c
133.431 86.121 l
133.431 85.004 134.345 84.089 135.463 84.089 c
146.638 84.089 l
h
B
146.949 85.092 m
147.37 85.092 147.711 85.433 147.711 85.854 c
B
135.167 93.38 m
134.746 93.38 134.405 93.039 134.405 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 138.3481 86.3933 Tm
(1)Tj
ET
0.125 0.071 0.055 0.004 k
164.138 84.089 m
165.255 84.089 166.17 85.004 166.17 86.121 c
166.17 92.216 l
166.17 93.334 165.255 94.249 164.138 94.249 c
152.963 94.249 l
151.845 94.249 150.931 93.334 150.931 92.216 c
150.931 86.121 l
150.931 85.004 151.845 84.089 152.963 84.089 c
164.138 84.089 l
h
B
164.449 85.092 m
164.87 85.092 165.211 85.433 165.211 85.854 c
B
152.667 93.38 m
152.246 93.38 151.905 93.039 151.905 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 155.8481 86.3933 Tm
(5)Tj
ET
0.125 0.071 0.055 0.004 k
181.638 84.089 m
182.755 84.089 183.67 85.004 183.67 86.121 c
183.67 92.216 l
183.67 93.334 182.755 94.249 181.638 94.249 c
170.463 94.249 l
169.345 94.249 168.431 93.334 168.431 92.216 c
168.431 86.121 l
168.431 85.004 169.345 84.089 170.463 84.089 c
181.638 84.089 l
h
B
181.949 85.092 m
182.37 85.092 182.711 85.433 182.711 85.854 c
B
170.167 93.38 m
169.746 93.38 169.405 93.039 169.405 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 173.3481 86.3933 Tm
(0)Tj
ET
0.125 0.071 0.055 0.004 k
199.138 84.089 m
200.255 84.089 201.17 85.004 201.17 86.121 c
201.17 92.216 l
201.17 93.334 200.255 94.249 199.138 94.249 c
187.963 94.249 l
186.845 94.249 185.931 93.334 185.931 92.216 c
185.931 86.121 l
185.931 85.004 186.845 84.089 187.963 84.089 c
199.138 84.089 l
h
B
199.449 85.092 m
199.87 85.092 200.211 85.433 200.211 85.854 c
B
187.667 93.38 m
187.246 93.38 186.905 93.039 186.905 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 190.8481 86.3933 Tm
(0)Tj
ET
0.125 0.071 0.055 0.004 k
216.638 84.089 m
217.756 84.089 218.67 85.004 218.67 86.121 c
218.67 92.216 l
218.67 93.334 217.756 94.249 216.638 94.249 c
205.463 94.249 l
204.345 94.249 203.431 93.334 203.431 92.216 c
203.431 86.121 l
203.431 85.004 204.345 84.089 205.463 84.089 c
216.638 84.089 l
h
B
216.949 85.092 m
217.37 85.092 217.711 85.433 217.711 85.854 c
B
205.167 93.38 m
204.746 93.38 204.405 93.039 204.405 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 208.3481 86.3933 Tm
(0)Tj
ET
0.188 0.137 0.075 0.008 k
234.138 84.089 m
235.256 84.089 236.17 85.004 236.17 86.121 c
236.17 92.216 l
236.17 93.334 235.256 94.249 234.138 94.249 c
222.963 94.249 l
221.845 94.249 220.931 93.334 220.931 92.216 c
220.931 86.121 l
220.931 85.004 221.845 84.089 222.963 84.089 c
234.138 84.089 l
h
B
234.449 85.092 m
234.87 85.092 235.211 85.433 235.211 85.854 c
B
222.667 93.38 m
222.246 93.38 221.905 93.039 221.905 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 225.8481 86.3933 Tm
(x)Tj
ET
0.125 0.071 0.055 0.004 k
251.638 84.089 m
252.756 84.089 253.67 85.004 253.67 86.121 c
253.67 92.216 l
253.67 93.334 252.756 94.249 251.638 94.249 c
240.463 94.249 l
239.345 94.249 238.431 93.334 238.431 92.216 c
238.431 86.121 l
238.431 85.004 239.345 84.089 240.463 84.089 c
251.638 84.089 l
h
B
251.949 85.092 m
252.37 85.092 252.711 85.433 252.711 85.854 c
B
240.167 93.38 m
239.746 93.38 239.405 93.039 239.405 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 243.3481 86.3933 Tm
(0)Tj
ET
0.188 0.137 0.075 0.008 k
269.138 84.089 m
270.256 84.089 271.17 85.004 271.17 86.121 c
271.17 92.216 l
271.17 93.334 270.256 94.249 269.138 94.249 c
257.963 94.249 l
256.845 94.249 255.931 93.334 255.931 92.216 c
255.931 86.121 l
255.931 85.004 256.845 84.089 257.963 84.089 c
269.138 84.089 l
h
B
269.449 85.092 m
269.87 85.092 270.211 85.433 270.211 85.854 c
B
257.667 93.38 m
257.246 93.38 256.905 93.039 256.905 92.618 c
B
0 g
BT
/T1_4 1 Tf
7.6799 0 0 7.6799 261.8481 86.3933 Tm
(\341)Tj
ET
0.125 0.071 0.055 0.004 k
286.638 84.089 m
287.756 84.089 288.67 85.004 288.67 86.121 c
288.67 92.216 l
288.67 93.334 287.756 94.249 286.638 94.249 c
275.463 94.249 l
274.345 94.249 273.431 93.334 273.431 92.216 c
273.431 86.121 l
273.431 85.004 274.345 84.089 275.463 84.089 c
286.638 84.089 l
h
B
286.949 85.092 m
287.37 85.092 287.711 85.433 287.711 85.854 c
B
275.167 93.38 m
274.746 93.38 274.405 93.039 274.405 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 278.3481 86.3933 Tm
(9)Tj
ET
0.125 0.071 0.055 0.004 k
304.138 84.089 m
305.256 84.089 306.17 85.004 306.17 86.121 c
306.17 92.216 l
306.17 93.334 305.256 94.249 304.138 94.249 c
292.963 94.249 l
291.845 94.249 290.931 93.334 290.931 92.216 c
290.931 86.121 l
290.931 85.004 291.845 84.089 292.963 84.089 c
304.138 84.089 l
h
B
304.449 85.092 m
304.87 85.092 305.211 85.433 305.211 85.854 c
B
292.667 93.38 m
292.246 93.38 291.905 93.039 291.905 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 295.8481 86.3933 Tm
(1)Tj
ET
0.125 0.071 0.055 0.004 k
339.138 84.089 m
340.256 84.089 341.17 85.004 341.17 86.121 c
341.17 92.216 l
341.17 93.334 340.256 94.249 339.138 94.249 c
327.963 94.249 l
326.845 94.249 325.931 93.334 325.931 92.216 c
325.931 86.121 l
325.931 85.004 326.845 84.089 327.963 84.089 c
339.138 84.089 l
h
B
339.449 85.092 m
339.87 85.092 340.211 85.433 340.211 85.854 c
B
327.667 93.38 m
327.246 93.38 326.905 93.039 326.905 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 330.8481 86.3933 Tm
(3)Tj
ET
0.188 0.137 0.075 0.008 k
356.638 84.089 m
357.756 84.089 358.67 85.004 358.67 86.121 c
358.67 92.216 l
358.67 93.334 357.756 94.249 356.638 94.249 c
345.463 94.249 l
344.345 94.249 343.431 93.334 343.431 92.216 c
343.431 86.121 l
343.431 85.004 344.345 84.089 345.463 84.089 c
356.638 84.089 l
h
B
356.949 85.092 m
357.37 85.092 357.711 85.433 357.711 85.854 c
B
345.167 93.38 m
344.746 93.38 344.405 93.039 344.405 92.618 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 348.3481 86.3933 Tm
(=)Tj
ET
Q Q Q 
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0 660.06 467.04 -660 re
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/T1_5 1 Tf
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[(Fractions, decimals and per)18(centages)]TJ
0 0 0 1 k
/T1_2 1 Tf
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(This section is a lot easier than you think. A variety of methods, inclu\
ding calculator)Tj
0 -1.3333 TD
[(methods ar)18(e shown.)]TJ
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418.83 565.69 l
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418.83 565.53 l
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W n
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BT
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(6)Tj
/T1_1 1 Tf
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(Easingwold School                               )Tj
/T1_2 1 Tf
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[(Some amounts incr)18(ease by a fixed amount over a fixed period of time. This fixed)]TJ
-0.0002 Tc 0 -1.3333 TD
[(amount is the gr)18(owth rate, eg a population may incr)18(ease by 5% each year)92(. Some)]TJ
-0.0001 Tc T*
[(amounts decr)18(ease by a fixed amount each year)92(. This is called the decay rate, eg)]TJ
T*
[(radioactive material may decay by 3% each year)92(.)]TJ
/T1_0 1 Tf
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(Important:)Tj
/T1_2 1 Tf
-0.0224 Tc 0.0278 Tw 5.0076 0 Td
[(If you ar)18(e going forwar)18(d in time )]TJ
/T1_0 1 Tf
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(multiply)Tj
/T1_2 1 Tf
-0.0224 Tc 0.0278 Tw 3.5714 0 Td
[(, it you ar)18(e going back in time )]TJ
/T1_0 1 Tf
-0.0239 Tc 0 Tw 13.0817 0 Td
(divide)Tj
/CS2 cs 1  scn
-0.0002 Tc 10 0 0 10 50.6063 480.2288 Tm
(Example)Tj
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/T1_2 1 Tf
0.0278 Tw 9 0 0 9 67.6142 465.3942 Tm
(A man)Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.9177 0 Td
(\325)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0277 Tw 0.1491 0 Td
[(s salary incr)18(eased by 6% per year)92(. In 1985 he ear)-18(ned \24312 000. In which year)]TJ
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(did his salary first exceed \24318 000?)Tj
/CS2 cs 1  scn
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0 Tw 10 0 0 10 50.6063 430.0556 Tm
(Method)Tj
0 0 0 1 k
/T1_2 1 Tf
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[(A 6% incr)18(ease means multiply by 1)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 15.6653 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(06 \(ie 1 + 0)Tj
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0 Tc 0 Tw 5.1675 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(06\))Tj
0.0278 Tw -21.3886 -6.4206 Td
[(this will work but it will take a long time. A quicker way is trial and \
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-0.0002 Tc 0 -5.2223 TD
[(try n = 10)-5053(\24312 000 x 1)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 14.7389 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(06)Tj
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(10)Tj
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[(= \24321 490)-979(too high)]TJ
-17.3228 -1.6483 Td
[(try n = 8)-5609(\24312 000 x 1)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 14.7389 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(06)Tj
0 Tc 6.3 0 0 6.3 212.7716 299.1998 Tm
(8)Tj
-0.0001 Tc 0.0277 Tw 9 0 0 9 223.5196 295.5999 Tm
[(= \24319 126)-979(too high)]TJ
-17.3228 -1.6483 Td
[(try n = 6)-5609(\24312 000 x 1)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 14.7389 0 Td
(\341)Tj
/T1_2 1 Tf
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(06)Tj
0 Tc 6.3 0 0 6.3 212.7716 284.3652 Tm
(6)Tj
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[(= \24317 022)-979(too low)]TJ
-17.3228 -1.6483 Td
[(try n = 7)-5609(\24312 000 x 1)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 14.7389 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(06)Tj
0 Tc 6.3 0 0 6.3 212.7716 269.5305 Tm
(7)Tj
-0.0001 Tc 0.0277 Tw 9 0 0 9 223.5196 265.9306 Tm
[(= \24318 044)-979(first year salary exceeded \24318000)]TJ
-0.0002 Tc -17.3228 -1.9633 Td
(Answer = 1992)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 50.6063 224.9227 Tm
(Question)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0279 Tc 0.0278 Tw 9 0 0 9 67.6142 212.9227 Tm
[(1)-1360(An island had 15 000 seals in 1980. The seal population is decr)18(easing by 2% each year: )]TJ
-0.0001 Tc 1.8898 -1.6483 Td
[(a)-1371(What was the population in 1986?)]TJ
0 -1.6483 TD
[(b)-1279(When will the population fall below 10 000? )]TJ
T*
[(c)-1408(What was the population in 1970?)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
0 Tw 8 0 0 8 50.6063 147.915 Tm
(Answers)Tj
ET
0 0 0 0 k
60.46 145.09 346.8 -52.62 re
f*
Q Q 
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS6 gs
284.25 122.51 m
273.484 117.345 l
S
0 g
272.592 116.417 m
273.451 116.505 274.035 116.5 274.75 116.51 c
273.778 118.837 l
273.603 118.642 272.862 117.917 272.195 117.368 c
271.482 116.781 270.812 116.303 270.357 116.042 c
270.862 116.183 271.673 116.323 272.592 116.417 c
f
325.839 122.32 m
341.998 119.712 l
S
343.25 120.01 m
342.48 120.4 341.991 120.721 341.385 121.099 c
340.943 118.616 l
341.197 118.685 342.212 118.894 343.07 118.995 c
343.987 119.104 344.809 119.143 345.333 119.117 c
344.832 119.272 344.074 119.592 343.25 120.01 c
f
BT
/T1_2 1 Tf
7 0 0 7 66.75 133.0101 Tm
(1    a     15 000 x 0.98)Tj
5 0 0 5 134.0842 136.0101 Tm
(6)Tj
7 0 0 7 136.8645 133.0101 Tm
( = 13 288 \()Tj
/T1_0 1 Tf
4.8181 0 Td
(Note:)Tj
/T1_2 1 Tf
2.665 0 Td
( Going)Tj
/T1_0 1 Tf
3.0561 0 Td
[( forwar)18(d)]TJ
/T1_2 1 Tf
3.9811 0 Td
( in time )Tj
/T1_0 1 Tf
3.6101 0 Td
(multiply)Tj
/T1_2 1 Tf
3.7621 0 Td
(\))Tj
-31.9087 -3.4286 Td
[(      b     Use trial and impr)18(ovement \(see example\) 15000 x 0.98)]TJ
0.0001 Tc 5 0 0 5 262.3054 112.0101 Tm
(21)Tj
0 Tc 7 0 0 7 267.8661 109.0101 Tm
[( = 9814            Answer = Y)92(ear 2001)]TJ
-28.7309 -1.7143 Td
(      c     15 000 )Tj
/T1_4 1 Tf
6.8761 0 Td
(\003)Tj
/T1_2 1 Tf
0.549 0 Td
( 0.98)Tj
0.0001 Tc 5 0 0 5 134.2942 100.0101 Tm
(10)Tj
0 Tc 7 0 0 7 139.8549 97.0101 Tm
( = 18 358 \()Tj
/T1_0 1 Tf
4.8181 0 Td
(Note:)Tj
/T1_2 1 Tf
2.665 0 Td
( Going )Tj
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180.86 123 m
180.86 115 l
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209.347 113.819 m
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238.86 115 l
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267.86 115 l
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267.347 113.819 m
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296.86 123 m
296.86 115 l
S
296.347 113.819 m
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325.86 123 m
325.86 115 l
S
325.347 113.819 m
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122.693 297.567 m
122.693 287.921 l
143.36 287.921 l
127.36 284.567 m
127.36 274.921 l
143.36 274.921 l
127.693 271.9 m
127.693 262.254 l
143.36 262.254 l
127.693 258.213 m
127.693 248.567 l
143.36 248.567 l
131.693 245.567 m
131.693 235.921 l
143.36 235.921 l
135.36 232.879 m
135.36 223.234 l
143.36 223.234 l
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BT
/T1_2 1 Tf
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(\(2 will not go into 147, so try 3\))Tj
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(\(5 will not go into 49, so try 7\))Tj
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(Note: )Tj
/T1_2 1 Tf
2.9611 0 Td
(Keep dividing by prime numbers until you get to 1)Tj
ET
170.693 255.9 m
150.026 254.9 l
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148.87 254.328 m
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170.693 216.359 m
150.026 215.359 l
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148.87 214.786 m
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170.693 243.567 m
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150.219 241.661 m
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170.693 236.9 m
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150.127 238.533 m
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(Note:)Tj
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(The use of the dot is a)Tj
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(quicker method of indicating)Tj
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(\324)Tj
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(9)Tj
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(Easingwold School                               )Tj
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[(This used to be called trial and err)18(or)92(. But mathematicians do not like err)18(ors so they)]TJ
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[(changed the name to impr)18(ovement. Make sur)18(e you r)18(emember the four columns.)]TJ
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[(W)18(ARNING: This topic can be a time-waster in the examination. If you ar)18(e short of time)]TJ
-0.0002 Tc 0 -1.3333 TD
(this is a question to leave and go back to at the end.)Tj
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[(T)92(rial and impr)18(ovement)]TJ
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[(Y)92(ou should draw four columns as )]TJ
-0.0001 Tc T*
[(shown below)55(.)]TJ
0 -1.9633 TD
(In the first column write down )Tj
0 -1.3333 TD
(your guess. In the second column )Tj
-0.0002 Tc T*
(work out the answer using your guess.)Tj
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(If your answer is too big write your )Tj
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(guess)Tj
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(in the )Tj
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(\324)Tj
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(too big)Tj
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(\325)Tj
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( column.)Tj
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(If your answer is too small write your )Tj
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(guess)Tj
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(in the )Tj
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0 Tc 0 Tw 2.8505 0 Td
(\324)Tj
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(too small)Tj
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0 Tc 0 Tw 4.0994 0 Td
(\325)Tj
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-0.0002 Tc 0.0278 Tw 0.2599 0 Td
( column.)Tj
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(Question)Tj
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(x)Tj
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(3)Tj
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(+ 2x = 161)Tj
-0.0001 Tc -1.1767 -1.9633 Td
[(Find the value of x corr)18(ect to one decimal place using trial and impr)18(ovement)]TJ
-0.0002 Tc 0 Tw 0 -1.3333 TD
(methods.)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
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(Answer )Tj
0 0 0 1 k
/T1_2 1 Tf
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[(Y)92(ou must show your working. For example, start by guessing 5. Y)92(ou may have used dif)18(fer)18(ent guesses in)]TJ
0 -1.7143 TD
(your calculations.)Tj
ET
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55.48 219.18 358.19 -167.31 re
f*
Q Q 
0 g
/GS5 gs
BT
/T1_2 1 Tf
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[(Guess x)-4498(Answer x)]TJ
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(2)Tj
7 0 0 7 284.2268 208.9301 Tm
( )Tj
0.278 -0.4286 Td
[(+ 2x)-4948(Too big)-2000(Too small)]TJ
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
190.93 200.93 m
408.68 200.93 l
229.18 215.93 m
229.18 113.93 l
326.18 215.93 m
326.18 113.93 l
367.18 215.93 m
367.18 113.93 l
190.68 113.93 218 102 re
S
0.047 0.02 0.486 0 k
309.68 78.43 69.5 23.5 re
B
0 g
BT
/T1_2 1 Tf
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(5)Tj
0 -1.8571 TD
(6)Tj
T*
(5)Tj
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0.556 0 Td
(\341)Tj
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(5)Tj
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(5)Tj
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0.556 0 Td
(\341)Tj
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0.278 0 Td
(3)Tj
-0.834 -1.8571 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(4)Tj
-0.834 -1.8571 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(35)Tj
3.5946 9.2857 Td
(5)Tj
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(2)Tj
7 0 0 7 241.3524 187.9301 Tm
( + 2 x 5 = 35)Tj
-0.9532 -1.8571 Td
(6)Tj
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(2)Tj
7 0 0 7 241.3524 174.9301 Tm
( + 2 x 6 = 48)Tj
-0.9532 -1.8571 Td
(5)Tj
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(\341)Tj
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0.278 0 Td
(5)Tj
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(2)Tj
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( + 2 x 5)Tj
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3.3721 0 Td
(\341)Tj
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(5 = 41)Tj
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2.89 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(25)Tj
-8.6053 -1.8571 Td
(5)Tj
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0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3)Tj
5 0 0 5 244.4102 151.9301 Tm
(2)Tj
7 0 0 7 247.1905 148.9301 Tm
( + 2 x 5)Tj
/T1_3 1 Tf
3.3721 0 Td
(\341)Tj
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0.278 0 Td
(3 = 38)Tj
/T1_3 1 Tf
2.89 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(69)Tj
-8.6053 -1.8571 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(4)Tj
5 0 0 5 244.4102 138.9301 Tm
(2)Tj
7 0 0 7 247.1905 135.9301 Tm
( + 2 x 5)Tj
/T1_3 1 Tf
3.3721 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(4 = 39)Tj
/T1_3 1 Tf
2.89 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(96)Tj
-8.6053 -1.8571 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(35)Tj
5 0 0 5 248.3022 125.9301 Tm
(2)Tj
7 0 0 7 251.0826 122.9301 Tm
( + 2 x 5)Tj
/T1_3 1 Tf
3.3721 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(35 = 39)Tj
/T1_3 1 Tf
3.4461 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3225)Tj
5.3541 7.4286 Td
(6)Tj
T*
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(5)Tj
-0.834 -3.7143 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(4)Tj
-0.834 -1.8571 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(35)Tj
5.5231 9.2857 Td
(5)Tj
0 -5.5714 TD
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3)Tj
-45.9167 5.7857 Td
(5 is too small. Guess higher.)Tj
0 -2.0714 TD
(5 is too small. 6 is too big.)Tj
0 -1.1429 TD
(Guess between 5 and 6.)Tj
0 -5.5714 TD
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 is too small. 5)Tj
/T1_3 1 Tf
6.9631 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(5 is too big.)Tj
-8.0751 -1.1429 Td
(Guess between 5)Tj
/T1_3 1 Tf
7.7431 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 and 5)Tj
/T1_3 1 Tf
3.3541 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(5.)Tj
-11.6532 4.5714 Td
(5 is too small. 5)Tj
/T1_3 1 Tf
6.9631 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(5 is too big.)Tj
-7.2411 -1.1429 Td
(Guess between 5 and 5)Tj
/T1_3 1 Tf
10.5412 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(5.)Tj
-10.8192 -6 Td
(The answer to one decimal place is )Tj
0 -1.1429 TD
(either 5)Tj
/T1_3 1 Tf
3.4061 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 or 5)Tj
/T1_3 1 Tf
2.593 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(4. To find out which )Tj
-6.5551 -1.1429 Td
(try the number in the middle of )Tj
T*
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 and 5)Tj
/T1_3 1 Tf
3.3541 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(4, ie 5)Tj
/T1_3 1 Tf
2.742 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(35. )Tj
28.0965 1.9286 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(35 is too )Tj
/T1_0 1 Tf
4.1301 0 Td
(big)Tj
/T1_2 1 Tf
-4.9641 -1.1429 Td
(so 5)Tj
/T1_3 1 Tf
1.853 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 is )Tj
/T1_0 1 Tf
1.778 0 Td
(nearer)Tj
ET
162.18 188.43 m
195.18 179.43 l
S
196.456 179.617 m
195.724 180.075 195.266 180.438 194.697 180.87 c
194.033 178.436 l
194.291 178.483 195.322 178.599 196.185 178.622 c
197.109 178.648 197.931 178.613 198.45 178.539 c
197.965 178.739 197.239 179.126 196.456 179.617 c
f
155.68 171.93 m
195.18 164.43 l
S
196.439 164.711 m
195.673 165.111 195.188 165.437 194.586 165.822 c
194.116 163.345 l
194.37 163.411 195.388 163.608 196.246 163.699 c
197.166 163.797 197.988 163.827 198.511 163.793 c
198.012 163.955 197.258 164.284 196.439 164.711 c
f
166.18 124.93 m
195.18 136.93 l
S
196.074 137.86 m
195.215 137.775 194.63 137.782 193.916 137.774 c
194.88 135.443 l
195.056 135.638 195.8 136.361 196.468 136.908 c
197.183 137.493 197.855 137.969 198.311 138.228 c
197.805 138.089 196.993 137.951 196.074 137.86 c
f
159.68 147.93 m
195.18 150.43 l
S
196.322 151.024 m
195.48 151.215 194.928 151.407 194.247 151.626 c
194.425 149.11 l
194.654 149.239 195.587 149.689 196.394 149.996 c
197.258 150.325 198.046 150.564 198.56 150.666 c
198.036 150.694 197.223 150.82 196.322 151.024 c
f
181.18 107.93 m
195.18 121.43 l
S
195.636 122.639 m
194.88 122.22 194.34 121.996 193.687 121.707 c
195.494 119.947 l
195.579 120.195 195.976 121.153 196.374 121.92 c
196.8 122.74 197.228 123.442 197.544 123.861 c
197.135 123.533 196.444 123.086 195.636 122.639 c
f
347.18 102.43 m
347.18 116.43 l
S
346.667 117.611 m
346.418 116.785 346.188 116.247 345.922 115.584 c
348.444 115.584 l
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(Start with )Tj
11.0271 15.2361 Td
[(Factorise)-1927(x\(x + 2\) = 8)]TJ
7.0183 -2.662 Td
(x + 2 =)Tj
1.778 -2.3333 Td
(x =)Tj
-11.4815 2.3287 Td
(x =)Tj
2.9999 0.5926 Td
(8)Tj
-0.852 -1.1111 Td
(x + 2)Tj
11.4075 1.1852 Td
(8)Tj
0.037 -1.1111 Td
(x)Tj
/T1_0 1 Tf
-18.0923 0.4444 Td
[(Either)-8129(or)]TJ
18.2963 -5.4028 Td
(or)Tj
ET
263.985 418.479 m
269.944 418.479 l
S
BT
/T1_3 1 Tf
9 0 0 9 264.4415 399.8536 Tm
(8)Tj
0.037 -1.1111 Td
(x)Tj
ET
263.985 397.145 m
269.944 397.145 l
161.652 418.52 m
182.61 418.52 l
S
BT
/T1_3 1 Tf
9 0 0 9 204.8863 366.5615 Tm
(x)Tj
0.0001 Tc 5 0 0 5 209.2242 364.5615 Tm
(n+1)Tj
6.7528 Tc -6.7528 Tw 9 0 0 9 218.1152 366.5615 Tm
( =x)Tj
0.0001 Tc 0 Tw 5 0 0 5 291.7242 364.5615 Tm
(n+1)Tj
0 Tc 9 0 0 9 300.6152 366.5615 Tm
( =)Tj
-6.649 0.5926 Td
(8)Tj
-1.0064 -1.1111 Td
(x)Tj
5 0 0 5 236.0544 359.8951 Tm
(n)Tj
9 0 0 9 238.8348 361.8951 Tm
( + 2)Tj
ET
232.985 369.895 m
253.943 369.895 l
S
BT
/T1_3 1 Tf
9 0 0 9 172.8863 329.5616 Tm
(x)Tj
0.0001 Tc 5 0 0 5 177.2242 327.5616 Tm
(n+1)Tj
0 Tc 9 0 0 9 186.1152 329.5616 Tm
( =)Tj
2.5177 0.5926 Td
(8)Tj
-1.0064 -1.1111 Td
(x)Tj
5 0 0 5 204.0544 322.8951 Tm
(n)Tj
9 0 0 9 206.8348 324.8951 Tm
( + 2)Tj
ET
200.985 332.895 m
221.944 332.895 l
S
BT
/T1_3 1 Tf
9 0 0 9 182.8863 304.0616 Tm
(x)Tj
0.0001 Tc 5 0 0 5 187.2242 302.0615 Tm
(n+1)Tj
0 Tc 9 0 0 9 196.1152 304.0615 Tm
( =)Tj
2.5177 0.5926 Td
(8)Tj
-0.889 -1.1111 Td
(1 + 2)Tj
ET
210.985 307.395 m
231.944 307.395 l
S
BT
/T1_3 1 Tf
9 0 0 9 182.8863 279.5616 Tm
(x)Tj
0.0001 Tc 5 0 0 5 187.2242 277.5616 Tm
(n+1)Tj
0 Tc 9 0 0 9 196.1152 279.5616 Tm
( =)Tj
3.4066 0.5926 Td
(8)Tj
-1.862 -1.1111 Td
(2)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(667 + 2)Tj
ET
210.985 282.895 m
247.943 282.895 l
S
BT
/T1_3 1 Tf
9 0 0 9 141.61 304.0616 Tm
(1)Tj
0 -2.7222 TD
(2)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(667)Tj
-0.834 -2.7222 Td
(1)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(714)Tj
12.2771 5.4444 Td
(= 2)Tj
/T1_4 1 Tf
1.4999 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(667)Tj
-1.7779 -2.7222 Td
(= 1)Tj
/T1_4 1 Tf
1.4999 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(714)Tj
-10.2224 -2.7222 Td
(and continue... )Tj
-7.0126 5.4444 Td
(x)Tj
5 0 0 5 124.834 302.0615 Tm
(1)Tj
9 0 0 9 127.6144 304.0615 Tm
( =)Tj
-0.7909 -2.7222 Td
(x)Tj
5 0 0 5 124.834 277.5616 Tm
(2)Tj
9 0 0 9 127.6144 279.5616 Tm
( =)Tj
-0.7909 -2.7222 Td
(x)Tj
5 0 0 5 124.834 253.0616 Tm
(3)Tj
9 0 0 9 127.6144 255.0616 Tm
( =)Tj
/T1_4 1 Tf
16.7399 15.5694 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 2)Tj
3.7038 -2.588 Td
(8)Tj
-0.1174 -1.1111 Td
(x)Tj
5 0 0 5 319.3888 359.8951 Tm
(n)Tj
ET
315.652 369.187 m
321.61 369.187 l
S
BT
/T1_4 1 Tf
9 0 0 9 327.9405 368.2285 Tm
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 2)Tj
-19.3949 -20.3519 Td
(x)Tj
0.0001 Tc 5 0 0 5 162.2242 183.0616 Tm
(n+1)Tj
0 Tc 9 0 0 9 171.1152 185.0616 Tm
( =)Tj
1.7214 0.5926 Td
(8)Tj
-0.1174 -1.1111 Td
(x)Tj
5 0 0 5 189.8888 178.3951 Tm
(n)Tj
ET
186.152 187.687 m
192.11 187.687 l
189.652 103.062 m
195.61 103.062 l
189.652 83.562 m
195.61 83.562 l
119.152 103.062 m
134.11 103.062 l
S
BT
/T1_4 1 Tf
9 0 0 9 198.9405 185.2285 Tm
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 2)Tj
5.0744 7.8148 Td
(Eventually we find the solution is x = 2)Tj
-20.1938 -5.8333 Td
(1)Tj
0 -2 TD
(2)Tj
7 0 0 7 67.3659 126.5616 Tm
(1)Tj
32.784 0 Td
[(2)-1874(Y)92(ou should obtain these values:)]TJ
2.4297 -1.7143 Td
(x)Tj
4 0 0 4 317.2361 112.5616 Tm
(2)Tj
7 0 0 7 319.4606 114.5616 Tm
( = )Tj
/T1_4 1 Tf
1.222 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 4)Tj
/T1_4 1 Tf
0.834 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(666...)Tj
-3.6338 -1.7143 Td
(x)Tj
4 0 0 4 317.2361 100.5616 Tm
(3)Tj
7 0 0 7 319.4606 102.5616 Tm
( = )Tj
/T1_4 1 Tf
1.222 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
(3)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(714...)Tj
-3.3558 -1.7143 Td
(x)Tj
4 0 0 4 317.2361 88.5616 Tm
(4)Tj
7 0 0 7 319.4606 90.5616 Tm
( = )Tj
/T1_4 1 Tf
1.222 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
(4)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(153...)Tj
-3.3558 -1.7143 Td
[(Eventually we find the answer)92(.)]TJ
0 -1.7143 TD
(                    Answer  x = -4)Tj
/T1_4 1 Tf
11.9872 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(00)Tj
-44.7743 8.5714 Td
(x)Tj
5 0 0 5 89.6724 129.5616 Tm
(2)Tj
7 0 0 7 92.4527 126.5616 Tm
( + 4x = 12)Tj
-1.002 -1.7143 Td
(x\(x + 4\) = 12)Tj
/T1_0 1 Tf
8.9541 -1.8571 Td
(or)Tj
/T1_3 1 Tf
2.9141 -2.7143 Td
(x)Tj
0.0001 Tc 4 0 0 4 171.8903 80.5615 Tm
(n+1)Tj
0 Tc 7 0 0 7 179.0038 82.5615 Tm
( =)Tj
-2.2602 2.7143 Td
(x + 4 =)Tj
-9.6666 -0.0714 Td
(x)Tj
0.0001 Tc 4 0 0 4 98.8903 99.0616 Tm
(n+1)Tj
0 Tc 7 0 0 7 106.0038 101.0616 Tm
( =)Tj
11.8163 0.5714 Td
(12)Tj
0.315 -1.1429 Td
(x)Tj
-0.315 -1.6429 Td
(12)Tj
0.1561 -1.1429 Td
(x)Tj
4 0 0 4 193.1851 75.5616 Tm
(n)Tj
7 0 0 7 123.218 105.0616 Tm
(12)Tj
-0.7328 -1.1429 Td
(x)Tj
4 0 0 4 121.4622 95.0616 Tm
(n)Tj
7 0 0 7 123.6867 97.0616 Tm
( + 4)Tj
/T1_4 1 Tf
10.9408 -2.0714 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 4)Tj
/T1_0 1 Tf
9 0 0 9 315.61 497.1868 Tm
(Note:)Tj
/T1_3 1 Tf
2.6649 0 Td
( Factorisation is )Tj
-2.6649 -1.3333 Td
(explained on page 17.)Tj
/T1_0 1 Tf
-27.5827 -2.7731 Td
(Method:)Tj
/T1_3 1 Tf
4.4345 0 Td
[(Put x ter)-18(ms to the left of equals; numbers to the right of equals.)]TJ
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 67.6142 557.2368 Tm
[(Iteration is a pr)18(ocess of r)18(epeating a sequence of instructions to pr)18(oduce a better and)]TJ
0 -1.3333 TD
[(better appr)18(oximation to the corr)18(ect answer)92(. A conver)18(ging sequence gets closer and)]TJ
T*
[(closer to a solution. A diver)18(ging sequence does not.)]TJ
ET
Q Q 
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1 g
1 i 
/RelativeColorimetric ri
/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(13)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 550.87 368.51 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0296 Tw 14 0 0 14 143.8643 539.2842 Tm
[(Dir)18(ect and inverse variation)]TJ
/CS3 cs 1  scn
/T1_2 1 Tf
0 Tw 18 0 0 18 342.8209 598.6229 Tm
[(V)55(ariation)]TJ
0 0 0 1 k
/T1_3 1 Tf
0.0278 Tw 9 0 0 9 51.3228 579.9141 Tm
(This page shows a useful mathematical technique.)Tj
ET
0 0 0 1 K
0.125 w 10 M 0 j 0 J []0 d 
50.32 560.61 m
418.83 560.61 l
S
0.042 w 
50.32 560.44 m
418.83 560.44 l
S
Q Q 
q
50.32 524.37 368.51 -477 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.039 0.02 0.486 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS3 gs
248.82 343.37 140.5 101 re
B
73.82 343.37 140.5 101 re
B
0 g
BT
/T1_3 1 Tf
9 0 0 9 262.32 497.8701 Tm
(a              means a is )Tj
/T1_0 1 Tf
9.3386 0 Td
(inversely)Tj
/T1_3 1 Tf
-4.9134 -1.3333 Td
(proportional to b)Tj
-25.2586 3.3056 Td
(These statements all mean the same:)Tj
0 -1.3333 TD
(a        b)Tj
T*
(a is proportional to b)Tj
T*
(a varies as b)Tj
T*
(a varies directly as b)Tj
0.6111 -4.3611 Td
(a       b)Tj
0 -2 TD
(a       b)Tj
6 0 0 6 108.0028 414.3701 Tm
(2)Tj
9 0 0 9 80.32 392.3701 Tm
(a       b)Tj
6 0 0 6 108.0028 396.3701 Tm
(3)Tj
9 0 0 9 176.32 428.37 Tm
(a = kb)Tj
T*
(a = kb)Tj
6 0 0 6 201.825 414.3701 Tm
(2)Tj
9 0 0 9 176.32 392.3701 Tm
(a = kb)Tj
6 0 0 6 201.825 396.3701 Tm
(3)Tj
9 0 0 9 124.32 427.8701 Tm
(this means)Tj
T*
(this means)Tj
T*
(this means)Tj
-4.4366 -3.0556 Td
(These are the )Tj
/T1_4 1 Tf
6.3527 0 Td
(\322)Tj
/T1_3 1 Tf
0.519 0 Td
(k)Tj
/T1_4 1 Tf
0.482 0 Td
(\322)Tj
/T1_3 1 Tf
0.519 0 Td
( equations)Tj
-5.6742 -1.3333 Td
(for direct variation)Tj
17.7459 1.3333 Td
(These are the )Tj
/T1_4 1 Tf
6.3527 0 Td
(\322)Tj
/T1_3 1 Tf
0.519 0 Td
(k)Tj
/T1_4 1 Tf
0.482 0 Td
(\322)Tj
/T1_3 1 Tf
0.519 0 Td
( equations)Tj
-5.9717 -1.3333 Td
(for inverse variation)Tj
-2.6866 8.4444 Td
(a)Tj
T*
(a)Tj
T*
(a)Tj
11 4 Td
(a =)Tj
T*
(a =)Tj
T*
(a =)Tj
7 0 0 7 284.82 492.8701 Tm
(b)Tj
9 0 0 9 300.82 427.8701 Tm
(this means)Tj
T*
(this means)Tj
T*
(this means)Tj
7 0 0 7 284.82 502.8701 Tm
(1)Tj
ET
284.32 501.37 m
289.82 501.37 l
S
BT
/T1_3 1 Tf
7 0 0 7 372.82 422.8701 Tm
(b)Tj
0 -2.5714 TD
(b)Tj
5 0 0 5 377.097 407.8701 Tm
(2)Tj
7 0 0 7 372.82 386.8701 Tm
(b)Tj
5 0 0 5 377.097 389.8701 Tm
(3)Tj
7 0 0 7 372.82 432.87 Tm
(k)Tj
T*
(k)Tj
T*
(k)Tj
ET
372.32 431.37 m
377.82 431.37 l
372.32 413.37 m
377.82 413.37 l
372.32 395.37 m
377.82 395.37 l
S
BT
/T1_3 1 Tf
7 0 0 7 280.32 422.8701 Tm
(b)Tj
T*
(b)Tj
5 0 0 5 284.5971 407.8701 Tm
(2)Tj
7 0 0 7 280.32 386.8701 Tm
(b)Tj
5 0 0 5 284.5971 389.8701 Tm
(3)Tj
7 0 0 7 280.32 432.87 Tm
(1)Tj
T*
(1)Tj
T*
(1)Tj
ET
279.82 431.37 m
285.32 431.37 l
279.82 413.37 m
285.32 413.37 l
279.82 395.37 m
285.32 395.37 l
S
0.172 0.89 0.796 0.047 k
BT
/T1_0 1 Tf
9 0 0 9 79.32 450.3701 Tm
[(Direct variation)-12387(Inverse variation)]TJ
0 g
/T1_3 1 Tf
-1.4532 -15.6667 Td
(y is proportional to x)Tj
6 0 0 6 149.209 313.3701 Tm
(2)Tj
9 0 0 9 152.5452 309.3701 Tm
(. y = 75 when x = 5. Find the value of:)Tj
-9.5893 -16.6111 Td
(y is inversely proportional to x)Tj
6 0 0 6 186.5395 163.8701 Tm
(2)Tj
9 0 0 9 189.8757 159.8701 Tm
(. y = 8 when x = 5. Find the value of y when x = 2.)Tj
-10.3951 15.1667 Td
[(a    y when x = 7)-6959(b    x when y = 192)]TJ
7 0 0 7 66.0499 127.37 Tm
(First write out the equation and find the value of k)Tj
6.4333 21 Td
(First write out the equation)Tj
1.0605 -1.4286 Td
(and find the value of k)Tj
20.0542 -19.5714 Td
(Write out the k equation)Tj
-6.9106 21 Td
[(a    Write out the k equation)-2770(b    Write out the k equation)]TJ
-7.4559 -3.3809 Td
(kx)Tj
5 0 0 5 165.0681 253.7041 Tm
(2)Tj
7 0 0 7 158.32 236.7041 Tm
(k x 5)Tj
5 0 0 5 172.8523 239.7041 Tm
(2)Tj
7 0 0 7 158.32 222.7041 Tm
(k)Tj
0 -2 TD
(3)Tj
14.6666 5.9523 Td
(kx)Tj
5 0 0 5 267.7341 253.3701 Tm
(2)Tj
7 0 0 7 260.986 236.3701 Tm
(3 x 7)Tj
5 0 0 5 276.0363 239.3701 Tm
(2)Tj
7 0 0 7 260.986 222.37 Tm
(147)Tj
5.9973 -15.5237 Td
(k)Tj
-0.1986 -1.2857 Td
(x)Tj
5 0 0 5 304.9511 107.704 Tm
(2)Tj
7 0 0 7 298.816 95.704 Tm
(200)Tj
0.3574 -1.2857 Td
(2)Tj
5 0 0 5 305.2101 89.704 Tm
(2)Tj
7 0 0 7 144.2995 113.704 Tm
(k)Tj
-0.1986 -1.2857 Td
(x)Tj
5 0 0 5 146.2836 107.704 Tm
(2)Tj
7 0 0 7 144.2995 95.704 Tm
(k)Tj
-0.2356 -1.2857 Td
(5)Tj
5 0 0 5 146.5426 89.704 Tm
(2)Tj
7 0 0 7 128.8381 110.0361 Tm
(y =)Tj
-0.074 -2.5714 Td
(8 =)Tj
-2.15 -2.5714 Td
(8 x 25 =)Tj
24.724 4.9049 Td
(y =)Tj
0 -2.5714 TD
(y =)Tj
T*
(y =)Tj
-20.1429 25.4763 Td
(y =)Tj
-0.63 -2 Td
(75 =)Tj
1.39 -2 Td
(=)Tj
-0.76 -2 Td
(k =)Tj
14.6191 5.9523 Td
(y =)Tj
0 -2 TD
(y =)Tj
T*
(y =)Tj
16.664 3.9523 Td
(kx)Tj
5 0 0 5 371.0681 253.036 Tm
(2)Tj
7 0 0 7 364.32 236.036 Tm
(3 x)Tj
5 0 0 5 373.5322 239.036 Tm
(2)Tj
7 0 0 7 364.32 222.036 Tm
(x)Tj
5 0 0 5 367.6941 225.036 Tm
(2)Tj
7 0 0 7 364.32 208.036 Tm
(x)Tj
5 0 0 5 367.6941 211.036 Tm
(2)Tj
7 0 0 7 364.32 194.036 Tm
(x)Tj
T*
(8)Tj
-1.9023 10 Td
(y =)Tj
-1.186 -2 Td
(192 =)Tj
1.668 -2 Td
( =)Tj
-1.112 -2 Td
(64 =)Tj
T*
(64 =)Tj
0.63 -2 Td
(x =)Tj
-7.4954 -15.4046 Td
(50)Tj
-22.1795 0.2617 Td
(k)Tj
-1.186 -2.5714 Td
(200)Tj
ET
142.654 94.704 m
149.487 94.704 l
142.654 112.37 m
149.487 112.37 l
140.486 224.37 m
147.32 224.37 l
343.32 223.829 m
353.154 223.829 l
300.32 112.536 m
307.154 112.536 l
299.32 94.204 m
310.154 94.204 l
S
BT
/T1_3 1 Tf
7 0 0 7 140.1325 226.3701 Tm
(75)Tj
0 -1.2857 TD
(25)Tj
28.9071 1.137 Td
(192)Tj
0.556 -1.2857 Td
(3)Tj
/CS4 cs 1  scn
/T1_0 1 Tf
8 0 0 8 51.2414 141.8701 Tm
(Answer)Tj
/CS5 cs 1  scn
10 0 0 10 51.32 174.3701 Tm
(Question)Tj
0 14.9 TD
(Example)Tj
0 -4.8 TD
(Method)Tj
ET
270.553 499.857 m
270.553 496.797 274.303 497.067 275.654 499.677 c
276.744 501.786 278.129 502.737 280.004 501.117 c
270.553 499.857 m
270.553 502.917 274.303 502.647 275.654 500.037 c
276.744 497.927 278.129 496.976 280.004 498.597 c
88.887 430.523 m
88.887 427.463 92.637 427.733 93.987 430.343 c
95.078 432.453 96.462 433.403 98.337 431.783 c
88.887 430.523 m
88.887 433.583 92.637 433.313 93.987 430.704 c
95.078 428.594 96.462 427.643 98.337 429.264 c
88.887 412.523 m
88.887 409.463 92.637 409.733 93.987 412.343 c
95.078 414.453 96.462 415.403 98.337 413.783 c
88.887 412.523 m
88.887 415.583 92.637 415.313 93.987 412.704 c
95.078 410.594 96.462 409.643 98.337 411.264 c
88.887 394.523 m
88.887 391.463 92.637 391.733 93.987 394.343 c
95.078 396.453 96.462 397.403 98.337 395.783 c
88.887 394.523 m
88.887 397.583 92.637 397.313 93.987 394.704 c
95.078 392.594 96.462 391.643 98.337 393.264 c
264.886 430.523 m
264.886 427.463 268.636 427.733 269.986 430.343 c
271.078 432.453 272.462 433.403 274.337 431.783 c
264.886 430.523 m
264.886 433.583 268.636 433.313 269.986 430.704 c
271.078 428.594 272.462 427.643 274.337 429.264 c
84.303 505.857 m
84.303 502.797 88.053 503.067 89.404 505.677 c
90.494 507.786 91.878 508.737 93.753 507.117 c
84.303 505.857 m
84.303 508.917 88.053 508.647 89.404 506.037 c
90.494 503.927 91.878 502.976 93.753 504.597 c
264.886 412.523 m
264.886 409.463 268.636 409.733 269.986 412.343 c
271.078 414.453 272.462 415.403 274.337 413.783 c
264.886 412.523 m
264.886 415.583 268.636 415.313 269.986 412.704 c
271.078 410.594 272.462 409.643 274.337 411.264 c
264.886 394.523 m
264.886 391.463 268.636 391.733 269.986 394.343 c
271.078 396.453 272.462 397.403 274.337 395.783 c
264.886 394.523 m
264.886 397.583 268.636 397.313 269.986 394.704 c
271.078 392.594 272.462 391.643 274.337 393.264 c
341.82 194.87 m
342.324 195.734 l
343.404 192.998 l
345.87 199.91 l
S
0 g
BT
/T1_3 1 Tf
7 0 0 7 122.3381 56.3701 Tm
(k =)Tj
ET
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90.713 311.175 89.621 310.082 89.621 308.746 c
89.621 301.463 l
89.621 300.128 90.713 299.035 92.049 299.035 c
105.402 299.035 l
h
B
105.773 300.233 m
106.276 300.233 106.684 300.641 106.684 301.143 c
B
91.695 310.137 m
91.192 310.137 90.785 309.729 90.785 309.226 c
B
148.326 299.035 m
149.662 299.035 150.754 300.128 150.754 301.463 c
150.754 308.746 l
150.754 310.082 149.662 311.175 148.326 311.175 c
134.973 311.175 l
133.638 311.175 132.545 310.082 132.545 308.746 c
132.545 301.463 l
132.545 300.128 133.638 299.035 134.973 299.035 c
148.326 299.035 l
h
B
148.698 300.233 m
149.201 300.233 149.608 300.641 149.608 301.143 c
B
134.619 310.137 m
134.117 310.137 133.709 309.729 133.709 309.226 c
B
191.251 299.035 m
192.586 299.035 193.679 300.128 193.679 301.463 c
193.679 308.746 l
193.679 310.082 192.586 311.175 191.251 311.175 c
177.898 311.175 l
176.562 311.175 175.47 310.082 175.47 308.746 c
175.47 301.463 l
175.47 300.128 176.562 299.035 177.898 299.035 c
191.251 299.035 l
h
B
191.622 300.233 m
192.125 300.233 192.533 300.641 192.533 301.143 c
B
177.544 310.137 m
177.041 310.137 176.634 309.729 176.634 309.226 c
B
234.176 299.035 m
235.511 299.035 236.603 300.128 236.603 301.463 c
236.603 308.746 l
236.603 310.082 235.511 311.175 234.176 311.175 c
220.822 311.175 l
219.487 311.175 218.394 310.082 218.394 308.746 c
218.394 301.463 l
218.394 300.128 219.487 299.035 220.822 299.035 c
234.176 299.035 l
h
B
234.547 300.233 m
235.05 300.233 235.457 300.641 235.457 301.143 c
B
220.469 310.137 m
219.966 310.137 219.558 309.729 219.558 309.226 c
B
0.188 0.141 0.039 0.004 k
83.94 299.035 m
85.275 299.035 86.368 300.128 86.368 301.463 c
86.368 308.746 l
86.368 310.082 85.275 311.175 83.94 311.175 c
70.586 311.175 l
69.251 311.175 68.159 310.082 68.159 308.746 c
68.159 301.463 l
68.159 300.128 69.251 299.035 70.586 299.035 c
83.94 299.035 l
h
B
84.311 300.233 m
84.814 300.233 85.222 300.641 85.222 301.143 c
B
70.233 310.137 m
69.73 310.137 69.322 309.729 69.322 309.226 c
B
126.865 299.035 m
128.2 299.035 129.292 300.128 129.292 301.463 c
129.292 308.746 l
129.292 310.082 128.2 311.175 126.865 311.175 c
113.511 311.175 l
112.176 311.175 111.083 310.082 111.083 308.746 c
111.083 301.463 l
111.083 300.128 112.176 299.035 113.511 299.035 c
126.865 299.035 l
h
B
127.236 300.233 m
127.738 300.233 128.146 300.641 128.146 301.143 c
B
113.157 310.137 m
112.654 310.137 112.246 309.729 112.246 309.226 c
B
169.789 299.035 m
171.124 299.035 172.217 300.128 172.217 301.463 c
172.217 308.746 l
172.217 310.082 171.124 311.175 169.789 311.175 c
156.435 311.175 l
155.1 311.175 154.008 310.082 154.008 308.746 c
154.008 301.463 l
154.008 300.128 155.1 299.035 156.435 299.035 c
169.789 299.035 l
h
B
170.16 300.233 m
170.663 300.233 171.071 300.641 171.071 301.143 c
B
156.081 310.137 m
155.579 310.137 155.171 309.729 155.171 309.226 c
B
212.713 299.035 m
214.049 299.035 215.142 300.128 215.142 301.463 c
215.142 308.746 l
215.142 310.082 214.049 311.175 212.713 311.175 c
199.36 311.175 l
198.025 311.175 196.932 310.082 196.932 308.746 c
196.932 301.463 l
196.932 300.128 198.025 299.035 199.36 299.035 c
212.713 299.035 l
h
B
213.085 300.233 m
213.587 300.233 213.995 300.641 213.995 301.143 c
B
199.006 310.137 m
198.503 310.137 198.096 309.729 198.096 309.226 c
B
255.638 299.035 m
256.973 299.035 258.066 300.128 258.066 301.463 c
258.066 308.746 l
258.066 310.082 256.973 311.175 255.638 311.175 c
242.285 311.175 l
240.949 311.175 239.857 310.082 239.857 308.746 c
239.857 301.463 l
239.857 300.128 240.949 299.035 242.285 299.035 c
255.638 299.035 l
h
B
256.009 300.233 m
256.512 300.233 256.92 300.641 256.92 301.143 c
B
241.93 310.137 m
241.428 310.137 241.02 309.729 241.02 309.226 c
B
277.1 299.035 m
278.435 299.035 279.528 300.128 279.528 301.463 c
279.528 308.746 l
279.528 310.082 278.435 311.175 277.1 311.175 c
263.747 311.175 l
262.411 311.175 261.319 310.082 261.319 308.746 c
261.319 301.463 l
261.319 300.128 262.411 299.035 263.747 299.035 c
277.1 299.035 l
h
B
277.472 300.233 m
277.974 300.233 278.382 300.641 278.382 301.143 c
B
263.393 310.137 m
262.89 310.137 262.482 309.729 262.482 309.226 c
B
0.129 0.063 0.035 0.004 k
105.589 314.33 m
106.925 314.33 108.018 315.423 108.018 316.758 c
108.018 324.042 l
108.018 325.377 106.925 326.47 105.589 326.47 c
92.236 326.47 l
90.901 326.47 89.808 325.377 89.808 324.042 c
89.808 316.758 l
89.808 315.423 90.901 314.33 92.236 314.33 c
105.589 314.33 l
h
B
105.961 315.528 m
106.463 315.528 106.871 315.936 106.871 316.438 c
B
91.882 325.432 m
91.379 325.432 90.972 325.024 90.972 324.521 c
B
148.514 314.33 m
149.849 314.33 150.942 315.423 150.942 316.758 c
150.942 324.042 l
150.942 325.377 149.849 326.47 148.514 326.47 c
135.16 326.47 l
133.825 326.47 132.733 325.377 132.733 324.042 c
132.733 316.758 l
132.733 315.423 133.825 314.33 135.16 314.33 c
148.514 314.33 l
h
B
148.885 315.528 m
149.388 315.528 149.796 315.936 149.796 316.438 c
B
134.806 325.432 m
134.304 325.432 133.896 325.024 133.896 324.521 c
B
0.188 0.141 0.039 0.004 k
169.976 314.33 m
171.311 314.33 172.404 315.423 172.404 316.758 c
172.404 324.042 l
172.404 325.377 171.311 326.47 169.976 326.47 c
156.623 326.47 l
155.287 326.47 154.195 325.377 154.195 324.042 c
154.195 316.758 l
154.195 315.423 155.287 314.33 156.623 314.33 c
169.976 314.33 l
h
B
170.347 315.528 m
170.85 315.528 171.258 315.936 171.258 316.438 c
B
156.269 325.432 m
155.766 325.432 155.358 325.024 155.358 324.521 c
B
0.129 0.063 0.035 0.004 k
191.438 314.33 m
192.774 314.33 193.866 315.423 193.866 316.758 c
193.866 324.042 l
193.866 325.377 192.774 326.47 191.438 326.47 c
178.085 326.47 l
176.75 326.47 175.657 325.377 175.657 324.042 c
175.657 316.758 l
175.657 315.423 176.75 314.33 178.085 314.33 c
191.438 314.33 l
h
B
191.81 315.528 m
192.312 315.528 192.72 315.936 192.72 316.438 c
B
177.731 325.432 m
177.228 325.432 176.821 325.024 176.821 324.521 c
B
234.363 314.33 m
235.698 314.33 236.791 315.423 236.791 316.758 c
236.791 324.042 l
236.791 325.377 235.698 326.47 234.363 326.47 c
221.01 326.47 l
219.674 326.47 218.581 325.377 218.581 324.042 c
218.581 316.758 l
218.581 315.423 219.674 314.33 221.01 314.33 c
234.363 314.33 l
h
B
234.734 315.528 m
235.237 315.528 235.644 315.936 235.644 316.438 c
B
220.656 325.432 m
220.153 325.432 219.745 325.024 219.745 324.521 c
B
277.288 314.33 m
278.623 314.33 279.715 315.423 279.715 316.758 c
279.715 324.042 l
279.715 325.377 278.623 326.47 277.288 326.47 c
263.934 326.47 l
262.598 326.47 261.506 325.377 261.506 324.042 c
261.506 316.758 l
261.506 315.423 262.598 314.33 263.934 314.33 c
277.288 314.33 l
h
B
277.659 315.528 m
278.161 315.528 278.569 315.936 278.569 316.438 c
B
263.58 325.432 m
263.077 325.432 262.67 325.024 262.67 324.521 c
B
0.188 0.141 0.039 0.004 k
298.75 314.33 m
300.085 314.33 301.178 315.423 301.178 316.758 c
301.178 324.042 l
301.178 325.377 300.085 326.47 298.75 326.47 c
285.396 326.47 l
284.061 326.47 282.969 325.377 282.969 324.042 c
282.969 316.758 l
282.969 315.423 284.061 314.33 285.396 314.33 c
298.75 314.33 l
h
B
299.121 315.528 m
299.624 315.528 300.031 315.936 300.031 316.438 c
B
285.042 325.432 m
284.54 325.432 284.132 325.024 284.132 324.521 c
B
0.129 0.063 0.035 0.004 k
320.212 314.33 m
321.547 314.33 322.64 315.423 322.64 316.758 c
322.64 324.042 l
322.64 325.377 321.547 326.47 320.212 326.47 c
306.858 326.47 l
305.523 326.47 304.43 325.377 304.43 324.042 c
304.43 316.758 l
304.43 315.423 305.523 314.33 306.858 314.33 c
320.212 314.33 l
h
B
320.583 315.528 m
321.086 315.528 321.493 315.936 321.493 316.438 c
B
306.505 325.432 m
306.002 325.432 305.594 325.024 305.594 324.521 c
B
0.188 0.141 0.039 0.004 k
84.127 314.33 m
85.462 314.33 86.555 315.423 86.555 316.758 c
86.555 324.042 l
86.555 325.377 85.462 326.47 84.127 326.47 c
70.774 326.47 l
69.438 326.47 68.346 325.377 68.346 324.042 c
68.346 316.758 l
68.346 315.423 69.438 314.33 70.774 314.33 c
84.127 314.33 l
h
B
84.498 315.528 m
85.001 315.528 85.409 315.936 85.409 316.438 c
B
70.42 325.432 m
69.917 325.432 69.51 325.024 69.51 324.521 c
B
127.052 314.33 m
128.387 314.33 129.479 315.423 129.479 316.758 c
129.479 324.042 l
129.479 325.377 128.387 326.47 127.052 326.47 c
113.698 326.47 l
112.363 326.47 111.27 325.377 111.27 324.042 c
111.27 316.758 l
111.27 315.423 112.363 314.33 113.698 314.33 c
127.052 314.33 l
h
B
127.423 315.528 m
127.926 315.528 128.333 315.936 128.333 316.438 c
B
113.345 325.432 m
112.842 325.432 112.434 325.024 112.434 324.521 c
B
212.901 314.33 m
214.236 314.33 215.328 315.423 215.328 316.758 c
215.328 324.042 l
215.328 325.377 214.236 326.47 212.901 326.47 c
199.547 326.47 l
198.212 326.47 197.12 325.377 197.12 324.042 c
197.12 316.758 l
197.12 315.423 198.212 314.33 199.547 314.33 c
212.901 314.33 l
h
B
213.272 315.528 m
213.775 315.528 214.182 315.936 214.182 316.438 c
B
199.193 325.432 m
198.691 325.432 198.283 325.024 198.283 324.521 c
B
255.825 314.33 m
257.16 314.33 258.253 315.423 258.253 316.758 c
258.253 324.042 l
258.253 325.377 257.16 326.47 255.825 326.47 c
242.472 326.47 l
241.137 326.47 240.044 325.377 240.044 324.042 c
240.044 316.758 l
240.044 315.423 241.137 314.33 242.472 314.33 c
255.825 314.33 l
h
B
256.196 315.528 m
256.699 315.528 257.107 315.936 257.107 316.438 c
B
242.118 325.432 m
241.615 325.432 241.207 325.024 241.207 324.521 c
B
341.674 314.33 m
343.01 314.33 344.102 315.423 344.102 316.758 c
344.102 324.042 l
344.102 325.377 343.01 326.47 341.674 326.47 c
328.321 326.47 l
326.985 326.47 325.893 325.377 325.893 324.042 c
325.893 316.758 l
325.893 315.423 326.985 314.33 328.321 314.33 c
341.674 314.33 l
h
B
342.045 315.528 m
342.548 315.528 342.956 315.936 342.956 316.438 c
B
327.967 325.432 m
327.464 325.432 327.056 325.024 327.056 324.521 c
B
363.137 314.33 m
364.472 314.33 365.564 315.423 365.564 316.758 c
365.564 324.042 l
365.564 325.377 364.472 326.47 363.137 326.47 c
349.783 326.47 l
348.448 326.47 347.355 325.377 347.355 324.042 c
347.355 316.758 l
347.355 315.423 348.448 314.33 349.783 314.33 c
363.137 314.33 l
h
B
363.508 315.528 m
364.011 315.528 364.418 315.936 364.418 316.438 c
B
349.429 325.432 m
348.927 325.432 348.519 325.024 348.519 324.521 c
B
384.599 314.33 m
385.934 314.33 387.027 315.423 387.027 316.758 c
387.027 324.042 l
387.027 325.377 385.934 326.47 384.599 326.47 c
371.245 326.47 l
369.91 326.47 368.817 325.377 368.817 324.042 c
368.817 316.758 l
368.817 315.423 369.91 314.33 371.245 314.33 c
384.599 314.33 l
h
B
384.97 315.528 m
385.473 315.528 385.88 315.936 385.88 316.438 c
B
370.892 325.432 m
370.389 325.432 369.981 325.024 369.981 324.521 c
B
0.039 0.02 0.486 0 k
96.62 244.01 310.5 19.5 re
B
0.188 0.141 0.039 0.004 k
374.12 246.51 m
375.571 246.51 376.759 247.698 376.759 249.149 c
376.759 257.066 l
376.759 258.517 375.571 259.705 374.12 259.705 c
359.605 259.705 l
358.154 259.705 356.966 258.517 356.966 257.066 c
356.966 249.149 l
356.966 247.698 358.154 246.51 359.605 246.51 c
374.12 246.51 l
h
B
374.523 247.812 m
375.07 247.812 375.513 248.255 375.513 248.802 c
B
359.221 258.577 m
358.674 258.577 358.231 258.134 358.231 257.587 c
B
398.135 246.51 m
399.586 246.51 400.774 247.698 400.774 249.149 c
400.774 257.066 l
400.774 258.517 399.586 259.705 398.135 259.705 c
383.62 259.705 l
382.168 259.705 380.981 258.517 380.981 257.066 c
380.981 249.149 l
380.981 247.698 382.168 246.51 383.62 246.51 c
398.135 246.51 l
h
B
398.538 247.812 m
399.085 247.812 399.528 248.255 399.528 248.802 c
B
383.235 258.577 m
382.689 258.577 382.246 258.134 382.246 257.587 c
B
0.039 0.02 0.486 0 k
244.62 411.01 153 19.5 re
B
139.786 481.51 m
171.12 481.51 l
190.14 277.6 m
190.77 278.68 l
192.12 275.26 l
195.202 283.9 l
S
0 g
BT
/T1_3 1 Tf
9 0 0 9 68.349 508.5101 Tm
(Find D given    a = 3)Tj
/T1_4 1 Tf
9.1136 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(2    b = 5)Tj
/T1_4 1 Tf
4.0568 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(4    c = -2)Tj
/T1_4 1 Tf
4.2608 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(1)Tj
-13.9574 -7.1111 Td
(First write the question replacing the letters with numbers.)Tj
/T1_0 1 Tf
-0.4329 -21.5556 Td
(Note: )Tj
/T1_3 1 Tf
2.9609 0 Td
(If you are finding a square root the last two keys will be)Tj
-2.528 25.3889 Td
(D =)Tj
3.7222 0.6111 Td
(3a )Tj
/T1_4 1 Tf
1.3529 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 2c)Tj
-1.8529 -1.3333 Td
(  a + c)Tj
ET
138.12 490.899 m
136.131 488.181 134.955 484.831 134.955 481.205 c
134.955 477.578 136.131 474.229 138.12 471.51 c
172.12 490.899 m
174.109 488.181 175.285 484.831 175.285 481.205 c
175.285 477.578 174.109 474.229 172.12 471.51 c
125.453 475.677 m
126.953 478.844 l
129.62 472.51 l
133.786 489.844 l
139.786 420.51 m
209.62 420.51 l
S
BT
/T1_3 1 Tf
9 0 0 9 107.12 418.0101 Tm
(D =)Tj
3.8771 0.6111 Td
(3 x 3)Tj
/T1_4 1 Tf
2.1499 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(2 )Tj
/T1_4 1 Tf
0.834 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 2 x -2)Tj
/T1_4 1 Tf
2.7609 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(1)Tj
-5.2897 -1.3333 Td
(3)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(2 + -2)Tj
/T1_4 1 Tf
2.6669 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(1)Tj
ET
139.786 361.51 m
217.12 361.51 l
S
BT
/T1_3 1 Tf
9 0 0 9 143.6736 364.51 Tm
(\(3 x 3)Tj
/T1_4 1 Tf
2.4099 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(2 )Tj
/T1_4 1 Tf
0.834 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 2 x -2)Tj
/T1_4 1 Tf
2.7609 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(1\))Tj
-5.5497 -1.3333 Td
(\(3)Tj
/T1_4 1 Tf
0.816 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(2 + -2)Tj
/T1_4 1 Tf
2.6669 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(1\))Tj
ET
138.12 429.899 m
136.131 427.181 134.955 423.831 134.955 420.205 c
134.955 416.578 136.131 413.229 138.12 410.51 c
211.62 429.899 m
213.609 427.181 214.785 423.831 214.785 420.205 c
214.785 416.578 213.609 413.229 211.62 410.51 c
125.453 414.677 m
126.953 417.844 l
129.62 411.51 l
133.786 428.844 l
S
BT
/T1_3 1 Tf
9 0 0 9 251.12 417.5101 Tm
(Look at )Tj
/T1_5 1 Tf
3.5749 0 Td
(Using a calculator )Tj
/T1_3 1 Tf
8.1667 0 Td
(\(page 2\).)Tj
-32.0494 -2.7222 Td
(Work out everything in the brackets.)Tj
0 -1.3333 TD
(Remember to put brackets at the start and end of each line.)Tj
0 -5 TD
(Calculator keys:)Tj
0 -6.6667 TD
(Now press           and finally           Answer 3)Tj
/T1_4 1 Tf
19.4862 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(54)Tj
/T1_4 1 Tf
1.112 0 Td
(\311)Tj
/T1_0 1 Tf
1.8948 Tc 9.1768 0 0 9.1768 75.8932 317.071 Tm
(\(3)Tj
0 Tc 4.557 0.0953 Td
(x)Tj
2.3113 -0.0953 Td
(3)Tj
/T1_6 1 Tf
2.4868 0 Td
(\341)Tj
/T1_0 1 Tf
2.1907 0 Td
(2)Tj
/T1_6 1 Tf
2.3848 0.0953 Td
(\320)Tj
/T1_0 1 Tf
2.2928 -0.0953 Td
(2)Tj
2.3663 0.0953 Td
(x)Tj
2.3112 -0.0953 Td
(2)Tj
/T1_6 1 Tf
2.4868 0 Td
(\341)Tj
/T1_0 1 Tf
4.2335 Tc 2.1908 0 Td
(1\))Tj
/T1_7 1 Tf
0 Tc 7.0377 0 Td
(\003)Tj
/T1_0 1 Tf
1.8947 Tc -32.6364 -1.6667 Td
(\(3)Tj
/T1_6 1 Tf
0 Tc 4.6775 0 Td
(\341)Tj
/T1_0 1 Tf
2.1907 0.0952 Td
(2)Tj
1.7098 Tc 2.3018 -0.0952 Td
(+2)Tj
/T1_6 1 Tf
0 Tc 4.8625 0 Td
(\341)Tj
/T1_0 1 Tf
4.2335 Tc 2.1907 0 Td
(1\))Tj
0 Tc 9.9748 0 0 9.9748 121.8249 275.4896 Tm
(=)Tj
ET
388.135 250.51 m
388.764 251.59 l
390.115 248.17 l
393.197 256.81 l
S
BT
/T1_0 1 Tf
9.9748 0 0 9.9748 363.3249 249.4896 Tm
(=)Tj
7.2 0 0 7.2 329.9226 319.9603 Tm
(+)Tj
/T1_6 1 Tf
0.8885 -0.4445 Td
(\320)Tj
ET
337.92 323.76 m
333.12 316.96 l
S
BT
/T1_0 1 Tf
7.2 0 0 7.2 243.6726 304.4602 Tm
(+)Tj
/T1_6 1 Tf
0.8885 -0.4445 Td
(\320)Tj
ET
251.67 308.26 m
246.87 301.46 l
S
Q Q Q 
q
49.61 217.8 368.5 -19.02 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS6 gs
295.334 209.172 m
295.334 209.505 l
295.313 209.504 295.296 209.503 295.261 209.503 c
295.162 209.503 294.862 209.503 294.725 209.72 c
294.652 209.837 294.617 210.003 294.617 210.23 c
294.617 213.413 l
294.816 213.613 l
295.481 213.613 l
295.481 213.975 l
290.256 213.975 l
290.256 213.613 l
290.92 213.613 l
291.12 213.413 l
291.12 209.17 l
291.623 209.17 l
291.623 213.413 l
291.823 213.613 l
293.913 213.613 l
294.113 213.413 l
294.113 209.976 l
294.113 209.602 294.208 209.362 294.401 209.245 c
294.477 209.199 294.635 209.146 294.953 209.146 c
294.999 209.146 295.04 209.147 295.076 209.15 c
295.307 209.17 295.305 209.169 v
295.334 209.172 l
f
BT
/T1_3 1 Tf
9 0 0 9 68.349 208.67 Tm
(Calculate the value of r given v = 90, h = 6 and  v = )Tj
6 0 0 6 277.2215 212.67 Tm
(1)Tj
9 0 0 9 280.5577 208.67 Tm
(/)Tj
6 0 0 6 283.8875 206.67 Tm
(3  )Tj
9 0 0 9 290.5599 208.67 Tm
(   r)Tj
6 0 0 6 301.0535 212.67 Tm
(2)Tj
9 0 0 9 304.3897 208.67 Tm
(h)Tj
ET
Q Q Q 
q
49.61 192.28 368.5 -100.9 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.141 0.039 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS7 gs
324.995 110.859 m
326.156 110.859 327.106 111.808 327.106 112.969 c
327.106 119.303 l
327.106 120.465 326.156 121.415 324.995 121.415 c
313.383 121.415 l
312.222 121.415 311.272 120.465 311.272 119.303 c
311.272 112.969 l
311.272 111.808 312.222 110.859 313.383 110.859 c
324.995 110.859 l
h
B
325.317 111.9 m
325.755 111.9 326.109 112.255 326.109 112.692 c
B
313.075 120.512 m
312.638 120.512 312.284 120.157 312.284 119.72 c
B
306.332 110.859 m
307.493 110.859 308.443 111.808 308.443 112.969 c
308.443 119.303 l
308.443 120.465 307.493 121.415 306.332 121.415 c
294.72 121.415 l
293.559 121.415 292.609 120.465 292.609 119.303 c
292.609 112.969 l
292.609 111.808 293.559 110.859 294.72 110.859 c
306.332 110.859 l
h
B
306.655 111.9 m
307.092 111.9 307.446 112.255 307.446 112.692 c
B
294.412 120.512 m
293.975 120.512 293.62 120.157 293.62 119.72 c
B
0.129 0.063 0.035 0.004 k
287.669 110.859 m
288.83 110.859 289.78 111.808 289.78 112.969 c
289.78 119.303 l
289.78 120.465 288.83 121.415 287.669 121.415 c
276.057 121.415 l
274.896 121.415 273.946 120.465 273.946 119.303 c
273.946 112.969 l
273.946 111.808 274.896 110.859 276.057 110.859 c
287.669 110.859 l
h
B
287.992 111.9 m
288.429 111.9 288.783 112.255 288.783 112.692 c
B
275.749 120.512 m
275.312 120.512 274.957 120.157 274.957 119.72 c
B
269.006 110.859 m
270.167 110.859 271.117 111.808 271.117 112.969 c
271.117 119.303 l
271.117 120.465 270.167 121.415 269.006 121.415 c
257.394 121.415 l
256.233 121.415 255.283 120.465 255.283 119.303 c
255.283 112.969 l
255.283 111.808 256.233 110.859 257.394 110.859 c
269.006 110.859 l
h
B
269.328 111.9 m
269.766 111.9 270.12 112.255 270.12 112.692 c
B
257.086 120.512 m
256.649 120.512 256.295 120.157 256.295 119.72 c
B
0.188 0.141 0.039 0.004 k
250.343 110.859 m
251.504 110.859 252.454 111.808 252.454 112.969 c
252.454 119.303 l
252.454 120.465 251.504 121.415 250.343 121.415 c
238.731 121.415 l
237.57 121.415 236.62 120.465 236.62 119.303 c
236.62 112.969 l
236.62 111.808 237.57 110.859 238.731 110.859 c
250.343 110.859 l
h
B
250.665 111.9 m
251.103 111.9 251.457 112.255 251.457 112.692 c
B
238.423 120.512 m
237.986 120.512 237.632 120.157 237.632 119.72 c
B
231.68 110.859 m
232.841 110.859 233.791 111.808 233.791 112.969 c
233.791 119.303 l
233.791 120.465 232.841 121.415 231.68 121.415 c
220.068 121.415 l
218.907 121.415 217.957 120.465 217.957 119.303 c
217.957 112.969 l
217.957 111.808 218.907 110.859 220.068 110.859 c
231.68 110.859 l
h
B
232.003 111.9 m
232.44 111.9 232.794 112.255 232.794 112.692 c
B
219.761 120.512 m
219.323 120.512 218.969 120.157 218.969 119.72 c
B
213.017 110.859 m
214.178 110.859 215.128 111.808 215.128 112.969 c
215.128 119.303 l
215.128 120.465 214.178 121.415 213.017 121.415 c
201.405 121.415 l
200.244 121.415 199.294 120.465 199.294 119.303 c
199.294 112.969 l
199.294 111.808 200.244 110.859 201.405 110.859 c
213.017 110.859 l
h
B
213.34 111.9 m
213.777 111.9 214.131 112.255 214.131 112.692 c
B
201.098 120.512 m
200.66 120.512 200.306 120.157 200.306 119.72 c
B
194.354 110.859 m
195.515 110.859 196.465 111.808 196.465 112.969 c
196.465 119.303 l
196.465 120.465 195.515 121.415 194.354 121.415 c
182.742 121.415 l
181.581 121.415 180.631 120.465 180.631 119.303 c
180.631 112.969 l
180.631 111.808 181.581 110.859 182.742 110.859 c
194.354 110.859 l
h
B
194.677 111.9 m
195.114 111.9 195.469 112.255 195.469 112.692 c
B
182.434 120.512 m
181.997 120.512 181.643 120.157 181.643 119.72 c
B
175.691 110.859 m
176.852 110.859 177.802 111.808 177.802 112.969 c
177.802 119.303 l
177.802 120.465 176.852 121.415 175.691 121.415 c
164.079 121.415 l
162.918 121.415 161.968 120.465 161.968 119.303 c
161.968 112.969 l
161.968 111.808 162.918 110.859 164.079 110.859 c
175.691 110.859 l
h
B
176.014 111.9 m
176.451 111.9 176.805 112.255 176.805 112.692 c
B
163.771 120.512 m
163.334 120.512 162.98 120.157 162.98 119.72 c
B
0.129 0.063 0.035 0.004 k
157.028 110.859 m
158.189 110.859 159.139 111.808 159.139 112.969 c
159.139 119.303 l
159.139 120.465 158.189 121.415 157.028 121.415 c
145.416 121.415 l
144.255 121.415 143.305 120.465 143.305 119.303 c
143.305 112.969 l
143.305 111.808 144.255 110.859 145.416 110.859 c
157.028 110.859 l
h
B
157.351 111.9 m
157.788 111.9 158.142 112.255 158.142 112.692 c
B
145.109 120.512 m
144.671 120.512 144.317 120.157 144.317 119.72 c
B
138.365 110.859 m
139.526 110.859 140.476 111.808 140.476 112.969 c
140.476 119.303 l
140.476 120.465 139.526 121.415 138.365 121.415 c
126.753 121.415 l
125.592 121.415 124.642 120.465 124.642 119.303 c
124.642 112.969 l
124.642 111.808 125.592 110.859 126.753 110.859 c
138.365 110.859 l
h
B
138.688 111.9 m
139.125 111.9 139.479 112.255 139.479 112.692 c
B
126.446 120.512 m
126.009 120.512 125.654 120.157 125.654 119.72 c
B
0.188 0.141 0.039 0.004 k
119.702 110.859 m
120.863 110.859 121.813 111.808 121.813 112.969 c
121.813 119.303 l
121.813 120.465 120.863 121.415 119.702 121.415 c
108.09 121.415 l
106.929 121.415 105.979 120.465 105.979 119.303 c
105.979 112.969 l
105.979 111.808 106.929 110.859 108.09 110.859 c
119.702 110.859 l
h
B
120.025 111.9 m
120.462 111.9 120.817 112.255 120.817 112.692 c
B
107.783 120.512 m
107.346 120.512 106.991 120.157 106.991 119.72 c
B
0.129 0.063 0.035 0.004 k
101.039 110.859 m
102.201 110.859 103.15 111.808 103.15 112.969 c
103.15 119.303 l
103.15 120.465 102.201 121.415 101.039 121.415 c
89.428 121.415 l
88.266 121.415 87.316 120.465 87.316 119.303 c
87.316 112.969 l
87.316 111.808 88.266 110.859 89.428 110.859 c
101.039 110.859 l
h
B
101.362 111.9 m
101.799 111.9 102.154 112.255 102.154 112.692 c
B
89.12 120.512 m
88.682 120.512 88.328 120.157 88.328 119.72 c
B
0.188 0.141 0.039 0.004 k
82.376 110.859 m
83.537 110.859 84.488 111.808 84.488 112.969 c
84.488 119.303 l
84.488 120.465 83.537 121.415 82.376 121.415 c
70.764 121.415 l
69.603 121.415 68.653 120.465 68.653 119.303 c
68.653 112.969 l
68.653 111.808 69.603 110.859 70.764 110.859 c
82.376 110.859 l
h
B
82.699 111.9 m
83.136 111.9 83.491 112.255 83.491 112.692 c
B
70.457 120.512 m
70.02 120.512 69.665 120.157 69.665 119.72 c
B
316.761 114.442 m
317.266 115.305 l
318.345 112.569 l
320.811 119.482 l
S
0 g
111.62 140.9 m
111.62 141.167 l
111.603 141.166 111.59 141.165 111.561 141.165 c
111.482 141.165 111.242 141.165 111.133 141.339 c
111.074 141.432 111.046 141.566 111.046 141.746 c
111.046 144.294 l
111.206 144.453 l
111.737 144.453 l
111.737 144.743 l
107.557 144.743 l
107.557 144.453 l
108.089 144.453 l
108.248 144.294 l
108.248 140.899 l
108.651 140.899 l
108.651 144.294 l
108.811 144.453 l
110.483 144.453 l
110.643 144.294 l
110.643 141.544 l
110.643 141.244 110.719 141.052 110.873 140.958 c
110.934 140.922 111.06 140.879 111.315 140.879 c
111.352 140.879 111.385 140.88 111.413 140.882 c
111.598 140.898 111.597 140.898 v
111.62 140.9 l
f
104.849 155.411 m
103.258 153.236 102.317 150.557 102.317 147.656 c
102.317 144.755 103.258 142.075 104.849 139.9 c
121.088 155.411 m
122.679 153.236 123.62 150.557 123.62 147.656 c
123.62 144.755 122.679 142.075 121.088 139.9 c
94.716 143.234 m
95.916 145.767 l
98.049 140.7 l
101.383 154.567 l
S
BT
/T1_0 1 Tf
1.8948 Tc 7.9799 0 0 7.9799 75.2163 113.2419 Tm
(\(3)Tj
0 Tc 4.557 -0.005 Td
(x)Tj
1.7468 Tc 2.3113 0.005 Td
[(90)-148(\))]TJ
/T1_7 1 Tf
0 Tc 7.0377 0 Td
(\003)Tj
/T1_0 1 Tf
2.4653 0 Td
(\()Tj
4.557 0.0952 Td
(x)Tj
ET
227.945 113.77 m
227.945 114.036 l
227.928 114.035 227.914 114.034 227.886 114.034 c
227.807 114.034 227.567 114.034 227.458 114.209 c
227.399 114.302 227.37 114.435 227.37 114.616 c
227.37 117.163 l
227.531 117.323 l
228.062 117.323 l
228.062 117.612 l
223.882 117.612 l
223.882 117.323 l
224.413 117.323 l
224.574 117.163 l
224.574 113.768 l
224.976 113.768 l
224.976 117.163 l
225.136 117.323 l
226.808 117.323 l
226.968 117.163 l
226.968 114.413 l
226.968 114.113 227.044 113.922 227.198 113.828 c
227.259 113.792 227.386 113.749 227.64 113.749 c
227.677 113.749 227.71 113.75 227.738 113.752 c
227.923 113.768 227.922 113.767 v
227.945 113.77 l
f
BT
/T1_0 1 Tf
7.9799 0 0 7.9799 280.5088 114.0421 Tm
(\))Tj
4.0485 Tc -2.4868 -0.1003 Td
(6=)Tj
/T1_3 1 Tf
0 Tc 7 0 0 7 68.349 166.4001 Tm
(First rewrite the formula making r the subject \(see Question 11 on page\
 11\) )Tj
1.9286 -3.0714 Td
(r = )Tj
3.7554 0.7857 Td
(3 v)Tj
0.76 -1.4286 Td
(h)Tj
ET
106.349 147.9 m
119.62 147.9 l
S
184.62 140.506 m
184.62 140.773 l
184.603 140.772 184.59 140.771 184.561 140.771 c
184.482 140.771 184.242 140.771 184.133 140.946 c
184.074 141.039 184.046 141.172 184.046 141.353 c
184.046 143.9 l
184.206 144.06 l
184.737 144.06 l
184.737 144.349 l
180.557 144.349 l
180.557 144.06 l
181.089 144.06 l
181.249 143.9 l
181.249 140.506 l
181.651 140.506 l
181.651 143.9 l
181.811 144.06 l
183.483 144.06 l
183.643 143.9 l
183.643 141.15 l
183.643 140.85 183.719 140.659 183.873 140.565 c
183.934 140.529 184.061 140.486 184.315 140.486 c
184.352 140.486 184.385 140.487 184.413 140.489 c
184.414 140.489 184.598 140.505 184.597 140.505 c
184.62 140.506 l
f
173.349 155.411 m
171.758 153.236 170.817 150.557 170.817 147.656 c
170.817 144.755 171.758 142.075 173.349 139.9 c
203.088 155.411 m
204.679 153.236 205.62 150.557 205.62 147.656 c
205.62 144.755 204.679 142.075 203.088 139.9 c
163.216 143.234 m
164.416 145.767 l
166.549 140.7 l
169.883 154.567 l
S
BT
/T1_3 1 Tf
7 0 0 7 150.349 144.9001 Tm
(r = )Tj
3.9756 0.7857 Td
(3 x 90)Tj
0.278 -1.4286 Td
(    x 6)Tj
ET
174.849 147.9 m
201.12 147.9 l
S
BT
/T1_3 1 Tf
7 0 0 7 67.5538 125.632 Tm
(Calculator keys:)Tj
33.2141 -3.4286 Td
(Answer 3)Tj
/T1_4 1 Tf
4.1121 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(78 \(approx\))Tj
ET
Q Q Q 
endstream
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994 1 obj
28468 
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<< /Length 467 2 R >> 
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1 g
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/GS0 gs
0 660 m
0 660 l
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q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
/CS2 cs 1  scn
/T1_1 1 Tf
0 Tw 14 0 0 14 204.9068 581.8038 Tm
(Contents)Tj
0 0 0 1 k
8 0 0 8 51.3228 557.9926 Tm
[(Intr)18(oduction)]TJ
/T1_2 1 Tf
-0.0002 Tc 16.5283 0 Td
[(........................................................................\
...................)-2685(vi)]TJ
/T1_1 1 Tf
-0.0001 Tc 0.0295 Tw -16.5283 -2.2087 Td
[(Examiner\325)74(s tips)]TJ
/T1_2 1 Tf
-0.0002 Tc 0 Tw 16.5283 0 Td
[(........................................................................\
...................)-2445(vii)]TJ
/T1_1 1 Tf
-0.0001 Tc 0.0295 Tw -16.5283 -2.2087 Td
(Number skills)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 16.2992 0 Td
[(Rational and irrational numbers)-138(.........................................)-2851(1)]TJ
/T1_1 1 Tf
0.0296 Tw -16.2992 -2.2087 Td
(Calculator skills)Tj
/T1_2 1 Tf
0.0278 Tw 16.2992 0 Td
[(Using a calculator: Brackets, memory and fractions)-129(..........)-2851(2)]TJ
0 -1.5 TD
[(Using a calculator: Powers, r)18(oots and memory)-258(.................)-2851(3)]TJ
T*
[(Standar)18(d for)-18(m)-207(....................................................................)-2851(4)]TJ
/T1_1 1 Tf
-0.0001 Tc 0.0296 Tw -16.2992 -2.2087 Td
(Fractions, decimals and)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 16.2992 0 Td
[(Per)18(centages and fractions)-68(..................................................)-2851(5)]TJ
/T1_1 1 Tf
-0.0001 Tc 0 Tw -16.2992 -1.125 Td
[(per)18(centages)]TJ
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 16.2992 -0.375 Td
[(Calculating gr)18(owth and decay rates)-219(..................................)-2851(6)]TJ
/T1_1 1 Tf
-0.0001 Tc 0.0296 Tw -16.2992 -2.2087 Td
[(Number patter)-18(ns)]TJ
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 16.2992 0 Td
[(Patter)-18(ns you must r)18(ecognise)-42(..............................................)-2851(7)]TJ
-0.0023 -1.5 Td
[(Pr)18(oduct of primes, highest common factor)92(,)]TJ
0 -1.125 TD
[(lowest common multiple and r)18(ecipr)18(ocals)-185(..........................)-2851(8)]TJ
/T1_1 1 Tf
-0.0001 Tc 0 Tw -16.2969 -2.5837 Td
(Equations)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 16.2992 0 Td
[(T)92(rial and impr)18(ovement)-179(.......................................................)-2851(9)]TJ
0 Tw 0 -1.5 TD
[(Equations)-250(........................................................................\
...)-2295(10)]TJ
0.0278 Tw T*
[(Rewriting for)-18(mulae)-117(.............................................................)-2295(11)]TJ
0 Tw 0 -1.6429 TD
[(Iteration)-118(........................................................................\
......)-2295(12)]TJ
/T1_1 1 Tf
-16.2992 -2.2087 Td
[(V)55(ariation)]TJ
/T1_2 1 Tf
0.0279 Tw 16.2992 0 Td
[(Dir)18(ect and inverse variation)-228(...............................................)-2295(13)]TJ
/T1_1 1 Tf
0.0296 Tw -16.2992 -2.0658 Td
(Algebraic skills)Tj
/T1_2 1 Tf
0.0278 Tw 16.2992 0 Td
[(Using algebraic for)-18(mulae)-143(...................................................)-2295(14)]TJ
0 -1.5 TD
[(Rules for indices \(powers\))-244(..................................................)-2295(15)]TJ
T*
[(Expansion of brackets)-140(........................................................)-2295(16)]TJ
T*
[(Factorisation \320 1)-68(.................................................................)-2295(17)]TJ
T*
[(Factorisation \320 2)-68(.................................................................)-2295(18)]TJ
T*
[(Factorisation \320 3)-68(.................................................................)-2295(19)]TJ
T*
[(Solving quadratic equations)-255(..............................................)-2295(20)]TJ
-0.0001 Tc T*
[(Simultaneous equations: Solving using algebra)-145(................)-2295(21)]TJ
-0.0002 Tc T*
[(Simplifying algebraic fractions \320 1)-147(.....................................)-2295(22)]TJ
T*
[(Simplifying algebraic fractions \320 2)-147(.....................................)-2295(23)]TJ
/T1_1 1 Tf
-0.0001 Tc 0 Tw -16.2992 -2.2087 Td
(Graphs)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0279 Tw 16.2992 0 Td
[(Drawing lines)-20(......................................................................)-2295(24)]TJ
-0.0001 Tc 0.0277 Tw T*
[(Simultaneous equations: Solving by drawing a graph)-258(......)-2295(25)]TJ
T*
[(Solving equations using graphical methods)-90(......................)-2295(26)]TJ
T*
[(The straight line equation y = mx + c)-239(...............................)-2295(27)]TJ
-0.0002 Tc T*
[(Using tangents to find gradients)-240(.......................................)-2295(28)]TJ
-0.0001 Tc T*
[(Expr)18(essing general rules in symbolic for)-18(m \320 1)-212(..................)-2295(29)]TJ
T*
[(Expr)18(essing general rules in symbolic for)-18(m \320 2)-212(..................)-2295(30)]TJ
-0.0002 Tc T*
[(Drawing graphs)-95(..................................................................)-2295(31)]TJ
0.0279 Tw T*
[(Sketching graphs \320 1.................................................\
.........)-2295(32)]TJ
T*
[(Sketching graphs \320 2.................................................\
.........)-2295(33)]TJ
T*
[(Speed, time and distance graphs)-125(......................................)-2295(34)]TJ
T*
[(Ar)18(ea under a curve)-36(.............................................................)-2295(35)]TJ
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
165.96 68.66 6.59 -6.58 re
413.063 62.969 m
165.96 80.66 6.59 -6.58 re
413.063 62.969 m
165.96 92.66 6.59 -6.58 re
413.063 62.969 m
165.96 104.66 6.59 -6.58 re
413.063 62.969 m
165.96 116.66 6.59 -6.58 re
413.063 62.969 m
165.96 128.66 6.59 -6.58 re
413.063 62.969 m
165.96 140.66 6.59 -6.58 re
413.063 62.969 m
165.96 152.66 6.59 -6.58 re
413.063 62.969 m
165.96 164.66 6.59 -6.58 re
413.063 62.969 m
165.96 176.66 6.59 -6.58 re
413.063 62.969 m
165.96 188.66 6.59 -6.58 re
413.063 62.969 m
165.96 200.66 6.59 -6.58 re
413.063 62.969 m
165.96 218.33 6.59 -6.58 re
413.063 62.969 m
165.96 230.33 6.59 -6.58 re
413.063 62.969 m
165.96 242.33 6.59 -6.58 re
413.063 62.969 m
165.96 254.33 6.59 -6.58 re
413.063 62.969 m
165.96 266.33 6.59 -6.58 re
413.063 62.969 m
165.96 278.33 6.59 -6.58 re
413.063 62.969 m
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-0.0003 Tc 0.9714 0 Td
(2a)Tj
0 Tc 6.3 0 0 6.3 102.6707 450.4272 Tm
(8)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 108.9234 446.8272 Tm
(= 4a)Tj
/T1_2 1 Tf
0 Tc 0 Tw 6.3 0 0 6.3 127.3383 450.4272 Tm
(\320)Tj
/T1_0 1 Tf
0.4998 0 Td
(5)Tj
/T1_1 1 Tf
-0.0002 Tc 9 0 0 9 152.9225 446.8272 Tm
(Divide)Tj
/T1_0 1 Tf
-0.0001 Tc 0.0278 Tw 3.3066 0 Td
(the whole numbers and )Tj
/T1_1 1 Tf
0 Tw 10.9061 0 Td
(subtract)Tj
/T1_0 1 Tf
-0.0002 Tc 0.0278 Tw 4.1389 0 Td
(the powers)Tj
ET
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_1 1 Tf
-0.0004 Tc 0 Tw 8 0 0 8 408.358 35.0006 Tm
(15)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 593.39 368.51 -22.68 re
f*
/CS3 cs 1  scn
BT
/T1_1 1 Tf
0.0296 Tw 14 0 0 14 150.114 581.8038 Tm
(Rules for indices \(powers\))Tj
0 0 0 1 k
/T1_4 1 Tf
0.0278 Tw 10 0 0 10 350.9156 604.6698 Tm
(Algebraic skills)Tj
ET
Q Q 
q
50.32 438.9 368.51 -36.39 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.039 0.02 0.486 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS4 gs
65.569 407.8 324.771 28.5 re
B
341.859 420.973 m
342.49 422.053 l
343.84 418.634 l
346.922 427.273 l
S
0 g
BT
/T1_0 1 Tf
9 0 0 9 122.84 420.3 Tm
(y)Tj
/T1_2 1 Tf
6 0 0 6 127.1778 424.3 Tm
(\320)Tj
/T1_0 1 Tf
0.5 0 Td
(3)Tj
9 0 0 9 133.5142 420.3 Tm
( =)Tj
1.5915 0.6667 Td
(1)Tj
-0.1483 -1.3333 Td
(y)Tj
6 0 0 6 150.8408 418.3 Tm
(3)Tj
ET
145.007 424.8 m
154.84 424.8 l
S
BT
/T1_0 1 Tf
9 0 0 9 198.34 424.3 Tm
(5a)Tj
6 0 0 6 208.0146 428.3 Tm
(2)Tj
9 0 0 9 211.3508 424.3 Tm
( means 5 x a x a)Tj
-1.4456 -1.3333 Td
(\(5a\))Tj
6 0 0 6 212.6944 416.3 Tm
(2)Tj
9 0 0 9 216.0306 412.3 Tm
( means 5a x 5a = 25a)Tj
6 0 0 6 301.5811 416.3 Tm
(2)Tj
6.5988 1.1944 Td
(5)Tj
9 0 0 9 344.5102 419.4666 Tm
( y = y)Tj
5 0 0 5 367.506 426.3 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.37 -0.4 Td
(5)Tj
/T1_1 1 Tf
9 0 0 9 70.84 424.9665 Tm
(Note:)Tj
ET
Q Q Q 
q
50.32 400.33 368.51 -345.53 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.141 0.039 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
388.82 145.328 m
389.938 145.328 390.852 146.242 390.852 147.359 c
390.852 153.455 l
390.852 154.573 389.938 155.487 388.82 155.487 c
377.645 155.487 l
376.527 155.487 375.613 154.573 375.613 153.455 c
375.613 147.359 l
375.613 146.242 376.527 145.328 377.645 145.328 c
388.82 145.328 l
h
B
389.13 146.33 m
389.551 146.33 389.893 146.671 389.893 147.092 c
B
377.349 154.618 m
376.928 154.618 376.587 154.277 376.587 153.856 c
B
0 g
BT
/T1_0 1 Tf
9 0 0 9 68.0759 372.3718 Tm
(Simplify:)Tj
0 -2.2963 TD
(1)Tj
ET
253.82 291.83 m
254.45 292.91 l
255.8 289.49 l
258.882 298.13 l
381.401 148.695 m
381.905 149.56 l
382.985 146.824 l
385.451 153.735 l
S
0.925 0.725 0.075 0.012 k
BT
/T1_1 1 Tf
10 0 0 10 51.068 390.33 Tm
(Questions)Tj
0.172 0.89 0.796 0.047 k
8 0 0 8 51.068 243.8716 Tm
(Answers)Tj
0 g
/T1_0 1 Tf
9 0 0 9 67.4094 307.3715 Tm
(Evaluate:)Tj
7 0 0 7 85.0837 188.6635 Tm
[(Calculator keys:)-16908(Calculator keys:)]TJ
0 -4.3334 TD
[(An alter)-18(native solution is:)]TJ
0 -2.2143 TD
(8)Tj
/T1_2 1 Tf
5 0 0 5 88.9758 145.83 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(2)Tj
7 0 0 7 94.2564 142.83 Tm
( =       =)Tj
22.6165 0.7143 Td
[(Y)92(ou may need)-6689(could be)]TJ
0 -5.2857 TD
(Any number to the power of 1 is itself)Tj
0 -1.7143 TD
(6)Tj
5 0 0 5 256.4641 101.83 Tm
(1)Tj
7 0 0 7 259.2444 98.83 Tm
( = 6         8)Tj
0.0001 Tc 5 0 0 5 293.097 101.83 Tm
(1 )Tj
0 Tc 7 0 0 7 297.2675 98.83 Tm
(= 8)Tj
-6.3851 -1.7143 Td
(-3)Tj
5 0 0 5 258.7951 89.83 Tm
(1)Tj
7 0 0 7 261.5754 86.83 Tm
( = -3        0)Tj
/T1_2 1 Tf
4.8911 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(56)Tj
0.0001 Tc 5 0 0 5 305.5432 89.83 Tm
(1 )Tj
0 Tc 7 0 0 7 309.7137 86.83 Tm
(= 0)Tj
/T1_2 1 Tf
1.5 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(56)Tj
-33.868 3.5 Td
(At GCSE you can assume any )Tj
T*
(number to the power of 0 is 1)Tj
T*
(5)Tj
5 0 0 5 88.9758 90.33 Tm
(0)Tj
7 0 0 7 91.7561 87.33 Tm
( = 1         7)Tj
0.0001 Tc 5 0 0 5 125.6087 90.33 Tm
(0 )Tj
0 Tc 7 0 0 7 129.7792 87.33 Tm
(=1)Tj
-6.3851 -1.7143 Td
(-3)Tj
5 0 0 5 91.3068 78.33 Tm
(0)Tj
7 0 0 7 94.0871 75.33 Tm
( = 1        0)Tj
/T1_2 1 Tf
4.5581 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(27)Tj
0.0001 Tc 5 0 0 5 135.7238 78.33 Tm
(0 )Tj
0 Tc 7 0 0 7 139.8943 75.33 Tm
(=1)Tj
9 0 0 9 183.32 333.3716 Tm
(5)Tj
24.4156 Tc -12.8049 0 Td
(46)Tj
0 Tc 0 -4.7037 TD
(7)Tj
0 -2.037 TD
(9)Tj
18.6098 2.037 Td
(8)Tj
T*
(10)Tj
-16.72 8.7778 Td
(y)Tj
6 0 0 6 89.4215 355.705 Tm
(3)Tj
9 0 0 9 92.7577 351.705 Tm
( x y)Tj
6 0 0 6 106.4372 355.705 Tm
(5)Tj
1.3338 Tc 9 0 0 9 292.82 351.705 Tm
(3y)Tj
0 Tc 5 0 0 5 314.1656 356.705 Tm
(1)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(3)Tj
9 0 0 9 321.5765 351.705 Tm
( x y)Tj
5 0 0 5 335.256 356.705 Tm
(2)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(5)Tj
9 0 0 9 85.0837 333.3716 Tm
(y)Tj
/T1_2 1 Tf
5 0 0 5 89.4215 338.3716 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(1)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(2)Tj
9 0 0 9 99.3327 333.3716 Tm
( x y)Tj
/T1_2 1 Tf
5 0 0 5 113.0122 338.3716 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(2)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(5)Tj
9 0 0 9 200.3278 333.33 Tm
(y)Tj
5 0 0 5 204.6656 338.33 Tm
(1)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(3)Tj
9 0 0 9 212.0765 333.33 Tm
( )Tj
/T1_5 1 Tf
0.278 0 Td
(\003)Tj
/T1_0 1 Tf
0.549 0 Td
( y)Tj
5 0 0 5 226.359 338.33 Tm
(1)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(2)Tj
9 0 0 9 309.8278 333.33 Tm
(y)Tj
/T1_2 1 Tf
5 0 0 5 314.1656 338.33 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(2)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(5)Tj
9 0 0 9 324.0768 333.33 Tm
( )Tj
/T1_5 1 Tf
0.278 0 Td
(\003)Tj
/T1_0 1 Tf
0.549 0 Td
( y)Tj
/T1_2 1 Tf
5 0 0 5 338.3593 338.33 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(3)Tj
0.5561 -0.2 Td
(/)Tj
0.37 -0.2 Td
(8)Tj
9 0 0 9 183.32 351.705 Tm
(2)Tj
1.8898 -0.0046 Td
(y)Tj
6 0 0 6 204.6656 355.6635 Tm
(4)Tj
9 0 0 9 208.0018 351.6635 Tm
( )Tj
/T1_5 1 Tf
0.278 0 Td
(\003)Tj
/T1_0 1 Tf
0.549 0 Td
( y)Tj
/T1_2 1 Tf
6 0 0 6 222.2843 355.6635 Tm
(\320)Tj
/T1_0 1 Tf
0.5 0 Td
(5)Tj
7 0 0 7 295.8122 225.33 Tm
(3)Tj
-16.5714 -2.6191 Td
(5)Tj
-15.9623 -2.619 Td
(7)Tj
31.9778 Tc 0 2.619 TD
(46)Tj
0 Tc 23.9269 -2.619 Td
(8)Tj
-23.9269 -11.0476 Td
(9)Tj
23.9269 -0.0714 Td
(10)Tj
11.0366 16.3571 Td
(y)Tj
4 0 0 4 316.1941 229.33 Tm
(1)Tj
0.5561 -0.25 Td
(/)Tj
0.0001 Tc 0.3701 -0.25 Td
(3 )Tj
0 Tc 0.8342 0.25 Td
(+)Tj
0.6661 -0.25 Td
( )Tj
0.2781 0.5 Td
(2)Tj
0.5561 -0.25 Td
(/)Tj
0.3701 -0.25 Td
(5)Tj
7 0 0 7 332.9416 225.33 Tm
( = y)Tj
0.0001 Tc 4 0 0 4 344.8698 229.33 Tm
(11)Tj
0 Tc 1.1122 -0.25 Td
(/)Tj
0.0001 Tc 0.3701 -0.25 Td
(15)Tj
0 Tc 7 0 0 7 85.0837 206.9965 Tm
(y)Tj
0.482 0.2857 Td
(\()Tj
/T1_2 1 Tf
4 0 0 4 90.2777 210.9965 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(1)Tj
0.5561 -0.25 Td
(/)Tj
0.0001 Tc 0.3701 -0.25 Td
(2 )Tj
0 Tc 0.8342 0.25 Td
(+)Tj
0.6661 -0.25 Td
( )Tj
/T1_2 1 Tf
0.2781 0.5 Td
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(2)Tj
0.5561 -0.25 Td
(/)Tj
0.3701 -0.25 Td
(5)Tj
7 0 0 7 111.0262 208.9965 Tm
(\))Tj
0.26 -0.2857 Td
( = y)Tj
/T1_2 1 Tf
4 0 0 4 124.7744 210.9965 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(9)Tj
0.5561 -0.25 Td
(/)Tj
0.0001 Tc 0.3701 -0.25 Td
(10)Tj
0 Tc 7 0 0 7 196.82 206.955 Tm
(y)Tj
0.482 0.2857 Td
(\()Tj
4 0 0 4 202.0141 210.955 Tm
(1)Tj
0.5561 -0.25 Td
(/)Tj
0.0001 Tc 0.3701 -0.25 Td
(3 )Tj
/T1_2 1 Tf
0 Tc 0.8342 0.25 Td
(\320)Tj
/T1_0 1 Tf
0.5001 -0.25 Td
( )Tj
0.2781 0.5 Td
(1)Tj
0.5561 -0.25 Td
(/)Tj
0.3701 -0.25 Td
(2)Tj
7 0 0 7 218.0975 208.955 Tm
(\))Tj
0.26 -0.2857 Td
( = y)Tj
/T1_2 1 Tf
4 0 0 4 231.8457 210.955 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(1)Tj
0.5561 -0.25 Td
(/)Tj
0.3701 -0.25 Td
(6)Tj
7 0 0 7 312.82 206.955 Tm
(y)Tj
0.482 0.2857 Td
(\()Tj
/T1_2 1 Tf
4 0 0 4 318.0141 210.955 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(2)Tj
0.5561 -0.25 Td
(/)Tj
0.0001 Tc 0.3701 -0.25 Td
(5 )Tj
/T1_2 1 Tf
0 Tc 0.8342 0 Td
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
( )Tj
/T1_2 1 Tf
0.2781 0.5 Td
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(3)Tj
0.5561 -0.25 Td
(/)Tj
0.3701 -0.25 Td
(8)Tj
7 0 0 7 338.0984 208.955 Tm
(\))Tj
0.26 -0.2857 Td
( = y)Tj
/T1_2 1 Tf
4 0 0 4 351.8466 210.955 Tm
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(1)Tj
0.5561 -0.25 Td
(/)Tj
0.0001 Tc 0.3701 -0.25 Td
(40)Tj
0 Tc 7 0 0 7 179.8122 225.33 Tm
(2)Tj
1.8737 Tc -15.9623 0 Td
(1y)Tj
0.0001 Tc -0.0001 Tw 5 0 0 5 88.4577 228.33 Tm
(3 + 5)Tj
0 Tc 0 Tw 7 0 0 7 100.1292 225.33 Tm
( = y)Tj
5 0 0 5 112.0574 228.33 Tm
(8)Tj
7 0 0 7 196.82 225.2885 Tm
(y)Tj
0.0001 Tc 5 0 0 5 200.194 228.2885 Tm
(4 )Tj
/T1_2 1 Tf
0 Tc 0.8341 0 Td
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
( )Tj
/T1_2 1 Tf
0.278 0 Td
(\320)Tj
/T1_0 1 Tf
0.5001 0 Td
(5)Tj
7 0 0 7 213.5357 225.2885 Tm
( = y)Tj
5 0 0 5 225.4639 228.2885 Tm
(9)Tj
9 0 0 9 85.0837 291.0385 Tm
(8)Tj
/T1_2 1 Tf
6 0 0 6 90.0875 295.0385 Tm
(\320)Tj
/T1_0 1 Tf
26.0247 Tc -26.0247 Tw 0.5 0 Td
[(27)26025(  )]TJ
0 Tc 0 Tw 9 0 0 9 259.2444 291.0385 Tm
(128)Tj
-19.3512 -2.0417 Td
(5)Tj
6 0 0 6 90.0875 276.6635 Tm
(0)Tj
9 0 0 9 252.572 272.6635 Tm
(6)Tj
6 0 0 6 257.5758 276.6635 Tm
(1)Tj
7 0 0 7 85.0837 126.8301 Tm
(Answer = 0)Tj
/T1_2 1 Tf
5.0561 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(015625)Tj
18.5928 -0.0714 Td
(Answer = 2)Tj
ET
0.188 0.141 0.039 0.004 k
187.32 172.531 m
188.438 172.531 189.352 173.445 189.352 174.563 c
189.352 180.659 l
189.352 181.776 188.438 182.69 187.32 182.69 c
176.145 182.69 l
175.027 182.69 174.112 181.776 174.112 180.659 c
174.112 174.563 l
174.112 173.445 175.027 172.531 176.145 172.531 c
187.32 172.531 l
h
B
187.63 173.534 m
188.051 173.534 188.393 173.874 188.393 174.295 c
175.848 181.822 m
175.428 181.822 175.087 181.481 175.087 181.06 c
S
0 g
179.827 178.448 4.018 -0.587 re
179.827 177.267 4.018 -0.587 re
f
0.188 0.141 0.039 0.004 k
388.32 172.531 m
389.438 172.531 390.352 173.445 390.352 174.563 c
390.352 180.659 l
390.352 181.776 389.438 182.69 388.32 182.69 c
377.145 182.69 l
376.027 182.69 375.112 181.776 375.112 180.659 c
375.112 174.563 l
375.112 173.445 376.027 172.531 377.145 172.531 c
388.32 172.531 l
h
B
388.63 173.534 m
389.051 173.534 389.393 173.874 389.393 174.295 c
376.848 181.822 m
376.428 181.822 376.087 181.481 376.087 181.06 c
S
0 g
380.827 178.448 4.018 -0.587 re
380.827 177.267 4.018 -0.587 re
f
0.129 0.063 0.035 0.004 k
283.995 172.531 m
285.113 172.531 286.027 173.445 286.027 174.563 c
286.027 180.659 l
286.027 181.776 285.113 182.69 283.995 182.69 c
272.82 182.69 l
271.702 182.69 270.788 181.776 270.788 180.659 c
270.788 174.563 l
270.788 173.445 271.702 172.531 272.82 172.531 c
283.995 172.531 l
h
B
284.306 173.534 m
284.727 173.534 285.068 173.874 285.068 174.295 c
B
272.524 181.822 m
272.103 181.822 271.762 181.481 271.762 181.06 c
B
0 g
BT
/T1_1 1 Tf
7.6799 0 0 7.6799 275.7053 174.835 Tm
(1)Tj
ET
0.188 0.141 0.039 0.004 k
313.509 156.828 m
314.627 156.828 315.541 157.742 315.541 158.859 c
315.541 164.955 l
315.541 166.073 314.627 166.987 313.509 166.987 c
302.334 166.987 l
301.216 166.987 300.302 166.073 300.302 164.955 c
300.302 158.859 l
300.302 157.742 301.216 156.828 302.334 156.828 c
313.509 156.828 l
h
B
313.82 157.83 m
314.241 157.83 314.582 158.171 314.582 158.592 c
B
302.038 166.118 m
301.617 166.118 301.276 165.777 301.276 165.356 c
B
0 g
BT
/T1_1 1 Tf
0.0001 Tc 5 0 0 5 303.2194 159.1314 Tm
(INV)Tj
ET
0.188 0.141 0.039 0.004 k
313.509 144.828 m
314.627 144.828 315.541 145.742 315.541 146.859 c
315.541 152.955 l
315.541 154.073 314.627 154.987 313.509 154.987 c
302.334 154.987 l
301.216 154.987 300.302 154.073 300.302 152.955 c
300.302 146.859 l
300.302 145.742 301.216 144.828 302.334 144.828 c
313.509 144.828 l
h
B
313.82 145.83 m
314.241 145.83 314.582 146.171 314.582 146.592 c
B
302.038 154.118 m
301.617 154.118 301.276 153.777 301.276 153.356 c
B
0 g
BT
/T1_1 1 Tf
4 0 0 4 302.2194 148.1313 Tm
(SHIFT)Tj
ET
0.188 0.141 0.039 0.004 k
313.509 132.828 m
314.627 132.828 315.541 133.742 315.541 134.859 c
315.541 140.955 l
315.541 142.073 314.627 142.987 313.509 142.987 c
302.334 142.987 l
301.216 142.987 300.302 142.073 300.302 140.955 c
300.302 134.859 l
300.302 133.742 301.216 132.828 302.334 132.828 c
313.509 132.828 l
h
B
313.82 133.83 m
314.241 133.83 314.582 134.171 314.582 134.592 c
B
302.038 142.118 m
301.617 142.118 301.276 141.777 301.276 141.356 c
B
0 g
BT
/T1_1 1 Tf
5 0 0 5 302.2194 135.1314 Tm
(2ND)Tj
ET
0.129 0.063 0.035 0.004 k
115.322 172.798 m
116.44 172.798 117.354 173.712 117.354 174.83 c
117.354 180.926 l
117.354 182.043 116.44 182.958 115.322 182.958 c
104.147 182.958 l
103.029 182.958 102.115 182.043 102.115 180.926 c
102.115 174.83 l
102.115 173.712 103.029 172.798 104.147 172.798 c
115.322 172.798 l
h
B
115.633 173.801 m
116.054 173.801 116.395 174.142 116.395 174.563 c
B
103.851 182.089 m
103.43 182.089 103.089 181.748 103.089 181.327 c
B
0 g
BT
/T1_1 1 Tf
0 Tc 7.6799 0 0 7.6799 107.0324 175.1021 Tm
(8)Tj
ET
0.129 0.063 0.035 0.004 k
370.081 172.531 m
371.198 172.531 372.112 173.445 372.112 174.563 c
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(4)Tj
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(+ 5y)Tj
0 Tc 0 Tw 6.3 0 0 6.3 279.1644 545.2462 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 285.4172 541.6462 Tm
(x 2ay = 15y)Tj
0 Tc 0 Tw 6.3 0 0 6.3 332.3517 545.2462 Tm
(7)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 338.6044 541.6462 Tm
(+ 10ay)Tj
0 Tc 0 Tw 6.3 0 0 6.3 366.3599 545.2462 Tm
(4)Tj
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 10 0 0 10 50.6063 521.1422 Tm
(Questions)Tj
0 0 0 1 k
/T1_3 1 Tf
1.3338 Tc 9 0 0 9 67.6142 506.3076 Tm
[(13)1334(a)]TJ
0 Tc 6.3 0 0 6.3 94.2944 509.9075 Tm
(5)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 100.5471 506.3076 Tm
(x 2a)Tj
-0.0003 Tc 0 Tw 6.3 0 0 6.3 117.3074 509.9075 Tm
(4 )Tj
11.4772 Tc 9 0 0 9 122.735 506.3076 Tm
[(=2)10143(5)11478(a)]TJ
0 Tc 6.3 0 0 6.3 258.7038 509.9075 Tm
(6)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 264.9565 506.3076 Tm
(x 2a =)Tj
1.3338 Tc 0 Tw -21.9269 -1.3333 Td
[(33)1334(a)]TJ
0 Tc 6.3 0 0 6.3 94.2944 497.9075 Tm
(2)Tj
-0.0001 Tc 9 0 0 9 97.7966 494.3076 Tm
(cy)Tj
0 Tc 6.3 0 0 6.3 106.4714 497.9075 Tm
(3)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 112.7241 494.3076 Tm
(x 4ac)Tj
0 Tc 0 Tw 6.3 0 0 6.3 133.8218 497.9075 Tm
(5)Tj
9 0 0 9 137.3241 494.3076 Tm
(y)Tj
/T1_4 1 Tf
6.3 0 0 6.3 141.6615 497.9075 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.4998 0 Td
(5 )Tj
-0.0002 Tc 9 0 0 9 150.2391 494.3076 Tm
[(=)-8421(4)-1334(12a)]TJ
0 Tc 6.3 0 0 6.3 263.707 497.9075 Tm
(3)Tj
-0.0002 Tc 9 0 0 9 267.2092 494.3076 Tm
(cd)Tj
0 Tc 6.3 0 0 6.3 277.0441 497.9075 Tm
(8)Tj
/T1_4 1 Tf
9 0 0 9 283.2969 494.3076 Tm
(\326)Tj
/T1_3 1 Tf
-0.0002 Tc 0.9714 0 Td
(3ac)Tj
0 Tc 6.3 0 0 6.3 306.0491 497.9075 Tm
(3)Tj
9 0 0 9 309.5514 494.3076 Tm
(d)Tj
-0.0003 Tc 6.3 0 0 6.3 315.0489 497.9075 Tm
(2 )Tj
0 Tc 9 0 0 9 320.4765 494.3076 Tm
(=)Tj
-0.0001 Tc 0.0278 Tw -28.0958 -1.8705 Td
(Expand the following:)Tj
-0.0002 Tc 0 Tw 0 -1.5556 TD
[(5)-1334(5\(2a )]TJ
/T1_4 1 Tf
0 Tc 4.0858 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[( 3\))-12561(6)-1334(3a\(5 )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 17.7679 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 6a\))Tj
1.3338 Tc 0 Tw -22.8533 -1.5556 Td
[(74)1334(y)]TJ
0 Tc 6.3 0 0 6.3 93.9626 453.0729 Tm
(6)Tj
-0.0002 Tc 9 0 0 9 97.4648 449.4729 Tm
(\(2y)Tj
0 Tc 6.3 0 0 6.3 109.1432 453.0729 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 115.396 449.4729 Tm
(+ 4y)Tj
0 Tc 0 Tw 6.3 0 0 6.3 133.4791 453.0729 Tm
(2)Tj
-0.0002 Tc 9 0 0 9 136.9813 449.4729 Tm
[(\))-10300(8)-1334(-3\(a)]TJ
0 Tc 6.3 0 0 6.3 264.0365 453.0729 Tm
(3)Tj
-0.0002 Tc 9 0 0 9 270.2893 449.4729 Tm
(+2y)Tj
0 Tc 6.3 0 0 6.3 285.6218 453.0729 Tm
(2)Tj
9 0 0 9 289.124 449.4729 Tm
(\))Tj
1.3338 Tc -24.6122 -1.5556 Td
[(94)1334(a)]TJ
0 Tc 6.3 0 0 6.3 94.2944 439.0729 Tm
(3)Tj
9 0 0 9 97.7966 435.473 Tm
(b)Tj
6.3 0 0 6.3 103.2941 439.0729 Tm
(2)Tj
-0.0002 Tc 9 0 0 9 106.7963 435.473 Tm
(cd)Tj
0 Tc 6.3 0 0 6.3 116.6313 439.0729 Tm
(2)Tj
-0.0002 Tc 9 0 0 9 120.1335 435.473 Tm
(\(3ab)Tj
0 Tc 6.3 0 0 6.3 137.6413 439.0729 Tm
(4)Tj
/T1_4 1 Tf
9 0 0 9 143.8941 435.473 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 6ac)Tj
0 Tc 0 Tw 6.3 0 0 6.3 165.1544 439.0729 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 168.6566 435.473 Tm
[(d\))-6170(10)-778(\(3a + 2\)\(5a )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 13.9978 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 3\))Tj
0 Tw -25.7246 -1.5556 Td
[(11)-778(\(6a )]TJ
/T1_4 1 Tf
0 Tc 3.5299 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 7\)\(4a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.7615 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[( 3\))-9855(12)-778(\(4y )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 14.4696 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 3\)\(7y + 6\))Tj
0 Tw -22.2605 -1.5556 Td
[(13)-778(\(6a )]TJ
/T1_4 1 Tf
0 Tc 3.5299 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\))Tj
0 Tc 0 Tw 6.3 0 0 6.3 113.9744 411.0729 Tm
(2)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 8 0 0 8 50.6063 386.969 Tm
(Answers)Tj
0 0 0 1 k
/T1_3 1 Tf
1.0638 Tc 7 0 0 7 67.6142 374.969 Tm
[(16)1064(a)]TJ
0 Tc 4.9 0 0 4.9 86.4757 377.769 Tm
(9)Tj
-0.0002 Tc 7 0 0 7 192.3385 374.969 Tm
[(2)-1064(10a)]TJ
0 Tc 4.9 0 0 4.9 215.0914 377.769 Tm
(7)Tj
7 0 0 7 219.9547 374.969 Tm
(\()Tj
/T1_0 1 Tf
-0.0001 Tc 0.2598 0 Td
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
(2a means 2a)Tj
0 Tc 0 Tw 4.9 0 0 4.9 282.2462 377.769 Tm
(1)Tj
7 0 0 7 284.9701 374.969 Tm
(\))Tj
-0.0002 Tc -31.0508 -1.7143 Td
[(3)-1064(12a)]TJ
0 Tc 4.9 0 0 4.9 90.3671 365.769 Tm
(3)Tj
7 0 0 7 93.091 362.969 Tm
(c)Tj
4.9 0 0 4.9 96.4645 365.769 Tm
(6)Tj
7 0 0 7 99.1885 362.969 Tm
(y)Tj
/T1_4 1 Tf
4.9 0 0 4.9 102.562 365.769 Tm
(\320)Tj
/T1_3 1 Tf
0.4999 0 Td
(2)Tj
1.0638 Tc 7 0 0 7 192.3385 362.969 Tm
[(44)1064(a)]TJ
0 Tc 4.9 0 0 4.9 211.2001 365.769 Tm
(2)Tj
7 0 0 7 213.924 362.969 Tm
(c)Tj
/T1_4 1 Tf
4.9 0 0 4.9 217.2975 365.769 Tm
(\320)Tj
/T1_3 1 Tf
0.4999 0 Td
(2)Tj
7 0 0 7 222.4715 362.969 Tm
(d)Tj
4.9 0 0 4.9 226.7474 365.769 Tm
(6)Tj
-0.0002 Tc 7 0 0 7 67.6142 337.2997 Tm
[(5)-1064(5\(2a )]TJ
/T1_4 1 Tf
0 Tc 3.8158 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[( 3\))-12381(6)-1064(3a\(5 )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 17.3179 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[( 6a\))-10242(7)-1064(4y)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 324.3278 340.0997 Tm
(6)Tj
-0.0002 Tc 7 0 0 7 327.0518 337.2997 Tm
(\(2y)Tj
0 Tc 4.9 0 0 4.9 336.135 340.0997 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 340.9983 337.2997 Tm
(+ 4y)Tj
0 Tc 0 Tw 4.9 0 0 4.9 355.0629 340.0997 Tm
(2)Tj
-0.0004 Tc 7 0 0 7 357.7868 337.2997 Tm
(\) )Tj
-0.0001 Tc -39.0235 -1.1429 Td
(10a )Tj
/T1_4 1 Tf
0 Tc 1.9363 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
[( 15)-13154(15a )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 16.508 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 18a)Tj
0 Tc 0 Tw 4.9 0 0 4.9 234.2844 332.0997 Tm
(2)Tj
-0.0002 Tc 7 0 0 7 317.0629 329.2997 Tm
(8y)Tj
0 Tc 4.9 0 0 4.9 324.3278 332.0997 Tm
(9)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 329.1911 329.2997 Tm
(+ 16y)Tj
0 Tc 0 Tw 4.9 0 0 4.9 347.147 332.0997 Tm
(8)Tj
-0.0003 Tc 7 0 0 7 67.6142 314.4651 Tm
[(8)-1064(-3\(a)]TJ
0 Tc 4.9 0 0 4.9 90.6234 317.265 Tm
(3)Tj
-0.0002 Tc 7 0 0 7 95.4867 314.4651 Tm
(+2y)Tj
0 Tc 4.9 0 0 4.9 107.412 317.265 Tm
(2)Tj
11.4832 Tc 7 0 0 7 110.1359 314.4651 Tm
[(\)9)10419(4)11484(a)]TJ
0 Tc 4.9 0 0 4.9 211.2001 317.265 Tm
(3)Tj
7 0 0 7 213.924 314.4651 Tm
(b)Tj
4.9 0 0 4.9 218.1999 317.265 Tm
(2)Tj
-0.0002 Tc 7 0 0 7 220.9238 314.4651 Tm
(cd)Tj
0 Tc 4.9 0 0 4.9 228.5732 317.265 Tm
(2)Tj
-0.0002 Tc 7 0 0 7 231.2972 314.4651 Tm
(\(3ab)Tj
0 Tc 4.9 0 0 4.9 244.9144 317.265 Tm
(4)Tj
/T1_4 1 Tf
7 0 0 7 249.7776 314.4651 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 6ac)Tj
0 Tc 0 Tw 4.9 0 0 4.9 266.3134 317.265 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 269.0373 314.4651 Tm
[(d\))-4371(10)-508(\(3a + 2\)\(5a )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 11.9281 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 3\))Tj
-0.0003 Tc 0 Tw -38.7729 -1.7143 Td
(-3a)Tj
0 Tc 4.9 0 0 4.9 94.4743 305.265 Tm
(3)Tj
/T1_4 1 Tf
7 0 0 7 99.3375 302.4651 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 6y)Tj
0 Tc 0 Tw 4.9 0 0 4.9 112.2417 305.265 Tm
(2)Tj
-0.0002 Tc 7 0 0 7 203.6771 302.4651 Tm
(12a)Tj
0 Tc 4.9 0 0 4.9 215.0914 305.265 Tm
(4)Tj
7 0 0 7 217.8154 302.4651 Tm
(b)Tj
4.9 0 0 4.9 222.0912 305.265 Tm
(6)Tj
-0.0002 Tc 7 0 0 7 224.8152 302.4651 Tm
(cd)Tj
0 Tc 4.9 0 0 4.9 232.4646 305.265 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 237.3278 302.4651 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 24a)Tj
0 Tc 0 Tw 4.9 0 0 4.9 254.3815 305.265 Tm
(4)Tj
7 0 0 7 257.1054 302.4651 Tm
(b)Tj
4.9 0 0 4.9 261.3813 305.265 Tm
(2)Tj
7 0 0 7 264.1052 302.4651 Tm
(c)Tj
4.9 0 0 4.9 267.4788 305.265 Tm
(4)Tj
7 0 0 7 270.2027 302.4651 Tm
(d)Tj
4.9 0 0 4.9 274.4786 305.265 Tm
(3)Tj
-0.0002 Tc 7 0 0 7 317.0629 302.4651 Tm
(3a\(5a )Tj
/T1_4 1 Tf
0 Tc 2.7148 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 3\) + 2\(5a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 4.5944 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 3\))Tj
0 Tw -8.3089 -1.7143 Td
(15a)Tj
0 Tc 4.9 0 0 4.9 328.4772 293.265 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 333.3405 290.4651 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 9a + 10a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 4.5937 0 Td
(\320)Tj
/T1_3 1 Tf
0.0276 Tc 0.4999 0 Td
( 6)Tj
-0.0002 Tc -7.9188 -1.7143 Td
(15a)Tj
0 Tc 4.9 0 0 4.9 328.4772 281.265 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 333.3405 278.4651 Tm
(+ a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 1.7959 0 Td
(\320)Tj
/T1_3 1 Tf
0.0276 Tc 0.4998 0 Td
( 6)Tj
-0.0002 Tc -40.2566 -2.1192 Td
[(11)-1318(\(6a )]TJ
/T1_4 1 Tf
0 Tc 4.0698 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 7\)\(4a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.7615 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[( 3\))-8865(12)-508(\(4y )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 13.2097 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[( 3\)\(7y + 6\))-7964(13)-508(\(6a )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 15.7351 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\))Tj
0 Tc 0 Tw 4.9 0 0 4.9 339.8926 266.4304 Tm
(2)Tj
-0.0001 Tc 7 0 0 7 84.622 251.6304 Tm
(6a\(4a )Tj
/T1_4 1 Tf
0 Tc 2.7149 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4999 0 Td
( 3\) )Tj
/T1_4 1 Tf
0 Tc 0 Tw 1.427 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 7\(4a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.5017 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[( 3\)   )-6827(4y\(7y + 6\) )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 13.5985 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4998 0 Td
[( 3\(7y + 6\)      )-4879(This means:)]TJ
-0.0002 Tc 0 Tw -22.2414 -1.7143 Td
(24a)Tj
0 Tc 4.9 0 0 4.9 96.0363 242.4304 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 100.8995 239.6304 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 18a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.2419 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( 28a + 21)-7116(28y)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 214.8334 242.4304 Tm
(2)Tj
-0.0001 Tc 0.0278 Tw 7 0 0 7 219.6966 239.6304 Tm
(+ 24y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.8709 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 21y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.205 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0279 Tw 0.4999 0 Td
[(18  )-6111(\(6a )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 9.474 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\)\(6a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.7615 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\) )Tj
0 Tw -38.6071 -1.7143 Td
(24a)Tj
0 Tc 4.9 0 0 4.9 96.0363 230.4304 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 100.8995 227.6304 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( 46a + 21)-9858(28y)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 214.8334 230.4304 Tm
(2)Tj
-0.0001 Tc 7 0 0 7 219.6966 227.6304 Tm
(+3y )Tj
/T1_4 1 Tf
0 Tc 2.0093 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
[( 18)-9983(6a\(6a )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 14.1152 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 4\) )Tj
/T1_4 1 Tf
0 Tc 0 Tw 1.427 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 4\(6a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.5017 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 4\))Tj
/T1_0 1 Tf
0 Tw -41.349 -1.7143 Td
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
(-7 x -3 = 21)Tj
/T1_0 1 Tf
-0.0001 Tc 0 Tw 14.0377 0 Td
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
[(-3 x 6 = -18)-7969(36a)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 328.4772 218.4304 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 333.3405 215.6304 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 24a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.2419 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 24a + 16)Tj
-0.0002 Tc 0 Tw -5.567 -1.7143 Td
(36a)Tj
0 Tc 4.9 0 0 4.9 328.4772 206.4304 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 333.3405 203.6304 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
( 48a +16)Tj
ET
Q Q 
q
110.55 370.19 52.7 -26.9 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS4 gs
BT
/T1_3 1 Tf
7 0 0 7 130.6165 360.6901 Tm
(12a)Tj
5 0 0 5 142.0337 363.6901 Tm
(3)Tj
7 0 0 7 144.814 360.6901 Tm
(c)Tj
5 0 0 5 148.1881 363.6901 Tm
(6)Tj
7 0 0 7 137.7134 350.6901 Tm
(y)Tj
5 0 0 5 141.0874 353.6901 Tm
(2)Tj
7 0 0 7 118.554 357.1901 Tm
(or)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
131.29 359.19 m
149.79 359.19 l
116.79 369.19 m
114.79 369.19 l
114.79 348.19 l
116.79 348.19 l
154.79 369.19 m
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[(4)-1334(Factorise x)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 128.022 374.9785 Tm
(2)Tj
/T1_4 1 Tf
9 0 0 9 134.2747 371.3785 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 5x )Tj
/T1_4 1 Tf
0 Tc 0 Tw 1.6492 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0279 Tw 0.4999 0 Td
[( 6)-4002(\(x )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 5.9107 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 6\)\(x + 1\))Tj
/CS3 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 50.6063 348.0399 Tm
(Example)Tj
0 0 0 1 k
/T1_3 1 Tf
0.0278 Tw 9 0 0 9 67.6142 333.2054 Tm
(Factorise a)Tj
0 Tc 0 Tw 6.3 0 0 6.3 111.3459 336.8053 Tm
(2)Tj
/T1_4 1 Tf
9 0 0 9 117.5987 333.2054 Tm
(\320)Tj
/T1_3 1 Tf
0.0165 Tc 0.0278 Tw 0.4998 0 Td
[( )17(7)17(a)17( )17(+)17( )17(1)17(0)17(.)17( )17(Last sign is +, ther)18(efor)18(e the signs in the brackets will both be)]TJ
-6.0537 -1.3333 Td
[(the same as the pr)18(evious sign, ie )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 15.5736 0 Td
(\320)Tj
/T1_3 1 Tf
0.0165 Tc 0.0278 Tw 0.5165 0 Td
( \(negative\).)Tj
/T1_0 1 Tf
0.0176 Tc 0.0296 Tw -16.0902 -9.3438 Td
[(The first ter)-18(m: )]TJ
/T1_3 1 Tf
0 Tc 0 Tw 7.3511 0 Td
(a)Tj
6.3 0 0 6.3 138.5933 240.7107 Tm
(2)Tj
0.0165 Tc 0.0278 Tw 9 0 0 9 145.1012 237.1109 Tm
[(is pr)18(oduced by multiplying the first ter)-18(m in each bracket.)]TJ
-8.6097 -1.3333 Td
(The only possibility is a x a.)Tj
/T1_0 1 Tf
0.0177 Tc 0.0296 Tw 0 -1.8058 TD
[(The last ter)-18(m:)]TJ
/T1_3 1 Tf
0.0165 Tc 0.0278 Tw 7.0999 0 Td
[(10 is pr)18(oduced by multiplying the last ter)-18(m in each bracket.)]TJ
-7.0999 -1.6483 Td
[(Possibilities ar)18(e 1 x 10, 2 x 5, 5 x 2, 10 x 1.)]TJ
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 0 -2.1207 TD
[(The middle ter)-18(m: )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 8.4569 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[(7a is pr)18(oduced by adding the last ter)-18(m in each bracket,)]TJ
-8.9568 -1.6483 Td
[(ie)-1400(-1 + -10 = -11)]TJ
1.8898 -1.3333 Td
[(-2 + -5 = -7)-4002(this works)]TJ
0 -1.3333 TD
[(-5 + -2 = -7)-4002(this works)]TJ
T*
(-10 + -1 = -11)Tj
/T1_0 1 Tf
-0.0001 Tc 0 Tw -1.8898 -2.1207 Td
(Solution: )Tj
/T1_3 1 Tf
-0.0002 Tc 4.4715 0 Td
(\(a )Tj
/T1_4 1 Tf
0 Tc 1.0843 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 2\)\(a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.2056 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 5\) )Tj
/T1_0 1 Tf
0 Tw 1.427 0 Td
(or)Tj
/T1_3 1 Tf
1.3044 0 Td
(\(a )Tj
/T1_4 1 Tf
0 Tc 1.0843 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 5\)\(a )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.2056 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 2\))Tj
ET
Q Q 
q
132.6 142.73 34.02 -6.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS10 gs
136.1 139.73 m
157.1 139.73 l
S
0 g
158.281 140.242 m
157.455 140.492 156.917 140.722 156.254 140.988 c
156.254 138.466 l
156.491 138.579 157.455 138.962 158.281 139.212 c
159.166 139.479 159.968 139.662 160.488 139.727 c
159.968 139.793 159.166 139.975 158.281 140.242 c
f
Q Q Q 
q
132.6 154.73 34.02 -6.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS11 gs
136.1 151.73 m
157.1 151.73 l
S
0 g
158.281 152.242 m
157.455 152.492 156.917 152.722 156.254 152.988 c
156.254 150.466 l
156.491 150.579 157.455 150.962 158.281 151.212 c
159.166 151.479 159.968 151.662 160.488 151.727 c
159.968 151.793 159.166 151.975 158.281 152.242 c
f
Q Q Q 
q
166.87 378.01 34.02 -6.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS12 gs
170.37 375.01 m
191.37 375.01 l
S
0 g
192.551 375.522 m
191.725 375.772 191.187 376.002 190.524 376.268 c
190.524 373.746 l
190.761 373.859 191.725 374.242 192.551 374.492 c
193.436 374.759 194.238 374.942 194.758 375.007 c
194.238 375.073 193.436 375.255 192.551 375.522 c
f
Q Q Q 
q
168.36 395.68 34.02 -6.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS13 gs
171.86 392.68 m
192.86 392.68 l
S
0 g
194.041 393.192 m
193.215 393.442 192.677 393.672 192.014 393.938 c
192.014 391.416 l
192.251 391.529 193.215 391.912 194.041 392.162 c
194.926 392.429 195.728 392.612 196.248 392.677 c
195.728 392.743 194.926 392.925 194.041 393.192 c
f
Q Q Q 
q
168.36 413.35 34.02 -6.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS14 gs
171.86 410.35 m
192.86 410.35 l
S
0 g
194.041 410.862 m
193.215 411.112 192.677 411.342 192.014 411.608 c
192.014 409.086 l
192.251 409.199 193.215 409.582 194.041 409.832 c
194.926 410.099 195.728 410.282 196.248 410.347 c
195.728 410.413 194.926 410.595 194.041 410.862 c
f
Q Q Q 
q
169.85 431.02 34.02 -6.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS15 gs
173.35 428.02 m
194.35 428.02 l
S
0 g
195.531 428.532 m
194.705 428.782 194.167 429.012 193.504 429.278 c
193.504 426.756 l
193.741 426.869 194.705 427.252 195.531 427.502 c
196.416 427.769 197.218 427.952 197.738 428.017 c
197.218 428.083 196.416 428.265 195.531 428.532 c
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_5 1 Tf
-0.0001 Tc 0.0278 Tw 10 0 0 10 50.6063 604.6697 Tm
(Algebraic skills)Tj
ET
Q Q 
q
102.03 454.48 139.44 -24.41 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS16 gs
136.19 444.98 m
136.19 439.48 l
S
0 g
136.702 438.299 m
136.952 439.126 137.182 439.663 137.448 440.326 c
134.926 440.326 l
135.039 440.089 135.422 439.126 135.672 438.299 c
135.939 437.414 136.122 436.612 136.187 436.092 c
136.253 436.612 136.435 437.414 136.702 438.299 c
f
158.678 444.98 m
158.678 439.48 l
S
159.19 438.299 m
159.439 439.126 159.67 439.663 159.936 440.326 c
157.414 440.326 l
157.526 440.089 157.91 439.126 158.159 438.299 c
158.427 437.414 158.609 436.612 158.675 436.092 c
158.74 436.612 158.923 437.414 159.19 438.299 c
f
BT
/T1_3 1 Tf
7 0 0 7 102.69 447.98 Tm
[(Pr)18(evious sign)]TJ
7.2143 0 Td
(Last sign)Tj
ET
Q Q Q 
q
142.64 312.76 159.76 -55.95 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS17 gs
188.848 298.47 m
188.848 292.97 l
S
0 g
189.36 291.789 m
189.609 292.616 189.839 293.153 190.106 293.816 c
187.584 293.816 l
187.696 293.579 188.08 292.616 188.329 291.789 c
188.597 290.904 188.779 290.102 188.845 289.582 c
188.91 290.102 189.093 290.904 189.36 291.789 c
f
221.36 298.47 m
221.36 292.97 l
S
221.872 291.789 m
222.122 292.616 222.352 293.153 222.618 293.816 c
220.096 293.816 l
220.209 293.579 220.592 292.616 220.842 291.789 c
221.109 290.904 221.292 290.102 221.357 289.582 c
221.422 290.102 221.605 290.904 221.872 291.789 c
f
237.118 270.316 m
237.118 275.816 l
S
236.606 276.997 m
236.356 276.171 236.126 275.633 235.86 274.97 c
238.382 274.97 l
238.27 275.207 237.886 276.171 237.636 276.997 c
237.369 277.882 237.186 278.684 237.121 279.204 c
237.056 278.684 236.873 277.882 236.606 276.997 c
f
204.606 270.316 m
204.606 275.816 l
S
204.093 276.997 m
203.844 276.171 203.614 275.633 203.348 274.97 c
205.87 274.97 l
205.757 275.207 205.374 276.171 205.124 276.997 c
204.857 277.882 204.674 278.684 204.608 279.204 c
204.544 278.684 204.36 277.882 204.093 276.997 c
f
BT
/T1_3 1 Tf
7 0 0 7 149.86 303.47 Tm
[(Multiply these to pr)18(oduce the first ter)-18(m, ie a)]TJ
5 0 0 5 287.3564 306.47 Tm
(2)Tj
10 0 0 10 180.86 281.97 Tm
(\(    )Tj
/T1_4 1 Tf
1.3719 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
(    \)\(    )Tj
/T1_4 1 Tf
2.7438 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
(    \))Tj
7 0 0 7 149.36 261.97 Tm
[(Multiply these to pr)18(oduce the last ter)-18(m, ie 10)]TJ
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS4 cs 1  scn
238.82 135.65 164.87 -70.92 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 9 0 0 9 245.0683 122.5975 Tm
(Note:)Tj
/T1_3 1 Tf
0.0278 Tw 2.9702 0 Td
[(Y)92(ou can check the answer by)]TJ
-2.9702 -1.3333 Td
(expanding the brackets \(see page)Tj
0 -1.3333 TD
(16, Question 10\). Expanding )Tj
-0.0002 Tc 0 Tw T*
(\(a )Tj
/T1_4 1 Tf
0 Tc 1.0842 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 1.0559 0 Td
(2\)\(a )Tj
/T1_4 1 Tf
0 Tc 1.9001 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( 5\) gives the expr)18(ession in)]TJ
-4.54 -1.3333 Td
(the question, ie a)Tj
0 Tc 0 Tw 6.3 0 0 6.3 315.4652 78.1974 Tm
(2)Tj
/T1_4 1 Tf
9 0 0 9 321.718 74.5975 Tm
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 1.0559 0 Td
(7a + 10.)Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
238.82 135.65 164.87 -70.92 re
S
Q Q 
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0 660 m
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f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(19)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 593.39 368.51 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0 Tw 14 0 0 14 180.0011 581.8038 Tm
(Factorisation )Tj
/T1_2 1 Tf
0 Tc 6.3789 0 Td
(\320)Tj
/T1_0 1 Tf
0.0295 Tc 0.4999 0 Td
( 3)Tj
0 0 0 1 k
/T1_3 1 Tf
0 Tc 9 0 0 9 68.3307 555.6776 Tm
(a)Tj
-0.0003 Tc 6.3 0 0 6.3 72.9999 559.2775 Tm
(2 )Tj
0.0278 Tw 9 0 0 9 78.4275 555.6776 Tm
(- b)Tj
0 Tc 0 Tw 6.3 0 0 6.3 89.6705 559.2775 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 95.9232 555.6776 Tm
(factorises as \(a + b\)\(a - b\))Tj
/CS3 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 51.3228 532.3391 Tm
(Example)Tj
0 0 0 1 k
/T1_3 1 Tf
0.0278 Tw 9 0 0 9 68.3307 517.5043 Tm
(Factorise x)Tj
0 Tc 0 Tw 6.3 0 0 6.3 111.7307 521.1043 Tm
(2)Tj
/T1_4 1 Tf
9 0 0 9 117.9834 517.5043 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 36)Tj
-0.0002 Tc -6.0169 -1.9632 Td
(Answer = \(x + 6\)\(x )Tj
/T1_4 1 Tf
0 Tc 0 Tw 8.4358 0 Td
(\320)Tj
/T1_3 1 Tf
0.0276 Tc 0.4998 0 Td
[( 6)28(\))28(     )]TJ
/T1_0 1 Tf
-0.0001 Tc 2.6496 0 Td
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
[(6 is the squar)18(e r)18(oot of 36)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 51.3228 476.4966 Tm
(Questions)Tj
0 0 0 1 k
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 461.6619 Tm
[(1)-1334(Factorise y)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 128.7385 465.2618 Tm
(2)Tj
/T1_4 1 Tf
9 0 0 9 134.9913 461.6619 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 2y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 1.6492 0 Td
(\320)Tj
/T1_3 1 Tf
0.0277 Tc 0.4999 0 Td
( 8)Tj
-0.0001 Tc 0.0278 Tw -10.0557 -1.9632 Td
[(2)-1334(Solve y)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 114.2651 447.5925 Tm
(2)Tj
/T1_4 1 Tf
9 0 0 9 120.5179 443.9926 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 2y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 1.649 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 8 = 0 by factorisation)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
0 Tw 8 0 0 8 51.3228 423.4886 Tm
(Answers)Tj
0 0 0 1 k
/T1_3 1 Tf
1.0638 Tc 7 0 0 7 68.3307 399.4886 Tm
(1y)Tj
0 Tc 4.9 0 0 4.9 83.0428 402.2886 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 87.9061 399.4886 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 2y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 1.6491 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 8 )Tj
-3.306 -1.7143 Td
[(Ther)18(efor)18(e the signs in the brackets ar)18(e dif)18(fer)18(ent.)]TJ
-0.0002 Tc -2.1393 -22.2857 Td
[(2)-1064(First factorise)-278(\(see above\))]TJ
1.6198 -1.7143 Td
(\(y + 2\)\(y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 3.8817 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\) = 0)Tj
-0.0001 Tc -4.3815 -1.7143 Td
[(If two numbers ar)18(e multiplied together to make 0,)]TJ
-0.0002 Tc 0 -1.7143 TD
(one of the numbers must be 0.)Tj
/T1_0 1 Tf
0 Tw 0 -3.4286 TD
(Example:)Tj
/T1_3 1 Tf
0.0277 Tw 4.6196 0 Td
[(7 x )-1818(= 0)]TJ
/T1_0 1 Tf
-0.0001 Tc 0 Tw -4.6196 -5.1429 Td
(Remember: )Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 5.7317 0 Td
(\(y + 2\)\(y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 3.8818 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\) means \(y + 2\) x \(y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 9.6157 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\))Tj
-20.2289 -1.7143 Td
(If \(y + 2\) x \(y )Tj
/T1_4 1 Tf
0 Tc 0 Tw 5.8402 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 4\) = 0)Tj
-0.0001 Tc -6.3401 -1.7143 Td
[(then either   y)-278(+ 2 = 0       )]TJ
/T1_0 1 Tf
-0.0002 Tc 0 Tw 12.0526 0 Td
(or)Tj
/T1_3 1 Tf
-0.0001 Tc 3.1381 0 Td
(y )Tj
/T1_4 1 Tf
0 Tc 0.7875 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
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ET
382.11 81.707 m
414.777 81.707 l
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ET
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S
BT
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ET
327.172 300.547 m
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351.61 309.847 l
306.277 295.707 m
353.61 295.707 l
S
BT
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ET
275.687 265.374 m
323.61 265.374 l
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ET
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(First check you have)Tj
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(   then  )Tj
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(x)Tj
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( then )Tj
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(number)Tj
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( then )Tj
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(y)Tj
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( then )Tj
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[(If not, r)18(earrange the equation:)]TJ
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[(Using the for)-18(mula:)]TJ
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(2)Tj
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(\320)Tj
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ET
284.11 454.54 m
284.11 460.54 l
S
283.597 461.721 m
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285.374 459.694 l
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284.361 462.605 284.178 463.408 284.113 463.928 c
284.048 463.408 283.865 462.605 283.597 461.721 c
f
326.61 454.54 m
326.61 460.54 l
S
326.097 461.721 m
325.848 460.894 325.618 460.357 325.352 459.694 c
327.874 459.694 l
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326.861 462.605 326.678 463.408 326.613 463.928 c
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f
366.11 454.54 m
366.11 460.54 l
S
365.597 461.721 m
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367.374 459.694 l
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366.047 463.408 365.865 462.605 365.597 461.721 c
f
BT
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[(First r)18(earrange the equation:)]TJ
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(y)Tj
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(2)Tj
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(\320)Tj
/T1_3 1 Tf
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(     5y     )Tj
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(\320)Tj
/T1_3 1 Tf
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[(a = 1)-1705(b = -5)-1700(c = -3)]TJ
ET
283.11 171.874 m
283.11 175.874 l
S
282.597 177.054 m
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284.374 175.027 l
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283.048 178.741 282.865 177.939 282.597 177.054 c
f
313.61 171.874 m
313.61 175.874 l
S
313.097 177.054 m
312.848 176.228 312.618 175.69 312.352 175.027 c
314.874 175.027 l
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313.861 177.939 313.678 178.741 313.613 179.262 c
313.547 178.741 313.365 177.939 313.097 177.054 c
f
302.36 96.54 m
327.551 105.641 l
S
328.524 106.483 m
327.661 106.474 327.079 106.532 326.366 106.587 c
327.123 104.181 l
327.316 104.359 328.119 105.015 328.833 105.5 c
329.597 106.021 330.307 106.436 330.784 106.654 c
330.268 106.561 329.448 106.494 328.524 106.483 c
f
343.11 171.874 m
343.11 175.874 l
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342.597 177.054 m
342.348 176.228 342.118 175.69 341.852 175.027 c
344.374 175.027 l
344.261 175.265 343.878 176.228 343.628 177.054 c
343.361 177.939 343.178 178.741 343.113 179.262 c
343.048 178.741 342.865 177.939 342.597 177.054 c
f
BT
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[(corr)18(ect to )]TJ
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/T1_3 1 Tf
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[(76)-6702(x = -1)]TJ
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(\341)Tj
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(26)Tj
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(\341)Tj
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[(54)-3048(x = -0)]TJ
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(\341)Tj
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(541)Tj
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(or)Tj
/T1_3 1 Tf
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(x =)Tj
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(-32 + 23)Tj
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(\341)Tj
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(3238)Tj
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(16)Tj
ET
101.374 81.707 m
145.041 81.707 l
S
BT
/T1_3 1 Tf
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(x =)Tj
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(-32 )Tj
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(\320)Tj
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( 23)Tj
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(\341)Tj
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(16)Tj
ET
179.874 81.707 m
223.541 81.707 l
S
BT
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(x = -0)Tj
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[(542)-4310(x = -3)]TJ
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(46)Tj
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ET
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B
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(Note)Tj
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[(3 significant figur)18(es)]TJ
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BT
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(21)Tj
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(Easingwold School                               )Tj
ET
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(Simultaneous equations: Solving using algebra)Tj
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(Algebraic skills)Tj
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[(I know ther)18(e ar)18(e quicker ways but her)18(e is a method for solving all simultaneous)]TJ
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(equations. I do not believe in lots of complicated rules and methods. Th\
is method will)Tj
T*
[(work every time in the same way)92(.)]TJ
/CS4 cs 1  scn
/T1_0 1 Tf
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(Question)Tj
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/T1_3 1 Tf
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[(Solve the simultaneous equations:)-2965(4x )]TJ
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(\320)Tj
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( 5y = 2 )Tj
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(3x )Tj
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(\320)Tj
/T1_3 1 Tf
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( 2y = 5)Tj
/CS3 cs 1  scn
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0 Tw 8 0 0 8 51.3228 462.5595 Tm
(Answer)Tj
0 0 0 1 k
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0.0277 Tw 7 0 0 7 68.3307 450.5595 Tm
[(Make the numbers in fr)18(ont of the )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 15.1358 0 Td
(\324)Tj
/T1_3 1 Tf
0.2598 0 Td
(x)Tj
/T1_4 1 Tf
0.4818 0 Td
(\325)Tj
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-0.0002 Tc 0.0278 Tw 0.2598 0 Td
( the same.)Tj
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(Substitute y = 2 into one of the original equations)Tj
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(4x )Tj
/T1_4 1 Tf
0 Tc 1.3435 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4999 0 Td
[( 5y)-393(= 2)]TJ
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(4x )Tj
/T1_4 1 Tf
0 Tc 1.3434 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( 5 x 2 )-88(= 2)]TJ
0 Tw -0.7501 -1.7143 Td
(4x )Tj
/T1_4 1 Tf
0 Tc 1.3434 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( 10 )-88(= 2)]TJ
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[(4x )-88(= 2 + 10)]TJ
0.1156 Tw 0 -1.7143 TD
[(4x = )88(12)]TJ
0.0278 Tw 0.5559 -1.7143 Td
[(x)-393(= 12 )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 3.264 0 Td
(\326)Tj
/T1_3 1 Tf
0.9714 0 Td
(4)Tj
-0.0002 Tc 0.1156 Tw -4.2354 -1.7143 Td
[(x = )88(3)]TJ
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(Answer: x = 3, y = 2)Tj
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(Now check by substituting x = 3 and y = 2 in the other original equation\
 )Tj
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(3x )Tj
/T1_4 1 Tf
0 Tc 1.3434 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( 2y )-88(= 5)]TJ
-4.1776 -1.7143 Td
(3 x 3 )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.5106 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( 2 x 2)-393(= 5)]TJ
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(9 )Tj
/T1_4 1 Tf
0 Tc 0.8615 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0277 Tw 0.4999 0 Td
[( 4 )-88(= 5)]TJ
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(Sometimes the question is shown like this:)Tj
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(Solve the simultaneous equations 5x = 13 )Tj
/T1_4 1 Tf
0 Tc 0 Tw 19.063 0 Td
(\320)Tj
/T1_3 1 Tf
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( 2y and 3y = 15 )Tj
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(\320)Tj
/T1_3 1 Tf
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( 3x)Tj
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(First )Tj
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(write each question like this:)Tj
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[(x ter)-18(ms)-4797(y ter)-18(ms)-2066(=)-1985(number)]TJ
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[(5x)-3198(+)-3198(2y)-3198(=)-3161(13)]TJ
T*
[(3x)-3198(+)-3198(3y)-3198(=)-3161(15)]TJ
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[(Now pr)18(oceed as above.)]TJ
ET
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f*
Q Q 
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BT
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(4   x )Tj
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(\320)Tj
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0.5 0 Td
( 5y = 2)Tj
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(3   x )Tj
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2.15 0 Td
(\320)Tj
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0.5 0 Td
( 2y = 5)Tj
7.3023 2 Td
(multiply by   3)Tj
0 -2 TD
(multiply by   4)Tj
18.1816 2 Td
(12x )Tj
/T1_4 1 Tf
1.872 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 15y = 6)Tj
-2.372 -2 Td
(12x )Tj
/T1_4 1 Tf
1.872 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( 8y = 20)Tj
0.3065 -3 Td
(-7y = -14)Tj
0 -4.2857 TD
(       )Tj
ET
0 G
0.25 w 4 M 0 j 0 J [1 2 1 2]0 d 
85.37 408.016 m
88.234 408.016 90.555 410.338 90.555 413.202 c
90.555 416.066 88.234 418.388 85.37 418.388 c
82.506 418.388 80.184 416.066 80.184 413.202 c
80.184 410.338 82.506 408.016 85.37 408.016 c
h
85.036 393.35 m
87.9 393.35 90.222 395.672 90.222 398.535 c
90.222 401.399 87.9 403.721 85.036 403.721 c
82.173 403.721 79.851 401.399 79.851 398.535 c
79.851 395.672 82.173 393.35 85.036 393.35 c
h
167.37 430.683 m
170.234 430.683 172.555 433.005 172.555 435.869 c
172.555 438.732 170.234 441.054 167.37 441.054 c
164.506 441.054 162.185 438.732 162.185 435.869 c
162.185 433.005 164.506 430.683 167.37 430.683 c
h
195.036 407.684 m
197.9 407.684 200.222 410.005 200.222 412.869 c
200.222 415.732 197.9 418.054 195.036 418.054 c
192.173 418.054 189.851 415.732 189.851 412.869 c
189.851 410.005 192.173 407.684 195.036 407.684 c
h
195.036 393.683 m
197.9 393.683 200.222 396.005 200.222 398.869 c
200.222 401.732 197.9 404.054 195.036 404.054 c
192.173 404.054 189.851 401.732 189.851 398.869 c
189.851 396.005 192.173 393.683 195.036 393.683 c
h
S
BT
/T1_3 1 Tf
7 0 0 7 87.0365 433.35 Tm
(Multiply the top line by   3)Tj
ET
177.307 371.869 m
180.171 371.869 182.493 374.19 182.493 377.054 c
182.493 379.918 180.171 382.24 177.307 382.24 c
174.444 382.24 172.122 379.918 172.122 377.054 c
172.122 374.19 174.444 371.869 177.307 371.869 c
h
S
BT
/T1_3 1 Tf
7 0 0 7 84.37 374.5355 Tm
(Multiply the bottom line by   4)Tj
ET
0.5 w []0 d 
281.391 388.35 m
333.391 388.35 l
320.484 357.631 m
332.453 357.631 l
335.391 420.016 m
339.724 420.35 340.057 415.017 v
340.547 407.186 339.057 407.684 342.724 406.017 c
335.391 392.016 m
339.724 391.683 340.057 397.017 v
340.547 404.847 339.057 404.35 342.724 406.017 c
S
BT
/T1_3 1 Tf
7 0 0 7 346.391 404.0165 Tm
(Subtract)Tj
-18.2887 -5.619 Td
(-15y )Tj
/T1_4 1 Tf
2.205 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
[( -8y = -7y)-14449(6 )]TJ
/T1_4 1 Tf
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ET
[]0 d 
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(y )Tj
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ET
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BT
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(y )Tj
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(4)Tj
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(6)Tj
ET
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353.987 498.706 l
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BT
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h
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BT
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[(Common err)18(or:)]TJ
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[(Many candidates put +25. This is wr)18(ong.)]TJ
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ET
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h
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(13y )Tj
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(\320)Tj
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ET
[]0 d 
162.82 347.54 m
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S
BT
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(2)Tj
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(24)Tj
ET
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S
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312.834 348.553 m
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f
258.028 347.019 m
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BT
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(24)Tj
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BT
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(Factorise)Tj
ET
171.32 188.04 m
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179.807 186.776 l
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182.719 187.789 183.521 187.972 184.042 188.037 c
183.521 188.103 182.719 188.285 181.834 188.553 c
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223.333 188.04 m
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S
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235.534 188.103 234.732 188.285 233.847 188.553 c
f
117.32 188.04 m
126.653 188.04 l
S
127.834 188.553 m
127.007 188.802 126.47 189.032 125.807 189.298 c
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[(1)-1334(Solve x)]TJ
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[(2)-1334(Solve x)]TJ
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[(3)-1351(Use graphical methods to solve x)]TJ
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[(4)-1334(Draw y = 2)]TJ
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(\005)Tj
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(x )Tj
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(\005)Tj
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(3  )Tj
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(Use your graph to solve 2)Tj
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(x)Tj
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/CS3 cs 1  scn
/T1_0 1 Tf
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(Answers)Tj
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[(cr)18(osses y = x)]TJ
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[(cr)18(osses y = x)]TJ
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[(45 \(appr)18(ox\).)]TJ
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(1)Tj
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(2)Tj
T*
(3)Tj
T*
(4)Tj
T*
(5)Tj
T*
(6)Tj
T*
(7)Tj
T*
(8)Tj
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B
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(-4)Tj
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(2)Tj
T*
(3)Tj
T*
(4)Tj
T*
(5)Tj
T*
(6)Tj
T*
(7)Tj
T*
(8)Tj
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(in the first 8 seconds.)Tj
0 -1.6483 TD
[(a)-1369(Estimate the total distance travelled )]TJ
-0.0001 Tc 1.888 -1.3333 Td
[(by dividing the ar)18(ea under the curve )]TJ
-0.0002 Tc 0 -1.3333 TD
(into four trapezia.)Tj
-0.0001 Tc -1.888 -1.6483 Td
[(b)-1279(Is the actual distance travelled mor)18(e )]TJ
1.8898 -1.3333 Td
[(or less than your estimate? Explain why)92(.)]TJ
/CS1 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 51.3228 425.8037 Tm
(Method)Tj
0 0 0 1 k
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 410.969 Tm
[(The ar)18(ea under the curve r)18(epr)18(esents )]TJ
-0.0001 Tc T*
(the distance travelled.)Tj
0 -1.6483 TD
[(a)-1371(The total distance is )]TJ
-0.0002 Tc 1.8898 -1.6483 Td
(40 m + 100 m + 130 m + 145 m = 415 m)Tj
-1.8898 -1.6483 Td
[(b)-1277(The total ar)18(ea of the trapezia is less )]TJ
1.888 -1.3333 Td
[(than the ar)18(ea under the curve. Ther)18(efor)18(e )]TJ
-0.0001 Tc 0 -1.3333 TD
(the estimate of 415 m is slightly less than )Tj
T*
(the actual distance travelled.)Tj
/CS1 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 51.3228 295.1266 Tm
(Question)Tj
0 0 0 1 k
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 280.2919 Tm
(This curve shows the )Tj
T*
(speed of a motor cycle )Tj
T*
(during a period of )Tj
T*
(12 seconds. Estimate )Tj
T*
(the total distance )Tj
-0.0001 Tc T*
(travelled by using )Tj
-0.0002 Tc T*
[(thr)18(ee trapezia.)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 51.3228 99.4416 Tm
(Answer)Tj
0 0 0 1 k
/T1_1 1 Tf
0.0277 Tw 7 0 0 7 68.3307 87.4416 Tm
(The total distance is )Tj
-0.0002 Tc 0 -1.7143 TD
(50 m + 100 m + 110 m = 260 m)Tj
ET
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 0 Tw 8 0 0 8 408.358 35.0006 Tm
(35)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 593.39 368.51 -22.68 re
f*
/CS3 cs 1  scn
BT
/T1_0 1 Tf
0.0296 Tw 14 0 0 14 171.6062 581.8038 Tm
[(Ar)18(ea under a curve)]TJ
0 0 0 1 k
/T1_3 1 Tf
-0.0002 Tc 0 Tw 10 0 0 10 385.4171 604.6698 Tm
(Graphs)Tj
ET
Q Q 
q
251.76 565.04 167.07 -137.48 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS6 gs
289.613 558.271 m
289.613 449.42 l
398.463 449.42 l
S
0.25 w 
288.013 544.664 m
289.613 544.664 l
289.613 447.82 m
289.613 449.42 l
303.219 447.82 m
303.219 449.42 l
316.826 447.82 m
316.826 449.42 l
330.432 447.82 m
330.432 449.42 l
344.038 447.82 m
344.038 449.42 l
357.645 447.82 m
357.645 449.42 l
371.251 447.82 m
371.251 449.42 l
384.857 447.82 m
384.857 449.42 l
398.464 447.82 m
398.464 449.42 l
288.013 558.271 m
289.613 558.271 l
288.013 531.058 m
289.613 531.058 l
288.013 517.452 m
289.613 517.452 l
288.013 503.846 m
289.613 503.846 l
288.013 490.239 m
289.613 490.239 l
288.013 476.633 m
289.613 476.633 l
288.013 463.027 m
289.613 463.027 l
288.013 449.42 m
289.613 449.42 l
S
0 g
BT
/T1_1 1 Tf
7 0 0 7 282.3465 447.4902 Tm
(0)Tj
1.3878 Tc 0.7626 -0.8675 Td
(012345678)Tj
-0.005 Tc -1.3135 2.8113 Td
(10)Tj
0 1.9438 TD
(20)Tj
T*
(30)Tj
T*
(40)Tj
T*
(50)Tj
T*
(60)Tj
T*
(70)Tj
T*
(80)Tj
ET
0.5 w 
289.613 449.42 m
306.931 490.239 316.826 503.845 v
326.72 517.452 334.736 524.335 344.038 531.058 c
352.97 537.514 362.603 541.604 371.251 544.664 c
380.87 548.068 398.464 551.551 y
S
BT
/T1_1 1 Tf
0 7 -7 0 274.2028 484.9742 Tm
(Speed m/s)Tj
7 0 0 7 319.0473 432.5635 Tm
[(T)7(ime in seconds)]TJ
ET
Q Q Q 
q
251.76 426.9 167.07 -137.48 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS7 gs
289.613 419.149 m
289.613 310.298 l
398.463 310.298 l
S
0.25 w 
288.013 405.543 m
289.613 405.543 l
289.613 308.698 m
289.613 310.298 l
303.219 308.698 m
303.219 310.298 l
316.826 308.698 m
316.826 310.298 l
330.432 308.698 m
330.432 310.298 l
344.038 308.698 m
344.038 310.298 l
357.645 308.698 m
357.645 310.298 l
371.251 308.698 m
371.251 310.298 l
384.857 308.698 m
384.857 310.298 l
398.464 308.698 m
398.464 310.298 l
288.013 419.149 m
289.613 419.149 l
288.013 391.936 m
289.613 391.936 l
288.013 378.33 m
289.613 378.33 l
288.013 364.724 m
289.613 364.724 l
288.013 351.118 m
289.613 351.118 l
288.013 337.511 m
289.613 337.511 l
288.013 323.905 m
289.613 323.905 l
288.013 310.298 m
289.613 310.298 l
S
0 g
BT
/T1_1 1 Tf
7 0 0 7 282.3465 308.3684 Tm
(0)Tj
1.3878 Tc 0.7626 -0.8675 Td
(012345678)Tj
-0.005 Tc -1.3135 2.8113 Td
(10)Tj
0 1.9438 TD
(20)Tj
T*
(30)Tj
T*
(40)Tj
T*
(50)Tj
T*
(60)Tj
T*
(70)Tj
T*
(80)Tj
ET
0.5 w 
289.613 310.298 m
306.931 351.117 316.826 364.724 v
326.72 378.33 334.736 385.213 344.038 391.936 c
352.97 398.392 362.603 402.483 371.251 405.543 c
380.87 408.946 398.464 412.43 y
S
0.25 w 
316.826 310.298 m
316.826 364.724 l
289.613 310.298 l
316.826 310.298 l
h
344.038 310.298 m
344.038 391.936 l
316.826 364.724 l
316.825 310.298 l
344.038 310.298 l
h
371.251 310.298 m
371.251 405.543 l
344.038 391.936 l
344.038 310.298 l
371.251 310.298 l
h
398.464 310.298 m
398.464 412.43 l
371.251 405.543 l
371.251 310.298 l
398.464 310.298 l
h
S
BT
/T1_1 1 Tf
0 7 -7 0 274.2028 345.8524 Tm
(Speed m/s)Tj
7 0 0 7 319.0473 294.58 Tm
[(T)7(ime in seconds)]TJ
0 6 -6 0 324.72 312.4167 Tm
[(Ar)18(ea)]TJ
9.5833 3.8333 Td
[(Ar)18(ea)]TJ
-7.1811 -3.9167 Td
(= )Tj
0 Tc 0 4 -4 0 321.22 332.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 325.22 338.3036 Tm
( x \(a +b\) x h)Tj
-1.9123 -1.3333 Td
(= )Tj
0 Tc 0 4 -4 0 329.22 332.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 333.22 338.3036 Tm
( x \(40 + 60\) x 2)Tj
-1.9123 -1.3333 Td
(= 100 m)Tj
-2.4022 -1.8333 Td
[(Ar)18(ea)]TJ
2.4022 -0.0833 Td
(= )Tj
0 Tc 0 4 -4 0 348.72 332.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 352.72 338.3036 Tm
( x \(a +b\) x h)Tj
-1.9123 -1.3333 Td
(= )Tj
0 Tc 0 4 -4 0 356.72 332.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 360.72 338.3036 Tm
( x \(60 + 70\) x 2)Tj
-1.9123 -1.3333 Td
(= 130 m)Tj
-2.4022 -1.8333 Td
[(Ar)18(ea)]TJ
2.4022 -0.0833 Td
(= )Tj
0 Tc 0 4 -4 0 376.22 332.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 380.22 338.3036 Tm
( x \(a +b\) x h)Tj
-1.9123 -1.3333 Td
(= )Tj
0 Tc 0 4 -4 0 384.22 332.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 388.22 338.3036 Tm
( x \(70 + 75\) x 2)Tj
-1.9123 -1.3333 Td
(= 145 m)Tj
9.6667 15.7083 Td
(= )Tj
0 Tc 0 4 -4 0 297.97 390.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 301.97 396.3036 Tm
( x b x h)Tj
-1.9123 -1.3333 Td
(= )Tj
0 Tc 0 4 -4 0 305.97 390.4344 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 0 6 -6 0 309.97 396.3036 Tm
( x 40 x 2)Tj
-1.9123 -1.3333 Td
(= 40 m)Tj
ET
0.5 w 
299.72 366.58 m
303.47 325.58 l
S
304.086 324.448 m
304.264 325.293 304.448 325.848 304.656 326.532 c
302.143 326.316 l
302.276 326.09 302.74 325.163 303.059 324.36 c
303.401 323.502 303.652 322.718 303.761 322.205 c
303.782 322.729 303.896 323.544 304.086 324.448 c
f
Q Q Q 
q
150.34 279.19 268.49 -101.08 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS8 gs
216.439 274.664 m
216.439 201.191 l
412.37 201.191 l
S
0.25 w 
213.439 274.664 m
216.439 274.664 l
213.439 262.419 m
216.439 262.419 l
213.439 250.173 m
216.439 250.173 l
213.439 237.928 m
216.439 237.928 l
213.439 225.682 m
216.439 225.682 l
213.439 213.437 m
216.439 213.437 l
213.439 201.191 m
216.439 201.191 l
216.439 198.191 m
216.439 201.191 l
249.094 198.191 m
249.094 201.191 l
281.749 198.191 m
281.749 201.191 l
314.404 198.191 m
314.404 201.191 l
347.06 198.19 m
347.06 201.19 l
379.715 198.19 m
379.715 201.19 l
412.37 198.19 m
412.37 201.19 l
S
0 g
BT
/T1_1 1 Tf
7 0 0 7 205.883 199.1629 Tm
(0)Tj
4.109 Tc 1.2325 -1.2817 Td
[(02468)275(1)4114(0)551(1)4114(2)]TJ
0 Tc -1.2325 3.031 Td
(5)Tj
-0.005 Tc -0.5509 1.7494 Td
(10)Tj
0 1.7494 TD
(15)Tj
T*
(20)Tj
T*
(25)Tj
T*
(30)Tj
12.2115 -13.1786 Td
[(T)7(ime in seconds)]TJ
0 7 -7 0 195.0159 220.0254 Tm
(Speed m/s)Tj
ET
0.5 w 
216.439 213.437 m
237.239 225.682 260.009 237.928 281.749 250.173 c
303.489 262.419 327.725 274.664 347.06 274.664 c
370.739 274.664 389.001 272.675 412.37 262.419 c
S
Q Q Q 
q
150.34 155.89 268.49 -101.09 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS9 gs
209.38 152.462 m
209.38 78.988 l
405.311 78.988 l
S
0.25 w 
206.38 152.462 m
209.38 152.462 l
206.38 140.216 m
209.38 140.216 l
206.38 127.971 m
209.38 127.971 l
206.38 115.725 m
209.38 115.725 l
206.38 103.479 m
209.38 103.479 l
206.38 91.234 m
209.38 91.234 l
206.38 78.988 m
209.38 78.988 l
209.38 75.988 m
209.38 78.988 l
242.035 75.988 m
242.035 78.988 l
274.69 75.988 m
274.69 78.988 l
307.345 75.988 m
307.345 78.988 l
340 75.988 m
340 78.988 l
372.655 75.987 m
372.655 78.987 l
405.311 75.987 m
405.311 78.987 l
S
0 g
BT
/T1_1 1 Tf
7 0 0 7 198.8237 76.9601 Tm
(0)Tj
4.109 Tc 1.2325 -1.2817 Td
[(02468)275(1)4114(0)551(1)4114(2)]TJ
0 Tc -1.2325 3.0311 Td
(5)Tj
-0.005 Tc -0.5509 1.7494 Td
(10)Tj
0 1.7494 TD
(15)Tj
T*
(20)Tj
T*
(25)Tj
T*
(30)Tj
12.2115 -13.1786 Td
[(T)7(ime in seconds)]TJ
0 7 -7 0 187.9566 97.8225 Tm
(Speed m/s)Tj
ET
0.5 w 
209.38 91.234 m
230.18 103.479 252.95 115.725 274.69 127.97 c
296.43 140.216 320.665 152.462 340 152.462 c
363.68 152.462 381.941 150.472 405.311 140.216 c
S
0.25 w 
274.69 78.988 m
274.69 127.971 l
209.38 91.234 l
209.38 78.988 l
274.69 78.988 l
h
340 78.988 m
340 152.462 l
274.69 127.97 l
274.69 78.988 l
340 78.988 l
h
405.311 78.987 m
405.311 140.216 l
340 152.462 l
340 78.987 l
405.311 78.987 l
h
S
BT
/T1_1 1 Tf
6 0 0 6 221.5167 149.7101 Tm
[(Ar)18(ea)]TJ
20.5833 -5.0833 Td
[(Ar)18(ea)]TJ
-10.7228 -1.7051 Td
(= )Tj
0 Tc 4 0 0 4 286.2843 112.9793 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 6 0 0 6 292.1536 108.9793 Tm
( x \(a +b\) x h)Tj
-1.9123 -1.3333 Td
(= )Tj
0 Tc 4 0 0 4 286.2843 104.9793 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 6 0 0 6 292.1536 100.9793 Tm
( x \(20 + 30\) x 4)Tj
-1.9123 -1.3333 Td
(= 100 m)Tj
-9.9167 7.75 Td
(= )Tj
0 Tc 4 0 0 4 226.7843 143.4792 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 6 0 0 6 232.6536 139.4792 Tm
( x \(a +b\) x h)Tj
-1.9123 -1.3333 Td
(= )Tj
0 Tc 4 0 0 4 226.7843 135.4793 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 6 0 0 6 232.6536 131.4793 Tm
( x \(5 + 20\) x 4)Tj
-1.9123 -1.3333 Td
(= 50 m)Tj
20.7083 -2.4167 Td
(= )Tj
0 Tc 4 0 0 4 351.0344 112.9793 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 6 0 0 6 356.9036 108.9793 Tm
( x \(a +b\) x h)Tj
-1.9123 -1.3333 Td
(= )Tj
0 Tc 4 0 0 4 351.0344 104.9793 Tm
(1)Tj
0.5511 -0.5 Td
(/)Tj
0.3651 -0.5 Td
(2)Tj
-0.005 Tc 6 0 0 6 356.9036 100.9793 Tm
( x \(30 + 25\) x 4)Tj
-1.9123 -1.3333 Td
(= 110 m)Tj
ET
0.5 w 
238.93 119.21 m
244.68 102.96 l
S
245.557 102.018 m
245.517 102.88 245.554 103.463 245.584 104.178 c
243.206 103.336 l
243.392 103.15 244.075 102.37 244.585 101.674 c
245.133 100.929 245.572 100.234 245.808 99.765 c
245.696 100.277 245.6 101.094 245.557 102.018 c
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/T1_2 1 Tf
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(Find the length of AB and AE.)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 50.6063 343.6934 Tm
(Answer)Tj
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/T1_2 1 Tf
0.0277 Tw 7 0 0 7 67.6142 331.6934 Tm
[(DE is parallel to BC. Ther)18(efor)18(e ADE is similar to ABC.)]TJ
0 -1.7143 TD
[(1)-1064(Draw the two triangles separately)92(.)]TJ
0 -3.4286 TD
[(2)-1064(Identify the big triangle and the )]TJ
1.6198 -1.7143 Td
(small triangle.)Tj
-0.0168 Tc -1.6198 -3.4286 Td
[(3)-1081(Find two sides with lengths given which ar)18(e in the same position on each triangle. In this example DE and BC.)]TJ
-0.0002 Tc 1.6198 -1.7143 Td
(DE = 6 cm,   BC = 9 cm)Tj
-1.6198 -3.4286 Td
[(4)-1064(The scale factor \(SF\) fr)18(om small to big is                    .)]TJ
-0.0001 Tc 1.6198 -1.7143 Td
[(T)111(o convert any length on the small triangle to a length on the lar)18(ge triangle, multiply by SF )]TJ
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(9)Tj
7 0 0 7 369.3406 211.6935 Tm
(/)Tj
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(6)Tj
7 0 0 7 374.6536 211.6935 Tm
(.)Tj
-0.0001 Tc 0.0277 Tw -42.243 -1.8571 Td
[(eg)-1263(AD \(small triangle\) x SF )]TJ
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(9)Tj
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(6)Tj
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(=  AB)Tj
-7.2139 -1.8571 Td
(5 cm  x )Tj
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(9)Tj
0.5559 -0.8571 Td
(6)Tj
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(=  7)Tj
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(\341)Tj
/T1_2 1 Tf
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(5 cm)Tj
-15.4376 -3.4286 Td
[(5)-1064(The scale factor fr)18(om big to small is                     .)]TJ
-0.0001 Tc 1.6198 -1.7143 Td
[(T)111(o convert any length on the lar)18(ge triangle to a length on the small triangle, multiply by SF )]TJ
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(6)Tj
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(/)Tj
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(9)Tj
7 0 0 7 374.6536 149.6935 Tm
(.)Tj
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[(eg  AC \(lar)18(ge triangle\)   x   SF )]TJ
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(6)Tj
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(9)Tj
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(=  AE)Tj
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(6 cm  x )Tj
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(6)Tj
0.5559 -0.8572 Td
(9)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 160.1538 125.6935 Tm
(=  4 cm)Tj
ET
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q
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q
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W n
q
0 660.06 467.04 -660 re
W n
0.063 0.231 0.502 0.008 k
0 G
0.4 w 4 M 0 j 0 J []0 d 
/GS7 gs
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381.895 366.45 l
332.816 437.836 l
251.87 366.45 l
B
278.906 390.245 m
365.535 390.245 l
B
326.24 441.345 m
276.003 397.25 l
S
0 g
275.869 399.105 m
276.376 397.578 l
277.827 396.882 l
274.213 395.674 l
275.869 399.105 l
f
326.379 439.493 m
325.872 441.02 l
324.42 441.716 l
328.034 442.925 l
326.379 439.493 l
f
1 g
296.22 417.317 m
301.203 415.117 l
308.937 422.05 l
304.403 424.45 l
296.22 417.317 l
f
0 g
BT
/T1_2 1 Tf
8.8 0 0 8.8 289.7368 418.1833 Tm
(5 cm)Tj
ET
1 g
339.722 439.789 m
386.682 370.974 l
B
0 g
384.826 371.063 m
386.403 371.383 l
387.268 372.741 l
388.036 369.008 l
384.826 371.063 l
f
341.581 439.704 m
340.003 439.383 l
339.139 438.026 l
338.371 441.758 l
341.581 439.704 l
f
1 g
357.947 409.436 m
363.331 410.264 l
368.995 401.557 l
363.993 400.419 l
357.947 409.436 l
f
0 g
BT
/T1_2 1 Tf
8.8 0 0 8.8 357.87 401.9833 Tm
(6 cm)Tj
ET
323.8 388.798 m
324.431 390.278 l
323.804 391.761 l
327.313 390.274 l
323.8 388.798 l
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318.7 388.798 m
319.331 390.278 l
318.704 391.761 l
322.213 390.274 l
318.7 388.798 l
f
323.639 364.97 m
324.27 366.45 l
323.643 367.932 l
327.152 366.446 l
323.639 364.97 l
f
318.539 364.97 m
319.17 366.45 l
318.543 367.932 l
322.052 366.446 l
318.539 364.97 l
f
281.603 383.65 m
362.27 383.65 l
S
361.147 382.168 m
361.776 383.65 l
361.147 385.132 l
364.658 383.65 l
361.147 382.168 l
f
282.727 385.132 m
282.097 383.65 l
282.727 382.168 l
279.216 383.65 l
282.727 385.132 l
f
254.503 360.45 m
379.237 360.45 l
S
378.113 358.968 m
378.743 360.45 l
378.113 361.932 l
381.624 360.45 l
378.113 358.968 l
f
255.627 361.932 m
254.997 360.45 l
255.627 358.968 l
252.116 360.45 l
255.627 361.932 l
f
0.063 0.231 0.502 0.008 k
312.403 386.983 m
333.87 387.25 l
334.27 379.65 l
312.537 379.783 l
312.403 386.983 l
f
1 g
310.403 363.517 m
332.67 363.65 l
332.67 356.45 l
310.537 356.317 l
310.403 363.517 l
f
0 g
BT
/T1_2 1 Tf
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(6 cm)Tj
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(9 cm)Tj
2.0909 9.3485 Td
(A)Tj
-9.7273 -8.8182 Td
(B)Tj
15.8636 -0.2727 Td
(C)Tj
-13 3.1364 Td
(D)Tj
11.8182 0.2273 Td
(E)Tj
ET
Q Q Q 
q
201.19 365.25 216.92 -97.69 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.063 0.231 0.502 0.008 k
0 G
0.325 w 4 M 0 j 0 J []0 d 
/GS8 gs
222.057 297.678 m
292.938 297.678 l
266.184 336.594 l
222.057 297.678 l
B
260.841 339.445 m
220.023 303.618 l
S
0 g
219.914 305.125 m
220.326 303.884 l
221.505 303.319 l
218.569 302.337 l
219.914 305.125 l
f
260.953 337.94 m
260.541 339.181 l
259.362 339.746 l
262.299 340.729 l
260.953 337.94 l
f
1 g
236.449 319.922 m
240.498 318.134 l
246.782 323.768 l
243.098 325.718 l
236.449 319.922 l
f
0 g
BT
/T1_2 1 Tf
7.15 0 0 7.15 231.8318 320.6258 Tm
(5 cm)Tj
ET
224.573 292.568 m
290.115 292.568 l
S
289.202 291.364 m
289.713 292.568 l
289.202 293.771 l
292.055 292.568 l
289.202 291.364 l
f
225.486 293.771 m
224.975 292.568 l
225.486 291.364 l
222.633 292.568 l
225.486 293.771 l
f
1 g
249.598 295.276 m
267.365 295.33 l
267.365 289.48 l
249.707 289.426 l
249.598 295.276 l
f
0 g
BT
/T1_2 1 Tf
7.15 0 0 7.15 250.8982 290.78 Tm
(6 cm)Tj
1.8485 6.7045 Td
(A)Tj
10.4863 Tc -6.8636 -5.9545 Td
(DE)Tj
ET
0.063 0.231 0.502 0.008 k
292.593 278.796 m
398.238 278.796 l
358.362 336.797 l
292.593 278.796 l
B
1 g
363.973 338.383 m
402.128 282.471 l
B
0 g
400.62 282.543 m
401.901 282.804 l
402.604 283.907 l
403.228 280.874 l
400.62 282.543 l
f
365.483 338.315 m
364.201 338.054 l
363.499 336.951 l
362.875 339.984 l
365.483 338.315 l
f
1 g
378.781 313.722 m
383.155 314.394 l
387.757 307.32 l
383.693 306.396 l
378.781 313.722 l
f
0 g
BT
/T1_2 1 Tf
0 Tc 7.15 0 0 7.15 378.7181 307.6664 Tm
(6 cm)Tj
ET
294.733 273.921 m
396.079 273.921 l
S
395.166 272.717 m
395.677 273.921 l
395.166 275.125 l
398.018 273.921 l
395.166 272.717 l
f
295.645 275.125 m
295.134 273.921 l
295.645 272.717 l
292.793 273.921 l
295.645 275.125 l
f
1 g
340.151 276.412 m
357.715 276.48 l
357.715 270.738 l
340.26 270.562 l
340.151 276.412 l
f
0 g
BT
/T1_2 1 Tf
7.15 0 0 7.15 341.3431 272.0789 Tm
(9 cm)Tj
2.0909 9.3485 Td
(A)Tj
-9.7273 -8.8182 Td
(B)Tj
15.8636 -0.2727 Td
(C)Tj
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(small)Tj
11.7917 -1.7083 Td
(big)Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS3 cs 1  scn
BT
/T1_4 1 Tf
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(Similarity)Tj
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/T1_2 1 Tf
-0.0057 Tc 0.0278 Tw 9 0 0 9 50.6063 579.9141 Tm
[(This usually appears on the exam paper)92(. Just r)18(ecognise the shapes, put them the same way)]TJ
0 -1.3333 TD
[(r)18(ound, then find the scale factor \(ie the r)18(elationship between the sizes of the shapes\).)]TJ
ET
0 0 0 1 K
0.125 w 10 M 0 j 0 J []0 d 
49.61 560.95 m
418.11 560.95 l
S
0.042 w 
49.61 560.78 m
418.11 560.78 l
S
Q Q 
q
69.45 479.18 207.47 -41.54 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.063 0.231 0.502 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS9 gs
185.24 441.83 m
266.505 441.83 l
241.74 473.33 l
185.24 441.83 l
B
0 g
BT
/T1_2 1 Tf
7 0 0 7 231.252 459.3301 Tm
(110)Tj
/T1_5 1 Tf
1.668 0 Td
(\006)Tj
/T1_2 1 Tf
-6.3424 -2.2857 Td
(30)Tj
/T1_5 1 Tf
1.112 0 Td
(\006)Tj
/T1_2 1 Tf
5.9118 0.0477 Td
(40)Tj
/T1_5 1 Tf
1.112 0 Td
(\006)Tj
ET
236.448 470.544 m
237.265 468.419 239.327 466.911 241.74 466.911 c
243.219 466.911 244.565 467.477 245.574 468.404 c
190.909 441.83 m
190.909 442.892 190.617 443.886 190.109 444.736 c
262.741 446.069 m
261.572 445.03 260.836 443.516 260.836 441.83 c
S
0.063 0.231 0.502 0.008 k
79.278 443.43 m
144.29 443.43 l
124.478 468.63 l
79.278 443.43 l
B
0 g
BT
/T1_2 1 Tf
7 0 0 7 114.6397 456.4302 Tm
(110)Tj
/T1_5 1 Tf
1.668 0 Td
(\006)Tj
/T1_2 1 Tf
-4.9234 -1.6858 Td
(30)Tj
/T1_5 1 Tf
1.112 0 Td
(\006)Tj
/T1_2 1 Tf
3.9356 0.0381 Td
(40)Tj
/T1_5 1 Tf
1.112 0 Td
(\006)Tj
ET
138.621 443.43 m
138.621 445.213 139.444 446.803 140.73 447.842 c
84.947 443.43 m
84.947 444.544 84.626 445.583 84.07 446.459 c
127.924 464.128 m
126.969 463.396 125.774 462.961 124.478 462.961 c
122.296 462.961 120.402 464.194 119.454 466.001 c
S
Q Q Q 
q
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W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS10 gs
BT
/T1_2 1 Tf
6 0 0 6 197.152 165.2601 Tm
(6)Tj
-0.278 -1.1667 Td
(  9)Tj
3.8342 1.1667 Td
(small)Tj
0.4075 -1.1667 Td
(big)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
197.486 162.177 m
201.82 165.344 l
218.82 163.823 m
232.07 163.823 l
S
BT
/T1_2 1 Tf
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(ie)Tj
ET
Q Q Q 
q
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W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS11 gs
210.839 223.456 m
215.172 226.623 l
232.61 224.852 m
245.86 224.852 l
S
0 g
BT
/T1_2 1 Tf
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(9)Tj
0 -1 TD
( 6)Tj
3.9637 1 Td
(big)Tj
-0.4075 -1.1667 Td
(small)Tj
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(ie)Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 K
0.25 w 10 M 0 j 0 J []0 d 
157.71 189.89 m
153.71 185.62 l
175.75 203.2 m
171.75 198.93 l
178.8 141.87 m
174.8 137.6 l
157.32 130.4 m
153.32 126.13 l
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f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 0.0277 Tw 9 0 0 9 68.3307 515.8036 Tm
[(Y)92(ou must be able to identify congruent triangles. )]TJ
ET
0 0 0 0 k
50.32 549.26 368.51 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_1 1 Tf
0.0296 Tw 14 0 0 14 156.7175 537.6771 Tm
(Congruent triangles )Tj
/T1_2 1 Tf
0 Tc 0 Tw 9.7051 0 Td
(\320)Tj
/T1_1 1 Tf
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( 1)Tj
ET
Q Q 
q
50.32 476.57 368.51 -421.77 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
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BT
/T1_0 1 Tf
-0.005 Tc 9 0 0 9 68.0759 314.945 Tm
(A )Tj
/T1_1 1 Tf
0.954 0 Td
[(common err)18(or)]TJ
/T1_0 1 Tf
6.5847 0 Td
[( is to think AAA is a test for congruency)92(. It is NOT)111(. )]TJ
-7.5387 -1.5556 Td
(But it is a test for similarity \(see page 38\).)Tj
ET
0.039 0.02 0.486 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
98.528 330.195 275.792 23 re
B
68.076 235.529 338.604 52.708 re
B
68.076 179.82 338.604 51.709 re
B
68.076 123.112 338.604 51.708 re
B
68.076 67.404 338.604 51.709 re
B
0 g
BT
/T1_0 1 Tf
9 0 0 9 68.0759 463.2786 Tm
[(When you test for congruency you may have to tur)-18(n one of the triangles or flip one over)92(.)]TJ
ET
0.031 0.243 0.502 0.004 k
121.32 445.237 m
98.653 421.237 l
159.987 424.57 l
121.32 445.237 l
h
B
360.653 445.237 m
337.986 421.237 l
399.32 424.57 l
360.653 445.237 l
h
B
227.163 404.778 m
259.395 397.647 l
225.049 448.57 l
227.163 404.778 l
h
B
0 g
BT
/T1_0 1 Tf
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(A)Tj
12.4884 -2 Td
(B)Tj
14.0301 2 Td
(B)Tj
7 0 0 7 268.3073 427.9035 Tm
[(T)92(ur)-18(n this triangle )]TJ
0.444 -1.2857 Td
(so that it is the )Tj
-1.6875 -1.2857 Td
(same way as triangle A)Tj
ET
325.12 438.266 m
317.494 443.307 306.811 446.44 294.986 446.44 c
279.772 446.44 266.448 441.253 259.092 433.489 c
S
326.392 438.044 m
325.841 438.708 325.519 439.196 325.112 439.784 c
323.722 437.68 l
323.982 437.643 324.997 437.432 325.824 437.184 c
326.71 436.919 327.48 436.63 327.95 436.397 c
327.551 436.738 326.983 437.333 326.392 438.044 c
f
BT
/T1_0 1 Tf
-0.005 Tc 9 0 0 9 68.0759 382.945 Tm
[(If two triangles obey any of the following tests they ar)18(e congruent. )]TJ
/T1_1 1 Tf
13.0597 -4.8912 Td
(SSS)Tj
-12.3601 -7.0764 Td
(SSS)Tj
18.3503 7.0764 Td
(SAS)Tj
-18.4243 -13.3773 Td
(SAS)Tj
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(AAS)Tj
-24.2748 -19.6782 Td
(AAS)Tj
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(RHS)Tj
-30.339 -26.0671 Td
(RHS)Tj
/T1_0 1 Tf
4.2671 26.0671 Td
(Memorise:)Tj
ET
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116.52 274.837 m
133.32 248.437 l
212.92 267.237 l
116.52 274.837 l
h
B
333.98 238.728 m
328.478 269.532 l
247.709 282.407 l
333.98 238.728 l
h
B
158.945 223.633 m
226.278 200.966 l
137.945 184.966 l
158.945 223.633 l
h
B
314.978 224.369 m
244.827 213.125 l
329.309 182.768 l
314.978 224.369 l
h
B
273.103 76.57 m
273.103 111.237 l
330.103 111.237 l
273.103 76.57 l
h
B
218.871 109.32 m
218.871 74.654 l
161.871 74.654 l
218.871 109.32 l
h
B
137.472 169.426 m
147.072 130.426 l
210.972 130.426 l
137.472 169.426 l
h
B
340.645 147.855 m
307.295 170.234 l
260.041 127.221 l
340.645 147.855 l
h
B
0 g
BT
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(\241)Tj
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(/)Tj
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[(enlar)18(gement the point \(5, 1\) to pr)18(oduce R)]TJ
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(\325)Tj
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(. The inverse to take R)Tj
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(\325)Tj
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( back to R is)Tj
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(4)Tj
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(/)Tj
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(3)Tj
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(point \(1, )Tj
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(\320)Tj
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[(4\) to pr)18(oduce T)]TJ
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(\325)Tj
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(\325)Tj
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[( to T)111(.)]TJ
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(Answers)Tj
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/T1_1 1 Tf
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[(1)-1064(T)92(ranslation by the vector)]TJ
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(\241)Tj
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(\241)Tj
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(\320)Tj
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(4\).)Tj
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BT
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BT
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(Easingwold School                               )Tj
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0 G
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226.07 331.18 19.84 -27 re
W* n
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-1 661 470 -662 re
W n
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0 660.06 467.04 -660 re
W n
0 g
/GS11 gs
BT
/T1_1 1 Tf
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(-a)Tj
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ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
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W n
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W n
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f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 50.6063 35.0006 Tm
(42)Tj
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(Easingwold School                               )Tj
ET
0 0 0 0 k
49.61 593.39 368.5 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
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[(Enlar)18(gement by a fractional scale factor)]TJ
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[(T)92(ransformations)]TJ
/T1_0 1 Tf
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(Note:)Tj
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-0.0002 Tc 0.0278 Tw 2.9702 0 Td
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(smaller)Tj
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(.)Tj
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(Question)Tj
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/T1_3 1 Tf
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[(Enlar)18(ge the triangle by a scale factor of )]TJ
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(2)Tj
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ET
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f*
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0 g
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BT
/T1_3 1 Tf
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ET
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306.307 198.931 m
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BT
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21.5 -0.5 Td
(x       =)Tj
ET
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BT
/T1_3 1 Tf
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(12 along)Tj
6.0119 2.2857 Td
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ET
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f
BT
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(8 along)Tj
4.9762 2.0357 Td
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ET
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f
BT
/T1_3 1 Tf
7 0 0 7 123.3065 102.6935 Tm
(12 along)Tj
6.0119 2.2857 Td
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ET
269.806 110.194 m
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S
313.39 130.681 m
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313.39 128.784 l
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BT
/T1_3 1 Tf
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(8 along)Tj
4.8334 2.0357 Td
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39 10.4286 Td
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(Point C)Tj
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3.4251 0 Td
(\324)Tj
/T1_3 1 Tf
-19.7822 10.5 Td
(2)Tj
0 -1.2143 TD
( 3)Tj
ET
227.723 187.527 m
234.057 191.194 l
S
BT
/T1_3 1 Tf
7 0 0 7 227.89 155.985 Tm
(2)Tj
T*
( 3)Tj
ET
227.723 152.152 m
234.057 155.819 l
S
BT
/T1_3 1 Tf
7 0 0 7 227.89 118.5475 Tm
(2)Tj
T*
( 3)Tj
ET
227.723 114.714 m
234.057 118.381 l
S
BT
/T1_3 1 Tf
7 0 0 7 219.89 151.6936 Tm
(x       =)Tj
0 -5.3334 TD
(x       =)Tj
ET
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
/GS7 gs
93.16 338.01 281.4 -101.56 re
f*
Q Q 
139.756 333.499 m
139.756 248.459 l
338.181 248.459 l
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0 0 0 1 k
BT
/T1_3 1 Tf
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(0)Tj
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(1)Tj
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(1)Tj
-2.8361 4.7857 Td
(2)Tj
4.8608 -4.7857 Td
(2)Tj
-4.8608 6.8571 Td
(3)Tj
6.8856 -6.8095 Td
(3)Tj
-6.8856 8.9524 Td
(4)Tj
8.9104 -9 Td
(4)Tj
-8.9104 10.8571 Td
(5)Tj
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(6)Tj
1.4688 Tc 10.9351 -12.9286 Td
(567)Tj
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(8)Tj
1.1908 Tc 2.0248 -0.0476 Td
[(91)1191(0)278(1)1191(1)278(1)1191(2)]TJ
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(13)Tj
2.0247 -0.0476 Td
(14)Tj
ET
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h
B
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 278.3625 309.3535 Tm
(A)Tj
-6.511 -2.1905 Td
(A)Tj
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0.686 0.3037 Td
(\324)Tj
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3.2098 1.5534 Td
(C)Tj
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0.704 0.3037 Td
(\324)Tj
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-0.0645 -3.7903 Td
(B)Tj
/T1_5 1 Tf
0.63 0.3037 Td
(\324)Tj
/T1_3 1 Tf
8.1801 2.4552 Td
(B)Tj
-0.6658 4 Td
(C)Tj
ET
[1 2]0 d 
153.929 262.632 m
281.488 262.632 l
281.488 305.152 l
S
198.936 262.609 m
196.449 261.593 l
197.039 262.609 l
196.449 263.625 l
198.936 262.609 l
f
258.897 262.609 m
256.409 261.593 l
256.999 262.609 l
256.409 263.625 l
258.897 262.609 l
f
239.06 278.414 m
240.076 275.926 l
239.06 276.517 l
238.043 275.926 l
239.06 278.414 l
f
281.726 285.747 m
282.742 283.26 l
281.726 283.85 l
280.71 283.26 l
281.726 285.747 l
f
238.968 262.632 m
238.968 290.979 l
S
0.043 0.369 0.757 0.004 k
[]0 d 
238.968 290.979 m
267.315 290.979 l
267.315 305.152 l
238.968 290.979 l
h
B
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 152.242 261.2804 Tm
(x)Tj
6.0372 0.8571 Td
(6)Tj
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-0.0001 Tc 0.0278 Tw 7 0 0 7 265.7926 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
49.61 555.39 368.5 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0296 Tw 14 0 0 14 164.5928 543.8038 Tm
[(Compound measur)18(es)]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0113 Tc 0.0278 Tw 9 0 0 9 67.6142 524.6384 Tm
[(Speed and density ar)18(e compound measur)18(es because we give the speed in m/s or km/h,)]TJ
-0.0112 Tc 0 -1.3333 TD
(ie two units. If mass is given in kg and volume in m)Tj
0 Tc 0 Tw 6.3 0 0 6.3 268.4199 516.2383 Tm
(3)Tj
-0.0112 Tc 0.0278 Tw 9 0 0 9 271.8522 512.6384 Tm
(, the density will be given in kg/m)Tj
0 Tc 0 Tw 6.3 0 0 6.3 405.3902 516.2383 Tm
(3)Tj
9 0 0 9 408.8224 512.6384 Tm
(.)Tj
-0.0002 Tc 0.0278 Tw -37.912 -1.9633 Td
[(The following for)-18(mulae must be memorised:)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 50.6063 284.5976 Tm
(Questions)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0224 Tc 0.0278 Tw 9 0 0 9 67.6142 269.763 Tm
[(1)-1356(A car takes 8 hours 10 minutes to travel 343 kilometr)18(es. Calculate the average speed.)]TJ
-0.0001 Tc 0 -1.9633 TD
[(2)-1332(A man walks at a speed of 24 metr)18(es in 10 seconds. Calculate his speed in)]TJ
-0.0002 Tc 1.888 -1.3333 Td
[(kilometr)18(es per hour)92(.)]TJ
-0.0001 Tc -1.888 -1.9633 Td
[(3)-1334(Mass is given in g, volume is given in cm)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 249.5383 226.0244 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 253.0405 222.4244 Tm
[(. What units ar)18(e used for density?)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 50.6063 201.9205 Tm
(Answers)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 7 0 0 7 67.6142 189.9205 Tm
[(1)-1064(Decide if you r)18(equir)18(e the answer in kilometr)18(es per hour or kilometr)18(es per minute.)]TJ
1.6198 -1.7143 Td
[(If you choose kilometr)18(es per hour change 8 hours 10 minutes into hours. )]TJ
0 -1.7143 TD
(10 minutes is )Tj
-0.0002 Tc 0 Tw 4.9 0 0 4.9 122.4334 168.7204 Tm
(10)Tj
0 Tc 7 0 0 7 127.8813 165.9205 Tm
(/)Tj
-0.0002 Tc 4.9 0 0 4.9 130.4704 164.5206 Tm
(60)Tj
0.0278 Tw 7 0 0 7 138.0576 165.9205 Tm
[(of an hour)92(. )]TJ
-0.0001 Tc -8.4436 -1.7143 Td
[(Ther)18(efor)18(e 8 hours 10 minutes = 8)]TJ
-0.0002 Tc 0 Tw 4.9 0 0 4.9 184.0686 156.7204 Tm
(10)Tj
0 Tc 7 0 0 7 189.5165 153.9205 Tm
(/)Tj
-0.0002 Tc 4.9 0 0 4.9 192.1056 152.5206 Tm
(60)Tj
7 0 0 7 199.6928 153.9205 Tm
(hours.)Tj
-0.0001 Tc 0.0277 Tw -17.2486 -1.7143 Td
[(Speed = Distance =  343  = 42 kilometr)18(es per hour)92(.)]TJ
0.0276 Tc 0 Tw 5.1955 -1.7143 Td
[(T)35(i)28(m)28(e)28(      8)]TJ
-0.0002 Tc 4.9 0 0 4.9 147.5522 132.7204 Tm
(10)Tj
0 Tc 7 0 0 7 153.0001 129.9205 Tm
(/)Tj
-0.0002 Tc 4.9 0 0 4.9 155.5892 128.5206 Tm
(60)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 67.6142 117.9205 Tm
[(2)-1064(24 metr)18(es in 10 seconds)]TJ
1.6198 -1.7143 Td
[(\(multiply by 6\))-5817(144 metr)18(es in 1 minute)]TJ
T*
[(\(multiply by 60\))-5261(8640 metr)18(es in 60 minutes \(ie 1 hour\))]TJ
T*
[(\(divide by 1000\))-4962(8.64 kilometr)18(es in 1 hour)]TJ
12.1485 -1.7143 Td
[(The speed is 8.64 kilometr)18(es per hour)92(.)]TJ
-0.0002 Tc 0 Tw -13.7683 -1.7143 Td
[(3)-1064(g/cm)]TJ
0 Tc 4.9 0 0 4.9 95.1539 60.7204 Tm
(3)Tj
ET
0 0 0 0 k
54.2 486.67 359.31 -181.57 re
f*
Q Q 
0.039 0.02 0.486 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS4 gs
191.613 318.506 116.101 161.102 re
B
62.011 318.506 116.101 161.102 re
B
0.035 0.028 0.874 0 k
120.212 472.208 m
172.173 394.407 l
68.252 394.407 l
120.212 472.208 l
h
B
0.039 0.02 0.486 0 k
360.396 417.56 m
381.18 386.44 l
339.612 386.44 l
360.396 417.56 l
h
B
91.012 428.207 m
149.412 428.207 l
121.437 377.807 m
149.812 377.807 l
S
0 0 0 1 k
BT
/T1_0 1 Tf
7 0 0 7 106.2122 438.0074 Tm
(Distance)Tj
0.0001 Tc 4 0 0 4 352.7122 403.0074 Tm
(Distance)Tj
2.875 -2.8919 Td
(Time)Tj
0 Tc 7 0 0 7 92.18 407.44 Tm
(Speed    x    Time)Tj
/T1_2 1 Tf
-1.8811 -4.5762 Td
(Speed =)Tj
6.1312 0.6286 Td
(Distance)Tj
0.815 -1.2143 Td
(Time)Tj
ET
121.437 353.806 m
149.812 353.806 l
S
BT
/T1_2 1 Tf
7 0 0 7 79.012 351.4063 Tm
(Time =)Tj
6.1312 0.6286 Td
(Distance)Tj
0.481 -1.2143 Td
(Speed)Tj
-6.6122 -2.8428 Td
(Distance = Speed x Time)Tj
ET
0.035 0.028 0.874 0 k
249.813 472.208 m
301.774 394.407 l
197.853 394.407 l
249.813 472.208 l
h
B
220.613 428.207 m
279.014 428.207 l
347.68 399.395 m
372.68 399.395 l
251.038 377.807 m
279.414 377.807 l
S
0 0 0 1 k
BT
/T1_0 1 Tf
7 0 0 7 241.0135 437.0074 Tm
(Mass)Tj
-3.4762 -4.5096 Td
(Density   x   Volume)Tj
/T1_2 1 Tf
-1.1524 -4.2905 Td
(Density =)Tj
6.9267 0.6286 Td
(Mass)Tj
-0.5735 -1.2143 Td
(Volume)Tj
ET
251.038 353.806 m
279.414 353.806 l
S
BT
/T1_2 1 Tf
7 0 0 7 208.6131 351.4063 Tm
(Volume =)Tj
6.9267 0.6286 Td
(Mass)Tj
-0.536 -1.2143 Td
(Density)Tj
-6.3907 -2.8428 Td
(Mass = Density x Volume)Tj
0 g
16.1524 2.9334 Td
(You will use this method in )Tj
0 -1.4286 TD
(trigonometry \(that is sin, )Tj
T*
(cos, tan\) on page 59.)Tj
0 19.8571 TD
(You may have used these )Tj
0 -1.4286 TD
(formulae in Science.)Tj
8.7169 -11.7857 Td
(Distance)Tj
0.815 -1.2143 Td
(Time)Tj
-9.5319 10.7857 Td
(Suppose you want to know )Tj
T*
(what speed equals. Cover )Tj
T*
(up speed. This shows:)Tj
-0.0714 -7.2143 Td
(Therefore Speed = )Tj
ET
383.18 372.44 m
409.68 372.44 l
S
1 g
360.68 381.94 m
361.18 386.94 370.18 410.44 333.68 399.94 c
B
345.68 379.955 m
352.709 379.955 358.408 383.754 358.408 388.44 c
358.408 393.126 352.709 396.925 345.68 396.925 c
338.651 396.925 332.952 393.126 332.952 388.44 c
332.952 383.754 338.651 379.955 345.68 379.955 c
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 K
10 M 
/GS5 gs
108.69 138.97 m
135.11 138.97 l
143.15 138.93 m
159.36 138.93 l
S
/CS3 cs 1  scn
BT
/T1_3 1 Tf
-0.0001 Tc 18 0 0 18 50.6063 598.6229 Tm
[(Measur)18(ement)]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0057 Tc 0.0278 Tw 9 0 0 9 50.6063 579.9141 Tm
(Quite a lot to memorise if you don)Tj
/T1_4 1 Tf
0 Tc 0 Tw 15.4075 0 Td
(\325)Tj
/T1_2 1 Tf
-0.0057 Tc 0.0277 Tw 0.2366 0 Td
[(t alr)18(eady know it. Most of this section is everyday Maths.)]TJ
-15.6441 -1.3333 Td
[(Nothing dif)18(ficult.)]TJ
ET
0.125 w 
49.61 560.95 m
418.11 560.95 l
S
0.042 w 
49.61 560.78 m
418.11 560.78 l
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f
q
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q
0 660.06 467.04 -660 re
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0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(45)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 592.71 368.51 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
-0.0002 Tc 0 Tw 14 0 0 14 218.6317 581.1277 Tm
(Time)Tj
0 0 0 1 k
/T1_2 1 Tf
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[(Y)92(our examination paper may contain a time question. W)18(e use time fr)18(equently so it)]TJ
0 -1.3333 TD
[(should be easy)92(. W)18(ARNING: At least half of the examination candidates will get the)]TJ
-0.0002 Tc T*
[(question wr)18(ong. T)92(r)18(eat the question with r)18(espect. Remember ther)18(e ar)18(e 60 minutes in)]TJ
-0.0001 Tc T*
(an hour NOT 10 or 100; lots of candidates will make this mistake.)Tj
/CS3 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 51.3228 362.8745 Tm
(Questions)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 9 0 0 9 68.3307 348.0399 Tm
[(1)-1332(A train leaves London at 07:42 and )]TJ
1.888 -1.3333 Td
(arrives in Glasgow at 13:16. How long )Tj
-0.0002 Tc T*
[(does the jour)-18(ney take?)]TJ
-1.888 -1.9633 Td
[(2)-1332(A car travels 378 km at 67)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 13.5899 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
(9 km/h. )Tj
-11.9797 -1.3333 Td
[(How long does the jour)-18(ney take? )]TJ
T*
[(Give your answer to the near)18(est second.)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 51.3228 261.8666 Tm
(Answers)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 7 0 0 7 68.3307 249.8667 Tm
[(1)-1064(If you have 5 hours 34 minutes, stick with your own method.)]TJ
1.6198 -1.7143 Td
(If you obtained the answer 5 hours 74 minutes or 6 hours 14 minutes you \
have fallen straight into the trap)Tj
-0.0002 Tc 0 -1.7143 TD
[(and must study the solution car)18(efully)92(. )]TJ
/T1_0 1 Tf
-0.0001 Tc 0 Tw 31.7601 -1.7143 Td
[(Hours)-3513(Minutes)]TJ
/T1_2 1 Tf
0.0277 Tw -31.7601 -1.7143 Td
[(First find the time to the next whole hour)92(.)-2338(07:42 to 08:00)-11829(18)]TJ
T*
[(Now the hours)-14367(08:00 to 13:00)-5346(5)]TJ
T*
[(Now the minutes)-13312(13:00 to 13:16)-11829(16)]TJ
31.477 -1.7143 Td
[(5 hours)-2632(34 minutes)]TJ
-0.0002 Tc -33.0968 -1.7143 Td
[(2)-1064(T)7(ime =                \(see page 44\).)]TJ
-0.0001 Tc 4.8899 -3.4286 Td
(= 5)Tj
/T1_3 1 Tf
0 Tc 0 Tw 1.5274 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0277 Tw 0.2779 0 Td
(567010309   )Tj
/T1_0 1 Tf
0 Tw 5.9199 0 Td
(Note:)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
(This does )Tj
/T1_0 1 Tf
-0.0001 Tc 0 Tw 4.5922 0 Td
(not)Tj
/T1_2 1 Tf
0.0277 Tw 1.8784 0 Td
(mean 5 hours 56 minutes or 5 hours 57 minutes.)Tj
-0.0002 Tc -20.4359 -1.7143 Td
(Use the         or          key to change your answer = 5 hours 34 minut\
es 1 second. )Tj
/T1_4 1 Tf
0 Tw 10 0 0 10 356.1398 604.6698 Tm
[(Measur)18(ement)]TJ
ET
/CS4 cs 1  scn
50.57 512.26 368.01 -132.73 re
f*
0 0 0 1 k
BT
/T1_2 1 Tf
0.0278 Tw 9 0 0 9 56.8228 499.2092 Tm
[(A common err)18(or is to think 3)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 12.8845 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
(5 hours equals 3 hours 50 minutes. It does not. It equals 3)Tj
-0.0001 Tc -13.1623 -1.3333 Td
[(hours 30 minutes. Y)92(our calculator will change hours \(as a decimal\))-278(into hours, minutes)]TJ
-0.0002 Tc 0 -1.3333 TD
(and seconds. \()Tj
/T1_0 1 Tf
-0.0001 Tc 0 Tw 6.4833 0 Td
(Note:)Tj
/T1_2 1 Tf
0.0278 Tw 2.9424 0 Td
[(Y)92(ou can only use this method if your calculator has these keys.\))]TJ
-0.0002 Tc -9.4257 -1.9633 Td
(Find the           key or         or          .)Tj
-0.0001 Tc 0 -1.9633 TD
[(These ar)18(e very useful keys.)]TJ
-0.0002 Tc T*
(Put 3)Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.3231 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
[(5 into your calculator and pr)18(ess the          key or you may have to pr)18(ess the top)]TJ
-2.6009 -1.3333 Td
(left key on your calculator \(ie         or         or         followed \
by          or         \). )Tj
T*
[(Y)92(ou should get 3)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 7.5834 0 Td
(\241)Tj
/T1_2 1 Tf
-0.0002 Tc 0.3999 0 Td
(30)Tj
/T1_3 1 Tf
0 Tc 1.1117 0 Td
(\325)Tj
/T1_2 1 Tf
-0.0002 Tc 0.2599 0 Td
(00)Tj
/T1_3 1 Tf
0 Tc 1.1117 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
(00 or 3)Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.2037 0 Td
(\241)Tj
/T1_2 1 Tf
-0.0002 Tc 0.3999 0 Td
(30)Tj
/T1_3 1 Tf
0 Tc 1.1117 0 Td
(\325)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2599 0 Td
(0 this means 3 hours 30 minutes.)Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
50.57 512.26 368.01 -132.73 re
S
/CS4 cs 1  scn
285.85 364.72 121.53 -76.59 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 9 0 0 9 292.0984 351.6629 Tm
[(Y)92(ou must know:)]TJ
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw T*
[(60 seconds )-139(= 1 minute)]TJ
-0.0001 Tc 0 -1.3333 TD
[(60 minutes )-271(= 1 hour)]TJ
-0.0002 Tc T*
[(24 hours )-1326(= 1 day)]TJ
T*
[(365 days )-1195(= 1 year)]TJ
ET
285.85 364.72 121.53 -76.59 re
S
Q Q 
q
92.84 467.16 22.68 -15.04 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS13 gs
110.136 453.54 m
111.446 453.54 112.517 454.611 112.517 455.921 c
112.517 463.064 l
112.517 464.374 111.446 465.445 110.136 465.445 c
97.04 465.445 l
95.73 465.445 94.659 464.374 94.659 463.064 c
94.659 455.921 l
94.659 454.611 95.73 453.54 97.04 453.54 c
110.136 453.54 l
h
B
110.5 454.715 m
110.993 454.715 111.393 455.115 111.393 455.608 c
B
96.693 464.428 m
96.2 464.428 95.8 464.028 95.8 463.535 c
B
0 g
BT
/T1_0 1 Tf
4 0 0 5 96.04 457.2065 Tm
(D)Tj
/T1_5 1 Tf
0.7592 0 Td
(\006)Tj
/T1_0 1 Tf
0.0002 Tc -0.0001 Tw 0.4001 0 Td
(M S)Tj
ET
106.706 441.207 m
107.21 441.391 107.49 441.687 107.49 442.054 c
107.49 442.246 107.41 442.374 107.274 442.374 c
107.226 442.374 107.139 442.358 107.082 442.358 c
106.819 442.358 106.683 442.542 106.683 442.726 c
106.683 442.974 106.867 443.142 107.139 443.142 c
107.554 443.142 107.89 442.758 107.89 442.294 c
107.89 441.742 107.458 441.239 106.779 441.007 c
106.706 441.207 l
h
108.54 441.207 m
109.044 441.391 109.324 441.687 109.324 442.054 c
109.324 442.246 109.244 442.374 109.108 442.374 c
109.06 442.374 108.972 442.358 108.916 442.358 c
108.652 442.358 108.516 442.542 108.516 442.726 c
108.516 442.974 108.7 443.142 108.972 443.142 c
109.388 443.142 109.724 442.758 109.724 442.294 c
109.724 441.742 109.291 441.239 108.612 441.007 c
108.54 441.207 l
h
108.373 460.374 m
108.877 460.557 109.157 460.853 109.157 461.221 c
109.157 461.413 109.077 461.54 108.941 461.54 c
108.893 461.54 108.805 461.525 108.749 461.525 c
108.485 461.525 108.349 461.708 108.349 461.893 c
108.349 462.14 108.533 462.308 108.805 462.308 c
109.221 462.308 109.557 461.924 109.557 461.461 c
109.557 460.909 109.125 460.405 108.445 460.173 c
108.373 460.374 l
h
110.206 460.374 m
110.71 460.557 110.99 460.853 110.99 461.221 c
110.99 461.413 110.91 461.54 110.774 461.54 c
110.726 461.54 110.639 461.525 110.582 461.525 c
110.319 461.525 110.183 461.708 110.183 461.893 c
110.183 462.14 110.367 462.308 110.639 462.308 c
111.054 462.308 111.39 461.924 111.39 461.461 c
111.39 460.909 110.959 460.405 110.279 460.173 c
110.206 460.374 l
h
102.914 441.207 m
103.418 441.391 103.698 441.687 103.698 442.054 c
103.698 442.246 103.618 442.374 103.482 442.374 c
103.434 442.374 103.346 442.358 103.29 442.358 c
103.026 442.358 102.891 442.542 102.891 442.726 c
102.891 442.974 103.074 443.142 103.346 443.142 c
103.762 443.142 104.098 442.758 104.098 442.294 c
104.098 441.742 103.666 441.239 102.986 441.007 c
102.914 441.207 l
h
104.706 460.54 m
105.21 460.724 105.49 461.02 105.49 461.388 c
105.49 461.58 105.41 461.708 105.274 461.708 c
105.226 461.708 105.139 461.691 105.082 461.691 c
104.819 461.691 104.683 461.875 104.683 462.059 c
104.683 462.307 104.867 462.475 105.139 462.475 c
105.554 462.475 105.89 462.091 105.89 461.627 c
105.89 461.076 105.458 460.572 104.779 460.34 c
104.706 460.54 l
f
Q Q Q 
q
146.7 467.16 22.68 -15.04 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS14 gs
163.996 452.945 m
165.306 452.945 166.377 454.017 166.377 455.327 c
166.377 462.47 l
166.377 463.779 165.306 464.851 163.996 464.851 c
150.9 464.851 l
149.59 464.851 148.519 463.779 148.519 462.47 c
148.519 455.327 l
148.519 454.017 149.59 452.945 150.9 452.945 c
163.996 452.945 l
h
B
164.36 454.12 m
164.853 454.12 165.253 454.52 165.253 455.013 c
B
150.553 463.833 m
150.06 463.833 149.66 463.434 149.66 462.94 c
B
0 g
BT
/T1_5 1 Tf
8 0 0 8 151.7335 455.3735 Tm
(\006)Tj
ET
160.566 459.207 m
161.07 459.391 161.35 459.687 161.35 460.054 c
161.35 460.246 161.27 460.374 161.134 460.374 c
161.086 460.374 160.999 460.358 160.942 460.358 c
160.679 460.358 160.543 460.542 160.543 460.726 c
160.543 460.974 160.727 461.142 160.999 461.142 c
161.414 461.142 161.75 460.758 161.75 460.294 c
161.75 459.742 161.318 459.239 160.639 459.007 c
160.566 459.207 l
h
162.4 459.207 m
162.904 459.391 163.184 459.687 163.184 460.054 c
163.184 460.246 163.104 460.374 162.968 460.374 c
162.92 460.374 162.832 460.358 162.776 460.358 c
162.512 460.358 162.376 460.542 162.376 460.726 c
162.376 460.974 162.56 461.142 162.832 461.142 c
163.248 461.142 163.584 460.758 163.584 460.294 c
163.584 459.742 163.151 459.239 162.472 459.007 c
162.4 459.207 l
h
162.233 478.374 m
162.737 478.557 163.017 478.853 163.017 479.221 c
163.017 479.413 162.937 479.54 162.801 479.54 c
162.753 479.54 162.665 479.525 162.609 479.525 c
162.345 479.525 162.209 479.708 162.209 479.893 c
162.209 480.14 162.393 480.308 162.665 480.308 c
163.081 480.308 163.417 479.924 163.417 479.461 c
163.417 478.909 162.985 478.405 162.305 478.173 c
162.233 478.374 l
h
164.066 478.374 m
164.57 478.557 164.85 478.853 164.85 479.221 c
164.85 479.413 164.77 479.54 164.634 479.54 c
164.586 479.54 164.499 479.525 164.442 479.525 c
164.179 479.525 164.043 479.708 164.043 479.893 c
164.043 480.14 164.227 480.308 164.499 480.308 c
164.914 480.308 165.25 479.924 165.25 479.461 c
165.25 478.909 164.818 478.405 164.139 478.173 c
164.066 478.374 l
h
156.774 459.207 m
157.278 459.391 157.558 459.687 157.558 460.054 c
157.558 460.246 157.478 460.374 157.342 460.374 c
157.294 460.374 157.206 460.358 157.15 460.358 c
156.886 460.358 156.751 460.542 156.751 460.726 c
156.751 460.974 156.934 461.142 157.206 461.142 c
157.622 461.142 157.958 460.758 157.958 460.294 c
157.958 459.742 157.526 459.239 156.846 459.007 c
156.774 459.207 l
h
158.566 478.54 m
159.07 478.724 159.35 479.02 159.35 479.388 c
159.35 479.58 159.27 479.708 159.134 479.708 c
159.086 479.708 158.999 479.691 158.942 479.691 c
158.679 479.691 158.543 479.875 158.543 480.059 c
158.543 480.307 158.727 480.475 158.999 480.475 c
159.414 480.475 159.75 480.091 159.75 479.627 c
159.75 479.076 159.318 478.572 158.639 478.34 c
158.566 478.54 l
f
Q Q Q 
q
182.33 467.02 22.68 -15.04 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS15 gs
199.626 453.221 m
200.936 453.221 202.007 454.292 202.007 455.602 c
202.007 462.745 l
202.007 464.055 200.936 465.126 199.626 465.126 c
186.53 465.126 l
185.22 465.126 184.149 464.055 184.149 462.745 c
184.149 455.602 l
184.149 454.292 185.22 453.221 186.53 453.221 c
199.626 453.221 l
h
B
199.99 454.396 m
200.483 454.396 200.883 454.796 200.883 455.289 c
B
186.183 464.109 m
185.69 464.109 185.29 463.709 185.29 463.216 c
B
0 g
191.814 461.091 m
191.31 460.907 191.03 460.611 191.03 460.244 c
191.03 460.052 191.11 459.924 191.246 459.924 c
191.294 459.924 191.382 459.939 191.438 459.939 c
191.701 459.939 191.838 459.756 191.838 459.572 c
191.838 459.324 191.653 459.156 191.382 459.156 c
190.966 459.156 190.63 459.54 190.63 460.004 c
190.63 460.555 191.062 461.059 191.741 461.291 c
191.814 461.091 l
h
189.855 461.091 m
189.351 460.907 189.071 460.611 189.071 460.244 c
189.071 460.052 189.151 459.924 189.287 459.924 c
189.335 459.924 189.423 459.939 189.479 459.939 c
189.743 459.939 189.879 459.756 189.879 459.572 c
189.879 459.324 189.695 459.156 189.423 459.156 c
189.007 459.156 188.671 459.54 188.671 460.004 c
188.671 460.555 189.103 461.059 189.783 461.291 c
189.855 461.091 l
f
196.774 459.356 m
197.278 459.54 197.558 459.835 197.558 460.203 c
197.558 460.395 197.478 460.523 197.342 460.523 c
197.294 460.523 197.206 460.507 197.15 460.507 c
196.886 460.507 196.75 460.691 196.75 460.875 c
196.75 461.123 196.934 461.291 197.206 461.291 c
197.622 461.291 197.958 460.907 197.958 460.443 c
197.958 459.891 197.526 459.388 196.846 459.156 c
196.774 459.356 l
h
194.815 459.356 m
195.319 459.54 195.599 459.835 195.599 460.203 c
195.599 460.395 195.519 460.523 195.383 460.523 c
195.335 460.523 195.247 460.507 195.191 460.507 c
194.927 460.507 194.791 460.691 194.791 460.875 c
194.791 461.123 194.975 461.291 195.247 461.291 c
195.663 461.291 195.999 460.907 195.999 460.443 c
195.999 459.891 195.567 459.388 194.887 459.156 c
194.815 459.356 l
f
Q Q Q 
q
225.21 435.42 22.68 -15.03 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS16 gs
242.506 422.06 m
243.816 422.06 244.887 423.131 244.887 424.441 c
244.887 431.584 l
244.887 432.894 243.816 433.965 242.506 433.965 c
229.41 433.965 l
228.1 433.965 227.029 432.894 227.029 431.584 c
227.029 424.441 l
227.029 423.131 228.1 422.06 229.41 422.06 c
242.506 422.06 l
h
B
242.87 423.235 m
243.363 423.235 243.763 423.635 243.763 424.128 c
B
229.063 432.948 m
228.57 432.948 228.17 432.548 228.17 432.055 c
B
0 g
BT
/T1_0 1 Tf
4 0 0 5 228.41 425.7266 Tm
(D)Tj
/T1_5 1 Tf
0.7592 0 Td
(\006)Tj
/T1_0 1 Tf
0.0002 Tc -0.0001 Tw 0.4001 0 Td
(M S)Tj
ET
239.076 409.727 m
239.58 409.911 239.86 410.207 239.86 410.574 c
239.86 410.766 239.78 410.894 239.644 410.894 c
239.596 410.894 239.509 410.878 239.452 410.878 c
239.189 410.878 239.053 411.062 239.053 411.246 c
239.053 411.494 239.237 411.662 239.509 411.662 c
239.924 411.662 240.26 411.278 240.26 410.814 c
240.26 410.262 239.828 409.759 239.149 409.527 c
239.076 409.727 l
h
240.91 409.727 m
241.414 409.911 241.694 410.207 241.694 410.574 c
241.694 410.766 241.614 410.894 241.478 410.894 c
241.43 410.894 241.342 410.878 241.286 410.878 c
241.022 410.878 240.886 411.062 240.886 411.246 c
240.886 411.494 241.07 411.662 241.342 411.662 c
241.758 411.662 242.094 411.278 242.094 410.814 c
242.094 410.262 241.661 409.759 240.982 409.527 c
240.91 409.727 l
h
240.743 428.894 m
241.247 429.077 241.527 429.373 241.527 429.741 c
241.527 429.933 241.447 430.061 241.311 430.061 c
241.263 430.061 241.175 430.045 241.119 430.045 c
240.855 430.045 240.719 430.229 240.719 430.413 c
240.719 430.66 240.903 430.828 241.175 430.828 c
241.591 430.828 241.927 430.444 241.927 429.981 c
241.927 429.429 241.495 428.925 240.815 428.693 c
240.743 428.894 l
h
242.576 428.894 m
243.08 429.077 243.36 429.373 243.36 429.741 c
243.36 429.933 243.28 430.061 243.144 430.061 c
243.096 430.061 243.009 430.045 242.952 430.045 c
242.689 430.045 242.553 430.229 242.553 430.413 c
242.553 430.66 242.737 430.828 243.009 430.828 c
243.424 430.828 243.76 430.444 243.76 429.981 c
243.76 429.429 243.328 428.925 242.649 428.693 c
242.576 428.894 l
h
235.284 409.727 m
235.788 409.911 236.068 410.207 236.068 410.574 c
236.068 410.766 235.988 410.894 235.852 410.894 c
235.804 410.894 235.716 410.878 235.66 410.878 c
235.396 410.878 235.261 411.062 235.261 411.246 c
235.261 411.494 235.444 411.662 235.716 411.662 c
236.132 411.662 236.468 411.278 236.468 410.814 c
236.468 410.262 236.036 409.759 235.356 409.527 c
235.284 409.727 l
h
237.076 429.06 m
237.58 429.244 237.86 429.54 237.86 429.908 c
237.86 430.1 237.78 430.228 237.644 430.228 c
237.596 430.228 237.509 430.211 237.452 430.211 c
237.189 430.211 237.053 430.395 237.053 430.579 c
237.053 430.827 237.237 430.995 237.509 430.995 c
237.924 430.995 238.26 430.611 238.26 430.147 c
238.26 429.596 237.828 429.092 237.149 428.86 c
237.076 429.06 l
f
Q Q Q 
q
349.38 419.42 22.68 -15.04 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS17 gs
366.666 406.121 m
367.976 406.121 369.047 407.192 369.047 408.502 c
369.047 415.645 l
369.047 416.955 367.976 418.026 366.666 418.026 c
353.57 418.026 l
352.26 418.026 351.189 416.955 351.189 415.645 c
351.189 408.502 l
351.189 407.192 352.26 406.121 353.57 406.121 c
366.666 406.121 l
h
B
367.03 407.296 m
367.523 407.296 367.923 407.696 367.923 408.189 c
B
353.223 417.009 m
352.73 417.009 352.33 416.609 352.33 416.116 c
B
0 g
358.854 413.991 m
358.35 413.807 358.07 413.511 358.07 413.144 c
358.07 412.952 358.15 412.824 358.286 412.824 c
358.334 412.824 358.422 412.839 358.478 412.839 c
358.741 412.839 358.878 412.656 358.878 412.472 c
358.878 412.224 358.693 412.056 358.422 412.056 c
358.006 412.056 357.67 412.44 357.67 412.904 c
357.67 413.455 358.102 413.959 358.781 414.191 c
358.854 413.991 l
h
356.895 413.991 m
356.391 413.807 356.111 413.511 356.111 413.144 c
356.111 412.952 356.191 412.824 356.327 412.824 c
356.375 412.824 356.463 412.839 356.519 412.839 c
356.783 412.839 356.919 412.656 356.919 412.472 c
356.919 412.224 356.735 412.056 356.463 412.056 c
356.047 412.056 355.711 412.44 355.711 412.904 c
355.711 413.455 356.143 413.959 356.823 414.191 c
356.895 413.991 l
f
363.814 412.256 m
364.318 412.44 364.598 412.735 364.598 413.104 c
364.598 413.295 364.518 413.423 364.382 413.423 c
364.334 413.423 364.246 413.407 364.19 413.407 c
363.926 413.407 363.79 413.591 363.79 413.775 c
363.79 414.023 363.974 414.191 364.246 414.191 c
364.662 414.191 364.998 413.807 364.998 413.343 c
364.998 412.791 364.566 412.288 363.886 412.056 c
363.814 412.256 l
h
361.855 412.256 m
362.359 412.44 362.639 412.735 362.639 413.104 c
362.639 413.295 362.559 413.423 362.423 413.423 c
362.375 413.423 362.287 413.407 362.231 413.407 c
361.967 413.407 361.831 413.591 361.831 413.775 c
361.831 414.023 362.015 414.191 362.287 414.191 c
362.703 414.191 363.039 413.807 363.039 413.343 c
363.039 412.791 362.607 412.288 361.927 412.056 c
361.855 412.256 l
f
Q Q Q 
q
174.64 418.97 22.68 -13.46 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS18 gs
192.644 406.275 m
193.954 406.275 195.025 407.346 195.025 408.656 c
195.025 415.799 l
195.025 417.109 193.954 418.18 192.644 418.18 c
179.548 418.18 l
178.239 418.18 177.167 417.109 177.167 415.799 c
177.167 408.656 l
177.167 407.346 178.239 406.275 179.548 406.275 c
192.644 406.275 l
h
B
193.008 407.45 m
193.502 407.45 193.901 407.849 193.901 408.343 c
B
179.201 417.162 m
178.708 417.162 178.308 416.763 178.308 416.269 c
B
192.644 392.796 m
193.954 392.796 195.025 393.867 195.025 395.177 c
195.025 402.32 l
195.025 403.63 193.954 404.701 192.644 404.701 c
179.548 404.701 l
178.239 404.701 177.167 403.63 177.167 402.32 c
177.167 395.177 l
177.167 393.867 178.239 392.796 179.548 392.796 c
192.644 392.796 l
h
S
0 g
BT
/T1_0 1 Tf
6 0 0 6 179.84 410.4335 Tm
(shift)Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_2 1 Tf
-0.0001 Tc 7 0 0 7 81.0866 133.8785 Tm
(378)Tj
0 -1.2857 TD
(67)Tj
/T1_3 1 Tf
0 Tc 1.1117 0 Td
(\341)Tj
/T1_2 1 Tf
0.2778 0 Td
(9)Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
80.65 131.67 m
95.68 131.67 l
S
Q Q 
q
104.18 126.67 19.18 -13.04 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.4 w 4 M 0 j 0 J []0 d 
/GS19 gs
118.407 115 m
119.455 115 120.312 115.857 120.312 116.905 c
120.312 122.62 l
120.312 123.667 119.455 124.524 118.407 124.524 c
107.93 124.524 l
106.882 124.524 106.025 123.667 106.025 122.62 c
106.025 116.905 l
106.025 115.857 106.882 115 107.93 115 c
118.407 115 l
h
B
118.698 115.94 m
119.092 115.94 119.412 116.26 119.412 116.654 c
B
107.652 123.71 m
107.258 123.71 106.938 123.39 106.938 122.996 c
B
0 g
BT
/T1_0 1 Tf
3.2 0 0 4 107.13 117.9332 Tm
(D)Tj
/T1_5 1 Tf
0.7592 0 Td
(\006)Tj
/T1_0 1 Tf
0.0002 Tc -0.0001 Tw 0.4001 0 Td
(M S)Tj
ET
115.663 105.133 m
116.066 105.281 116.29 105.517 116.29 105.811 c
116.29 105.965 116.226 106.067 116.118 106.067 c
116.079 106.067 116.009 106.055 115.964 106.055 c
115.753 106.055 115.644 106.202 115.644 106.349 c
115.644 106.547 115.791 106.681 116.009 106.681 c
116.341 106.681 116.61 106.374 116.61 106.003 c
116.61 105.562 116.265 105.159 115.721 104.973 c
115.663 105.133 l
h
117.13 105.133 m
117.533 105.281 117.757 105.517 117.757 105.811 c
117.757 105.965 117.693 106.067 117.584 106.067 c
117.546 106.067 117.475 106.055 117.431 106.055 c
117.219 106.055 117.111 106.202 117.111 106.349 c
117.111 106.547 117.258 106.681 117.475 106.681 c
117.808 106.681 118.077 106.374 118.077 106.003 c
118.077 105.562 117.731 105.159 117.187 104.973 c
117.13 105.133 l
h
116.997 120.467 m
117.4 120.614 117.623 120.85 117.623 121.145 c
117.623 121.298 117.56 121.4 117.451 121.4 c
117.412 121.4 117.342 121.388 117.297 121.388 c
117.086 121.388 116.977 121.535 116.977 121.682 c
116.977 121.88 117.125 122.015 117.342 122.015 c
117.675 122.015 117.943 121.708 117.943 121.337 c
117.943 120.895 117.598 120.492 117.054 120.307 c
116.997 120.467 l
h
118.463 120.467 m
118.866 120.614 119.09 120.85 119.09 121.145 c
119.09 121.298 119.026 121.4 118.918 121.4 c
118.879 121.4 118.809 121.388 118.764 121.388 c
118.553 121.388 118.444 121.535 118.444 121.682 c
118.444 121.88 118.591 122.015 118.809 122.015 c
119.141 122.015 119.41 121.708 119.41 121.337 c
119.41 120.895 119.065 120.492 118.521 120.307 c
118.463 120.467 l
h
112.63 105.133 m
113.032 105.281 113.257 105.517 113.257 105.811 c
113.257 105.965 113.192 106.067 113.084 106.067 c
113.045 106.067 112.975 106.055 112.93 106.055 c
112.719 106.055 112.61 106.202 112.61 106.349 c
112.61 106.547 112.757 106.681 112.975 106.681 c
113.307 106.681 113.576 106.374 113.576 106.003 c
113.576 105.562 113.231 105.159 112.687 104.973 c
112.63 105.133 l
h
114.063 120.6 m
114.466 120.747 114.69 120.984 114.69 121.278 c
114.69 121.432 114.626 121.534 114.518 121.534 c
114.479 121.534 114.409 121.521 114.364 121.521 c
114.153 121.521 114.044 121.668 114.044 121.815 c
114.044 122.014 114.191 122.148 114.409 122.148 c
114.741 122.148 115.01 121.841 115.01 121.47 c
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114.063 120.6 l
f
Q Q Q 
q
131.11 127.18 22.68 -13.55 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.4 w 4 M 0 j 0 J []0 d 
/GS20 gs
145.587 114.499 m
146.635 114.499 147.492 115.356 147.492 116.404 c
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135.11 124.023 l
134.062 124.023 133.205 123.166 133.205 122.118 c
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133.205 115.356 134.062 114.499 135.11 114.499 c
145.587 114.499 l
h
B
145.878 115.439 m
146.272 115.439 146.592 115.759 146.592 116.153 c
B
134.832 123.209 m
134.438 123.209 134.118 122.889 134.118 122.495 c
B
0 g
139.337 120.795 m
138.934 120.648 138.71 120.411 138.71 120.117 c
138.71 119.963 138.774 119.861 138.883 119.861 c
138.921 119.861 138.991 119.873 139.036 119.873 c
139.247 119.873 139.356 119.727 139.356 119.579 c
139.356 119.381 139.209 119.247 138.991 119.247 c
138.659 119.247 138.39 119.554 138.39 119.925 c
138.39 120.366 138.736 120.769 139.279 120.955 c
139.337 120.795 l
h
137.77 120.795 m
137.367 120.648 137.143 120.411 137.143 120.117 c
137.143 119.963 137.207 119.861 137.315 119.861 c
137.354 119.861 137.424 119.873 137.469 119.873 c
137.68 119.873 137.789 119.727 137.789 119.579 c
137.789 119.381 137.642 119.247 137.424 119.247 c
137.092 119.247 136.823 119.554 136.823 119.925 c
136.823 120.366 137.169 120.769 137.712 120.955 c
137.77 120.795 l
f
143.305 119.407 m
143.708 119.554 143.932 119.79 143.932 120.085 c
143.932 120.238 143.868 120.341 143.76 120.341 c
143.721 120.341 143.651 120.328 143.606 120.328 c
143.395 120.328 143.286 120.475 143.286 120.622 c
143.286 120.82 143.433 120.955 143.651 120.955 c
143.983 120.955 144.252 120.648 144.252 120.277 c
144.252 119.835 143.906 119.432 143.363 119.247 c
143.305 119.407 l
h
141.738 119.407 m
142.141 119.554 142.365 119.79 142.365 120.085 c
142.365 120.238 142.301 120.341 142.192 120.341 c
142.154 120.341 142.083 120.328 142.039 120.328 c
141.828 120.328 141.719 120.475 141.719 120.622 c
141.719 120.82 141.866 120.955 142.083 120.955 c
142.416 120.955 142.685 120.648 142.685 120.277 c
142.685 119.835 142.339 119.432 141.796 119.247 c
141.738 119.407 l
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_2 1 Tf
-0.0001 Tc 7 0 0 7 106.4487 159.0634 Tm
(Distance)Tj
-0.0002 Tc 0.4808 -1.2857 Td
(Speed)Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
105.63 156.85 m
133.67 156.85 l
S
Q Q 
q
208.61 418.97 22.68 -13.46 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS21 gs
226.114 419.775 m
227.424 419.775 228.495 420.846 228.495 422.156 c
228.495 429.299 l
228.495 430.609 227.424 431.68 226.114 431.68 c
213.018 431.68 l
211.709 431.68 210.637 430.609 210.637 429.299 c
210.637 422.156 l
210.637 420.846 211.709 419.775 213.018 419.775 c
226.114 419.775 l
h
S
0.188 0.137 0.075 0.008 k
226.114 406.296 m
227.424 406.296 228.495 407.367 228.495 408.677 c
228.495 415.82 l
228.495 417.13 227.424 418.201 226.114 418.201 c
213.018 418.201 l
211.709 418.201 210.637 417.13 210.637 415.82 c
210.637 408.677 l
210.637 407.367 211.709 406.296 213.018 406.296 c
226.114 406.296 l
h
B
226.479 407.471 m
226.972 407.471 227.371 407.871 227.371 408.363 c
B
212.671 417.183 m
212.178 417.183 211.778 416.784 211.778 416.29 c
B
226.114 392.816 m
227.424 392.816 228.495 393.888 228.495 395.198 c
228.495 402.341 l
228.495 403.65 227.424 404.722 226.114 404.722 c
213.018 404.722 l
211.709 404.722 210.637 403.65 210.637 402.341 c
210.637 395.198 l
210.637 393.888 211.709 392.816 213.018 392.816 c
226.114 392.816 l
h
S
0 g
BT
/T1_0 1 Tf
6 0 0 6 214.31 410.1 Tm
(INV)Tj
ET
Q Q Q 
q
241.66 418.97 22.68 -13.46 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS22 gs
259.414 419.296 m
260.724 419.296 261.796 420.367 261.796 421.677 c
261.796 428.82 l
261.796 430.13 260.724 431.201 259.414 431.201 c
246.318 431.201 l
245.009 431.201 243.937 430.13 243.937 428.82 c
243.937 421.677 l
243.937 420.367 245.009 419.296 246.318 419.296 c
259.414 419.296 l
h
S
0.188 0.137 0.075 0.008 k
259.414 405.816 m
260.724 405.816 261.796 406.888 261.796 408.198 c
261.796 415.341 l
261.796 416.65 260.724 417.722 259.414 417.722 c
246.318 417.722 l
245.009 417.722 243.937 416.65 243.937 415.341 c
243.937 408.198 l
243.937 406.888 245.009 405.816 246.318 405.816 c
259.414 405.816 l
h
B
259.779 406.991 m
260.272 406.991 260.671 407.391 260.671 407.884 c
B
245.971 416.704 m
245.478 416.704 245.078 416.305 245.078 415.811 c
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 247.4435 409.7665 Tm
(2nd)Tj
ET
Q Q Q 
q
313.94 419.83 22.68 -15.03 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS23 gs
331.236 405.625 m
332.546 405.625 333.617 406.697 333.617 408.007 c
333.617 415.15 l
333.617 416.459 332.546 417.531 331.236 417.531 c
318.14 417.531 l
316.83 417.531 315.759 416.459 315.759 415.15 c
315.759 408.007 l
315.759 406.697 316.83 405.625 318.14 405.625 c
331.236 405.625 l
h
B
331.6 406.8 m
332.093 406.8 332.493 407.2 332.493 407.693 c
B
317.793 416.513 m
317.3 416.513 316.9 416.114 316.9 415.62 c
B
0 g
BT
/T1_5 1 Tf
8 0 0 8 318.9735 408.0535 Tm
(\006)Tj
ET
327.807 411.887 m
328.31 412.071 328.59 412.367 328.59 412.734 c
328.59 412.926 328.51 413.054 328.374 413.054 c
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328.654 413.822 328.99 413.438 328.99 412.974 c
328.99 412.422 328.559 411.919 327.879 411.687 c
327.807 411.887 l
h
329.64 411.887 m
330.144 412.071 330.424 412.367 330.424 412.734 c
330.424 412.926 330.344 413.054 330.208 413.054 c
330.16 413.054 330.072 413.038 330.016 413.038 c
329.752 413.038 329.616 413.222 329.616 413.406 c
329.616 413.654 329.8 413.822 330.072 413.822 c
330.488 413.822 330.824 413.438 330.824 412.974 c
330.824 412.422 330.392 411.919 329.712 411.687 c
329.64 411.887 l
h
329.474 431.054 m
329.977 431.237 330.257 431.533 330.257 431.901 c
330.257 432.093 330.177 432.221 330.041 432.221 c
329.993 432.221 329.905 432.205 329.849 432.205 c
329.585 432.205 329.449 432.389 329.449 432.573 c
329.449 432.82 329.633 432.988 329.905 432.988 c
330.321 432.988 330.657 432.604 330.657 432.141 c
330.657 431.589 330.225 431.085 329.545 430.853 c
329.474 431.054 l
h
331.307 431.054 m
331.81 431.237 332.09 431.533 332.09 431.901 c
332.09 432.093 332.01 432.221 331.874 432.221 c
331.826 432.221 331.739 432.205 331.682 432.205 c
331.419 432.205 331.283 432.389 331.283 432.573 c
331.283 432.82 331.467 432.988 331.739 432.988 c
332.154 432.988 332.49 432.604 332.49 432.141 c
332.49 431.589 332.059 431.085 331.379 430.853 c
331.307 431.054 l
h
324.014 411.887 m
324.518 412.071 324.798 412.367 324.798 412.734 c
324.798 412.926 324.718 413.054 324.582 413.054 c
324.534 413.054 324.446 413.038 324.39 413.038 c
324.126 413.038 323.991 413.222 323.991 413.406 c
323.991 413.654 324.174 413.822 324.446 413.822 c
324.862 413.822 325.198 413.438 325.198 412.974 c
325.198 412.422 324.766 411.919 324.086 411.687 c
324.014 411.887 l
h
325.807 431.22 m
326.31 431.404 326.59 431.7 326.59 432.068 c
326.59 432.26 326.51 432.388 326.374 432.388 c
326.326 432.388 326.239 432.371 326.182 432.371 c
325.919 432.371 325.783 432.555 325.783 432.739 c
325.783 432.987 325.967 433.155 326.239 433.155 c
326.654 433.155 326.99 432.771 326.99 432.307 c
326.99 431.756 326.559 431.252 325.879 431.02 c
325.807 431.22 l
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f
q
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W n
q
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W n
0 0 0 0 k
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f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 50.6063 35.0006 Tm
(46)Tj
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(Easingwold School                               )Tj
/T1_2 1 Tf
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[(Some numbers can be written exactly)92(, eg 3 girls \(you cannot have 3)]TJ
/T1_3 1 Tf
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(\341)Tj
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(72 girls\). Some)Tj
-30.6273 -1.3333 Td
[(numbers, particularly measur)18(es, have a degr)18(ee of accuracy)92(, eg a height may be given)]TJ
0 -1.3333 TD
[(as 172 cm, corr)18(ect to the near)18(est centimetr)18(e. This means that the height is 172 cm\261)]TJ
0 Tc 0 Tw T*
(0)Tj
/T1_3 1 Tf
0.5559 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(5 cm, ie between 171)Tj
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(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(5 cm and 172)Tj
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(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(5 cm.)Tj
-17.2908 -1.9633 Td
(Finding the upper and lower bounds of numbers means calculating the maxi\
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-0.0002 Tc T*
[(minimum possible values. Y)92(ou need to know how to do easy questions first.)]TJ
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(Example)Tj
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(5)Tj
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(\341)Tj
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[(72 is corr)18(ect to two decimal places. Find:)]TJ
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[(a)-1371(the maximum possible value)-3611(b)-1279(the minimum possible value)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
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(Method )Tj
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0 Tc 0 -1.6483 TD
(5)Tj
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(\341)Tj
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[(72 is corr)18(ect to two decimal places, ie corr)18(ect to 0)]TJ
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(\341)Tj
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(01. )Tj
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[(The err)18(or can be half of this, ie 0)]TJ
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(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(005)Tj
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[(a)-1371(maximum = 5)]TJ
/T1_3 1 Tf
0 Tc 0 Tw 8.0747 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(72 + 0)Tj
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(\341)Tj
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(005 = 5)Tj
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(\341)Tj
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[(725)-1246(b)-1279(minimum = 5)]TJ
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(\341)Tj
/T1_2 1 Tf
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(72 )Tj
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(\320)Tj
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0.0277 Tc 0.4999 0 Td
( 0)Tj
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(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(005 = 5)Tj
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(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.2779 0 Td
(715)Tj
/CS2 cs 1  scn
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(Question)Tj
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[(A, B, C and D ar)18(e measur)18(ed corr)18(ect to one decimal place:)]TJ
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(A  5)Tj
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(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
(3,   B  4)Tj
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0 Tc 0 Tw 3.5476 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
(2,  C  3)Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.316 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
(8,  D  1)Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.353 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.2779 0 Td
(7.)Tj
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(Calculate the upper and lower bounds for )Tj
/CS3 cs 1  scn
/T1_0 1 Tf
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(Answer)Tj
ET
0 0 0 0 k
49.61 592.71 368.5 -22.68 re
f*
/CS3 cs 1  scn
BT
/T1_0 1 Tf
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(Upper and lower bounds of numbers )Tj
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(\320)Tj
/T1_0 1 Tf
0.0295 Tc 0.4999 0 Td
( 1)Tj
0 0 0 1 k
/T1_5 1 Tf
-0.0002 Tc 10 0 0 10 50.6063 604.6698 Tm
[(Measur)18(ement)]TJ
ET
Q Q 
q
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W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS4 gs
BT
/T1_2 1 Tf
9 0 0 9 245.66 298.42 Tm
(\(A + B\)  )Tj
/T1_3 1 Tf
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(\320)Tj
/T1_2 1 Tf
0.5 0 Td
( )Tj
0.5528 0.4444 Td
(C)Tj
0 -1.1111 TD
(D)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
287.66 300.92 m
294.66 300.92 l
S
Q Q Q 
q
49.61 305.6 368.5 -250.8 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.039 0.02 0.486 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
67.564 74.59 298.238 155.5 re
B
0 g
BT
/T1_2 1 Tf
7 0 0 7 75.8 216.59 Tm
[(Ther)18(e ar)18(e several complicated rules for finding minimum and maximum values.)]TJ
0 -1.4286 TD
(When you )Tj
/T1_0 1 Tf
4.7991 0 Td
(add)Tj
/T1_2 1 Tf
1.797 0 Td
( or )Tj
/T1_0 1 Tf
1.481 0 Td
(multiply)Tj
/T1_2 1 Tf
3.7621 0 Td
( it is )Tj
/T1_0 1 Tf
2.072 0 Td
(obvious)Tj
/T1_2 1 Tf
3.6471 0 Td
(.)Tj
-13.6635 7 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(35 \(max\))Tj
-0.834 -1.4286 Td
(5)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(25 \(min\))Tj
11.0231 1.4286 Td
(4)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(25 \(max\))Tj
-0.834 -1.4286 Td
(4)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(15 \(min\))Tj
11.0231 1.4286 Td
(3)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(85 \(max\))Tj
-0.834 -1.4286 Td
(3)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(75 \(min\))Tj
11.0231 1.4286 Td
(1)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(75 \(max\))Tj
-0.834 -1.4286 Td
(1)Tj
/T1_3 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(65 \(min\))Tj
-41.4769 0.7857 Td
(A = 5)Tj
/T1_3 1 Tf
2.464 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
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( All you have to do is multiply by)Tj
ET
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ET
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B
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(The following questions )Tj
0 -1.3333 TD
[(show you what you ar)18(e )]TJ
T*
(expected to do.)Tj
0.925 0.725 0.075 0.012 k
/T1_0 1 Tf
10 0 0 10 50.358 332.97 Tm
(Questions)Tj
0.172 0.89 0.796 0.047 k
8 0 0 8 50.358 230.97 Tm
(Answers)Tj
0 g
/T1_2 1 Tf
9 0 0 9 84.3737 317.97 Tm
(Find)Tj
0 -4.6667 TD
[(Find the shaded ar)18(ea. )]TJ
/T1_0 1 Tf
9.9836 0 Td
(Note:)Tj
/T1_2 1 Tf
2.6649 0 Td
[( The shaded ar)18(ea is a segment.)]TJ
-12.6485 -1.5556 Td
[(The volume of a spher)18(e is 80 cm)]TJ
6 0 0 6 214.4184 265.97 Tm
(2)Tj
9 0 0 9 217.7546 261.97 Tm
(. Find the radius.)Tj
-14.8201 -1.5556 Td
[(Find the total surface ar)18(ea of a cylinder)92(, radius 4 cm, height 6 cm.)]TJ
2.9707 7.9444 Td
[(a     the ar)18(ea of the sector OAB)]TJ
0 -1.3333 TD
[(b     the length of the ar)18(c AB)]TJ
-4.7222 1.1667 Td
(1)Tj
0 -4.6667 TD
(2)Tj
0 -1.5556 TD
(3)Tj
T*
(4)Tj
ET
305.444 410.137 m
305.444 410.443 l
305.425 410.442 305.408 410.441 305.376 410.441 c
305.285 410.441 305.009 410.441 304.883 410.641 c
304.816 410.748 304.783 410.902 304.783 411.11 c
304.783 414.037 l
304.967 414.221 l
305.578 414.221 l
305.578 414.554 l
300.773 414.554 l
300.773 414.221 l
301.384 414.221 l
301.568 414.037 l
301.568 410.135 l
302.031 410.135 l
302.031 414.037 l
302.215 414.221 l
304.136 414.221 l
304.32 414.037 l
304.32 410.876 l
304.32 410.532 304.407 410.311 304.585 410.204 c
304.655 410.162 304.8 410.113 305.093 410.113 c
305.135 410.113 305.174 410.114 305.206 410.116 c
305.419 410.135 305.417 410.134 v
305.444 410.137 l
f
311.61 396.303 m
311.61 396.61 l
311.591 396.609 311.575 396.607 311.543 396.607 c
311.452 396.607 311.175 396.607 311.05 396.808 c
310.983 396.915 310.95 397.068 310.95 397.276 c
310.95 400.204 l
311.134 400.388 l
311.745 400.388 l
311.745 400.721 l
306.94 400.721 l
306.94 400.388 l
307.551 400.388 l
307.735 400.204 l
307.735 396.302 l
308.197 396.302 l
308.197 400.204 l
308.382 400.388 l
310.303 400.388 l
310.487 400.204 l
310.487 397.043 l
310.487 396.698 310.574 396.478 310.752 396.37 c
310.822 396.329 310.967 396.279 311.259 396.279 c
311.302 396.279 311.34 396.281 311.372 396.283 c
311.585 396.301 311.584 396.301 v
311.61 396.303 l
f
311.36 382.137 m
311.36 382.443 l
311.341 382.442 311.325 382.441 311.293 382.441 c
311.202 382.441 310.925 382.441 310.8 382.641 c
310.733 382.748 310.7 382.902 310.7 383.11 c
310.7 386.037 l
310.884 386.221 l
311.495 386.221 l
311.495 386.554 l
306.69 386.554 l
306.69 386.221 l
307.301 386.221 l
307.485 386.037 l
307.485 382.135 l
307.947 382.135 l
307.947 386.037 l
308.132 386.221 l
310.053 386.221 l
310.237 386.037 l
310.237 382.876 l
310.237 382.532 310.324 382.311 310.502 382.204 c
310.572 382.162 310.717 382.113 311.009 382.113 c
311.052 382.113 311.09 382.114 311.122 382.117 c
311.335 382.135 311.334 382.134 v
311.36 382.137 l
f
299.11 354.137 m
299.11 354.443 l
299.091 354.442 299.075 354.441 299.043 354.441 c
298.952 354.441 298.675 354.441 298.55 354.641 c
298.483 354.748 298.45 354.902 298.45 355.11 c
298.45 358.037 l
298.634 358.221 l
299.245 358.221 l
299.245 358.554 l
294.44 358.554 l
294.44 358.221 l
295.051 358.221 l
295.235 358.037 l
295.235 354.135 l
295.697 354.135 l
295.697 358.037 l
295.882 358.221 l
297.803 358.221 l
297.987 358.037 l
297.987 354.876 l
297.987 354.532 298.074 354.311 298.252 354.204 c
298.322 354.162 298.467 354.113 298.759 354.113 c
298.802 354.113 298.84 354.114 298.872 354.117 c
299.085 354.135 299.084 354.134 v
299.11 354.137 l
f
153.277 219.637 m
153.277 219.867 l
153.262 219.866 153.25 219.865 153.226 219.865 c
153.158 219.865 152.951 219.865 152.857 220.015 c
152.806 220.095 152.781 220.21 152.781 220.367 c
152.781 222.562 l
152.92 222.7 l
153.378 222.7 l
153.378 222.95 l
149.774 222.95 l
149.774 222.7 l
150.232 222.7 l
150.37 222.562 l
150.37 219.635 l
150.717 219.635 l
150.717 222.562 l
150.855 222.7 l
152.297 222.7 l
152.434 222.562 l
152.434 220.191 l
152.434 219.933 152.5 219.768 152.633 219.687 c
152.686 219.655 152.795 219.618 153.014 219.618 c
153.046 219.618 153.074 219.619 153.098 219.621 c
153.258 219.635 153.257 219.635 v
153.277 219.637 l
f
137.61 176.97 m
137.61 177.2 l
137.596 177.199 137.584 177.198 137.559 177.198 c
137.491 177.198 137.284 177.198 137.19 177.348 c
137.139 177.429 137.115 177.544 137.115 177.7 c
137.115 179.895 l
137.253 180.034 l
137.711 180.034 l
137.711 180.283 l
134.107 180.283 l
134.107 180.034 l
134.566 180.034 l
134.704 179.895 l
134.704 176.969 l
135.05 176.969 l
135.05 179.895 l
135.189 180.034 l
136.63 180.034 l
136.768 179.895 l
136.768 177.525 l
136.768 177.266 136.833 177.101 136.966 177.02 c
137.019 176.989 137.128 176.952 137.347 176.952 c
137.379 176.952 137.407 176.953 137.432 176.955 c
137.591 176.968 l
137.61 176.97 l
f
159.61 176.97 m
159.61 177.2 l
159.596 177.199 159.584 177.198 159.559 177.198 c
159.491 177.198 159.284 177.198 159.19 177.348 c
159.139 177.429 159.115 177.544 159.115 177.7 c
159.115 179.895 l
159.253 180.034 l
159.711 180.034 l
159.711 180.283 l
156.107 180.283 l
156.107 180.034 l
156.566 180.034 l
156.704 179.895 l
156.704 176.969 l
157.05 176.969 l
157.05 179.895 l
157.189 180.034 l
158.63 180.034 l
158.768 179.895 l
158.768 177.525 l
158.768 177.266 158.833 177.101 158.966 177.02 c
159.019 176.989 159.128 176.952 159.347 176.952 c
159.379 176.952 159.407 176.953 159.432 176.955 c
159.591 176.968 l
159.61 176.97 l
f
306.61 98.47 m
306.61 98.7 l
306.596 98.699 306.584 98.698 306.559 98.698 c
306.491 98.698 306.284 98.698 306.19 98.848 c
306.139 98.929 306.115 99.044 306.115 99.2 c
306.115 101.395 l
306.253 101.534 l
306.711 101.534 l
306.711 101.783 l
303.107 101.783 l
303.107 101.534 l
303.566 101.534 l
303.704 101.395 l
303.704 98.469 l
304.05 98.469 l
304.05 101.395 l
304.189 101.534 l
305.63 101.534 l
305.768 101.395 l
305.768 99.025 l
305.768 98.766 305.833 98.601 305.966 98.52 c
306.019 98.489 306.128 98.452 306.347 98.452 c
306.379 98.452 306.407 98.453 306.432 98.455 c
306.591 98.469 306.591 98.468 v
306.61 98.47 l
f
275.36 98.22 m
275.36 98.45 l
275.346 98.449 275.334 98.448 275.309 98.448 c
275.241 98.448 275.034 98.448 274.94 98.598 c
274.889 98.678 274.865 98.794 274.865 98.95 c
274.865 101.145 l
275.003 101.284 l
275.461 101.284 l
275.461 101.533 l
271.857 101.533 l
271.857 101.284 l
272.316 101.284 l
272.454 101.145 l
272.454 98.219 l
272.8 98.219 l
272.8 101.145 l
272.939 101.284 l
274.38 101.284 l
274.518 101.145 l
274.518 98.775 l
274.518 98.516 274.583 98.351 274.716 98.27 c
274.769 98.239 274.878 98.202 275.097 98.202 c
275.129 98.202 275.157 98.203 275.182 98.205 c
275.341 98.219 275.341 98.218 v
275.36 98.22 l
f
282.11 73.97 m
282.11 74.2 l
282.096 74.199 282.084 74.198 282.059 74.198 c
281.991 74.198 281.784 74.198 281.69 74.348 c
281.639 74.428 281.615 74.544 281.615 74.7 c
281.615 76.895 l
281.753 77.034 l
282.211 77.034 l
282.211 77.283 l
278.607 77.283 l
278.607 77.034 l
279.066 77.034 l
279.204 76.895 l
279.204 73.969 l
279.55 73.969 l
279.55 76.895 l
279.689 77.034 l
281.13 77.034 l
281.268 76.895 l
281.268 74.525 l
281.268 74.266 281.333 74.101 281.466 74.02 c
281.519 73.989 281.628 73.952 281.847 73.952 c
281.879 73.952 281.907 73.953 281.932 73.955 c
282.091 73.969 282.091 73.968 v
282.11 73.97 l
f
313.016 73.972 m
313.016 74.201 l
313.002 74.2 312.99 74.2 312.966 74.2 c
312.898 74.2 312.691 74.2 312.596 74.35 c
312.546 74.43 312.522 74.545 312.522 74.701 c
312.522 76.897 l
312.659 77.035 l
313.118 77.035 l
313.118 77.284 l
309.514 77.284 l
309.514 77.035 l
309.972 77.035 l
310.11 76.897 l
310.11 73.97 l
310.457 73.97 l
310.457 76.897 l
310.595 77.035 l
312.036 77.035 l
312.175 76.897 l
312.175 74.526 l
312.175 74.268 312.24 74.102 312.373 74.021 c
312.425 73.991 312.534 73.953 312.754 73.953 c
312.785 73.953 312.814 73.954 312.839 73.956 c
312.998 73.97 312.997 73.97 v
313.016 73.972 l
f
141.966 76.97 m
141.966 77.2 l
141.952 77.199 141.94 77.198 141.916 77.198 c
141.847 77.198 141.64 77.198 141.546 77.348 c
141.496 77.428 141.471 77.544 141.471 77.7 c
141.471 79.895 l
141.609 80.034 l
142.067 80.034 l
142.067 80.283 l
138.464 80.283 l
138.464 80.034 l
138.922 80.034 l
139.06 79.895 l
139.06 76.969 l
139.406 76.969 l
139.406 79.895 l
139.545 80.034 l
140.986 80.034 l
141.124 79.895 l
141.124 77.525 l
141.124 77.266 141.189 77.101 141.322 77.02 c
141.375 76.989 141.484 76.952 141.703 76.952 c
141.735 76.952 141.764 76.953 141.788 76.955 c
141.947 76.969 141.946 76.968 v
141.966 76.97 l
f
167.61 96.47 m
167.61 96.7 l
167.596 96.699 167.584 96.698 167.559 96.698 c
167.491 96.698 167.284 96.698 167.19 96.848 c
167.139 96.929 167.115 97.044 167.115 97.2 c
167.115 99.395 l
167.253 99.534 l
167.711 99.534 l
167.711 99.783 l
164.107 99.783 l
164.107 99.534 l
164.566 99.534 l
164.704 99.395 l
164.704 96.469 l
165.05 96.469 l
165.05 99.395 l
165.189 99.534 l
166.63 99.534 l
166.768 99.395 l
166.768 97.025 l
166.768 96.766 166.833 96.601 166.966 96.52 c
167.019 96.489 167.128 96.452 167.347 96.452 c
167.379 96.452 167.407 96.453 167.432 96.455 c
167.591 96.469 167.591 96.468 v
167.61 96.47 l
f
167.61 110.47 m
167.61 110.7 l
167.596 110.699 167.584 110.698 167.559 110.698 c
167.491 110.698 167.284 110.698 167.19 110.848 c
167.139 110.929 167.115 111.044 167.115 111.2 c
167.115 113.395 l
167.253 113.534 l
167.711 113.534 l
167.711 113.783 l
164.107 113.783 l
164.107 113.534 l
164.566 113.534 l
164.704 113.395 l
164.704 110.469 l
165.05 110.469 l
165.05 113.395 l
165.189 113.534 l
166.63 113.534 l
166.768 113.395 l
166.768 111.025 l
166.768 110.766 166.833 110.601 166.966 110.52 c
167.019 110.489 167.128 110.452 167.347 110.452 c
167.379 110.452 167.407 110.453 167.432 110.455 c
167.591 110.469 167.591 110.468 v
167.61 110.47 l
f
174.277 219.637 m
174.277 219.867 l
174.262 219.866 174.25 219.865 174.226 219.865 c
174.158 219.865 173.951 219.865 173.857 220.015 c
173.806 220.095 173.781 220.21 173.781 220.367 c
173.781 222.562 l
173.92 222.7 l
174.378 222.7 l
174.378 222.95 l
170.774 222.95 l
170.774 222.7 l
171.232 222.7 l
171.37 222.562 l
171.37 219.635 l
171.717 219.635 l
171.717 222.562 l
171.855 222.7 l
173.297 222.7 l
173.434 222.562 l
173.434 220.191 l
173.434 219.933 173.5 219.768 173.633 219.687 c
173.686 219.655 173.795 219.618 174.014 219.618 c
174.046 219.618 174.074 219.619 174.098 219.621 c
174.258 219.635 174.257 219.635 v
174.277 219.637 l
f
BT
/T1_2 1 Tf
7 0 0 7 67.3659 219.47 Tm
(1)Tj
0 -4.4286 TD
(2)Tj
23.4789 Tc 0 -11.2143 TD
(34)Tj
-0.01 Tc 3.9634 15.6429 Td
[(Ar)18(ea of a cir)18(cle)]TJ
0 Tc 0 -1.9286 TD
[(Ar)18(ea of sector)]TJ
-1.5338 1.9286 Td
[(a)-7729(=    r)]TJ
0.0001 Tc -0.0001 Tw 5 0 0 5 156.8803 222.47 Tm
(2  )Tj
0 Tc 0 Tw 7 0 0 7 162.4409 219.47 Tm
(=     x 8)Tj
0.0001 Tc -0.0001 Tw 5 0 0 5 186.0454 222.47 Tm
(2  )Tj
0 Tc 0 Tw 7 0 0 7 191.606 219.47 Tm
(= 201 cm)Tj
5 0 0 5 221.1746 222.47 Tm
(2)Tj
7 0 0 7 142.11 205.97 Tm
(=  )Tj
0.0001 Tc 5 0 0 5 150.6642 209.97 Tm
(40)Tj
0 Tc 1.1121 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(360)Tj
0 Tc 7 0 0 7 166.4161 205.97 Tm
( x 201 = 22)Tj
/T1_4 1 Tf
5.0401 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 cm)Tj
5 0 0 5 218.819 208.97 Tm
(2)Tj
ET
342.86 219.637 m
342.86 219.867 l
342.846 219.866 342.834 219.865 342.809 219.865 c
342.741 219.865 342.534 219.865 342.44 220.015 c
342.389 220.095 342.365 220.21 342.365 220.367 c
342.365 222.562 l
342.503 222.7 l
342.961 222.7 l
342.961 222.95 l
339.358 222.95 l
339.358 222.7 l
339.816 222.7 l
339.954 222.562 l
339.954 219.635 l
340.3 219.635 l
340.3 222.562 l
340.439 222.7 l
341.88 222.7 l
342.018 222.562 l
342.018 220.191 l
342.018 219.933 342.083 219.768 342.216 219.687 c
342.269 219.655 342.378 219.618 342.597 219.618 c
342.629 219.618 342.657 219.619 342.682 219.621 c
342.841 219.635 l
342.86 219.637 l
f
371.277 219.637 m
371.277 219.867 l
371.262 219.866 371.25 219.865 371.226 219.865 c
371.158 219.865 370.951 219.865 370.857 220.015 c
370.806 220.095 370.781 220.21 370.781 220.367 c
370.781 222.562 l
370.92 222.7 l
371.378 222.7 l
371.378 222.95 l
367.774 222.95 l
367.774 222.7 l
368.232 222.7 l
368.37 222.562 l
368.37 219.635 l
368.717 219.635 l
368.717 222.562 l
368.855 222.7 l
370.297 222.7 l
370.434 222.562 l
370.434 220.191 l
370.434 219.933 370.5 219.768 370.633 219.687 c
370.686 219.655 370.795 219.618 371.014 219.618 c
371.045 219.618 371.074 219.619 371.098 219.621 c
371.258 219.635 371.257 219.635 v
371.277 219.637 l
f
BT
/T1_2 1 Tf
-0.01 Tc 7 0 0 7 249.0128 219.47 Tm
[(Cir)18(cumfer)18(ence of a cir)18(cle)]TJ
0 Tc 0 -2.0238 TD
[(Length of ar)18(c)]TJ
-1.5338 2.0238 Td
[(b)-11960(=  2   r = 2 x     x 8 = 50)]TJ
/T1_4 1 Tf
23.0936 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 cm)Tj
-10.8002 -2.0238 Td
(=  )Tj
0.0001 Tc 5 0 0 5 334.8307 209.3035 Tm
(40)Tj
0 Tc 1.1121 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(360)Tj
0 Tc 7 0 0 7 350.5826 205.3035 Tm
( x 50)Tj
/T1_4 1 Tf
2.15 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(3 = 5)Tj
/T1_4 1 Tf
2.334 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(59 cm)Tj
-33.8219 -5.7619 Td
(=  )Tj
0.0001 Tc 5 0 0 5 157.6642 168.97 Tm
(60)Tj
0 Tc 1.1121 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(360)Tj
0 Tc 7 0 0 7 173.4161 164.97 Tm
( x 78)Tj
/T1_4 1 Tf
2.15 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(5398 )Tj
-5.9003 -1.7143 Td
(= 13.089969 cm)Tj
5 0 0 5 200.0849 155.97 Tm
(2)Tj
7 0 0 7 251.11 109.97 Tm
[(Ar)18(ea of the curved sector is:)]TJ
0 -1.7143 TD
(        2   rh = 2 x     x 4 x 6 = 150.796 cm)Tj
5 0 0 5 375.6282 100.97 Tm
(2)Tj
7 0 0 7 251.11 85.97 Tm
[(plus ar)18(ea of the cir)18(cles:)]TJ
T*
(        2 x    r)Tj
5 0 0 5 285.9986 76.97 Tm
(2)Tj
7 0 0 7 288.779 73.97 Tm
( = 2 x     x 4)Tj
5 0 0 5 325.4876 76.97 Tm
(2)Tj
7 0 0 7 328.2679 73.97 Tm
( = 100.531 cm)Tj
5 0 0 5 373.4047 76.97 Tm
(2)Tj
7 0 0 7 251.11 61.97 Tm
[(total ar)18(ea = 150)]TJ
/T1_4 1 Tf
7.0921 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(8 +100)Tj
/T1_4 1 Tf
3.1681 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(5 = 251 cm)Tj
5 0 0 5 362.23 64.97 Tm
(2)Tj
/T1_0 1 Tf
7 0 0 7 237.11 188.97 Tm
(Second)Tj
/T1_2 1 Tf
3.4441 0 Td
[(, find the ar)18(ea of triangle OCD.)]TJ
-3.4441 -1.7143 Td
[(\(OC and OD ar)18(e radii ther)18(efor)18(e OC = OD = 5 cm\))]TJ
T*
[(Ar)18(ea of a triangle )]TJ
/T1_0 1 Tf
-21.8195 -5.6607 Td
[(Thir)18(d)]TJ
/T1_2 1 Tf
2.409 0 Td
[(, ar)18(ea of sector )]TJ
/T1_4 1 Tf
6.9081 0 Td
(\320)Tj
/T1_2 1 Tf
0.5 0 Td
[( ar)18(ea of triangle = shaded ar)18(ea = 13.089969 )]TJ
/T1_4 1 Tf
19.9303 0 Td
(\320)Tj
/T1_2 1 Tf
0.5 0 Td
( 10.825318 = 2.26 cm)Tj
5 0 0 5 364.5956 128.345 Tm
(2)Tj
ET
[]0 d 
384.893 165.104 m
385.437 164.942 386.013 164.855 386.61 164.855 c
388.238 164.855 389.715 165.502 390.797 166.554 c
S
BT
/T1_2 1 Tf
7 0 0 7 295.11 163.6365 Tm
(= )Tj
5 0 0 5 301.7181 167.6365 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 310.5192 163.6365 Tm
(ab sin c)Tj
-2.2013 -1.7143 Td
(= )Tj
5 0 0 5 301.7181 155.6365 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 310.5192 151.6365 Tm
(x 5 x 5 x sin60)Tj
/T1_3 1 Tf
6.2821 0 Td
(\006)Tj
/T1_2 1 Tf
-8.4834 -1.7143 Td
(= 10)Tj
/T1_4 1 Tf
2.056 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(825318 cm)Tj
5 0 0 5 346.0849 142.6365 Tm
(2)Tj
7 0 0 7 84.3109 109.97 Tm
[(V)55(olume of a spher)18(e)]TJ
7.5022 -2 Td
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(y)Tj
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B
0 g
BT
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(c)Tj
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(b)Tj
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(d)Tj
ET
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S
BT
/T1_2 1 Tf
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/T1_0 1 Tf
5.2968 0 Td
(equal)Tj
/T1_2 1 Tf
2.5749 0 Td
[( angles.)-9164(Cyclic quadrilateral)]TJ
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[(A 4-sided shape inside a cir)18(cle.)]TJ
0 -1.3333 TD
(All 4 vertices lie on the )Tj
T*
[(cir)18(cumfer)18(ence of the cir)18(cle)]TJ
/T1_0 1 Tf
0 -2.0701 TD
(Remember:)Tj
/T1_2 1 Tf
0 -1.3333 TD
(Opposite angles )Tj
T*
(add up to 180)Tj
/T1_5 1 Tf
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(\006)Tj
/T1_2 1 Tf
0.37 0 Td
(,)Tj
-0.03 Tc -6.3147 -1.3333 Td
(ie   a + c = b + d = 180)Tj
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(\006)Tj
/T1_0 1 Tf
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[(Y)92(ou also need to know the obvious)]TJ
0.925 0.725 0.075 0.012 k
0 Tc 10 0 0 10 51.068 532.5917 Tm
(Angle rule 1 )Tj
0 -14.941 TD
(Angle rule 2)Tj
0 -12.4131 TD
(Radius)Tj
0 g
3.0748 0 Td
( )Tj
0.925 0.725 0.075 0.012 k
15.3748 12.4131 Td
(Angle rule 3)Tj
0 g
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( )Tj
/T1_2 1 Tf
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[(The angle at the centr)18(e of a cir)18(cle is twice the angle at the cir)18(cumfer)18(ence.)]TJ
0 -1.3333 TD
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T*
[(Actually they ar)18(e all the same, they just look dif)18(fer)18(ent.)]TJ
1.416 -40.8819 Td
(1)Tj
T*
(2)Tj
T*
(3)Tj
T*
(4)Tj
-0.03 Tc 1.9331 4 Td
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(\006)Tj
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(\006)Tj
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(\006)Tj
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-0.03 Tc -13.2934 -1.3333 Td
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(This is an examiners)Tj
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(\325)Tj
/T1_2 1 Tf
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( favourite which is often missed by candidates.)Tj
-0.7151 -1.6342 Td
[(O is the centr)18(e)]TJ
T*
(OA is a radius)Tj
T*
(OB is a radius)Tj
T*
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T*
(and angle A = angle B)Tj
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(Easingwold School                               )Tj
ET
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[(Angle and tangent pr)18(operties of cir)18(cles )]TJ
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[(Cir)18(cles)]TJ
ET
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h
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(A)Tj
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(tangent)Tj
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(O)Tj
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(O)Tj
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(an angle of 90)Tj
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(\006)Tj
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( )Tj
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(with the radius.)Tj
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(If we combine rules 1 and 2:)Tj
-0.0741 -12.1481 Td
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(\325)Tj
/T1_4 1 Tf
0.242 0 Td
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(but if it does most candidates will miss it.)Tj
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[(If A)68(T and BT ar)18(e both )]TJ
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ET
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99.429 518.898 5 5 re
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[0.5 2]0 d 
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229.444 373.827 l
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[]0 d 
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229.444 373.827 l
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314.406 381.675 m
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292.382 344.211 m
289.252 342.887 287.056 339.787 287.056 336.175 c
291.699 345.198 m
288.266 343.644 285.877 340.189 285.877 336.175 c
305.676 336.175 m
305.676 339.71 303.823 342.813 301.035 344.564 c
276.62 379.121 m
279.688 380.482 281.936 383.357 282.414 386.798 c
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(That)Tj
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(\325)Tj
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(must)Tj
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(be one of these rules \(but don)Tj
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(\325)Tj
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[(t for)18(get the )]TJ
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(obvious)Tj
/T1_4 1 Tf
-0.0003 Tc 3.646 0 Td
(\). )Tj
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(The easiest way to work out the size of angles is to:)Tj
0 -1.6483 TD
[(1)-1334(Draw a lar)18(ge diagram)6(.)]TJ
-0.0001 Tc T*
[(2)-1332(For)18(get what the question asks you to find. Instead fill in all the angles y\
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1.888 -1.3333 Td
[(work out easily)92(. If you ar)18(e certain, fill in the angle on your diagram in pen. If you)]TJ
0 -1.3333 TD
[(ar)18(e not certain use pencil.)]TJ
-0.0002 Tc 0 Tw -1.888 -1.6483 Td
[(3)-1334(Do )]TJ
/T1_0 1 Tf
-0.0001 Tc 3.5291 0 Td
(not)Tj
/T1_4 1 Tf
-0.0002 Tc 0.0278 Tw 1.8784 0 Td
[(for)18(get the )]TJ
/T1_0 1 Tf
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(obvious.)Tj
/T1_4 1 Tf
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[(4)-1334(T)92(ur)-18(n your diagram ar)18(ound. Things can look dif)18(fer)18(ent fr)18(om other dir)18(ections.)]TJ
0 -1.6483 TD
[(5)-1332(Look for the )]TJ
/T1_0 1 Tf
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[(thr)18(ee)]TJ
/T1_4 1 Tf
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[(thr)18(ee)]TJ
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(obvious)Tj
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(.)Tj
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T*
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T*
(miss this)Tj
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[(Y)92(ou ar)18(e expected to know how to use these for)-18(mulae:)]TJ
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(1)Tj
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[(V)55(olume of a cuboid)]TJ
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(Questions)Tj
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(Answers)Tj
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/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 7 0 0 7 67.6142 106.2194 Tm
[(1)-1064(a  8 cm + 3 cm + 8 cm + 3 cm = 22 cm)-6527(b)-1009(8 cm x 3 cm = 24 cm)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 326.9531 109.0193 Tm
(2)Tj
7 0 0 7 67.6142 94.2194 Tm
(2)Tj
4.9 0 0 4.9 78.9527 97.0193 Tm
(1)Tj
7 0 0 7 81.6767 94.2194 Tm
(/)Tj
4.9 0 0 4.9 84.2658 92.8193 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 89.129 94.2194 Tm
(x 7 cm x 6 cm = 21 cm)Tj
0 Tc 0 Tw 4.9 0 0 4.9 161.225 97.0193 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 249.0314 94.2194 Tm
[(3)-1064(12 m x 5 m = 60 m)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 320.7238 97.0193 Tm
(2)Tj
7 0 0 7 325.5871 94.2194 Tm
(\()Tj
/T1_0 1 Tf
-0.0001 Tc 0.2598 0 Td
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
(7m is not used\))Tj
-0.0003 Tc 0.0271 Tw -40.0832 -1.7143 Td
[(4)-1064(Ar)18(ea = )]TJ
0 Tc 0 Tw 4.9 0 0 4.9 102.406 85.0193 Tm
(1)Tj
7 0 0 7 105.1299 82.2194 Tm
(/)Tj
4.9 0 0 4.9 107.7191 80.8193 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 112.5823 82.2194 Tm
[(x \(12 cm + 20 cm\) x 8 cm)-8118(5)-1064(5 m x 4 m x 3 m = 60 m)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 336.4779 85.0193 Tm
(3)Tj
-0.0004 Tc 7 0 0 7 95.4813 70.2194 Tm
(= )Tj
0 Tc 4.9 0 0 4.9 102.281 73.0193 Tm
(1)Tj
7 0 0 7 105.0049 70.2194 Tm
(/)Tj
4.9 0 0 4.9 107.5941 68.8193 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 112.4573 70.2194 Tm
(x 32 cm  x 8 cm)Tj
-0.0002 Tc -2.4251 -1.7143 Td
(= 128 cm)Tj
4.9 0 0 4.9 125.4306 61.0193 Tm
(2  )Tj
0 Tc 0 Tw 7 0 0 7 131.1495 58.2194 Tm
(\()Tj
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 0.2598 0 Td
[(Common err)18(or:)]TJ
/T1_3 1 Tf
0.0277 Tw 7.4502 0 Td
(128 cm)Tj
0 Tc 0 Tw 4.9 0 0 4.9 208.2692 61.0193 Tm
(2)Tj
-0.0002 Tc 7 0 0 7 213.1324 58.2194 Tm
(does )Tj
/T1_0 1 Tf
-0.0001 Tc 2.4909 0 Td
(not)Tj
/T1_3 1 Tf
0.0277 Tw 1.8784 0 Td
(equal 1)Tj
/T1_4 1 Tf
0 Tc 0 Tw 3.3428 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.2779 0 Td
(28 m)Tj
0 Tc 0 Tw 4.9 0 0 4.9 284.9477 61.0193 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 289.811 58.2194 Tm
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4998 0 Td
( see page 56\))Tj
/CS3 cs 1  scn
/T1_5 1 Tf
0.0296 Tw 18 0 0 18 50.6063 598.6229 Tm
[(Perimeter)92(, ar)18(ea and volume)]TJ
0 0 0 1 k
/T1_3 1 Tf
-0.0113 Tc 0.0278 Tw 9 0 0 9 50.6063 579.9141 Tm
[(Fairly straightforwar)18(d. They give you the for)-18(mulae on the exam paper so that makes it easier)92(.)]TJ
ET
0 0 0 1 K
0.125 w 10 M 0 j 0 J []0 d 
49.61 572.61 m
418.11 572.61 l
S
0.042 w 
49.61 572.44 m
418.11 572.44 l
S
Q Q 
q
264.34 451.01 147.34 -119.41 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.051 0.235 0.502 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS4 gs
313.72 446.707 m
292.46 404.187 l
377.5 404.187 l
313.72 446.707 l
h
B
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 321.8555 396.1968 Tm
(Base)Tj
ET
0.051 0.235 0.502 0.008 k
306.855 420.572 16.5 9 re
f
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 308.3555 422.0718 Tm
(P.H.)Tj
ET
313.718 418.197 m
313.718 407.711 l
S
0 g
314.23 406.53 m
314.479 407.356 314.71 407.894 314.976 408.557 c
312.454 408.557 l
312.566 408.32 312.95 407.356 313.199 406.53 c
313.467 405.645 313.649 404.843 313.715 404.323 c
313.78 404.843 313.963 405.645 314.23 406.53 c
f
313.718 431.197 m
313.718 443.318 l
S
313.205 444.499 m
312.956 443.672 312.726 443.135 312.46 442.472 c
314.981 442.472 l
314.869 442.71 314.485 443.672 314.236 444.499 c
313.969 445.384 313.786 446.186 313.72 446.707 c
313.655 446.186 313.472 445.384 313.205 444.499 c
f
0.051 0.235 0.502 0.008 k
390.167 343.187 m
358.277 368.699 l
298.749 368.699 l
283.868 343.187 l
390.167 343.187 l
h
B
321.496 351.943 16.5 9 re
f
0 0 0 0 k
325.033 369.958 7.5 5.501 re
f
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 322.9956 353.443 Tm
(P.H.)Tj
0.541 2.5714 Td
(a)Tj
ET
0 0 0 0 k
325.033 335.796 7.5 5.5 re
f
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 326.5171 335.943 Tm
(b)Tj
ET
333.892 338.048 m
387.964 338.048 l
S
0 g
389.145 338.56 m
388.318 338.81 387.781 339.04 387.118 339.306 c
387.118 336.784 l
387.355 336.897 388.318 337.28 389.145 337.529 c
390.03 337.797 390.832 337.98 391.353 338.045 c
390.832 338.11 390.03 338.293 389.145 338.56 c
f
322.226 338.523 m
287.256 338.523 l
S
286.075 338.011 m
286.901 337.761 287.439 337.531 288.102 337.265 c
288.102 339.787 l
287.865 339.674 286.901 339.291 286.075 339.042 c
285.19 338.774 284.388 338.591 283.868 338.526 c
284.388 338.461 285.19 338.278 286.075 338.011 c
f
324.226 373.19 m
302.138 373.19 l
S
300.956 372.677 m
301.783 372.428 302.321 372.198 302.984 371.932 c
302.984 374.454 l
302.747 374.341 301.783 373.958 300.956 373.708 c
300.072 373.441 299.27 373.258 298.749 373.193 c
299.27 373.127 300.072 372.945 300.956 372.677 c
f
327.892 351.345 m
327.892 346.345 l
S
328.404 345.164 m
328.654 345.991 328.884 346.528 329.15 347.191 c
326.628 347.191 l
326.741 346.954 327.124 345.991 327.374 345.164 c
327.641 344.279 327.824 343.477 327.889 342.957 c
327.955 343.477 328.137 344.279 328.404 345.164 c
f
334.226 373.195 m
354.889 373.195 l
S
356.07 373.708 m
355.243 373.958 354.706 374.188 354.043 374.454 c
354.043 371.932 l
354.28 372.044 355.243 372.428 356.07 372.677 c
356.954 372.944 357.757 373.127 358.277 373.193 c
357.757 373.258 356.954 373.44 356.07 373.708 c
f
327.892 360.526 m
327.892 365.526 l
S
327.379 366.707 m
327.13 365.88 326.9 365.343 326.634 364.68 c
329.156 364.68 l
329.043 364.917 328.66 365.88 328.41 366.707 c
328.143 367.592 327.96 368.394 327.895 368.914 c
327.83 368.394 327.647 367.592 327.379 366.707 c
f
Q Q Q 
q
49.61 315.28 368.5 -217.28 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.051 0.235 0.502 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
196.488 137.33 m
185.858 162.842 l
126.33 162.842 l
105.07 137.33 l
196.488 137.33 l
h
B
283.267 127.36 57.391 21.232 re
B
0.043 0.369 0.757 0.004 k
355.501 163.424 m
340.67 148.592 l
283.267 148.592 l
298.098 163.424 l
355.489 163.424 l
B
0.051 0.235 0.502 0.008 k
340.67 127.33 m
355.501 142.161 l
355.501 163.424 l
340.67 148.592 l
340.67 127.33 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 348.835 129.5957 Tm
(4 m)Tj
-6.1189 -1.2522 Td
(5 m)Tj
7.4242 4.32 Td
(3 m)Tj
ET
303.57 124.497 m
285.638 124.558 l
S
284.812 124.199 m
285.391 124.024 285.767 123.864 286.231 123.677 c
286.231 125.443 l
286.065 125.364 285.391 125.096 284.812 124.921 c
284.193 124.734 283.631 124.606 283.267 124.56 c
283.631 124.514 284.193 124.387 284.812 124.199 c
f
359.003 148.033 m
359.003 144.533 l
S
359.362 143.707 m
359.536 144.285 359.697 144.661 359.884 145.125 c
358.118 145.125 l
358.197 144.959 358.466 144.285 358.64 143.707 c
358.827 143.087 358.955 142.525 359.001 142.161 c
359.047 142.525 359.174 143.087 359.362 143.707 c
f
318.748 124.532 m
338.298 124.532 l
S
339.125 124.891 m
338.546 125.065 338.17 125.227 337.706 125.413 c
337.706 123.647 l
337.872 123.726 338.546 123.995 339.125 124.169 c
339.744 124.356 340.306 124.484 340.67 124.53 c
340.306 124.576 339.744 124.704 339.125 124.891 c
f
358.999 157.552 m
358.999 161.052 l
S
358.64 161.878 m
358.466 161.3 358.305 160.924 358.118 160.459 c
359.884 160.459 l
359.805 160.625 359.536 161.3 359.362 161.878 c
359.174 162.498 359.047 163.06 359.001 163.424 c
358.955 163.06 358.827 162.498 358.64 161.878 c
f
347.148 129.66 m
344.631 127.228 l
S
344.286 126.395 m
344.823 126.672 345.206 126.817 345.669 127.006 c
344.442 128.276 l
344.378 128.103 344.079 127.442 343.784 126.914 c
343.469 126.35 343.154 125.867 342.924 125.581 c
343.217 125.801 343.711 126.1 344.286 126.395 c
f
353.99 136.277 m
356.507 138.709 l
S
356.853 139.542 m
356.315 139.266 355.933 139.12 355.469 138.931 c
356.696 137.662 l
356.761 137.834 357.059 138.495 357.354 139.023 c
357.669 139.588 357.984 140.07 358.214 140.356 c
357.921 140.136 357.428 139.837 356.853 139.542 c
f
0.051 0.235 0.502 0.008 k
106.554 204.323 m
149.074 204.323 l
174.586 236.212 l
106.554 204.323 l
h
B
[1 2]0 d 
174.695 236.212 m
174.695 204.33 l
149.57 204.33 l
S
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 176.1891 218.5801 Tm
(6 cm)Tj
-8.0625 -3.1429 Td
(7 cm)Tj
ET
[]0 d 
169.82 204.33 4.875 4.875 re
117.03 199.32 m
109.943 199.32 l
S
0 g
108.761 198.808 m
109.588 198.558 110.126 198.328 110.789 198.061 c
110.789 200.584 l
110.551 200.471 109.588 200.087 108.761 199.838 c
107.877 199.571 107.074 199.388 106.554 199.323 c
107.074 199.257 107.877 199.075 108.761 198.808 c
f
137.519 199.333 m
146.182 199.333 l
S
147.363 199.845 m
146.536 200.095 145.999 200.325 145.336 200.591 c
145.336 198.069 l
145.573 198.182 146.536 198.565 147.363 198.814 c
148.247 199.082 149.05 199.265 149.57 199.33 c
149.05 199.395 148.247 199.578 147.363 199.845 c
f
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 263.7922 270.065 Tm
(8 cm)Tj
ET
260.07 272.805 m
240.751 272.805 l
S
0 g
239.57 272.292 m
240.397 272.042 240.934 271.812 241.597 271.546 c
241.597 274.068 l
241.36 273.956 240.397 273.572 239.57 273.323 c
238.685 273.056 237.883 272.873 237.363 272.808 c
237.883 272.742 238.685 272.56 239.57 272.292 c
f
282.07 272.818 m
298.682 272.818 l
S
299.863 273.33 m
299.036 273.58 298.499 273.81 297.836 274.076 c
297.836 271.554 l
298.073 271.667 299.036 272.05 299.863 272.299 c
300.747 272.567 301.549 272.749 302.07 272.815 c
301.549 272.88 300.747 273.063 299.863 273.33 c
f
178.698 214.718 m
178.698 207.718 l
S
179.21 206.538 m
179.46 207.364 179.69 207.901 179.956 208.564 c
177.434 208.564 l
177.547 208.327 177.93 207.364 178.179 206.538 c
178.447 205.653 178.63 204.851 178.695 204.33 c
178.76 204.851 178.943 205.653 179.21 206.538 c
f
178.692 226.824 m
178.692 232.824 l
S
178.18 234.005 m
177.93 233.179 177.7 232.641 177.434 231.978 c
179.956 231.978 l
179.843 232.215 179.46 233.179 179.211 234.005 c
178.943 234.89 178.76 235.692 178.695 236.212 c
178.63 235.692 178.447 234.89 178.18 234.005 c
f
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 307.549 294.2466 Tm
(3 cm)Tj
ET
310.058 290.385 m
310.058 283.385 l
S
0 g
310.57 282.204 m
310.82 283.031 311.049 283.568 311.316 284.232 c
308.794 284.232 l
308.906 283.994 309.29 283.031 309.539 282.204 c
309.807 281.319 309.989 280.517 310.055 279.997 c
310.12 280.517 310.303 281.319 310.57 282.204 c
f
310.052 302.491 m
310.052 308.491 l
S
309.54 309.672 m
309.29 308.845 309.06 308.308 308.794 307.645 c
311.316 307.645 l
311.203 307.882 310.82 308.845 310.57 309.672 c
310.303 310.557 310.12 311.359 310.055 311.879 c
309.989 311.359 309.807 310.557 309.54 309.672 c
f
0.051 0.235 0.502 0.008 k
354.58 200.695 m
375.84 243.215 l
290.801 243.215 l
269.541 200.695 l
354.58 200.695 l
h
B
331.445 221.58 13.875 7.5 re
f
0 0 0 0 k
383.723 214.677 m
384.848 225.177 l
370.973 225.177 l
366.098 214.677 l
383.723 214.677 l
f
306.695 190.83 18.375 7.5 re
f
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 332.195 222.3301 Tm
(5 m)Tj
-3.5893 -4.2321 Td
(12 m)Tj
8.9504 3.7639 Td
(7 m)Tj
ET
282.999 221.525 m
281.544 224.982 l
278.087 223.526 l
366.695 219.33 m
365.239 222.786 l
361.783 221.331 l
301.445 197.955 m
304.096 200.606 l
301.445 203.258 l
303.32 197.955 m
305.971 200.606 l
303.32 203.258 l
327.695 240.33 m
330.346 242.982 l
327.695 245.633 l
329.57 240.33 m
332.221 242.982 l
329.57 245.633 l
305.016 194.692 m
272.929 194.692 l
S
0 g
271.748 194.18 m
272.574 193.93 273.112 193.7 273.775 193.434 c
273.775 195.956 l
273.538 195.844 272.574 195.46 271.748 195.21 c
270.863 194.943 270.061 194.76 269.541 194.695 c
270.061 194.63 270.863 194.447 271.748 194.18 c
f
338.07 218.083 m
338.07 204.083 l
S
338.582 202.902 m
338.832 203.729 339.062 204.267 339.328 204.93 c
336.806 204.93 l
336.919 204.692 337.302 203.729 337.552 202.902 c
337.819 202.018 338.002 201.215 338.067 200.695 c
338.133 201.215 338.315 202.018 338.582 202.902 c
f
327.529 194.698 m
351.192 194.698 l
S
352.373 195.21 m
351.546 195.46 351.009 195.69 350.345 195.956 c
350.345 193.434 l
350.583 193.547 351.546 193.93 352.373 194.18 c
353.258 194.447 354.059 194.63 354.58 194.695 c
354.059 194.76 353.258 194.943 352.373 195.21 c
f
338.07 229.955 m
338.07 239.955 l
S
337.557 241.136 m
337.308 240.31 337.078 239.772 336.812 239.109 c
339.334 239.109 l
339.221 239.346 338.838 240.31 338.588 241.136 c
338.321 242.021 338.138 242.823 338.073 243.343 c
338.008 242.823 337.825 242.021 337.557 241.136 c
f
366.869 215.277 m
360.637 202.741 l
S
360.57 201.455 m
361.161 202.084 361.607 202.463 362.14 202.938 c
359.882 204.061 l
359.877 203.798 359.792 202.765 359.647 201.914 c
359.493 201.003 359.299 200.203 359.126 199.708 c
359.416 200.145 359.937 200.782 360.57 201.455 c
f
373.877 229.728 m
378.329 238.682 l
S
378.396 239.968 m
377.804 239.338 377.359 238.96 376.825 238.484 c
379.084 237.362 l
379.089 237.624 379.174 238.658 379.319 239.509 c
379.473 240.42 379.667 241.22 379.84 241.715 c
379.549 241.278 379.029 240.641 378.396 239.968 c
f
BT
/T1_3 1 Tf
9 0 0 9 83.4035 297.3716 Tm
[(Find)-704(a   the perimeter; and)]TJ
2.6667 -1.3333 Td
(b   the area of this shape.)Tj
-2.6667 -3.7268 Td
[(Find the area.)-12629(Find the area.)]TJ
0.0185 -8.8333 Td
[(Find the area.)-12611(Find the volume.)]TJ
-1.731 13.8935 Td
(1)Tj
18.2305 Tc 0 -5.0602 TD
(23)Tj
0 -8.8333 TD
(45)Tj
ET
0.051 0.235 0.502 0.008 k
237.404 279.997 66 32 re
B
148.757 146.086 16.5 9 re
f
0 0 0 1 k
BT
/T1_3 1 Tf
0 Tc 7 0 0 7 149.882 148.336 Tm
(8 cm)Tj
-0.0536 2.5714 Td
(12 cm)Tj
-0.8571 -5.4643 Td
(20 cm)Tj
ET
144.404 160.211 m
147.055 162.863 l
144.404 165.514 l
146.279 160.211 m
148.93 162.863 l
146.279 165.514 l
136.904 134.336 m
139.555 136.988 l
136.904 139.639 l
138.779 134.336 m
141.43 136.988 l
138.779 139.639 l
157.641 146.059 m
157.641 140.059 l
S
0 g
158.154 138.878 m
158.404 139.704 158.634 140.242 158.9 140.905 c
156.377 140.905 l
156.49 140.667 156.874 139.704 157.123 138.878 c
157.39 137.993 157.573 137.19 157.638 136.67 c
157.704 137.19 157.886 137.993 158.154 138.878 c
f
157.641 153.24 m
157.641 159.24 l
S
157.129 160.421 m
156.879 159.594 156.649 159.057 156.383 158.394 c
158.905 158.394 l
158.793 158.631 158.409 159.594 158.159 160.421 c
157.892 161.305 157.709 162.107 157.644 162.628 c
157.579 162.107 157.396 161.305 157.129 160.421 c
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS4 cs 1  scn
114.87 503.26 232.75 -46.5 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 9 0 0 9 121.1184 490.2092 Tm
(Remember:)Tj
/T1_3 1 Tf
0.0277 Tw 5.7119 0 Td
[(Perimeter is the distance ar)18(ound a shape.)]TJ
-0.0002 Tc -5.7119 -1.3333 Td
[(Ar)18(ea is measur)18(ed in units)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 222.4305 481.8091 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 225.9327 478.2092 Tm
(, eg mm)Tj
0 Tc 0 Tw 6.3 0 0 6.3 259.7675 481.8091 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 263.2697 478.2092 Tm
(, cm)Tj
0 Tc 0 Tw 6.3 0 0 6.3 280.5244 481.8091 Tm
(2)Tj
-0.0002 Tc 0.0277 Tw 9 0 0 9 284.0266 478.2092 Tm
(, m)Tj
0 Tc 0 Tw 6.3 0 0 6.3 296.9439 481.8091 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 9 0 0 9 121.1184 466.2092 Tm
[(V)55(olume is measur)18(ed in units)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 233.9309 469.8091 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 237.4332 466.2092 Tm
(, eg mm)Tj
0 Tc 0 Tw 6.3 0 0 6.3 271.268 469.8091 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 274.7702 466.2092 Tm
(, cm)Tj
0 Tc 0 Tw 6.3 0 0 6.3 292.0249 469.8091 Tm
(3)Tj
-0.0003 Tc 0.0278 Tw 9 0 0 9 295.5271 466.2092 Tm
(, m)Tj
0 Tc 0 Tw 6.3 0 0 6.3 308.4444 469.8091 Tm
(3)Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
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(\(a+b\) x perpendicular height.)Tj
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(Answers)Tj
0 0 0 1 k
/T1_4 1 Tf
-0.0002 Tc 0.0278 Tw 7 0 0 7 67.6142 261.111 Tm
[(1)-1064(a   Split the shape into thr)18(ee parts.)]TJ
7.9308 -1.7143 Td
[(Ar)18(ea = 32 m)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 162.4745 251.9108 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 78.9527 237.1109 Tm
(b   8 m + 5 m + 3 m + 2 m )Tj
1.5281 -1.7143 Td
(+ 4 m + 2 m + 1 m + 5 m = 30 m)Tj
-0.0001 Tc -3.1479 -10.2857 Td
[(2)-1064(Find the ar)18(ea of the lar)18(ge r)18(ectangle = 10 x 16 )-3513(= 160 m)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 275.6071 155.9108 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 78.9527 141.1109 Tm
[(Find the ar)18(ea of the small r)18(ectangle = 6 x 12 )-4032(=   72 m)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 275.9944 143.9108 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 78.9527 129.1109 Tm
[(T)111(ake away )-19425(=   88 m)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 275.9944 131.9108 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 67.6142 105.1109 Tm
[(3)-1064(Be car)18(eful with this. Note the units. Either change everything to metr)18(es or everything to centimetr)18(es.)]TJ
1.6198 -1.7143 Td
(Answer 168 000 cm)Tj
0 Tc 0 Tw 4.9 0 0 4.9 140.9947 95.9108 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 145.858 93.1109 Tm
(or 0)Tj
/T1_5 1 Tf
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(\341)Tj
/T1_4 1 Tf
-0.0002 Tc 0.2778 0 Td
(168m)Tj
0 Tc 4.9 0 0 4.9 177.9421 95.9108 Tm
(3)Tj
ET
Q Q 
q
191.06 559.35 172.55 -113.04 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.063 0.231 0.502 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS6 gs
196.472 459.11 m
196.472 545.459 l
334.63 545.459 l
334.63 459.11 l
282.82 459.11 l
282.82 493.649 l
213.742 493.649 l
213.742 459.11 l
196.472 459.11 l
h
B
0 g
BT
/T1_4 1 Tf
7 0 0 7 198.0625 449.7766 Tm
(1 m)Tj
9.7144 3.4286 Td
(2 m)Tj
5.238 -3.3333 Td
(3 m)Tj
5.1429 6.8571 Td
(5 m)Tj
-11.6191 7.3333 Td
(8 m)Tj
ET
Q Q Q 
q
223.24 267.08 145.51 -93.44 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.063 0.231 0.502 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS7 gs
236.027 185.156 m
236.027 254.236 l
346.553 254.236 l
346.553 185.156 l
305.106 185.156 l
305.106 212.788 l
249.843 212.788 l
249.843 185.156 l
236.027 185.156 l
h
B
0 g
BT
/T1_4 1 Tf
0 7 -7 0 245.1225 192.9497 Tm
(1 m x 5 m = 5 m)Tj
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(2)Tj
7 0 0 7 262.296 235.3921 Tm
(4 m x 3 m)Tj
0.4134 -1.2857 Td
(= 12 m)Tj
5 0 0 5 287.4924 229.3921 Tm
(2)Tj
7 0 0 7 310.256 225.7123 Tm
(5 m x 3 m)Tj
0.4134 -1.2857 Td
(= 15 m)Tj
5 0 0 5 335.4524 219.7123 Tm
(2)Tj
ET
[2 3]0 d 
249.843 212.788 m
249.843 254.212 l
305.162 212.788 m
305.162 254.212 l
S
BT
/T1_4 1 Tf
7 0 0 7 236.119 177.6899 Tm
(1 m)Tj
7.7429 2.2857 Td
(2 m)Tj
-5.362 -0.0381 Td
(2 m)Tj
2.7239 1.5714 Td
(4 m)Tj
6.8571 -3.7429 Td
(3 m)Tj
4.1143 5.4856 Td
(5 m)Tj
-18.2001 0 Td
(5 m)Tj
8.9049 5.8668 Td
(8 m)Tj
ET
Q Q Q 
q
226.16 415.55 116.43 -75.19 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.122 0.082 0.063 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS8 gs
234.749 356.107 87.081 54.425 re
B
0.255 0.051 0.502 0.004 k
245.634 366.992 65.311 32.654 re
B
0 g
BT
/T1_4 1 Tf
7 0 0 7 270.2497 381.1739 Tm
(Lawn)Tj
0.158 2.9841 Td
(Path)Tj
-0.1305 -7.8114 Td
(16 m)Tj
7.5619 4.7542 Td
(10 m)Tj
ET
289.719 349.431 m
321.83 349.431 l
S
320.203 349.824 m
319.568 350.016 319.156 350.193 318.647 350.397 c
318.647 348.46 l
318.829 348.546 319.568 348.841 320.203 349.032 c
320.883 349.237 321.5 349.378 321.898 349.428 c
321.5 349.479 320.883 349.618 320.203 349.824 c
f
329.069 378.103 m
329.069 356.215 l
S
329.463 357.842 m
329.654 358.477 329.831 358.889 330.035 359.398 c
328.099 359.398 l
328.185 359.216 328.48 358.477 328.672 357.842 c
328.877 357.162 329.018 356.546 329.066 356.147 c
329.117 356.546 329.258 357.162 329.463 357.842 c
f
328.813 388.582 m
328.813 410.469 l
S
328.42 408.843 m
328.227 408.209 328.052 407.796 327.848 407.287 c
329.784 407.287 l
329.697 407.469 329.402 408.209 329.211 408.843 c
329.006 409.523 328.865 410.139 328.815 410.539 c
328.766 410.139 328.625 409.523 328.42 408.843 c
f
266.871 350.486 m
234.76 350.486 l
S
236.386 350.093 m
237.021 349.901 237.434 349.725 237.942 349.52 c
237.942 351.457 l
237.761 351.371 237.021 351.076 236.386 350.885 c
235.706 350.679 235.09 350.539 234.69 350.488 c
235.09 350.439 235.706 350.298 236.386 350.093 c
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS4 cs 1  scn
297.33 160.32 120.53 -37.87 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 7 0 0 7 303.5791 148.7785 Tm
(Note:)Tj
/T1_4 1 Tf
0.0277 Tw 2.9424 0 Td
(It is 6 x 12)Tj
-0.0002 Tc -2.9424 -1.2857 Td
[(A common err)18(or is 8 x 14.)]TJ
0 -1.2857 TD
(Remember 2 m wide at both ends )Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
297.33 160.32 120.53 -37.87 re
282.73 144.09 m
296.22 144.09 l
S
Q Q 
q
232.44 338.81 96.38 -59.04 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.063 0.231 0.502 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS9 gs
257.157 292.053 43.541 29.027 re
B
315.162 306.517 m
315.162 335.545 l
S
0.051 0.365 0.761 0.004 k
315.174 335.545 m
300.71 321.08 l
257.157 321.08 l
271.621 335.545 l
315.174 335.545 l
h
B
0.063 0.231 0.502 0.008 k
315.174 306.488 m
300.71 292.024 l
300.71 321.08 l
315.174 335.545 l
315.174 306.488 l
h
B
0 g
BT
/T1_4 1 Tf
7 0 0 7 237.0086 303.2835 Tm
(4 cm)Tj
5.0476 -2.9524 Td
(6 cm)Tj
5.5238 1.2381 Td
(3 cm)Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
256 137.5 m
278.5 137.5 l
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/GS0 gs
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0 660 l
f
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W n
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0 660.06 467.04 -660 re
W n
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0 0 0 1 k
BT
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(55)Tj
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(Easingwold School                               )Tj
ET
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[(Perimeter)92(, ar)18(ea and volume)]TJ
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[(Y)92(ou need to r)18(ecognise for)-18(mulae. Which ones ar)18(e 1-D \(length\), 2-D \(ar)18(ea\) and 3-D \(volume\)?)]TJ
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(Length has 1 dimension)Tj
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[(V)55(olume has 3 dimensions)]TJ
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[(Length x length = ar)18(ea)]TJ
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(Length x length x length = volume)Tj
T*
[(Length x ar)18(ea = volume)]TJ
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(Length + length = length)Tj
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(For example:)Tj
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(r is a length)Tj
0 Tc 0 Tw -20.0654 -1.3333 Td
(r)Tj
6.3 0 0 6.3 99.6632 310.821 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 105.9159 307.2211 Tm
[(is an ar)18(ea)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 17.9341 0 Td
(\007)Tj
/T1_3 1 Tf
0.5488 0 Td
(r)Tj
6.3 0 0 6.3 275.2484 310.821 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 281.5011 307.2211 Tm
[(is an ar)18(ea)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 51.3228 254.2131 Tm
(Questions )Tj
0 0 0 1 k
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 239.3785 Tm
[(a, b, c and d ar)18(e lengths.)]TJ
0 -1.9633 TD
[(State whether each for)-18(mula gives a length, ar)18(ea, volume or none of these.)]TJ
0 Tw T*
[(1)-1334(3ab)-14693(2)]TJ
1.3338 Tc T*
[(3a)1334(b)]TJ
0 Tc 6.3 0 0 6.3 95.5053 189.9707 Tm
(2)Tj
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(+ 3cd)Tj
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(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 232.7401 186.3707 Tm
[(4)-1334(ab + d)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 51.3228 165.8667 Tm
(Answers)Tj
0 0 0 1 k
/T1_3 1 Tf
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(bcd)Tj
-0.0003 Tc 0.3144 -1.315 Td
(3a)Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
251.74 207.2 m
264.82 207.2 l
S
Q Q 
q
302.642 466.857 m
302.642 447.064 l
302.649 433.94 l
302.649 431.774 306.38 430.018 310.983 430.018 c
315.586 430.018 319.318 431.774 319.318 433.94 c
319.292 445.564 l
319.292 466.857 l
W n
q
16.6758 0 0 -40.8384 302.642 468.8566 cm
0.5069 0.0416 m
0 0.0416 l
0 0.9011 l
0.5069 0.9011 l
0.5069 0.0416 l
h
W n
/GS1 gs q
0.5056 0 0 -0.8595 0 0.9085 cm
/Im0 Do
Q
Q 
q
16.6758 0 0 -40.8384 302.642 468.8566 cm
0.5069 0.8938 m
0 0.8938 l
0 0.9452 l
0.5069 0.9452 l
0.5069 0.8938 l
h
W n
/GS1 gs q
0.5056 0 0 -0.0499 0 0.951 cm
/Im1 Do
Q
Q 
q
16.6758 0 0 -40.8384 302.642 468.8566 cm
1.0052 0.0416 m
0.5056 0.0416 l
0.5056 0.9158 l
1.0052 0.9158 l
1.0052 0.0416 l
h
W n
/GS1 gs q
0.4944 0 0 -0.8742 0.5056 0.9232 cm
/Im2 Do
Q
Q 
q
16.6758 0 0 -40.8384 302.642 468.8566 cm
1.0052 0.9085 m
0.5056 0.9085 l
0.5056 0.9452 l
1.0052 0.9452 l
1.0052 0.9085 l
h
W n
/GS1 gs q
0.4944 0 0 -0.0352 0.5056 0.951 cm
/Im3 Do
Q
Q Q 
q
294.1 477.97 34.57 -55.49 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
302.642 466.857 m
302.642 447.064 l
302.649 433.94 l
302.649 431.774 306.38 430.018 310.983 430.018 c
315.586 430.018 319.318 431.774 319.318 433.94 c
319.292 445.564 l
319.292 466.857 l
S
0.051 0.365 0.761 0.004 k
310.983 462.935 m
315.586 462.935 319.318 464.69 319.318 466.857 c
319.318 469.023 315.586 470.779 310.983 470.779 c
306.38 470.779 302.649 469.023 302.649 466.857 c
302.649 464.69 306.38 462.935 310.983 462.935 c
h
B
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS4 cs 1  scn
232.86 471.91 m
250.16 497.85 l
293.36 497.85 l
274.78 471.75 l
232.86 471.91 l
f*
Q Q 
q
232.39 471.66 m
250.03 498.1 l
293.84 498.1 l
274.91 471.5 l
232.39 471.66 l
W* n
0 0 0 1 K
1 w 10 M 0 j 0 J []0 d 
232.39 471.66 m
250.03 498.1 l
293.84 498.1 l
274.91 471.5 l
232.39 471.66 l
h
S
Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
271.43 528.19 m
319.58 528.19 l
S
/CS5 cs 1  scn
95.93 296.52 229.1 -22.49 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 9 0 0 9 102.1772 283.4692 Tm
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
[(Perimeter)92(, radius and diameter ar)18(e all lengths)]TJ
ET
95.93 296.52 229.1 -22.49 re
S
Q Q 
q
50.32 164.83 368.51 -96.75 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS6 gs
BT
/T1_3 1 Tf
7 0 0 7 83.07 155.0901 Tm
[(length x length = ar)18(ea)]TJ
-0.02 Tc 8.0843 -5.4286 Td
(ab)Tj
0 Tc 5 0 0 5 147.2902 120.0901 Tm
(2)Tj
-0.02 Tc 7 0 0 7 75.2758 107.0901 Tm
(length x length x length  )Tj
6.9899 -1.4286 Td
(volume  )Tj
0 Tc 26.2078 2.8571 Td
(ab)Tj
-5.6099 -1.4286 Td
(length x length)Tj
4.2758 -1.4286 Td
[(ar)18(ea  )]TJ
3.107 2.8571 Td
(+  d)Tj
0 -1.4286 TD
(+  length)Tj
T*
(+  length)Tj
-7.6377 8.2857 Td
(bcd)Tj
0.3145 -1.4286 Td
(3a)Tj
3.2231 1.4286 Td
(length x length x length)Tj
3.889 -1.4286 Td
(length)Tj
9.1431 1.4286 Td
(volume)Tj
0.214 -1.4286 Td
(length)Tj
-16.7394 -9 Td
[(ar)18(ea cannot be added to length)]TJ
0.0221 -1.3571 Td
(Answer    none of these)Tj
0.2857 8.8571 Td
[(Answer    ar)18(ea)]TJ
-26.5 1.3571 Td
[(Answer   ar)18(ea)]TJ
0 -8.8571 TD
(Answer   volume)Tj
25.6695 Tc -2.2892 10.4286 Td
(12)Tj
0 -5.4286 TD
(34)Tj
12.1911 Tc 30.6705 4.6429 Td
(==)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
266.57 152.59 m
278.07 152.59 l
291.07 152.59 m
365.57 152.59 l
382.07 152.59 m
406.07 152.59 l
S
BT
/T1_3 1 Tf
-0.02 Tc 7 0 0 7 154.07 117.0901 Tm
(+  3cd)Tj
0 Tc 5 0 0 5 173.3273 120.0901 Tm
(2)Tj
-0.02 Tc 7 0 0 7 154.07 107.0901 Tm
(+  length x length x length)Tj
0 -1.4286 TD
(+  volume)Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_3 1 Tf
-0.0002 Tc 9 0 0 9 332.8057 524.83 Tm
(1-D)Tj
0 -8.5564 TD
(3-D)Tj
-3.7701 3.8556 Td
(2-D)Tj
ET
Q Q 
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stream
1 g
1 i 
/RelativeColorimetric ri
/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
49.61 42.05 368.5 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 50.6063 35.0006 Tm
(56)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 265.7926 35.5258 Tm
(Easingwold School                               )Tj
/CS2 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 50.6063 222.7955 Tm
(Questions)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 67.6142 210.7955 Tm
[(1)-1334(Cube A has a side of 3 cm. Cube B has a side of 5 cm.)]TJ
-0.0001 Tc 1.8898 -1.6483 Td
[(a)-1371(What is the ratio of their lengths?)]TJ
-0.0002 Tc 0 -1.6483 TD
[(b)-1279(What is the ratio of their ar)18(eas?)]TJ
T*
[(c)-1408(What is the ratio of their volumes?)]TJ
-1.8898 -1.6483 Td
[(2)-1332(A map is drawn to a scale of 2 cm r)18(epr)18(esents 5 km. A for)18(est has an ar)18(ea of )]TJ
-0.0001 Tc 1.888 -1.3333 Td
(60 km)Tj
0 Tc 0 Tw 6.3 0 0 6.3 109.3668 143.0568 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 112.8691 139.4568 Tm
[(. What is the ar)18(ea of the for)18(est on the map?)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 50.6063 118.9529 Tm
(Answers)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 7 0 0 7 67.6142 106.9529 Tm
[(1)-1064(a)-1101(3 : 5)-8528(b)-1009(3)]TJ
-0.0003 Tc 0 Tw 4.9 0 0 4.9 179.222 109.7529 Tm
(2 )Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 183.4435 106.9529 Tm
(: 5)Tj
0 Tc 0 Tw 4.9 0 0 4.9 191.419 109.7529 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 212.0657 106.9529 Tm
[(9 : 25)-2724(c)-1138(3)]TJ
-0.0003 Tc 0 Tw 4.9 0 0 4.9 264.2613 109.7529 Tm
(3 )Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 268.4828 106.9529 Tm
(: 5)Tj
0 Tc 0 Tw 4.9 0 0 4.9 276.4583 109.7529 Tm
(3)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 297.105 106.9529 Tm
(27 : 125)Tj
-32.7844 -1.7143 Td
[(2)-1064(Length ratio 2 cm : 5 km)]TJ
-0.0002 Tc 1.6198 -1.7143 Td
[(Ar)18(ea ratio \(2 cm\))]TJ
-0.0003 Tc 0 Tw 4.9 0 0 4.9 130.8621 85.7529 Tm
(2 )Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 135.0836 82.9529 Tm
(: \(5 km\))Tj
0 Tc 0 Tw 4.9 0 0 4.9 158.1713 85.7529 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 202.0155 82.9529 Tm
(4 cm)Tj
0 Tc 0 Tw 4.9 0 0 4.9 217.3824 85.7529 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 222.6063 82.9529 Tm
(: 25 km)Tj
0 Tc 0 Tw 4.9 0 0 4.9 245.9486 85.7529 Tm
(2)Tj
-0.0002 Tc 7 0 0 7 78.9527 70.9529 Tm
[(Ther)18(efor)18(e)-11877(0)]TJ
/T1_3 1 Tf
0 Tc 16.7466 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0277 Tw 0.2778 0 Td
(16 cm)Tj
0 Tc 0 Tw 4.9 0 0 4.9 217.3824 73.7528 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 222.6063 70.9529 Tm
(: 1 km)Tj
0 Tc 0 Tw 4.9 0 0 4.9 242.0573 73.7528 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 196.1793 58.9529 Tm
(9.6 cm)Tj
0 Tc 0 Tw 4.9 0 0 4.9 217.3824 61.7528 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 222.6063 58.9529 Tm
(: 60 km)Tj
0 Tc 0 Tw 4.9 0 0 4.9 245.9486 61.7528 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 257.2298 58.9529 Tm
(Answer 9.6 cm)Tj
0 Tc 0 Tw 4.9 0 0 4.9 303.5119 61.7528 Tm
(2)Tj
ET
Q Q 
q
168.31 87.58 32.33 -4.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.4 w 4 M 0 j 0 J []0 d 
/GS7 gs
174.48 85.27 m
191.28 85.27 l
S
0 g
192.225 85.68 m
191.564 85.88 191.134 86.064 190.603 86.277 c
190.603 84.259 l
190.793 84.349 191.564 84.656 192.225 84.856 c
192.933 85.069 193.574 85.215 193.991 85.268 c
193.574 85.32 192.933 85.466 192.225 85.68 c
f
Q Q Q 
q
282.32 111.58 13.79 -4.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.4 w 4 M 0 j 0 J []0 d 
/GS8 gs
273.7 108.77 m
290.5 108.77 l
S
0 g
291.445 109.18 m
290.784 109.38 290.354 109.564 289.823 109.777 c
289.823 107.759 l
290.013 107.849 290.784 108.156 291.445 108.356 c
292.153 108.569 292.794 108.715 293.211 108.768 c
292.794 108.82 292.153 108.966 291.445 109.18 c
f
Q Q Q 
q
197.28 111.58 13.79 -4.63 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.4 w 4 M 0 j 0 J []0 d 
/GS9 gs
188.66 108.77 m
205.46 108.77 l
S
0 g
206.405 109.18 m
205.744 109.38 205.314 109.564 204.783 109.777 c
204.783 107.759 l
204.973 107.849 205.744 108.156 206.405 108.356 c
207.113 108.569 207.754 108.715 208.171 108.768 c
207.754 108.82 207.113 108.966 206.405 109.18 c
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
49.61 593.39 368.5 -22.68 re
f*
/CS3 cs 1  scn
BT
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 14 0 0 14 122.7999 581.8038 Tm
[(Ratio for length, ar)18(ea and volume)]TJ
0 0 0 1 k
/T1_4 1 Tf
0.0277 Tw 10 0 0 10 50.6063 604.6698 Tm
[(Perimeter)92(, ar)18(ea and volume)]TJ
ET
Q Q 
q
49.61 565.04 368.5 -327.4 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS10 gs
BT
/T1_2 1 Tf
9 0 0 9 84.3737 306.54 Tm
(Length ratio is)Tj
0 -1.3333 TD
[(Ar)18(ea ratio is)]TJ
0 -1.7778 TD
(\(divide by 16 to find 1 cm)Tj
6 0 0 6 186.8885 282.54 Tm
(3)Tj
9 0 0 9 190.2247 278.54 Tm
(\))Tj
-3.2724 3.1111 Td
(4 cm : 10 km)Tj
-0.8443 -1.3333 Td
(\(4 cm\))Tj
6 0 0 6 177.3654 298.54 Tm
(2 )Tj
9 0 0 9 182.3697 294.54 Tm
(: \(10 km\))Tj
6 0 0 6 216.5683 298.54 Tm
(2)Tj
ET
0.031 0.243 0.502 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
84.374 433.94 m
84.374 447.111 l
73.584 451.315 l
73.584 438.144 l
84.374 433.94 l
h
B
96.148 438.144 m
96.148 451.315 l
84.374 447.111 l
84.374 433.94 l
96.148 438.144 l
h
B
0.028 0.373 0.753 0.004 k
96.148 451.315 m
85.359 455.52 l
73.584 451.315 l
84.374 447.111 l
96.148 451.315 l
h
B
0.031 0.243 0.502 0.004 k
137.789 430.04 m
137.789 448.856 l
122.375 454.862 l
122.375 436.046 l
137.789 430.04 l
h
B
154.61 436.046 m
154.61 454.862 l
137.789 448.856 l
137.789 430.04 l
154.61 436.046 l
h
B
0.028 0.373 0.753 0.004 k
154.61 454.862 m
139.196 460.868 l
122.375 454.862 l
137.789 448.856 l
154.61 454.862 l
h
B
0.031 0.243 0.502 0.004 k
147.777 519.853 33 33 re
B
217.11 519.54 33 33 re
B
0.039 0.02 0.486 0 k
275.173 494.04 142.938 58.938 re
B
67.366 374.04 349.25 31.5 re
B
84.374 241.54 274.25 19 re
B
0 g
BT
/T1_2 1 Tf
7.1473 Tc 9 0 0 9 161.61 540.8735 Tm
(AB)Tj
0 Tc 7 0 0 7 134.61 535.3735 Tm
(1 m)Tj
3.3571 2.7143 Td
(1 m)Tj
5 -3.0714 Td
(100 cm)Tj
4.4286 3.1429 Td
(100 cm)Tj
/T1_0 1 Tf
6 0 0 6 157.4976 531.8735 Tm
[(Ar)18(ea)]TJ
/T1_2 1 Tf
0.0737 -1.3333 Td
(1 m)Tj
4 0 0 4 168.0566 526.8735 Tm
(2)Tj
/T1_0 1 Tf
6 0 0 6 226.9976 531.8735 Tm
[(Ar)18(ea)]TJ
/T1_2 1 Tf
-1.4183 -1.3333 Td
(10 000 cm)Tj
4 0 0 4 246.5097 526.8735 Tm
(2)Tj
9 0 0 9 67.3659 506.04 Tm
[(The two squar)18(es ar)18(e identical.)]TJ
0 -1.3333 TD
[(The ar)18(ea of A is 1 m)]TJ
6 0 0 6 147.5617 498.04 Tm
(2)Tj
9 0 0 9 150.8979 494.04 Tm
[(. The ar)18(ea of B is 10 000 cm)]TJ
6 0 0 6 262.4483 498.04 Tm
(2)Tj
9 0 0 9 265.7845 494.04 Tm
(. )Tj
/T1_0 1 Tf
1.8695 4.9444 Td
(Note:)Tj
/T1_2 1 Tf
2.6649 0 Td
[( Common err)18(or)92(, 1 m)]TJ
6 0 0 6 387.4377 542.54 Tm
(2)Tj
9 0 0 9 390.7739 538.54 Tm
( )Tj
-12.0182 -1.3333 Td
(does not equal 100 cm)Tj
6 0 0 6 374.9733 530.54 Tm
(2)Tj
9 0 0 9 378.3095 526.54 Tm
(. )Tj
-10.6333 -1.3333 Td
[(Be very car)18(eful when converting )]TJ
T*
[(units of ar)18(ea and volume.)]TJ
0.918 0.722 0.09 0.012 k
/T1_0 1 Tf
10 0 0 10 50.358 555.04 Tm
(Look at this)Tj
0 -20.05 TD
(Example)Tj
0 g
4.0188 0 Td
( )Tj
9 0 0 9 67.3659 475.54 Tm
(Let us see why this happens)Tj
/T1_2 1 Tf
14.0271 -2.8889 Td
(Ratio of sides \(length\))Tj
0 -1.3333 TD
[(Ratio of ar)18(eas)]TJ
T*
(Ratio of volumes)Tj
11.7677 2.6667 Td
(x : y)Tj
-0.3243 -1.3333 Td
(x)Tj
6 0 0 6 300.9378 441.54 Tm
(2 )Tj
9 0 0 9 305.9421 437.54 Tm
(: y)Tj
6 0 0 6 315.2838 441.54 Tm
(2)Tj
9 0 0 9 296.6 425.54 Tm
(x)Tj
6 0 0 6 300.9378 429.54 Tm
(3 )Tj
9 0 0 9 305.9421 425.54 Tm
(: y)Tj
6 0 0 6 315.2838 429.54 Tm
(3)Tj
9 0 0 9 349.353 449.54 Tm
(2 : 3)Tj
-0.3243 -1.3333 Td
(2)Tj
6 0 0 6 351.4378 441.54 Tm
(2 )Tj
9 0 0 9 356.4421 437.54 Tm
(: 3)Tj
6 0 0 6 366.4497 441.54 Tm
(2)Tj
9 0 0 9 346.434 425.54 Tm
(2)Tj
6 0 0 6 351.4378 429.54 Tm
(3 )Tj
9 0 0 9 356.4421 425.54 Tm
(: 3)Tj
6 0 0 6 366.4497 429.54 Tm
(3)Tj
9 0 0 9 333.11 449.54 Tm
(ie)Tj
T*
(ie)Tj
T*
(ie)Tj
6.5555 1.3333 Td
(4 : 9)Tj
T*
(8 : 27)Tj
ET
374.429 440.526 m
383.929 440.526 l
S
385.11 441.039 m
384.283 441.288 383.746 441.519 383.083 441.785 c
383.083 439.263 l
383.32 439.375 384.283 439.759 385.11 440.008 c
385.995 440.276 386.797 440.459 387.318 440.524 c
386.797 440.589 385.995 440.772 385.11 441.039 c
f
374.429 428.527 m
383.929 428.527 l
S
385.11 429.04 m
384.283 429.29 383.746 429.52 383.083 429.786 c
383.083 427.264 l
383.32 427.376 384.283 427.76 385.11 428.009 c
385.995 428.277 386.797 428.459 387.318 428.525 c
386.797 428.59 385.995 428.773 385.11 429.04 c
f
227.86 297.027 m
237.36 297.027 l
S
238.54 297.54 m
237.714 297.79 237.176 298.02 236.513 298.286 c
236.513 295.764 l
236.751 295.876 237.714 296.26 238.54 296.509 c
239.425 296.777 240.227 296.959 240.748 297.025 c
240.227 297.09 239.425 297.273 238.54 297.54 c
f
BT
/T1_2 1 Tf
9 0 0 9 144.6891 440.54 Tm
(y)Tj
-6.231 -0.0556 Td
(x)Tj
-2.4444 -2.2222 Td
[(side 2 cm)-1666(side 3 cm)]TJ
/T1_0 1 Tf
0.6111 -2.9444 Td
(Note:)Tj
/T1_2 1 Tf
8 0 0 8 99.11 393.54 Tm
[(If you ar)18(e given the ar)18(ea ratio you can find the length ratio by taking the squar)18(e r)18(oot.)]TJ
0 -1.5 TD
[(If you ar)18(e given the volume ratio you can find the length ratio by taking the cub\
e r)18(oot.)]TJ
9 0 0 9 84.3737 339.54 Tm
[(A map is drawn to a scale of 4 cm r)18(epr)18(esents 10 km. )]TJ
0 -1.3333 TD
[(The ar)18(ea of a lake on the map is 20 cm)]TJ
6 0 0 6 239.7614 331.54 Tm
(2)Tj
9 0 0 9 243.0976 327.54 Tm
[(. What is the ar)18(ea of the r)18(eal lake?)]TJ
0.5656 -3.7222 Td
(16 cm)Tj
6 0 0 6 272.7033 298.04 Tm
(2)Tj
9 0 0 9 253.1923 282.04 Tm
(1 cm)Tj
6 0 0 6 272.7036 286.04 Tm
(2)Tj
9 0 0 9 248.1883 270.04 Tm
(20 cm)Tj
6 0 0 6 272.7033 274.04 Tm
(2)Tj
9 0 0 9 280.0402 294.04 Tm
(: 100 km)Tj
6 0 0 6 314.5628 298.04 Tm
(2)Tj
9 0 0 9 280.0402 282.04 Tm
(: 6.25 km)Tj
6 0 0 6 317.0647 286.04 Tm
(2)Tj
9 0 0 9 280.0402 270.04 Tm
(: 125 km)Tj
6 0 0 6 314.5628 274.04 Tm
[(2      )-1522( )]TJ
9 0 0 9 338.7083 270.04 Tm
(Answer  125 km)Tj
6 0 0 6 402.7318 274.04 Tm
(2)Tj
/T1_0 1 Tf
9 0 0 9 91.6178 247.54 Tm
(or)Tj
/T1_2 1 Tf
0.999 0 Td
( you could use the scale factor method ie 20 x \()Tj
6 0 0 6 290.3207 251.54 Tm
(10)Tj
9 0 0 9 296.9932 247.54 Tm
(/)Tj
6 0 0 6 300.323 247.54 Tm
(4)Tj
9 0 0 9 303.6592 247.54 Tm
(\))Tj
6 0 0 6 305.9991 251.54 Tm
(2)Tj
9 0 0 9 309.3353 247.54 Tm
( = 125 km)Tj
6 0 0 6 349.8517 251.54 Tm
(2)Tj
ET
Q Q Q 
q
283.78 211.75 119.13 -44.42 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.031 0.243 0.502 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS11 gs
319.443 175.203 m
319.443 190.883 l
306.598 195.888 l
306.598 180.208 l
319.443 175.203 l
h
B
333.46 180.208 m
333.46 195.888 l
319.443 190.883 l
319.443 175.203 l
333.46 180.208 l
h
B
0.028 0.373 0.753 0.004 k
333.46 195.888 m
320.615 200.893 l
306.598 195.888 l
319.443 190.883 l
333.46 195.888 l
h
B
0.031 0.243 0.502 0.004 k
361.089 172.088 m
361.089 193.909 l
343.213 200.874 l
343.213 179.053 l
361.089 172.088 l
h
B
380.596 179.053 m
380.596 200.874 l
361.089 193.909 l
361.089 172.088 l
380.596 179.053 l
h
B
0.028 0.373 0.753 0.004 k
380.596 200.874 m
362.721 207.84 l
343.213 200.874 l
361.089 193.909 l
380.596 200.874 l
h
B
0 g
BT
/T1_2 1 Tf
7 0 0 7 288.3226 185.5227 Tm
(3 cm)Tj
13.619 0.3096 Td
(5 cm)Tj
9 0 0 9 309.6556 182.8562 Tm
(A)Tj
4.3704 0.0926 Td
(B)Tj
ET
Q Q Q 
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1 g
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/RelativeColorimetric ri
/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(57)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 567.39 368.51 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0 Tw 14 0 0 14 165.822 555.8038 Tm
(Pythagoras)Tj
/T1_2 1 Tf
0 Tc 5.2389 0 Td
(\325)Tj
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 0.2959 0 Td
[( theor)18(em)]TJ
0 0 0 1 k
/T1_3 1 Tf
0.0278 Tw 9 0 0 9 68.3307 538.3044 Tm
(When you know the lengths of two sides of a right-angled triangle you ca\
n use)Tj
-0.0002 Tc 0 Tw 0 -1.3333 TD
(Pythagoras)Tj
/T1_4 1 Tf
0 Tc 4.9422 0 Td
(\325)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.2598 0 Td
[( theor)18(em to find the thir)18(d side.)]TJ
0 Tw -5.202 -1.9632 Td
(Pythagoras)Tj
/T1_4 1 Tf
0 Tc 4.9422 0 Td
(\325)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.2598 0 Td
[( theor)18(em: a)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 161.6433 512.2352 Tm
(2)Tj
-0.0003 Tc 0.0278 Tw 9 0 0 9 167.8961 508.6353 Tm
(+ b)Tj
0 Tc 0 Tw 6.3 0 0 6.3 182.1361 512.2352 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 188.3889 508.6353 Tm
(= c)Tj
0 Tc 0 Tw 6.3 0 0 6.3 201.4688 512.2352 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 210.4721 508.6353 Tm
[(\(wher)18(e c is the longest side\))]TJ
/T1_0 1 Tf
-0.0001 Tc 0 Tw -15.7935 -1.9633 Td
(Note: )Tj
/T1_3 1 Tf
0.0278 Tw 2.99 0 Td
(The longest side is always opposite the right angle.)Tj
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0002 Tc 0 Tw 10 0 0 10 51.3228 473.2966 Tm
(Examples)Tj
0 0 0 1 k
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 9 0 0 9 68.3307 458.4619 Tm
(Find x)Tj
0 -7.2231 TD
(Find y)Tj
/CS3 cs 1  scn
/T1_0 1 Tf
0 Tw 10 0 0 10 51.3228 268.312 Tm
(Questions)Tj
0 0 0 1 k
/T1_3 1 Tf
0.0278 Tw 9 0 0 9 68.3307 253.4774 Tm
[(1)-1334(Find x)-13628(2)-1334(Find the height of this isosceles triangle:)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
0 Tw 8 0 0 8 51.3228 167.9656 Tm
(Answers)Tj
0 0 0 1 k
/T1_3 1 Tf
0.0277 Tw 7 0 0 7 68.3307 155.9656 Tm
[(1)-1064(T)111(o find a short side:)-15449(2)-1064(An isosceles triangle can be split into )]TJ
-0.0002 Tc 1.6198 -1.7143 Td
[(Squar)18(e both numbers)-2447(12)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 172.4913 146.7654 Tm
(2)Tj
7 0 0 7 185.9118 143.9656 Tm
(7)Tj
4.9 0 0 4.9 189.8031 146.7654 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 261.0865 143.9656 Tm
(two right)Tj
/T1_4 1 Tf
0 Tc 0 Tw 4.0225 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
(angled triangles.)Tj
-0.0002 Tc 0 Tw -30.4391 -1.7143 Td
[(Subtract)-8430(144 )]TJ
/T1_4 1 Tf
0 Tc 14.1218 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
[( 49)-9950(h)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 265.4855 134.7654 Tm
(2)Tj
-0.0002 Tc 0.0277 Tw 7 0 0 7 270.3487 131.9656 Tm
(+ 4)Tj
0 Tc 0 Tw 4.9 0 0 4.9 281.0398 134.7654 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 288.6521 131.9656 Tm
(= 10)Tj
0 Tc 0 Tw 4.9 0 0 4.9 303.2345 134.7654 Tm
(2)Tj
7 0 0 7 79.6693 119.9656 Tm
(\()Tj
/T1_0 1 Tf
-0.0001 Tc 0.2598 0 Td
(Note:)Tj
/T1_3 1 Tf
0.0277 Tw 2.9702 0 Td
(Big number )Tj
/T1_4 1 Tf
0 Tc 0 Tw 5.5541 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.4999 0 Td
[( small number)92(.)-12391(h)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 281.0398 122.7654 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 288.6521 119.9656 Tm
(= 10)Tj
0 Tc 0 Tw 4.9 0 0 4.9 303.2345 122.7654 Tm
(2)Tj
/T1_4 1 Tf
7 0 0 7 308.0977 119.9656 Tm
(\320)Tj
/T1_3 1 Tf
0.0277 Tc 0.4999 0 Td
( 4)Tj
0 Tc 4.9 0 0 4.9 317.6284 122.7654 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 79.6693 107.9656 Tm
[(If you do it the wr)18(ong way you will)-12766(h)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 281.0398 110.7654 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 288.6521 107.9656 Tm
(= 100 )Tj
/T1_4 1 Tf
0 Tc 0 Tw 2.9448 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 16)Tj
-0.0002 Tc 0 Tw -33.2993 -1.7143 Td
(get )Tj
/T1_4 1 Tf
0 Tc 1.804 0 Td
(\322)Tj
/T1_3 1 Tf
-0.0001 Tc 0.5188 0 Td
[(err)18(or)]TJ
/T1_4 1 Tf
0 Tc 2.1264 0 Td
(\323)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.5188 0 Td
[( when you pr)18(ess          \))-12658(h)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 281.0398 98.7654 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 288.6521 95.9656 Tm
(= 84)Tj
-29.8547 -1.7143 Td
[(Squar)18(e r)18(oot)]TJ
/T1_5 1 Tf
0 Tc 0 Tw 12.1485 0 Td
(\002)Tj
/T1_3 1 Tf
-0.0002 Tc 0.5488 0 Td
[(95)-14792(h)-698(= )]TJ
/T1_5 1 Tf
0 Tc 18.1288 0 Td
(\002)Tj
/T1_3 1 Tf
-0.0002 Tc 0.5488 0 Td
(84)Tj
0.0278 Tw -31.3749 -1.7143 Td
[(Answer x = )-6807(9)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 12.7043 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.2778 0 Td
[(75 m)-13349(h)-698(= 9.165 cm)]TJ
ET
0 0 0 0 k
61.34 367.48 346.47 -78.66 re
f*
Q Q 
0 g
/GS5 gs
BT
/T1_3 1 Tf
9 0 0 9 76.42 338.8002 Tm
(To find the )Tj
/T1_0 1 Tf
5.1478 0 Td
(long)Tj
/T1_3 1 Tf
2.0739 0 Td
( side)Tj
-7.3887 -2 Td
(Square both numbers)Tj
/T1_0 1 Tf
0.4735 -1 Td
(Add )Tj
/T1_3 1 Tf
2.2779 0 Td
(them together)Tj
-3.6299 -1 Td
(Take square root of result)Tj
14.6711 4 Td
(To find either )Tj
/T1_0 1 Tf
6.2757 0 Td
(short)Tj
/T1_3 1 Tf
2.4059 0 Td
( side)Tj
-8.1187 -2 Td
(Square both numbers)Tj
/T1_0 1 Tf
-3.2104 -1 Td
(Subtract )Tj
/T1_3 1 Tf
4.2598 0 Td
(the smaller from the larger)Tj
-1.9279 -1 Td
(Take square root of result)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
63.85 295.2 259.481 55.2 re
63.85 332.8 m
323.331 332.8 l
172.218 350.4 m
172.218 295.2 l
S
0.063 0.231 0.502 0.008 k
327.593 298.123 m
395.625 298.123 l
395.625 343.477 l
327.593 298.123 l
h
B
0 g
BT
/T1_3 1 Tf
0 -7 7 0 398.6088 336.8799 Tm
(Short side)Tj
7 0 0 7 347.7288 290.3997 Tm
(Short side)Tj
5.9017 3.7646 -3.7646 5.9017 346.5106 315.9727 Tm
(Long side)Tj
ET
395.391 302.7 m
390.891 302.7 l
390.891 298.2 l
S
0.063 0.231 0.502 0.008 k
376.173 479.361 m
342.157 479.361 l
376.173 531.546 l
376.173 479.361 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 379.1835 503.1902 Tm
(a)Tj
-3.0205 -4.7144 Td
(b)Tj
-0.9506 4.9541 Td
(c)Tj
ET
376.208 483.99 m
371.708 483.99 l
371.708 479.49 l
S
0.051 0.235 0.502 0.008 k
198.256 377.186 m
137.527 377.186 l
137.527 416.589 l
198.256 377.186 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 169.868 400.1241 Tm
(10 cm)Tj
-1.1217 -4.3278 Td
(8 cm)Tj
-4.4572 3.7238 Td
(y)Tj
ET
137.625 381.717 m
142.058 381.717 l
142.058 377.284 l
S
0.051 0.235 0.502 0.008 k
119.966 436.517 m
189.167 436.517 l
189.167 476.517 l
119.966 436.517 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 191.7667 452.9167 Tm
(5 cm)Tj
-6.3715 -3.5429 Td
(12 cm)Tj
0.4 4.6286 Td
(x)Tj
ET
189.066 441.116 m
184.566 441.116 l
184.566 436.616 l
S
0.063 0.231 0.502 0.008 k
376.667 80.017 m
376.667 131.539 l
356.058 80.017 l
376.667 80.017 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 344.454 105.9171 Tm
(10 cm)Tj
5.082 -0.8557 Td
(h)Tj
-2.912 -3.8737 Td
(4 cm)Tj
ET
373.387 80.017 3.28 3.28 re
S
0.063 0.231 0.502 0.008 k
347.981 171.657 m
322.31 235.834 l
296.639 171.657 l
347.981 171.657 l
h
B
322.31 175.634 m
322.31 170.464 l
337.857 204.113 m
333.128 201.882 l
338.622 202.75 m
333.893 200.519 l
306.763 204.113 m
311.492 201.882 l
305.997 202.75 m
310.727 200.519 l
S
0 g
BT
/T1_3 1 Tf
7 0 0 7 289.4189 207.6675 Tm
[(10 cm)-3713(10 cm)]TJ
3.7985 -6.3617 Td
(8 cm)Tj
ET
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
/GS6 gs
BT
/T1_3 1 Tf
9 0 0 9 225.6552 472.3328 Tm
(5)Tj
6.3 0 0 6.3 230.6584 475.9328 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 236.9112 472.3328 Tm
(+ 12)Tj
0 Tc 0 Tw 6.3 0 0 6.3 255.66 475.9328 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 263.2712 472.3328 Tm
(= x)Tj
0 Tc 0 Tw 6.3 0 0 6.3 276.3511 475.9328 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 9 0 0 9 222.6533 460.3328 Tm
[(25 + 144)-457(= x)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 276.3511 463.9328 Tm
(2)Tj
-0.0001 Tc 0.0277 Tw 9 0 0 9 244.1527 448.3328 Tm
[(169)-457(= x)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 276.3511 451.9328 Tm
(2)Tj
/T1_5 1 Tf
9 0 0 9 239.2133 436.3328 Tm
(\002)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.5488 0 Td
[(169)-457(= x)]TJ
-1.0834 -1.3333 Td
[(13 cm)-457(= x)]TJ
0 Tc 0 Tw 7.6577 -0.0586 Td
(y)Tj
6.3 0 0 6.3 307.6584 427.4059 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 313.9111 423.8058 Tm
(+ 8)Tj
0 Tc 0 Tw 6.3 0 0 6.3 327.6568 427.4059 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 335.268 423.8058 Tm
(= 10)Tj
0 Tc 0 Tw 6.3 0 0 6.3 354.0168 427.4059 Tm
(2)Tj
9 0 0 9 323.3194 411.8058 Tm
(y)Tj
6.3 0 0 6.3 327.6568 415.4059 Tm
(2)Tj
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BT
/T1_3 1 Tf
7.2 0 0 7.2 193.4302 266.7124 Tm
(TAN =            = )Tj
3.7431 0.5741 Td
(OPP)Tj
0 -1.1111 TD
(ADJ)Tj
T*
(  )Tj
ET
0 G
0.4 w 4 M 0 j 0 J []0 d 
219.773 269.346 m
235.773 269.346 l
246.707 269.346 m
253.507 269.346 l
S
BT
/T1_3 1 Tf
7.2 0 0 7.2 248.2314 270.9268 Tm
(5)Tj
T*
(3)Tj
ET
Q Q Q 
q
49.61 250.87 368.5 -85.52 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS10 gs
129.259 225.423 m
130.787 225.423 132.037 226.673 132.037 228.2 c
132.037 236.534 l
132.037 238.062 130.787 239.312 129.259 239.312 c
113.981 239.312 l
112.453 239.312 111.203 238.062 111.203 236.534 c
111.203 228.2 l
111.203 226.673 112.453 225.423 113.981 225.423 c
129.259 225.423 l
h
B
129.684 226.793 m
130.259 226.793 130.726 227.259 130.726 227.835 c
B
113.576 238.125 m
113.001 238.125 112.534 237.658 112.534 237.083 c
B
0.125 0.067 0.051 0.004 k
103.298 225.423 m
104.826 225.423 106.076 226.673 106.076 228.2 c
106.076 236.534 l
106.076 238.062 104.826 239.312 103.298 239.312 c
88.02 239.312 l
86.492 239.312 85.241 238.062 85.241 236.534 c
85.241 228.2 l
85.241 226.673 86.492 225.423 88.02 225.423 c
103.298 225.423 l
h
B
103.723 226.793 m
104.298 226.793 104.764 227.259 104.764 227.835 c
B
87.615 238.125 m
87.039 238.125 86.573 237.658 86.573 237.083 c
B
155.159 225.423 m
156.687 225.423 157.937 226.673 157.937 228.2 c
157.937 236.534 l
157.937 238.062 156.687 239.312 155.159 239.312 c
139.881 239.312 l
138.353 239.312 137.103 238.062 137.103 236.534 c
137.103 228.2 l
137.103 226.673 138.353 225.423 139.881 225.423 c
155.159 225.423 l
h
B
155.584 226.793 m
156.159 226.793 156.626 227.259 156.626 227.835 c
B
139.476 238.125 m
138.9 238.125 138.434 237.658 138.434 237.083 c
B
0.188 0.137 0.063 0.008 k
180.928 225.423 m
182.456 225.423 183.706 226.673 183.706 228.2 c
183.706 236.534 l
183.706 238.062 182.456 239.312 180.928 239.312 c
165.65 239.312 l
164.122 239.312 162.872 238.062 162.872 236.534 c
162.872 228.2 l
162.872 226.673 164.122 225.423 165.65 225.423 c
180.928 225.423 l
h
B
181.353 226.793 m
181.928 226.793 182.395 227.259 182.395 227.835 c
B
165.245 238.125 m
164.669 238.125 164.203 237.658 164.203 237.083 c
B
0 g
BT
/T1_0 1 Tf
10.4998 0 0 10.4998 169.2146 228.5587 Tm
(=)Tj
ET
0.188 0.137 0.063 0.008 k
357.21 176.13 m
358.519 176.13 359.589 177.201 359.589 178.509 c
359.589 185.648 l
359.589 186.957 358.519 188.028 357.21 188.028 c
344.123 188.028 l
342.813 188.028 341.743 186.957 341.743 185.648 c
341.743 178.509 l
341.743 177.201 342.813 176.13 344.123 176.13 c
357.21 176.13 l
h
B
357.574 177.304 m
358.066 177.304 358.466 177.704 358.466 178.196 c
B
343.775 187.01 m
343.283 187.01 342.883 186.611 342.883 186.118 c
B
0 g
BT
/T1_0 1 Tf
8.9941 0 0 8.9941 347.5265 179.1666 Tm
(=)Tj
10.4998 0 0 10.4998 92.3228 228.5587 Tm
(5)Tj
/T1_4 1 Tf
2.4941 0 Td
(\003)Tj
/T1_0 1 Tf
2.4452 0 Td
(3)Tj
ET
0.188 0.137 0.063 0.008 k
249.476 225.425 m
251.004 225.425 252.254 226.675 252.254 228.203 c
252.254 236.537 l
252.254 238.065 251.004 239.315 249.476 239.315 c
234.198 239.315 l
232.67 239.315 231.42 238.065 231.42 236.537 c
231.42 228.203 l
231.42 226.675 232.67 225.425 234.198 225.425 c
249.476 225.425 l
h
B
249.901 226.796 m
250.477 226.796 250.943 227.262 250.943 227.838 c
B
233.793 238.128 m
233.218 238.128 232.751 237.661 232.751 237.086 c
B
0 g
BT
/T1_0 1 Tf
7.6998 0 0 7.6998 233.5555 229.6115 Tm
(TAN)Tj
ET
0.188 0.137 0.063 0.008 k
216.664 225.425 m
218.192 225.425 219.442 226.675 219.442 228.203 c
219.442 236.537 l
219.442 238.065 218.192 239.315 216.664 239.315 c
201.385 239.315 l
199.858 239.315 198.607 238.065 198.607 236.537 c
198.607 228.203 l
198.607 226.675 199.858 225.425 201.385 225.425 c
216.664 225.425 l
h
B
217.089 226.796 m
217.664 226.796 218.13 227.262 218.13 227.838 c
B
200.981 238.128 m
200.405 238.128 199.939 237.661 199.939 237.086 c
B
0 g
BT
/T1_0 1 Tf
7.6998 0 0 7.6998 202.0943 229.6115 Tm
(INV)Tj
ET
0.188 0.137 0.063 0.008 k
325.601 225.425 m
327.129 225.425 328.379 226.675 328.379 228.203 c
328.379 236.537 l
328.379 238.065 327.129 239.315 325.601 239.315 c
310.322 239.315 l
308.795 239.315 307.544 238.065 307.544 236.537 c
307.544 228.203 l
307.544 226.675 308.795 225.425 310.322 225.425 c
325.601 225.425 l
h
B
326.026 226.796 m
326.601 226.796 327.067 227.262 327.067 227.838 c
B
309.917 238.128 m
309.342 238.128 308.876 237.661 308.876 237.086 c
B
0 g
BT
/T1_0 1 Tf
7.6998 0 0 7.6998 309.68 229.6115 Tm
(TAN)Tj
ET
0.188 0.137 0.063 0.008 k
371.743 225.425 m
373.271 225.425 374.521 226.675 374.521 228.203 c
374.521 236.537 l
374.521 238.065 373.271 239.315 371.743 239.315 c
350.951 239.315 l
349.423 239.315 348.173 238.065 348.173 236.537 c
348.173 228.203 l
348.173 226.675 349.423 225.425 350.951 225.425 c
371.743 225.425 l
h
B
372.168 226.796 m
372.744 226.796 373.21 227.262 373.21 227.838 c
B
350.546 238.128 m
349.971 238.128 349.505 237.661 349.505 237.086 c
B
0 g
BT
/T1_0 1 Tf
7.6998 0 0 7.6998 351.6968 229.6115 Tm
(TAN)Tj
4.8998 0 0 4.8998 367.8044 233.8114 Tm
(-1)Tj
ET
0.188 0.137 0.063 0.008 k
297.455 225.425 m
298.983 225.425 300.233 226.675 300.233 228.203 c
300.233 236.537 l
300.233 238.065 298.983 239.315 297.455 239.315 c
282.177 239.315 l
280.649 239.315 279.399 238.065 279.399 236.537 c
279.399 228.203 l
279.399 226.675 280.649 225.425 282.177 225.425 c
297.455 225.425 l
h
B
297.88 226.796 m
298.455 226.796 298.922 227.262 298.922 227.838 c
B
281.772 238.128 m
281.197 238.128 280.73 237.661 280.73 237.086 c
B
0 g
BT
/T1_0 1 Tf
7.6998 0 0 7.6998 282.8858 229.6115 Tm
(INV)Tj
/T1_3 1 Tf
7 0 0 7 122.9345 196.3805 Tm
(Do )Tj
/T1_0 1 Tf
1.612 0 Td
(not)Tj
/T1_3 1 Tf
1.573 0 Td
( forget )Tj
-3.4641 -1.2143 Td
(to press equals)Tj
9.4612 1.2143 Td
(Top left key on)Tj
0 -1.2143 TD
(most calculators;)Tj
T*
(it will show Shift,)Tj
-0.015 Tc -0.015 Tw 6.72 0 0 7 187.21 170.8805 Tm
[(Inv o)15(r)15( )]TJ
-0.03 Tc 0 Tw 2.618 0 Td
(2nd Function)Tj
0 Tc 7 0 0 7 255.6607 196.3805 Tm
(The answer displayed should be)Tj
T*
(59.0362...              )Tj
/T1_5 1 Tf
8.3401 0 Td
(59.0\274)Tj
/T1_3 1 Tf
-8.3401 -1.2143 Td
(If it is not displayed, press )Tj
ET
159.849 204.299 m
169.783 220.273 l
S
171.584 223.224 m
170.747 218.024 l
169.648 220.049 l
167.346 220.098 l
171.584 223.224 l
f
257.148 204.299 m
247.214 220.273 l
S
245.412 223.224 m
246.25 218.024 l
247.348 220.049 l
249.651 220.098 l
245.412 223.224 l
f
209.33 204.43 m
209.33 219.393 l
S
209.33 222.853 m
211.321 217.977 l
209.33 219.134 l
207.338 217.977 l
209.33 222.853 l
f
291.71 191.08 m
307.75 191.08 l
S
311.21 191.08 m
306.335 189.089 l
307.491 191.08 l
306.335 193.072 l
311.21 191.08 l
f
BT
/T1_6 1 Tf
15.3999 0 0 15.3999 271.4395 227.7633 Tm
(\002)Tj
6.894 0.0455 Td
(\003)Tj
12.5999 0 0 12.5999 335.3726 229.63 Tm
(\004)Tj
ET
Q Q Q 
q
111.44 176.69 55.55 -125.89 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.063 0.231 0.502 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS11 gs
145.013 106.906 m
145.013 65.18 l
117.713 65.18 l
145.013 106.906 l
h
B
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 126.4212 86.0804 Tm
(8)Tj
0.3857 -3.8429 Td
(3)Tj
-1.0403 1.0536 Td
(x)Tj
ET
128.213 65.18 m
128.138 69.23 126.038 72.08 123.638 74.18 c
S
0.063 0.231 0.502 0.008 k
145.013 168.639 m
145.013 126.913 l
117.713 126.913 l
145.013 168.639 l
h
B
0 0 0 1 k
BT
/T1_3 1 Tf
7 0 0 7 125.9212 147.3138 Tm
(8)Tj
0.4857 -3.8572 Td
(3)Tj
-0.1165 1.6393 Td
(x)Tj
ET
128.213 126.913 m
128.138 130.963 126.038 133.813 123.638 135.913 c
S
BT
/T1_3 1 Tf
6 0 0 6 133.3593 54.9135 Tm
(ADJ)Tj
0.0001 Tc 2.2826 4.6556 Td
(OPP)Tj
0 Tc 3.3594 4.9716 -4.9716 3.3594 118.2978 77.1168 Tm
(HYP)Tj
ET
145.755 86.147 m
159.613 82.314 l
134.813 122.733 m
143.846 122.733 l
S
144.905 122.733 m
143.413 122.124 l
143.767 122.733 l
143.413 123.343 l
144.905 122.733 l
f
130.492 154.001 m
140.917 168.863 l
S
141.522 169.732 m
141.169 168.159 l
140.872 168.798 l
140.169 168.856 l
141.522 169.732 l
f
125.634 145.824 m
115.817 131.158 l
S
115.212 130.288 m
115.565 131.861 l
115.863 131.223 l
116.565 131.165 l
115.212 130.288 l
f
131.213 89.88 m
142.248 106.497 l
S
142.854 107.366 m
142.501 105.793 l
142.203 106.432 l
141.5 106.49 l
142.854 107.366 l
f
127.013 83.88 m
115.636 66.704 l
S
115.031 65.835 m
115.383 67.408 l
115.681 66.769 l
116.384 66.711 l
115.031 65.835 l
f
127.425 122.733 m
118.392 122.733 l
S
117.333 122.733 m
118.825 123.343 l
118.471 122.733 l
118.825 122.124 l
117.333 122.733 l
f
134.813 62.69 m
143.846 62.69 l
S
144.905 62.69 m
143.413 62.08 l
143.767 62.69 l
143.413 63.299 l
144.905 62.69 l
f
127.425 62.69 m
118.392 62.69 l
S
117.333 62.69 m
118.825 63.299 l
118.471 62.69 l
118.825 62.08 l
117.333 62.69 l
f
145.013 131.247 m
140.68 131.247 l
140.68 126.913 l
145.013 69.347 m
140.68 69.347 l
140.68 65.014 l
S
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
184.99 102.73 181.4 -47.93 re
f*
Q Q 
0 g
/GS12 gs
BT
/T1_3 1 Tf
7 0 0 7 194.4613 82.1204 Tm
(COS  = )Tj
0 -2.2857 TD
(         =   67.975687...         68.0)Tj
/T1_7 1 Tf
14.0102 0 Td
(\274)Tj
/T1_3 1 Tf
0.385 0 Td
( )Tj
-10.3953 2.8333 Td
(ADJ)Tj
0 -1.1429 TD
(HYP)Tj
T*
(  )Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
222.482 84.37 m
235.411 84.37 l
247.948 84.43 m
252.723 84.43 l
265.39 68.721 m
272.932 68.721 l
S
275.403 68.721 m
271.92 67.299 l
272.747 68.721 l
271.92 70.144 l
275.403 68.721 l
f
BT
/T1_3 1 Tf
7 0 0 7 248.39 85.9534 Tm
(3)Tj
T*
(8)Tj
-1.1905 0.5953 Td
(=)Tj
ET
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS4 cs 1  scn
/GS13 gs
49.86 523.92 368 -91.86 re
f*
0 0 0 1 k
BT
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.1142 509.4937 Tm
[(Infor)-18(mation similar to )]TJ
-0.0001 Tc 0 -1.3333 TD
(this will be given on )Tj
-0.0002 Tc T*
[(your examination paper)92(.)]TJ
/T1_0 1 Tf
-0.0001 Tc 0 Tw 0 -3.2966 TD
(Note:)Tj
/T1_3 1 Tf
0.0277 Tw 2.9702 0 Td
(This only works for)Tj
-2.9702 -1.3333 Td
(right-angled triangles.)Tj
ET
0 0 0 1 K
10 M 
49.86 523.92 368 -91.86 re
S
Q Q 
q
184.06 516.82 225.65 -87.84 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
BT
/T1_3 1 Tf
7 0 0 7 216.5439 450.6535 Tm
(x)Tj
19.8832 6.2854 Td
[(SIN)-1402(= )]TJ
0 -2.8 TD
[(COS)-906(= )]TJ
T*
[(TAN)-962(=  )]TJ
4.5 6.2167 Td
(OPP)Tj
0 -1.4 TD
(HYP)Tj
T*
(ADJ)Tj
T*
(HYP)Tj
T*
(OPP)Tj
T*
(ADJ)Tj
ET
385.126 496.82 m
404.493 496.82 l
385.126 476.72 m
404.493 476.72 l
385.126 456.887 m
404.493 456.887 l
S
0.063 0.231 0.502 0.008 k
269.393 449.72 m
269.393 514.353 l
211.06 449.72 l
269.393 449.72 l
h
B
222.466 449.72 m
222.467 449.779 222.475 449.836 222.475 449.895 c
222.475 453.184 221.011 456.125 218.706 458.122 c
211.06 449.72 l
222.466 449.72 l
h
263.094 449.72 6.3 6.3 re
S
0 g
BT
/T1_3 1 Tf
7 0 0 7 226.3603 441.1452 Tm
(Adjacent)Tj
0 7 -7 0 277.2104 463.0203 Tm
(Opposite)Tj
-0.0001 Tc 4.7012 5.1863 -5.1863 4.7012 221.3857 467.3952 Tm
(Hypotenuse)Tj
ET
Q Q Q 
q
295.41 554.47 22.68 -13.46 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.075 0.008 k
313.414 541.775 m
314.724 541.775 315.796 542.846 315.796 544.156 c
315.796 551.299 l
315.796 552.609 314.724 553.68 313.414 553.68 c
300.318 553.68 l
299.009 553.68 297.937 552.609 297.937 551.299 c
297.937 544.156 l
297.937 542.846 299.009 541.775 300.318 541.775 c
313.414 541.775 l
h
B
313.779 542.95 m
314.272 542.95 314.671 543.35 314.671 543.843 c
B
299.971 552.663 m
299.478 552.663 299.078 552.263 299.078 551.769 c
B
313.414 528.296 m
314.724 528.296 315.796 529.367 315.796 530.677 c
315.796 537.82 l
315.796 539.13 314.724 540.201 313.414 540.201 c
300.318 540.201 l
299.009 540.201 297.937 539.13 297.937 537.82 c
297.937 530.677 l
297.937 529.367 299.009 528.296 300.318 528.296 c
313.414 528.296 l
h
S
0 g
BT
/T1_0 1 Tf
6 0 0 6 300.61 545.9335 Tm
(shift)Tj
ET
Q Q Q 
q
319.38 554.47 22.68 -13.46 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
336.884 555.275 m
338.194 555.275 339.266 556.346 339.266 557.656 c
339.266 564.799 l
339.266 566.109 338.194 567.18 336.884 567.18 c
323.788 567.18 l
322.479 567.18 321.407 566.109 321.407 564.799 c
321.407 557.656 l
321.407 556.346 322.479 555.275 323.788 555.275 c
336.884 555.275 l
h
S
0.188 0.137 0.075 0.008 k
336.884 541.796 m
338.194 541.796 339.266 542.867 339.266 544.177 c
339.266 551.32 l
339.266 552.63 338.194 553.701 336.884 553.701 c
323.788 553.701 l
322.479 553.701 321.407 552.63 321.407 551.32 c
321.407 544.177 l
321.407 542.867 322.479 541.796 323.788 541.796 c
336.884 541.796 l
h
B
337.249 542.971 m
337.742 542.971 338.141 543.371 338.141 543.863 c
B
323.441 552.684 m
322.948 552.684 322.548 552.284 322.548 551.79 c
B
336.884 528.316 m
338.194 528.316 339.266 529.388 339.266 530.698 c
339.266 537.841 l
339.266 539.15 338.194 540.222 336.884 540.222 c
323.788 540.222 l
322.479 540.222 321.407 539.15 321.407 537.841 c
321.407 530.698 l
321.407 529.388 322.479 528.316 323.788 528.316 c
336.884 528.316 l
h
S
0 g
BT
/T1_0 1 Tf
6 0 0 6 325.08 545.6 Tm
(INV)Tj
ET
Q Q Q 
q
352.43 554.47 22.68 -13.46 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
370.434 555.296 m
371.744 555.296 372.815 556.368 372.815 557.678 c
372.815 564.821 l
372.815 566.13 371.744 567.202 370.434 567.202 c
357.339 567.202 l
356.029 567.202 354.957 566.13 354.957 564.821 c
354.957 557.678 l
354.957 556.368 356.029 555.296 357.339 555.296 c
370.434 555.296 l
h
S
0.188 0.137 0.075 0.008 k
370.434 541.734 m
371.744 541.734 372.815 542.806 372.815 544.115 c
372.815 551.258 l
372.815 552.568 371.744 553.64 370.434 553.64 c
357.339 553.64 l
356.029 553.64 354.957 552.568 354.957 551.258 c
354.957 544.115 l
354.957 542.806 356.029 541.734 357.339 541.734 c
370.434 541.734 l
h
B
370.799 542.909 m
371.292 542.909 371.691 543.308 371.691 543.802 c
B
356.991 552.622 m
356.498 552.622 356.098 552.222 356.098 551.729 c
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 356.13 545.684 Tm
(2nd F)Tj
ET
Q Q Q 
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0 660 m
0 660 l
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q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(59)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 593.39 368.51 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0296 Tw 14 0 0 14 139.9849 581.8038 Tm
[(T)92(rigonometry: Finding a side)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 10 0 0 10 242.0909 604.6698 Tm
[(Pythagoras\325 theor)18(em and trigonometry)]TJ
/T1_3 1 Tf
-0.0002 Tc 9 0 0 9 68.3307 557.2368 Tm
[(W)18(e have used this method befor)18(e \(see page 44\).)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10.7087 -13.9003 Td
(Method)Tj
0 0 0 1 k
/T1_3 1 Tf
0.0278 Tw 0 -1.6483 TD
[(1)-1334(Label the triangle)]TJ
-0.0113 Tc 1.8898 -1.3333 Td
(Hypotenuse = the longest side, opposite the right angle)Tj
-0.0001 Tc 0 -1.3333 TD
(Opposite = opposite the angle being used)Tj
T*
(Adjacent = next to the angle being used)Tj
-1.8898 -1.9632 Td
[(2)-1334(Y)92(ou need the side you ar)18(e finding \(x\).)]TJ
1.8898 -1.3333 Td
[(Y)92(ou need the side you know \(10 m\).)]TJ
-0.0057 Tc T*
[(Cr)18(oss out the side not being used. In this question ADJ.)]TJ
-0.0224 Tc -1.8898 -1.9633 Td
[(3)-1356(Look at the for)-18(mulae above. Which uses OPP and HYP?)]TJ
-0.0001 Tc 0 -1.9633 TD
[(4)-1334(W)18(e need OPP)153(, cover up OPP to find the for)-18(mula:)]TJ
-10.7087 -5.8898 Td
[(5)-1334(Calculator keys)]TJ
0 -4.5333 TD
(This should give you an answer 4)Tj
/T1_4 1 Tf
0 Tc 0 Tw 14.8705 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0001 Tc 4.7105 Tw 0.2779 0 Td
(6947.. 4)Tj
/T1_4 1 Tf
0 Tc 0 Tw 8.3235 0 Td
(\341)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
(69 m)Tj
/T1_0 1 Tf
-0.0001 Tc 0 Tw -23.7497 -1.9633 Td
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
[(If this does not work ask your teacher to show you how to work your calc\
ulator)92(.)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 51.3228 169.4764 Tm
(Question)Tj
/CS2 cs 1  scn
8 0 0 8 159.3228 169.4764 Tm
(Answer)Tj
ET
0 0 0 0 k
233.43 219.5 37.39 -9.02 re
f*
Q Q 
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS3 gs
239.63 214.99 m
260.63 214.99 l
S
0 g
261.811 215.502 m
260.984 215.752 260.447 215.982 259.784 216.248 c
259.784 213.726 l
260.021 213.839 260.984 214.222 261.811 214.472 c
262.696 214.739 263.498 214.922 264.018 214.987 c
263.498 215.053 262.696 215.235 261.811 215.502 c
f
0.188 0.137 0.075 0.008 k
0.375 w 
302.325 227.222 m
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285.955 242.103 l
284.318 242.103 282.979 240.764 282.979 239.127 c
282.979 230.198 l
282.979 228.561 284.318 227.222 285.955 227.222 c
302.325 227.222 l
h
B
302.78 228.69 m
303.397 228.69 303.896 229.19 303.896 229.806 c
B
285.521 240.831 m
284.905 240.831 284.405 240.332 284.405 239.715 c
B
219.955 227.222 m
221.592 227.222 222.932 228.561 222.932 230.198 c
222.932 239.127 l
222.932 240.764 221.592 242.103 219.955 242.103 c
203.585 242.103 l
201.948 242.103 200.609 240.764 200.609 239.127 c
200.609 230.198 l
200.609 228.561 201.948 227.222 203.585 227.222 c
219.955 227.222 l
h
B
220.41 228.69 m
221.027 228.69 221.526 229.19 221.526 229.806 c
B
203.151 240.831 m
202.535 240.831 202.035 240.332 202.035 239.715 c
B
192.329 227.225 m
193.966 227.225 195.305 228.565 195.305 230.201 c
195.305 239.13 l
195.305 240.767 193.966 242.107 192.329 242.107 c
175.959 242.107 l
174.322 242.107 172.983 240.767 172.983 239.13 c
172.983 230.201 l
172.983 228.565 174.322 227.225 175.959 227.225 c
192.329 227.225 l
h
B
192.784 228.693 m
193.4 228.693 193.9 229.193 193.9 229.81 c
B
175.525 240.835 m
174.909 240.835 174.409 240.335 174.409 239.719 c
B
0.125 0.071 0.055 0.004 k
275.08 227.222 m
276.717 227.222 278.057 228.561 278.057 230.198 c
278.057 239.127 l
278.057 240.764 276.717 242.103 275.08 242.103 c
258.71 242.103 l
257.073 242.103 255.734 240.764 255.734 239.127 c
255.734 230.198 l
255.734 228.561 257.073 227.222 258.71 227.222 c
275.08 227.222 l
h
B
275.535 228.69 m
276.152 228.69 276.651 229.19 276.651 229.806 c
B
258.276 240.831 m
257.66 240.831 257.16 240.332 257.16 239.715 c
B
247.746 227.222 m
249.383 227.222 250.723 228.561 250.723 230.198 c
250.723 239.127 l
250.723 240.764 249.383 242.103 247.746 242.103 c
231.376 242.103 l
229.739 242.103 228.4 240.764 228.4 239.127 c
228.4 230.198 l
228.4 228.561 229.739 227.222 231.376 227.222 c
247.746 227.222 l
h
B
248.201 228.69 m
248.818 228.69 249.317 229.19 249.317 229.806 c
B
230.942 240.831 m
230.326 240.831 229.826 240.332 229.826 239.715 c
B
137.775 227.222 m
139.412 227.222 140.751 228.561 140.751 230.198 c
140.751 239.127 l
140.751 240.764 139.412 242.103 137.775 242.103 c
121.405 242.103 l
119.768 242.103 118.428 240.764 118.428 239.127 c
118.428 230.198 l
118.428 228.561 119.768 227.222 121.405 227.222 c
137.775 227.222 l
h
B
138.23 228.69 m
138.846 228.69 139.346 229.19 139.346 229.806 c
B
120.971 240.831 m
120.354 240.831 119.855 240.332 119.855 239.715 c
B
164.775 227.222 m
166.412 227.222 167.751 228.561 167.751 230.198 c
167.751 239.127 l
167.751 240.764 166.412 242.103 164.775 242.103 c
148.405 242.103 l
146.768 242.103 145.428 240.764 145.428 239.127 c
145.428 230.198 l
145.428 228.561 146.768 227.222 148.405 227.222 c
164.775 227.222 l
h
B
165.23 228.69 m
165.846 228.69 166.346 229.19 166.346 229.806 c
B
147.971 240.831 m
147.354 240.831 146.855 240.332 146.855 239.715 c
B
0 g
BT
/T1_0 1 Tf
11.2499 0 0 11.2499 289.7748 230.5819 Tm
(=)Tj
-2.3515 0 Td
(0)Tj
-2.4297 0 Td
(1)Tj
-2.4429 0.0667 Td
(x)Tj
1.808 Tc -7.3325 -0.0667 Td
(28)Tj
0.0001 Tc 8.2498 0 0 8.2498 177.1024 231.7102 Tm
(SIN)Tj
ET
0.063 0.231 0.502 0.008 k
0.5 w 
69.68 309.48 m
125.68 309.48 l
125.68 346.28 l
69.68 309.48 l
h
B
0 g
BT
/T1_3 1 Tf
0 Tc 8.8 0 0 8.8 128.905 327.4798 Tm
(x)Tj
-5.6994 0.2803 Td
(10 m)Tj
7.2 0 0 7.2 82.1016 311.4798 Tm
(28)Tj
/T1_4 1 Tf
1.112 0 Td
(\274)Tj
ET
95.69 309.534 m
95.578 315.549 92.723 320.216 89.869 322.713 c
S
BT
/T1_3 1 Tf
7.3638 4.818 -4.818 7.3638 95.6431 337.8038 Tm
(HYP)Tj
8.8 0 0 8.8 126.839 319.4798 Tm
(OPP)Tj
-4.0255 -2.1288 Td
(ADJ)Tj
ET
89.563 301.846 m
109.413 304.947 l
S
0.063 0.231 0.502 0.008 k
69.68 378.28 m
125.68 378.28 l
125.68 415.08 l
69.68 378.28 l
h
B
0 g
BT
/T1_3 1 Tf
8.8 0 0 8.8 128.905 394.2801 Tm
(x)Tj
-5.6994 0.5076 Td
(10 m)Tj
7.2 0 0 7.2 82.1016 380.0804 Tm
(28)Tj
/T1_4 1 Tf
1.112 0 Td
(\274)Tj
ET
95.69 378.335 m
95.578 384.349 92.723 389.016 89.869 391.513 c
S
0.925 0.725 0.075 0.012 k
BT
/T1_0 1 Tf
10 0 0 10 52.13 431.7801 Tm
(To find a side)Tj
ET
122.28 348.48 m
100.08 334.08 l
S
0 g
123.466 349.251 m
122.239 347.486 l
122.193 348.426 l
121.354 348.85 l
123.466 349.251 l
f
68.991 313.269 m
91.349 327.422 l
S
67.796 312.512 m
69.043 314.262 l
69.079 313.323 l
69.912 312.888 l
67.796 312.512 l
f
122.73 416.187 m
100.53 401.787 l
S
123.916 416.958 m
122.689 415.194 l
122.643 416.133 l
121.804 416.557 l
123.916 416.958 l
f
68.991 382.027 m
91.349 396.18 l
S
67.796 381.268 m
69.043 383.019 l
69.079 382.08 l
69.912 381.646 l
67.796 381.268 l
f
125.68 384.28 m
119.68 384.28 l
119.68 378.28 l
125.68 315.28 m
119.68 315.28 l
119.68 309.28 l
S
0.039 0.02 0.486 0 k
240.684 267.467 m
216.673 291.478 l
192.661 267.467 l
240.684 267.467 l
h
B
0 g
BT
/T1_3 1 Tf
9 0 0 9 258.55 282.4901 Tm
(OPP = SIN x HYP)Tj
0 -1.6667 TD
(OPP = SIN28)Tj
/T1_5 1 Tf
5.9138 0 Td
(\006)Tj
/T1_3 1 Tf
0.4 0 Td
( x 10)Tj
-0.0001 Tc 5.6 0 0 5.6 209.8401 279.5135 Tm
(OPP)Tj
0.0001 Tw -1.0211 -1.6713 Td
(SIN X HYP)Tj
ET
201.917 277.088 m
230.984 277.088 l
S
1 g
201.439 292.013 m
201.439 288.013 207.406 280.034 216.673 279.524 c
225.939 279.013 233.439 290.013 233.439 292.513 c
B
0.039 0.02 0.486 0 k
357.65 109.07 m
333.638 133.082 l
309.626 109.07 l
357.65 109.07 l
h
B
0.184 0.137 0.082 0.012 k
336.532 75.07 m
337.58 75.07 338.437 75.927 338.437 76.975 c
338.437 82.69 l
338.437 83.737 337.58 84.594 336.532 84.594 c
326.055 84.594 l
325.007 84.594 324.15 83.737 324.15 82.69 c
324.15 76.975 l
324.15 75.927 325.007 75.07 326.055 75.07 c
336.532 75.07 l
h
B
336.823 76.01 m
337.217 76.01 337.537 76.33 337.537 76.724 c
B
325.777 83.78 m
325.383 83.78 325.063 83.461 325.063 83.066 c
B
385.747 75.07 m
386.794 75.07 387.651 75.927 387.651 76.975 c
387.651 82.69 l
387.651 83.737 386.794 84.594 385.747 84.594 c
375.27 84.594 l
374.222 84.594 373.365 83.737 373.365 82.69 c
373.365 76.975 l
373.365 75.927 374.222 75.07 375.27 75.07 c
385.747 75.07 l
h
B
386.038 76.01 m
386.432 76.01 386.752 76.33 386.752 76.724 c
B
374.992 83.78 m
374.597 83.78 374.277 83.461 374.277 83.066 c
B
402.151 75.07 m
403.199 75.07 404.056 75.927 404.056 76.975 c
404.056 82.69 l
404.056 83.737 403.199 84.594 402.151 84.594 c
391.674 84.594 l
390.627 84.594 389.77 83.737 389.77 82.69 c
389.77 76.975 l
389.77 75.927 390.627 75.07 391.674 75.07 c
402.151 75.07 l
h
B
402.443 76.01 m
402.837 76.01 403.157 76.33 403.157 76.724 c
B
391.397 83.78 m
391.003 83.78 390.683 83.461 390.683 83.066 c
B
0.122 0.075 0.059 0.004 k
320.127 75.07 m
321.174 75.07 322.032 75.927 322.032 76.975 c
322.032 82.69 l
322.032 83.737 321.174 84.594 320.127 84.594 c
309.65 84.594 l
308.602 84.594 307.745 83.737 307.745 82.69 c
307.745 76.975 l
307.745 75.927 308.602 75.07 309.65 75.07 c
320.127 75.07 l
h
B
320.418 76.01 m
320.813 76.01 321.132 76.33 321.132 76.724 c
B
309.372 83.78 m
308.978 83.78 308.658 83.461 308.658 83.066 c
B
352.937 75.07 m
353.984 75.07 354.841 75.927 354.841 76.975 c
354.841 82.69 l
354.841 83.737 353.984 84.594 352.937 84.594 c
342.46 84.594 l
341.412 84.594 340.555 83.737 340.555 82.69 c
340.555 76.975 l
340.555 75.927 341.412 75.07 342.46 75.07 c
352.937 75.07 l
h
B
353.228 76.01 m
353.623 76.01 353.942 76.33 353.942 76.724 c
B
342.182 83.78 m
341.788 83.78 341.468 83.461 341.468 83.066 c
B
369.341 75.07 m
370.389 75.07 371.247 75.927 371.247 76.975 c
371.247 82.69 l
371.247 83.737 370.389 84.594 369.341 84.594 c
358.865 84.594 l
357.817 84.594 356.96 83.737 356.96 82.69 c
356.96 76.975 l
356.96 75.927 357.817 75.07 358.865 75.07 c
369.341 75.07 l
h
B
369.633 76.01 m
370.027 76.01 370.347 76.33 370.347 76.724 c
B
358.587 83.78 m
358.193 83.78 357.873 83.461 357.873 83.066 c
B
0 g
BT
/T1_3 1 Tf
0 Tc 0 Tw 7 0 0 7 108.3707 103.2653 Tm
(40)Tj
/T1_4 1 Tf
1.112 0 Td
(\274)Tj
/T1_3 1 Tf
-3.1885 -0.2 Td
(x)Tj
ET
0.063 0.231 0.502 0.008 k
77.125 135.07 m
121.149 135.07 l
121.15 80.47 l
77.125 135.07 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 123.3476 107.3366 Tm
(8 m)Tj
ET
121.149 101.095 m
114.086 100.964 111.866 100.27 108.203 96.084 c
S
BT
/T1_3 1 Tf
7 0 0 7 217.4702 95.9865 Tm
(ADJ)Tj
-4.2802 5.9524 Td
(OPP)Tj
-0.0001 Tc 4.7374 -5.1532 5.1532 4.7374 167.7912 119.2063 Tm
(HYP)Tj
ET
188.083 140.92 m
201.149 138.12 l
S
BT
/T1_3 1 Tf
0 Tc 7 0 0 7 237.3841 122.5699 Tm
[(COS)-278(=)]TJ
3.7046 0.5 Td
(ADJ)Tj
0 -1.1429 TD
(HYP)Tj
ET
262.85 124.403 m
276.15 124.403 l
S
BT
/T1_3 1 Tf
7 0 0 7 246.9524 89.57 Tm
[(HYP)-278(=)]TJ
3.4806 0.5 Td
(ADJ)Tj
T*
(COS)Tj
ET
270.85 91.403 m
284.15 91.403 l
S
BT
/T1_3 1 Tf
7 0 0 7 246.9524 72.1949 Tm
[(HYP)-278(=)]TJ
4.6788 0.5 Td
(8)Tj
-1.3675 -1.1429 Td
(cos 40)Tj
/T1_5 1 Tf
2.8911 0 Td
(\006)Tj
ET
270.85 74.028 m
292.15 74.028 l
75.006 130.631 m
92.794 109.364 l
S
73.106 132.912 m
77.092 130.794 l
75.146 130.464 l
74.469 128.609 l
73.106 132.912 l
f
101.485 96.904 m
116.671 79.033 l
S
117.95 77.47 m
113.942 79.549 l
115.885 79.899 l
116.544 81.76 l
117.95 77.47 l
f
BT
/T1_3 1 Tf
7 0 0 7 203.1632 103.2653 Tm
(40)Tj
/T1_4 1 Tf
1.112 0 Td
(\274)Tj
/T1_3 1 Tf
-3.1885 -0.2 Td
(x)Tj
ET
0.063 0.231 0.502 0.008 k
171.917 135.07 m
215.942 135.07 l
215.942 80.47 l
171.917 135.07 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 218.1401 107.3366 Tm
(8 m)Tj
ET
215.942 101.095 m
208.878 100.964 206.658 100.27 202.996 96.084 c
169.799 130.631 m
187.587 109.364 l
S
167.898 132.912 m
171.885 130.794 l
169.939 130.464 l
169.262 128.609 l
167.898 132.912 l
f
196.277 96.904 m
211.464 79.033 l
S
212.742 77.47 m
208.735 79.549 l
210.678 79.899 l
211.337 81.76 l
212.742 77.47 l
f
284.334 124.374 m
307.54 120.985 l
S
309.532 120.655 m
305.15 119.57 l
306.378 121.116 l
305.644 122.948 l
309.532 120.655 l
f
BT
/T1_3 1 Tf
9 0 0 9 71.4762 82.2365 Tm
(Find x)Tj
-0.0001 Tc 5.6 0 0 5.6 327.2146 121.1173 Tm
(ADJ)Tj
0.0001 Tw -1.5902 -1.6714 Td
(COS X HYP)Tj
ET
318.882 118.691 m
347.949 118.691 l
S
BT
/T1_3 1 Tf
0 Tc 0 Tw 7 0 0 7 354.65 127.57 Tm
(Cover up HYP)Tj
T*
(to find the formula)Tj
-6.8666 -4.2857 Td
(Calculator keys:)Tj
5.7701 -3.8571 Td
(Answer x = 10)Tj
/T1_4 1 Tf
6.3721 0 Td
(\341)Tj
/T1_3 1 Tf
0.278 0 Td
(4 m)Tj
/T1_0 1 Tf
7.2 0 0 7.2 312.6013 77.2203 Tm
(8)Tj
/T1_5 1 Tf
2.2999 0.1389 Td
(\003)Tj
/T1_0 1 Tf
1.6865 Tc 2.2569 -0.1389 Td
(40)Tj
0 Tc 6 0 0 6 375.7438 78.2204 Tm
(cos)Tj
7.2 0 0 7.2 394.3589 77.2203 Tm
(=)Tj
ET
115.649 129.57 5.5 5.5 re
210.442 129.57 5.5 5.5 re
S
0.039 0.02 0.486 0 k
329.735 501.723 m
305.723 525.734 l
281.711 501.723 l
329.735 501.723 l
h
B
329.735 464.598 m
305.723 488.609 l
281.711 464.598 l
329.735 464.598 l
h
B
196.235 519.723 m
172.223 543.734 l
148.211 519.723 l
196.235 519.723 l
h
B
196.235 490.27 m
172.223 514.282 l
148.211 490.27 l
196.235 490.27 l
h
B
196.235 460.818 m
172.223 484.83 l
148.211 460.818 l
196.235 460.818 l
h
B
0 g
BT
/T1_3 1 Tf
7 0 0 7 84.6962 528.7701 Tm
[(SIN)-278(=)]TJ
3.2086 0.5 Td
(OPP)Tj
T*
(HYP)Tj
ET
106.69 530.603 m
119.99 530.603 l
S
BT
/T1_3 1 Tf
7 0 0 7 331.5746 509.8951 Tm
(OPP  = SIN x HYP)Tj
1.2454 -4.7857 Td
(HYP =)Tj
3.4806 0.5 Td
(OPP)Tj
T*
(SIN)Tj
ET
364.19 478.229 m
377.49 478.229 l
S
BT
/T1_3 1 Tf
-0.0001 Tc 5.6 0 0 5.6 165.3909 531.7701 Tm
(OPP)Tj
0.0001 Tw -1.0211 -1.6714 Td
(SIN X HYP)Tj
ET
157.467 529.344 m
186.534 529.344 l
S
BT
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[(Remember to put the whole answer into your calculator memory)92(. )]TJ
0 -1.2857 TD
[(Y)92(ou may need to use it again \(do not work with the shortened answer 32)]TJ
/T1_2 1 Tf
32.2446 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(5\).)Tj
-20.3808 4.6429 Td
[(Always write the whole number down befor)18(e )]TJ
0 -1.1429 TD
[(you shorten it to 3 significant figur)18(es)]TJ
12.3777 5.4714 Td
(opp)Tj
-0.9286 -1.6429 Td
[(tan)-807(adj)]TJ
ET
246.94 303.48 m
276.065 303.48 l
261.69 303.355 m
261.69 293.48 l
162.946 278.23 m
155.118 280.528 l
S
153.839 280.378 m
154.559 279.9 155.007 279.525 155.565 279.079 c
156.292 281.494 l
156.032 281.455 155 281.365 154.136 281.364 c
153.212 281.363 152.391 281.42 151.874 281.507 c
152.353 281.295 153.069 280.888 153.839 280.378 c
f
0.031 0.243 0.502 0.004 k
318.19 290.73 m
401.19 321.23 l
401.19 290.73 l
318.19 290.73 l
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 338.5235 292.23 Tm
(18)Tj
/T1_5 1 Tf
1.1121 0 Td
(\006)Tj
/T1_0 1 Tf
10.0824 1.3333 Td
(?)Tj
-4.5 -2.6667 Td
(adj)Tj
4.4167 4.3333 Td
(opp)Tj
-15.5 -3.0833 Td
(D)Tj
15.3333 4.5833 Td
(F)Tj
0 -5.1667 TD
(A)Tj
-9.1667 -0.75 Td
(100 m)Tj
ET
0.25 w 
349.19 302.23 m
351.995 298.295 350.857 290.897 v
S
0.031 0.243 0.502 0.004 k
0.5 w 
212.19 64.23 m
270.19 89.73 l
270.19 64.23 l
212.19 64.23 l
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 274.69 72.73 Tm
(short)Tj
-4 -2.75 Td
(short)Tj
-4.1944 3.7222 Td
(long)Tj
8.1111 0.1944 Td
(32)Tj
/T1_2 1 Tf
1.1121 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(491969)Tj
-13.0568 -2.9167 Td
(C)Tj
11.4167 4.3333 Td
(F)Tj
0.0833 -4.4167 Td
(A)Tj
7 0 0 7 83.9537 91.73 Tm
(b)Tj
0 19.7857 TD
(a)Tj
-2.4297 0 Td
(2)Tj
4.392 -19.7857 Td
(Use Pythagoras)Tj
/T1_2 1 Tf
6.8901 0 Td
(\325)Tj
/T1_0 1 Tf
0.26 0 Td
[( theor)18(em.)]TJ
-7.1501 -1.7143 Td
[(T)111(o find a long side:)]TJ
6 0 0 6 105.186 66.459 Tm
[(Squar)18(e )]TJ
-0.6194 -1.1667 Td
(both sides)Tj
19.7034 -0.5382 Td
(122)Tj
/T1_2 1 Tf
1.6681 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(06555)Tj
7 0 0 7 321.19 89.23 Tm
(=    122)Tj
/T1_2 1 Tf
3.4461 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(06555)Tj
5 0 0 5 366.7188 92.23 Tm
(2)Tj
7 0 0 7 369.4991 89.23 Tm
( + 32)Tj
/T1_2 1 Tf
2.334 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(491969)Tj
5 0 0 5 411.1358 92.23 Tm
(2)Tj
7 0 0 7 321.19 77.23 Tm
(=    15955)Tj
/T1_2 1 Tf
4.5581 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(72)Tj
-4.8361 -1.7143 Td
(= 126)Tj
/T1_2 1 Tf
2.612 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(3159)Tj
-2.89 -1.7143 Td
(= 126 m)Tj
-1.5714 5.1429 Td
(CF)Tj
ET
329.44 90.269 m
329.943 91.133 l
331.023 88.397 l
333.489 97.709 l
413.857 97.709 l
329.44 77.769 m
329.943 78.633 l
331.023 75.897 l
333.489 85.209 l
362.357 85.209 l
S
BT
/T1_0 1 Tf
6 0 0 6 309.69 193.73 Tm
(short)Tj
-4 -2.75 Td
(short)Tj
-4.1944 3.7223 Td
(long)Tj
8.1111 0.1944 Td
(70 m)Tj
-11.6667 -2.9167 Td
(C)Tj
11.4167 4.3333 Td
(A)Tj
0.0833 -4.4167 Td
(B)Tj
-7.4722 -0.9167 Td
(100 m)Tj
ET
0.031 0.243 0.502 0.004 k
151.69 126.73 m
209.69 152.23 l
209.69 126.73 l
151.69 126.73 l
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 214.19 135.23 Tm
(opp)Tj
-7.1667 1.5 Td
(hyp)Tj
3.8333 -4.0833 Td
(adj)Tj
3.25 3.75 Td
(32)Tj
/T1_2 1 Tf
1.1121 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(491969)Tj
-13.0568 -2.9167 Td
(C)Tj
11.4167 4.3333 Td
(F)Tj
0.0833 -4.4167 Td
(A)Tj
-9.1389 -0.75 Td
(122)Tj
/T1_2 1 Tf
1.6681 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(06555)Tj
7 0 0 7 356.19 210.23 Tm
(=    100)Tj
5 0 0 5 380.3124 213.23 Tm
(2)Tj
7 0 0 7 383.0928 210.23 Tm
( + 70)Tj
5 0 0 5 399.4311 213.23 Tm
(2)Tj
7 0 0 7 356.19 198.23 Tm
(=    14900)Tj
0 -1.7143 TD
(= 122)Tj
/T1_2 1 Tf
2.612 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(06555)Tj
-4.4615 3.4286 Td
(AC)Tj
0 -3.4286 TD
(AC)Tj
ET
364.44 211.269 m
364.943 212.133 l
366.023 209.397 l
368.489 218.709 l
403.857 218.709 l
364.44 198.769 m
364.943 199.633 l
366.023 196.897 l
368.489 206.209 l
388.19 206.209 l
S
BT
/T1_0 1 Tf
-0.022 Tc 7 0 0 7 97.69 229.8965 Tm
(Look at your model \(desk and ruler\). Find the right-angled triangle yo\
u need. First you need to calculate AC.)Tj
6.5179 -2.1429 Td
[(This is or)18(dinary Pythagoras)]TJ
/T1_2 1 Tf
0 Tc 11.2932 0 Td
(\325)Tj
/T1_0 1 Tf
-0.022 Tc 0.238 0 Td
[( theor)18(em)]TJ
0 Tc -11.5312 -1.7143 Td
[(T)111(o find a long side:)]TJ
6 0 0 6 140.7996 61.959 Tm
(Add)Tj
3.6757 0.75 Td
[(Squar)18(e)]TJ
0.64 -1.1667 Td
[(r)18(oot)]TJ
ET
187.126 184.937 m
182.149 189.916 l
182.149 179.959 l
187.126 184.937 l
f
208.793 184.937 m
203.815 189.916 l
203.815 179.959 l
208.793 184.937 l
f
0.039 0.02 0.486 0 k
143.482 175.897 39.375 20.062 re
B
187.148 175.897 18.042 20.062 re
B
208.815 175.897 26.375 20.062 re
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 146.7012 187.7925 Tm
[(Squar)18(e both )]TJ
0.4921 -1.1667 Td
(short sides)Tj
6.7951 0.4167 Td
(Add)Tj
3.6757 0.75 Td
[(Squar)18(e)]TJ
0.64 -1.1667 Td
[(r)18(oot)]TJ
-7.8825 -8.7327 Td
(?)Tj
ET
0.25 w 
173.023 135.73 m
173.69 133.73 175.024 130.73 175.024 127.064 c
169.69 144.73 m
183.357 147.73 l
S
BT
/T1_0 1 Tf
7 0 0 7 234.19 155.23 Tm
(tan =          =                     = 0)Tj
/T1_2 1 Tf
13.1352 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(2661845 )Tj
-10.3656 0.5238 Td
(opp)Tj
0 -1.2857 TD
(adj)Tj
3.3809 1.2857 Td
(32)Tj
/T1_2 1 Tf
1.112 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(491969)Tj
-1.39 -1.2857 Td
(122)Tj
/T1_2 1 Tf
1.668 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(06555)Tj
ET
0.5 w 
279.857 157.23 m
312.523 157.23 l
255.19 157.23 m
266.524 157.23 l
S
BT
/T1_0 1 Tf
7 0 0 7 365.19 120.8965 Tm
(14)Tj
/T1_2 1 Tf
1.112 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(90562)Tj
-1.39 -1.2857 Td
(Answer = 14)Tj
/T1_2 1 Tf
5.6121 0 Td
(\341)Tj
/T1_0 1 Tf
0.278 0 Td
(9)Tj
/T1_5 1 Tf
0.556 0 Td
(\006)Tj
/T1_1 1 Tf
-24.7318 2.7381 Td
(Remember:)Tj
/T1_0 1 Tf
5.4071 0 Td
[( T)111(o find)]TJ
-5.4071 -1.2857 Td
[(an angle, last thr)18(ee )]TJ
T*
(calculator keys:)Tj
ET
0.188 0.141 0.039 0.004 k
320.88 130.728 m
321.997 130.728 322.911 131.642 322.911 132.759 c
322.911 138.855 l
322.911 139.973 321.997 140.887 320.88 140.887 c
309.704 140.887 l
308.587 140.887 307.672 139.973 307.672 138.855 c
307.672 132.759 l
307.672 131.642 308.587 130.728 309.704 130.728 c
320.88 130.728 l
h
B
321.19 131.73 m
321.611 131.73 321.952 132.071 321.952 132.492 c
B
309.408 140.018 m
308.987 140.018 308.646 139.677 308.646 139.256 c
B
0 g
BT
/T1_1 1 Tf
0.0001 Tc 5 0 0 5 311.0894 133.5313 Tm
(INV)Tj
ET
0.188 0.141 0.039 0.004 k
339.119 118.728 m
340.236 118.728 341.15 119.642 341.15 120.759 c
341.15 126.855 l
341.15 127.973 340.236 128.887 339.119 128.887 c
327.943 128.887 l
326.826 128.887 325.911 127.973 325.911 126.855 c
325.911 120.759 l
325.911 119.642 326.826 118.728 327.943 118.728 c
339.119 118.728 l
h
B
339.429 119.73 m
339.85 119.73 340.191 120.071 340.191 120.492 c
B
327.647 128.018 m
327.226 128.018 326.885 127.677 326.885 127.256 c
B
0 g
BT
/T1_1 1 Tf
5 0 0 5 328.0782 121.7813 Tm
(TAN)Tj
ET
0.188 0.141 0.039 0.004 k
357.358 118.728 m
358.475 118.728 359.39 119.642 359.39 120.759 c
359.39 126.855 l
359.39 127.973 358.475 128.887 357.358 128.887 c
346.182 128.887 l
345.065 128.887 344.15 127.973 344.15 126.855 c
344.15 120.759 l
344.15 119.642 345.065 118.728 346.182 118.728 c
357.358 118.728 l
h
B
357.669 119.73 m
358.089 119.73 358.43 120.071 358.43 120.492 c
B
345.886 128.018 m
345.465 128.018 345.125 127.677 345.125 127.256 c
B
0 g
BT
/T1_1 1 Tf
0 Tc 8 0 0 8 349.0674 121.0313 Tm
(=)Tj
ET
0.188 0.141 0.039 0.004 k
320.88 118.728 m
321.997 118.728 322.911 119.642 322.911 120.759 c
322.911 126.855 l
322.911 127.973 321.997 128.887 320.88 128.887 c
309.704 128.887 l
308.587 128.887 307.672 127.973 307.672 126.855 c
307.672 120.759 l
307.672 119.642 308.587 118.728 309.704 118.728 c
320.88 118.728 l
h
B
321.19 119.73 m
321.611 119.73 321.952 120.071 321.952 120.492 c
B
309.408 128.018 m
308.987 128.018 308.646 127.677 308.646 127.256 c
B
0 g
BT
/T1_1 1 Tf
0.0001 Tc 4 0 0 4 309.5894 122.0313 Tm
(SHIFT)Tj
ET
0.188 0.141 0.039 0.004 k
320.88 106.728 m
321.997 106.728 322.911 107.642 322.911 108.759 c
322.911 114.855 l
322.911 115.973 321.997 116.887 320.88 116.887 c
309.704 116.887 l
308.587 116.887 307.672 115.973 307.672 114.855 c
307.672 108.759 l
307.672 107.642 308.587 106.728 309.704 106.728 c
320.88 106.728 l
h
B
321.19 107.73 m
321.611 107.73 321.952 108.071 321.952 108.492 c
B
309.408 116.018 m
308.987 116.018 308.646 115.677 308.646 115.256 c
B
0 g
BT
/T1_1 1 Tf
5 0 0 5 310.0894 109.7813 Tm
(2ND)Tj
/T1_0 1 Tf
0 Tc 6 0 0 6 300.19 121.73 Tm
(or)Tj
0 -1.7917 TD
(or)Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_1 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(61)Tj
/T1_6 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
Q Q 
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/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
49.61 42.05 368.5 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 50.6063 35.0006 Tm
(62)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 265.7926 35.5258 Tm
(Easingwold School                               )Tj
/T1_0 1 Tf
-0.0297 Tc 0 Tw 9 0 0 9 67.6142 61.67 Tm
(Note:)Tj
/T1_2 1 Tf
-0.0279 Tc 0.0278 Tw 2.7945 0 Td
(By extending the graphs above you can find values above 360)Tj
/T1_3 1 Tf
0 Tc 0 Tw 26.3815 0 Td
(\241)Tj
/T1_2 1 Tf
-0.0279 Tc 0.0278 Tw 0.6499 0 Td
(and negative values.)Tj
ET
0 0 0 0 k
49.61 593.39 368.5 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 14 0 0 14 97.4307 581.8038 Tm
(Sine, cosine and tangent of any angle )Tj
/T1_4 1 Tf
0 Tc 0 Tw 18.0723 0 Td
(\320)Tj
/T1_0 1 Tf
0.0295 Tc 0.4999 0 Td
( 1)Tj
0 0 0 1 k
/T1_5 1 Tf
-0.0001 Tc 0.0277 Tw 10 0 0 10 50.6063 604.6698 Tm
[(Pythagoras\325 theor)18(em and trigonometry)]TJ
ET
Q Q 
q
49.61 565.04 368.5 -490.77 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.039 0.02 0.486 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS3 gs
85.318 75.373 287.292 33.333 re
B
313.276 519.374 91.334 39.333 re
B
164.61 478.54 57 21 re
B
193.319 314.165 54 36.5 re
B
355.631 370.499 53 28 re
B
0.25 w 
64.658 352.698 m
67.358 352.698 l
64.658 327.187 m
67.358 327.187 l
64.658 301.675 m
67.358 301.675 l
64.658 276.163 m
67.358 276.163 l
64.658 250.651 m
67.358 250.651 l
S
0.5 w 
67.38 354.532 m
67.38 248.045 l
S
0 g
67.842 246.982 m
68.066 247.727 68.273 248.21 68.513 248.807 c
66.243 248.807 l
66.344 248.593 66.69 247.727 66.914 246.982 c
67.155 246.186 67.319 245.464 67.378 244.996 c
67.437 245.464 67.601 246.186 67.842 246.982 c
f
66.919 356.106 m
66.695 355.363 66.488 354.879 66.248 354.282 c
68.518 354.282 l
68.417 354.496 68.071 355.363 67.847 356.106 c
67.606 356.903 67.441 357.625 67.383 358.093 c
67.324 357.625 67.16 356.903 66.919 356.106 c
f
222.874 301.675 m
67.358 301.675 l
S
223.937 302.136 m
223.193 302.36 222.71 302.567 222.112 302.807 c
222.112 300.537 l
222.326 300.639 223.193 300.984 223.937 301.208 c
224.733 301.449 225.455 301.613 225.923 301.672 c
225.455 301.731 224.733 301.896 223.937 302.136 c
f
BT
/T1_2 1 Tf
6 0 0 6 59.6657 299.416 Tm
(0)Tj
-0.005 Tc 6.909 -1.1495 Td
(90)Tj
/T1_6 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 5.0004 0 Td
(180)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7247 0 Td
(270)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7248 0.0374 Td
(360)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc -23.6397 -0.0374 Td
(45)Tj
/T1_6 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 5.0004 0 Td
(135)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7248 0 Td
(225)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.6209 -0.023 Td
(315)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
ET
0.25 w 
182.16 301.675 m
182.16 298.975 l
143.893 301.675 m
143.893 298.975 l
220.428 301.675 m
220.428 298.975 l
105.626 301.675 m
105.626 298.975 l
163.027 301.675 m
163.027 298.975 l
124.759 301.675 m
124.759 298.975 l
201.294 301.675 m
201.294 298.975 l
86.492 301.675 m
86.492 298.975 l
247.277 489.075 m
249.976 489.075 l
247.277 463.563 m
249.976 463.563 l
247.277 438.051 m
249.976 438.051 l
247.277 412.54 m
249.976 412.54 l
247.277 387.028 m
249.976 387.028 l
S
0.5 w 
249.999 490.908 m
249.999 384.422 l
S
250.46 383.359 m
250.685 384.103 250.891 384.586 251.131 385.184 c
248.861 385.184 l
248.963 384.97 249.308 384.103 249.532 383.359 c
249.773 382.562 249.937 381.841 249.996 381.372 c
250.055 381.841 250.219 382.562 250.46 383.359 c
f
249.538 492.483 m
249.313 491.739 249.106 491.256 248.866 490.659 c
251.136 490.659 l
251.035 490.872 250.69 491.739 250.465 492.483 c
250.224 493.279 250.06 494.001 250.001 494.47 c
249.942 494.001 249.778 493.279 249.538 492.483 c
f
249.976 438.051 m
405.492 438.051 l
S
406.555 438.513 m
405.811 438.737 405.328 438.944 404.731 439.184 c
404.731 436.913 l
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(\006)Tj
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(180)Tj
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(\006)Tj
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(270)Tj
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(\006)Tj
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(360)Tj
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(\006)Tj
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(45)Tj
/T1_6 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 5.0004 0 Td
(135)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
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(225)Tj
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(\006)Tj
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(315)Tj
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364.778 438.051 m
364.778 435.352 l
326.511 438.051 m
326.511 435.352 l
403.046 438.051 m
403.046 435.352 l
288.244 438.051 m
288.244 435.352 l
345.645 438.051 m
345.645 435.352 l
307.378 438.051 m
307.378 435.352 l
383.912 438.051 m
383.912 435.352 l
269.11 438.051 m
269.11 435.352 l
249.976 489.075 m
267.448 489.075 288.244 438.051 y
309.075 387.028 326.511 387.028 v
403.046 489.075 m
385.574 489.075 364.778 438.051 y
343.948 387.028 326.511 387.028 v
64.682 507.075 m
67.383 507.075 l
64.682 481.563 m
67.383 481.563 l
64.682 456.051 m
67.383 456.051 l
64.682 430.54 m
67.383 430.54 l
64.682 405.028 m
67.383 405.028 l
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67.405 508.908 m
67.405 402.422 l
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67.866 401.359 m
68.09 402.103 68.298 402.586 68.537 403.184 c
66.267 403.184 l
66.369 402.97 66.714 402.103 66.939 401.359 c
67.179 400.563 67.343 399.841 67.402 399.372 c
67.461 399.841 67.626 400.563 67.866 401.359 c
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66.943 510.483 m
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68.542 508.659 l
68.441 508.872 68.095 509.739 67.871 510.483 c
67.63 511.279 67.466 512.001 67.407 512.47 c
67.348 512.001 67.184 511.279 66.943 510.483 c
f
67.383 456.051 m
222.898 456.051 l
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223.961 456.513 m
223.217 456.737 222.734 456.944 222.137 457.184 c
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222.35 455.015 223.217 455.36 223.961 455.585 c
224.757 455.826 225.479 455.99 225.948 456.049 c
225.479 456.107 224.757 456.272 223.961 456.513 c
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BT
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(0)Tj
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(1)Tj
-0.005 Tc -0.45 -16.9874 Td
(-1)Tj
7.359 7.3255 Td
(90)Tj
/T1_6 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
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-0.005 Tc 5.0003 0 Td
(180)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7248 0 Td
(270)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
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-0.005 Tc 4.7248 0.0375 Td
(360)Tj
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0 Tc 1.6531 0 Td
(\006)Tj
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-0.005 Tc -23.6397 -0.0375 Td
(45)Tj
/T1_6 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 5.0003 0 Td
(135)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7248 0 Td
(225)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.6209 -0.0231 Td
(315)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
ET
0.25 w 
182.185 456.051 m
182.185 453.352 l
143.917 456.051 m
143.917 453.352 l
220.452 456.051 m
220.452 453.352 l
105.65 456.051 m
105.65 453.352 l
163.051 456.051 m
163.051 453.352 l
124.783 456.051 m
124.783 453.352 l
201.318 456.051 m
201.318 453.352 l
86.516 456.051 m
86.516 453.352 l
67.383 456.013 m
88.178 507.036 105.65 507.036 v
123.122 507.036 143.917 456.013 y
164.748 404.99 182.185 404.99 v
199.621 404.99 220.452 456.013 y
245.349 227.908 m
248.049 227.908 l
245.349 176.885 m
248.049 176.885 l
245.349 125.861 m
248.049 125.861 l
S
0.5 w 
248.071 229.742 m
248.071 123.255 l
S
248.533 122.192 m
248.757 122.936 248.964 123.42 249.204 124.017 c
246.934 124.017 l
247.035 123.803 247.381 122.936 247.605 122.192 c
247.845 121.396 248.01 120.674 248.069 120.206 c
248.128 120.674 248.292 121.396 248.533 122.192 c
f
247.61 231.316 m
247.385 230.573 247.178 230.089 246.939 229.492 c
249.209 229.492 l
249.108 229.706 248.762 230.573 248.538 231.316 c
248.297 232.113 248.132 232.835 248.074 233.303 c
248.015 232.835 247.851 232.113 247.61 231.316 c
f
248.049 176.885 m
403.565 176.885 l
S
404.628 177.346 m
403.884 177.57 403.4 177.777 402.803 178.017 c
402.803 175.747 l
403.017 175.849 403.884 176.194 404.628 176.418 c
405.424 176.659 406.146 176.823 406.614 176.882 c
406.146 176.941 405.424 177.105 404.628 177.346 c
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BT
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(0)Tj
0 8.5124 TD
(1)Tj
-0.5 -4.875 Td
(0)Tj
/T1_3 1 Tf
0.551 0 Td
(\341)Tj
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0.273 0 Td
(4)Tj
-0.005 Tc -0.7741 -12.1123 Td
(-1)Tj
7.359 7.3254 Td
(90)Tj
/T1_6 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 5.0004 0 Td
(180)Tj
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0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7247 0 Td
(270)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7248 0.0375 Td
(360)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc -23.6397 -0.0375 Td
(45)Tj
/T1_6 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 5.0004 0 Td
(135)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.7247 0 Td
(225)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 4.6209 -0.023 Td
(315)Tj
/T1_6 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
ET
0.25 w 
362.851 176.885 m
362.851 174.185 l
324.584 176.885 m
324.584 174.185 l
401.119 176.885 m
401.119 174.185 l
286.317 176.885 m
286.317 174.185 l
343.717 176.885 m
343.717 174.185 l
305.45 176.885 m
305.45 174.185 l
381.985 176.885 m
381.985 174.185 l
267.183 176.885 m
267.183 174.185 l
248.049 176.846 m
268.844 227.869 286.317 227.869 v
303.788 227.869 324.584 176.846 y
345.415 125.823 362.851 125.823 v
380.288 125.823 401.119 176.846 y
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[0.5 2]0 d 
105.626 355.657 m
105.626 247.657 l
182.182 355.657 m
182.182 247.657 l
248.033 198.374 m
403.276 198.374 l
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[]0 d 
67.358 301.675 m
96.323 306.382 100.373 314.431 104.423 352.698 c
143.893 301.675 m
172.858 306.382 176.907 314.431 180.958 352.698 c
143.893 301.675 m
114.928 296.967 110.879 288.919 106.829 250.651 c
220.428 301.675 m
191.463 296.967 187.413 288.919 183.363 250.651 c
258.521 196.214 m
258.521 179.214 l
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258.777 178.624 m
258.901 179.037 259.016 179.305 259.15 179.637 c
257.888 179.637 l
257.945 179.518 258.136 179.037 258.261 178.624 c
258.395 178.181 258.487 177.78 258.519 177.52 c
258.552 177.78 258.643 178.181 258.777 178.624 c
f
258.264 196.804 m
258.139 196.391 258.025 196.122 257.891 195.791 c
259.153 195.791 l
259.096 195.909 258.904 196.391 258.779 196.804 c
258.646 197.247 258.554 197.648 258.522 197.908 c
258.489 197.648 258.398 197.247 258.264 196.804 c
f
314.271 196.214 m
314.271 179.214 l
S
314.527 178.624 m
314.651 179.037 314.766 179.305 314.9 179.637 c
313.638 179.637 l
313.695 179.518 313.886 179.037 314.011 178.624 c
314.145 178.181 314.237 177.78 314.269 177.52 c
314.302 177.78 314.393 178.181 314.527 178.624 c
f
314.014 196.804 m
313.889 196.391 313.775 196.122 313.641 195.791 c
314.902 195.791 l
314.846 195.909 314.654 196.391 314.529 196.804 c
314.396 197.247 314.304 197.648 314.272 197.908 c
314.239 197.648 314.148 197.247 314.014 196.804 c
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0.925 0.725 0.075 0.012 k
BT
/T1_0 1 Tf
-0.005 Tc 9 0 0 9 203.9435 507.04 Tm
(Sine)Tj
19.6296 -31.1852 Td
(Sine)Tj
0 g
/T1_2 1 Tf
-35.6938 36.6342 Td
[(Y)92(ou must memorise these graphs.)]TJ
0 -1.3333 TD
[(In an emer)18(gency you can draw them by using your calculator)92(,)]TJ
T*
(eg for sin find values at 45)Tj
/T1_6 1 Tf
0 Tc 11.5825 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( intervals, ie 0)Tj
/T1_6 1 Tf
0 Tc 6.0667 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
(, 45)Tj
/T1_6 1 Tf
0 Tc 1.6479 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
(, 90)Tj
/T1_6 1 Tf
0 Tc 1.6479 0 Td
(\006)Tj
/T1_3 1 Tf
0.395 0 Td
(\311)Tj
/T1_2 1 Tf
-0.005 Tc 0.995 0 Td
( , 360)Tj
/T1_6 1 Tf
0 Tc 2.4719 0 Td
(\006)Tj
0.925 0.725 0.075 0.012 k
/T1_0 1 Tf
-0.005 Tc 9.5537 -14.1713 Td
(Cosine)Tj
-20.8889 -4.9815 Td
[(T)100(angent)]TJ
0 g
/T1_2 1 Tf
7 0 0 7 318.5851 547.04 Tm
[(Y)92(ou can r)18(emember these )]TJ
1.4932 -1.4286 Td
(important facts by )Tj
-0.7065 -1.4286 Td
(looking at the graphs.)Tj
6 0 0 6 169.5738 491.54 Tm
(+ve for 0)Tj
/T1_6 1 Tf
0 Tc 3.9922 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 180)Tj
/T1_6 1 Tf
0 Tc 3.1142 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc -7.886 -1.3333 Td
(-ve for 180)Tj
/T1_6 1 Tf
0 Tc 4.7613 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 360)Tj
/T1_6 1 Tf
0 Tc 3.1142 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 9 0 0 9 262.9435 339.3735 Tm
(Look at the symmetry of all )Tj
T*
[(thr)18(ee graphs.)]TJ
0 -2.2222 TD
(The graphs continue the same )Tj
0 -1.3333 TD
[(symmetrical patter)-18(ns for negative )]TJ
T*
[(angles and angles gr)18(eater than 360)]TJ
/T1_6 1 Tf
0 Tc 15.5724 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
(. )Tj
-15.9673 -2.4444 Td
[(Notice ther)18(e ar)18(e no values for )]TJ
T*
(tangents at 90)Tj
/T1_6 1 Tf
0 Tc 6.3367 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
(, 270)Tj
/T1_6 1 Tf
0 Tc 2.1989 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
(, 450)Tj
/T1_6 1 Tf
0 Tc 2.1989 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
(, etc.)Tj
-34.5392 -4.1806 Td
[(Y)92(ou can use the graphs to find angles.)]TJ
0 -1.7778 TD
[(Suppose you ar)18(e given the question )]TJ
0 -1.4 TD
(sin x = 0)Tj
/T1_3 1 Tf
0 Tc 3.7148 0 Td
(\341)Tj
/T1_2 1 Tf
-0.005 Tc 0.273 0 Td
(4. Find values of x )Tj
-3.9878 -1.4 Td
(between 0)Tj
/T1_6 1 Tf
0 Tc 4.6778 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( and 360)Tj
/T1_6 1 Tf
0 Tc 3.8698 0 Td
(\006)Tj
/T1_2 1 Tf
0.395 0 Td
(.)Tj
/T1_0 1 Tf
-0.005 Tc -9.3376 -1.8667 Td
(Method:)Tj
/T1_2 1 Tf
3.9638 0 Td
( Draw a horizontal line at 0)Tj
/T1_3 1 Tf
0 Tc 11.7465 0 Td
(\341)Tj
/T1_2 1 Tf
-0.005 Tc 0.273 0 Td
(4. )Tj
-15.9833 -1.4 Td
[(This gives appr)18(oximate values x = 25)]TJ
/T1_6 1 Tf
0 Tc 16.2663 0 Td
(\006)Tj
/T1_2 1 Tf
0.395 0 Td
( )Tj
-0.005 Tc -16.6613 -1.4 Td
(and x= 155)Tj
/T1_6 1 Tf
0 Tc 5.0078 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc -1.6349 -3.538 Td
(Note:)Tj
/T1_2 1 Tf
2.6399 0 Td
[( Y)92(ou would use the same method if you wer)18(e given the graph of)]TJ
0.6157 -1.4 Td
(y = 2cosx and asked )Tj
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(\322)Tj
/T1_2 1 Tf
-0.005 Tc 0.514 0 Td
(2cosx = 0)Tj
/T1_3 1 Tf
0 Tc 4.2718 0 Td
(\341)Tj
/T1_2 1 Tf
-0.005 Tc 0.273 0 Td
(4. Find the value of x)Tj
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(\323)Tj
/T1_2 1 Tf
0.514 0 Td
(.)Tj
-0.005 Tc 6 0 0 6 197.9353 342.665 Tm
(+ve for 0)Tj
/T1_6 1 Tf
0 Tc 3.9922 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 90)Tj
/T1_6 1 Tf
0 Tc 2.5632 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc -7.0284 -1.3333 Td
(and 180)Tj
/T1_6 1 Tf
0 Tc 3.5972 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 270)Tj
/T1_6 1 Tf
0 Tc 3.1142 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc -7.4129 -1.3333 Td
(-ve for 90)Tj
/T1_6 1 Tf
0 Tc 4.2103 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 180)Tj
/T1_6 1 Tf
0 Tc 3.1142 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc -7.413 -1.3333 Td
(and 270)Tj
/T1_6 1 Tf
0 Tc 3.5972 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 360)Tj
/T1_6 1 Tf
0 Tc 3.1142 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 19.9392 11.9722 Td
(+ve for 0)Tj
/T1_6 1 Tf
0 Tc 3.9922 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 90)Tj
/T1_6 1 Tf
0 Tc 2.5632 0 Td
(\006)Tj
/T1_2 1 Tf
0.395 0 Td
( )Tj
-0.005 Tc -7.287 -1.3333 Td
(and 270)Tj
/T1_6 1 Tf
0 Tc 3.5972 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 360)Tj
/T1_6 1 Tf
0 Tc 3.1142 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc -7.4129 -1.3333 Td
(-ve for 90)Tj
/T1_6 1 Tf
0 Tc 4.2103 0 Td
(\006)Tj
/T1_2 1 Tf
-0.005 Tc 0.395 0 Td
( to 270)Tj
/T1_6 1 Tf
0 Tc 3.1142 0 Td
(\006)Tj
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/GS3 gs
257.488 211.06 m
258.605 211.06 259.52 211.974 259.52 213.092 c
259.52 219.187 l
259.52 220.305 258.605 221.22 257.488 221.22 c
246.312 221.22 l
245.195 221.22 244.28 220.305 244.28 219.187 c
244.28 213.092 l
244.28 211.974 245.195 211.06 246.312 211.06 c
257.488 211.06 l
h
B
257.798 212.062 m
258.219 212.062 258.56 212.404 258.56 212.825 c
B
246.016 220.351 m
245.595 220.351 245.254 220.01 245.254 219.589 c
B
275.727 196.06 m
276.844 196.06 277.759 196.974 277.759 198.092 c
277.759 204.187 l
277.759 205.305 276.844 206.22 275.727 206.22 c
264.551 206.22 l
263.434 206.22 262.52 205.305 262.52 204.187 c
262.52 198.092 l
262.52 196.974 263.434 196.06 264.551 196.06 c
275.727 196.06 l
h
B
276.038 197.062 m
276.458 197.062 276.799 197.404 276.799 197.825 c
B
264.255 205.351 m
263.834 205.351 263.494 205.01 263.494 204.589 c
B
293.966 196.06 m
295.083 196.06 295.998 196.974 295.998 198.092 c
295.998 204.187 l
295.998 205.305 295.083 206.22 293.966 206.22 c
282.79 206.22 l
281.673 206.22 280.759 205.305 280.759 204.187 c
280.759 198.092 l
280.759 196.974 281.673 196.06 282.79 196.06 c
293.966 196.06 l
h
B
294.277 197.062 m
294.698 197.062 295.038 197.404 295.038 197.825 c
B
282.495 205.351 m
282.074 205.351 281.733 205.01 281.733 204.589 c
B
257.488 196.06 m
258.605 196.06 259.52 196.974 259.52 198.092 c
259.52 204.187 l
259.52 205.305 258.605 206.22 257.488 206.22 c
246.312 206.22 l
245.195 206.22 244.28 205.305 244.28 204.187 c
244.28 198.092 l
244.28 196.974 245.195 196.06 246.312 196.06 c
257.488 196.06 l
h
B
257.798 197.062 m
258.219 197.062 258.56 197.404 258.56 197.825 c
B
246.016 205.351 m
245.595 205.351 245.254 205.01 245.254 204.589 c
B
257.488 184.06 m
258.605 184.06 259.52 184.974 259.52 186.092 c
259.52 192.187 l
259.52 193.305 258.605 194.22 257.488 194.22 c
246.312 194.22 l
245.195 194.22 244.28 193.305 244.28 192.187 c
244.28 186.092 l
244.28 184.974 245.195 184.06 246.312 184.06 c
257.488 184.06 l
h
B
257.798 185.062 m
258.219 185.062 258.56 185.404 258.56 185.825 c
B
246.016 193.351 m
245.595 193.351 245.254 193.01 245.254 192.589 c
B
0.039 0.02 0.486 0 k
0.58 w 
278.06 320.56 138.5 43.5 re
B
89.06 136.56 115 51 re
B
89.06 248.56 119 51 re
B
89.06 386.06 128.5 51 re
B
0 g
BT
/T1_0 1 Tf
-0.005 Tc 7 0 0 7 101.2137 426.0601 Tm
(Between)Tj
/T1_4 1 Tf
0 Tc 0.3885 -1.2857 Td
(0)Tj
/T1_5 1 Tf
0.551 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 90)Tj
/T1_5 1 Tf
0 Tc 1.976 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -3.4731 -1.2857 Td
(90)Tj
/T1_5 1 Tf
0 Tc 1.102 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 180)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.2996 -1.2857 Td
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 270)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.5751 -1.2857 Td
(270)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 360)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc -4.4228 -14.3571 Td
(Between)Tj
/T1_4 1 Tf
0 Tc 0.3885 -1.2857 Td
(0)Tj
/T1_5 1 Tf
0.551 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 90)Tj
/T1_5 1 Tf
0 Tc 1.976 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -3.473 -1.2857 Td
(90)Tj
/T1_5 1 Tf
0 Tc 1.102 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 180)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.2996 -1.2857 Td
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 270)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.5751 -1.2857 Td
(270)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 360)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc -4.1371 -10.8571 Td
(Between)Tj
/T1_4 1 Tf
0 Tc 0.3885 -1.2857 Td
(0)Tj
/T1_5 1 Tf
0.551 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 90)Tj
/T1_5 1 Tf
0 Tc 1.976 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -3.473 -1.2857 Td
(90)Tj
/T1_5 1 Tf
0 Tc 1.102 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 180)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.2996 -1.2857 Td
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 270)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.5751 -1.2857 Td
(270)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 360)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc 2.8591 40.6429 Td
(Method)Tj
/T1_4 1 Tf
1.088 -1.2857 Td
(20)Tj
/T1_5 1 Tf
0 Tc 1.102 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.6465 -1.2857 Td
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
( )Tj
/T1_6 1 Tf
0.273 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( 20)Tj
/T1_5 1 Tf
0 Tc 1.375 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.2741 -1.2857 Td
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( + 20)Tj
/T1_5 1 Tf
0 Tc 2.309 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.4131 -1.2857 Td
(360)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
( )Tj
/T1_6 1 Tf
0.273 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( 20)Tj
/T1_5 1 Tf
0 Tc 1.375 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc 2.3735 5.1429 Td
(Angle)Tj
/T1_4 1 Tf
0.619 -1.2857 Td
(20)Tj
/T1_5 1 Tf
0 Tc 1.102 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.3775 -1.2857 Td
(160)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.653 -1.2857 Td
(200)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.792 -1.2857 Td
(340)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc -9.059 -30.3571 Td
(Method)Tj
/T1_4 1 Tf
0 -2.5714 TD
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
( )Tj
/T1_6 1 Tf
0.273 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( 28)Tj
/T1_5 1 Tf
0 Tc 1.375 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.1911 -1.2857 Td
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( + 28)Tj
/T1_5 1 Tf
0 Tc 2.309 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.3571 -1.2857 Td
(360)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
( )Tj
/T1_6 1 Tf
0.273 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( 28)Tj
/T1_5 1 Tf
0 Tc 1.375 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc 1.1661 5.1429 Td
(Angle)Tj
/T1_4 1 Tf
0 -1.2857 TD
(= 28)Tj
/T1_5 1 Tf
0 Tc 2.036 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.036 -1.2857 Td
(= 152)Tj
/T1_5 1 Tf
0 Tc 2.587 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.587 -1.2857 Td
(= 208)Tj
/T1_5 1 Tf
0 Tc 2.587 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.587 -1.2857 Td
(= 332)Tj
/T1_5 1 Tf
0 Tc 2.587 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 2.913 3.8571 Td
(0.4694715)Tj
T*
(0.4694715)Tj
T*
(-0.4694715)Tj
T*
(-0.4694715)Tj
0.172 0.89 0.796 0.047 k
/T1_0 1 Tf
8 0 0 8 54.808 452.5601 Tm
(Answers)Tj
0 g
/T1_4 1 Tf
7 0 0 7 88.8237 442.5601 Tm
(If you have one value for an angle, eg cos 20)Tj
/T1_5 1 Tf
0 Tc 19.7533 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
[( = 0.9396926. Y)92(ou can find the )]TJ
/T1_6 1 Tf
0 Tc 13.7962 0 Td
(\322)Tj
/T1_4 1 Tf
-0.005 Tc 0.514 0 Td
(friends)Tj
/T1_6 1 Tf
0 Tc 2.9821 0 Td
(\323)Tj
/T1_4 1 Tf
-0.005 Tc 0.514 0 Td
( of 20)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( like this.)Tj
-19.0572 -3.8571 Td
(The cos of all of these angles will be 0.9396926 )Tj
/T1_0 1 Tf
T*
(but)Tj
/T1_4 1 Tf
1.578 0 Td
( two will be +ve and two will be )Tj
/T1_6 1 Tf
0 Tc 14.2393 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(ve)Tj
0 Tc -40.5614 5.1429 Td
(1)Tj
0 -19.4286 TD
(2)Tj
0 -15 TD
(3)Tj
ET
0.5 w 
231.56 428.56 m
235.06 428.56 231.56 412.06 235.06 412.06 c
231.56 395.56 m
235.06 395.56 231.56 412.06 235.06 412.06 c
193.747 364.06 m
197.248 364.06 193.747 347.56 197.248 347.56 c
193.747 331.06 m
197.248 331.06 193.747 347.56 197.248 347.56 c
259.185 174.498 m
262.685 174.498 259.185 157.998 262.685 157.998 c
259.185 141.498 m
262.685 141.498 259.185 157.998 262.685 157.998 c
258.247 286.498 m
261.748 286.498 258.247 269.998 261.748 269.998 c
258.247 253.498 m
261.748 253.498 258.247 269.998 261.748 269.998 c
328.06 358.56 m
324.56 358.56 328.06 342.06 324.56 342.06 c
328.06 325.56 m
324.56 325.56 328.06 342.06 324.56 342.06 c
S
BT
/T1_4 1 Tf
-0.005 Tc 7 0 0 7 98.06 359.0601 Tm
(cos 20)Tj
/T1_5 1 Tf
0 Tc 2.8611 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.8611 -1.2857 Td
(cos 160)Tj
/T1_5 1 Tf
0 Tc 3.4121 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -3.4121 -1.2857 Td
(cos 200)Tj
/T1_5 1 Tf
0 Tc 3.4121 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -3.4121 -1.2857 Td
(cos 340)Tj
/T1_5 1 Tf
0 Tc 3.4121 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 1.6594 3.8571 Td
(0.9396926 \(+ve\))Tj
0 -1.2857 TD
(-0.9396926 \()Tj
/T1_6 1 Tf
0 Tc 5.5371 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(ve\))Tj
-6.0321 -1.2857 Td
(-0.9396926 \()Tj
/T1_6 1 Tf
0 Tc 5.5371 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(ve\))Tj
-6.0321 -1.2857 Td
(0.9396926 \(+ve\))Tj
-6.3909 5.6429 Td
[(Either use the cosine graph you have memorised or check using your calcu\
lator)92(,)]TJ
16.3195 -3.6429 Td
(Answer 160)Tj
/T1_5 1 Tf
0 Tc 5.1741 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( and 200)Tj
/T1_5 1 Tf
0 Tc 3.8701 0 Td
(\006)Tj
/T1_4 1 Tf
8.7751 1 Td
(0)Tj
/T1_5 1 Tf
0.551 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 90)Tj
/T1_5 1 Tf
0 Tc 1.976 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 1.7065 0 Td
(     angle)Tj
-4.6285 -1.2857 Td
(90)Tj
/T1_5 1 Tf
0 Tc 1.102 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 180)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.6045 0 Td
(     180 )Tj
/T1_6 1 Tf
0 Tc 3.2911 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( angle)Tj
-8.4146 -1.2857 Td
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 270)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
(    180 + angle)Tj
-4.9701 -1.2857 Td
(270)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 360)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
(    360 )Tj
/T1_6 1 Tf
0 Tc 3.0181 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( angle)Tj
/T1_0 1 Tf
-14.9831 2.0714 Td
(It is always)Tj
-20.748 -7.2857 Td
(Method)Tj
/T1_4 1 Tf
T*
(must be)Tj
T*
(given as)Tj
T*
(180)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( + 50)Tj
/T1_5 1 Tf
0 Tc 2.309 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -4.3571 -1.2857 Td
(360)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
( )Tj
/T1_6 1 Tf
0.273 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( 50)Tj
/T1_5 1 Tf
0 Tc 1.375 0 Td
(\006)Tj
/T1_0 1 Tf
-0.005 Tc 1.6284 5.1429 Td
(Angle)Tj
/T1_4 1 Tf
T*
(= 50)Tj
/T1_5 1 Tf
0 Tc 2.036 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.036 -1.2857 Td
(= 130)Tj
/T1_5 1 Tf
0 Tc 2.587 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.587 -1.2857 Td
(= 230)Tj
/T1_5 1 Tf
0 Tc 2.587 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -2.587 -1.2857 Td
(= 310)Tj
/T1_5 1 Tf
0 Tc 2.587 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 2.4844 3.9286 Td
(1.1917535)Tj
T*
(-1.1917535)Tj
T*
(1.1917535)Tj
T*
(-1.1917535)Tj
-18.1766 -2.2857 Td
(Answer is 50)Tj
/T1_5 1 Tf
0 Tc 5.5521 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( and 230)Tj
/T1_5 1 Tf
0 Tc 3.8701 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
[(. T)111(o find other values, keep adding or subtracting 360)]TJ
/T1_5 1 Tf
0 Tc 23.6384 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
(,)Tj
-0.005 Tc -34.2456 -1.4286 Td
(eg 50)Tj
/T1_5 1 Tf
0 Tc 2.532 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
( )Tj
/T1_6 1 Tf
0.273 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( 360)Tj
/T1_5 1 Tf
0 Tc 1.926 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( = )Tj
/T1_6 1 Tf
0 Tc 1.207 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(310)Tj
/T1_5 1 Tf
0 Tc 1.653 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
(, 230)Tj
/T1_5 1 Tf
0 Tc 2.199 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( + 360)Tj
/T1_5 1 Tf
0 Tc 2.8601 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( = 590)Tj
/T1_5 1 Tf
0 Tc 2.8601 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
(.)Tj
-0.005 Tc -18.8703 11.2143 Td
[(Y)92(ou ar)18(e given )]TJ
/T1_6 1 Tf
0 Tc 6.2291 0 Td
(\322)Tj
/T1_4 1 Tf
-0.005 Tc 0.514 0 Td
(friend 2)Tj
/T1_6 1 Tf
0 Tc 3.3851 0 Td
(\323)Tj
/T1_4 1 Tf
-0.005 Tc 0.514 0 Td
( \(90)Tj
/T1_5 1 Tf
0 Tc 1.63 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 180)Tj
/T1_5 1 Tf
0 Tc 2.527 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
(\). Friend 2 is 180)Tj
/T1_5 1 Tf
0 Tc 7.3011 0 Td
(\006)Tj
/T1_4 1 Tf
0.395 0 Td
( )Tj
/T1_6 1 Tf
0.273 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
( ? = 130)Tj
/T1_5 1 Tf
0 Tc 3.6101 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
(. So )Tj
/T1_6 1 Tf
0 Tc 1.958 0 Td
(\322)Tj
/T1_4 1 Tf
-0.005 Tc 0.514 0 Td
(friend 1)Tj
/T1_6 1 Tf
0 Tc 3.3851 0 Td
(\323)Tj
/T1_4 1 Tf
-0.005 Tc 0.514 0 Td
( = 50)Tj
/T1_5 1 Tf
0 Tc 2.309 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -11.062 -4.2143 Td
(Use the tangent graph you have )Tj
T*
(memorised or your calculator to find )Tj
T*
[(which ar)18(e +ve and which ar)18(e )]TJ
/T1_6 1 Tf
0 Tc 12.8082 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(ve.)Tj
-38.9798 -8.2143 Td
(Put )Tj
/T1_6 1 Tf
0 Tc 1.72 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
[(0.469471562 into your calculator then pr)18(ess)]TJ
23.3187 -5.3571 Td
(Use the sine graph you have )Tj
T*
(memorised or your calculator )Tj
T*
[(to find which ar)18(e )]TJ
/T1_6 1 Tf
0 Tc 7.5951 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(ve.)Tj
-33.6239 -3 Td
(Answer = x = 208)Tj
/T1_5 1 Tf
0 Tc 7.7921 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( or 332)Tj
/T1_5 1 Tf
0 Tc 3.1141 0 Td
(\006)Tj
/T1_0 1 Tf
0.0001 Tc 5 0 0 5 247.6972 213.8643 Tm
(INV)Tj
3.5979 -2.95 Td
(SIN)Tj
0 Tc 8 0 0 8 285.6865 199.1143 Tm
(=)Tj
0.0001 Tc 4 0 0 4 246.1972 199.3643 Tm
(SHIFT)Tj
5 0 0 5 246.6972 187.1143 Tm
(2ND)Tj
/T1_4 1 Tf
-0.005 Tc 7 0 0 7 302.3935 212.0601 Tm
(This will give )Tj
/T1_6 1 Tf
0 Tc 5.8861 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(28)Tj
/T1_5 1 Tf
0 Tc 1.102 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
(. \(If the calculator )Tj
-7.8781 -1.2857 Td
(gives a )Tj
/T1_6 1 Tf
0 Tc 3.3501 0 Td
(\320)Tj
/T1_4 1 Tf
-0.005 Tc 0.495 0 Td
(ve value, the 0)Tj
/T1_5 1 Tf
0 Tc 6.4281 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( - 90)Tj
/T1_5 1 Tf
0 Tc 1.976 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( value )Tj
-13.0392 -1.2857 Td
(will be the same angle but )Tj
T*
(positive, ie 28)Tj
/T1_5 1 Tf
0 Tc 6.1471 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
(.\))Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS3 cs 1  scn
BT
/T1_0 1 Tf
-0.0001 Tc 10 0 0 10 51.3228 556.4808 Tm
(Questions)Tj
0 0 0 1 k
/T1_4 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 544.4808 Tm
[(1)-1332(Cos 20)]TJ
/T1_6 1 Tf
0 Tc 0 Tw 5.0279 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.7055 0 Td
(= 0)Tj
/T1_6 1 Tf
0 Tc 0 Tw 1.5274 0 Td
(\341)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(9396926. Find the angles between 0)Tj
/T1_6 1 Tf
0 Tc 0 Tw 16.4547 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.7055 0 Td
(and 360)Tj
/T1_6 1 Tf
0 Tc 0 Tw 3.6589 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0002 Tc 0.7055 0 Td
[(wher)18(e )]TJ
0.0278 Tw -27.1753 -1.3333 Td
(cos x)Tj
/T1_6 1 Tf
0 Tc 0 Tw 2.288 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.7055 0 Td
(= -0)Tj
/T1_6 1 Tf
0 Tc 0 Tw 1.8602 0 Td
(\341)Tj
/T1_4 1 Tf
-0.0001 Tc 0.2779 0 Td
(9396926)Tj
0.0278 Tw -7.0197 -1.6483 Td
[(2)-1332(T)111(an 130)]TJ
/T1_6 1 Tf
0 Tc 0 Tw 5.3992 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0277 Tw 0.7055 0 Td
[(= -1.1917535. Find four angles wher)18(e tan x)]TJ
/T1_6 1 Tf
0 Tc 0 Tw 19.3791 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.7055 0 Td
(= 1)Tj
/T1_6 1 Tf
0 Tc 0 Tw 1.5274 0 Td
(\341)Tj
/T1_4 1 Tf
-0.0001 Tc 0.2779 0 Td
(1917535)Tj
0.0278 Tw -27.9946 -1.6483 Td
[(3)-1334(Sin x)]TJ
/T1_6 1 Tf
0 Tc 0 Tw 4.0291 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.7055 0 Td
(= -0)Tj
/T1_6 1 Tf
0 Tc 0 Tw 1.8603 0 Td
(\341)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(4694715. Find two values of x between 0)Tj
/T1_6 1 Tf
0 Tc 0 Tw 18.5104 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0277 Tw 0.7055 0 Td
(and 360)Tj
/T1_6 1 Tf
0 Tc 0 Tw 3.6589 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0002 Tc 0.0278 Tw -29.7476 -1.6483 Td
[(4)-1332(Draw the graph of y = 2cos x )]TJ
/T1_6 1 Tf
0 Tc 0 Tw 15.2929 0 Td
(\320)Tj
/T1_4 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 1 for 0 )Tj
/T1_5 1 Tf
0 Tc 0 Tw 3.5549 0 Td
(\005)Tj
/T1_4 1 Tf
-0.0002 Tc 0.8544 0 Td
(x )Tj
/T1_5 1 Tf
0 Tc 0.7876 0 Td
(\005)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.5488 0 Td
(360 using 30)Tj
/T1_6 1 Tf
0 Tc 0 Tw 5.7792 0 Td
(\241)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.7055 0 Td
(intervals and hence find)Tj
-26.1352 -1.3334 Td
(values of x for which 2cos x )Tj
/T1_6 1 Tf
0 Tc 0 Tw 12.6026 0 Td
(\320)Tj
/T1_4 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 1 = -1)Tj
/T1_6 1 Tf
0 Tc 0 Tw 3.0274 0 Td
(\341)Tj
/T1_4 1 Tf
0.2779 0 Td
(5)Tj
ET
Q Q 
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0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
49.61 42.05 368.5 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 50.6063 35.0006 Tm
(64)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 265.7926 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
49.61 593.39 368.5 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0296 Tw 14 0 0 14 97.4307 581.8038 Tm
(Sine, cosine and tangent of any angle )Tj
/T1_2 1 Tf
0 Tc 0 Tw 18.0723 0 Td
(\320)Tj
/T1_0 1 Tf
0.0295 Tc 0.4999 0 Td
( 3)Tj
0 0 0 1 k
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 10 0 0 10 50.6063 604.6698 Tm
[(Pythagoras\325 theor)18(em and trigonometry)]TJ
ET
Q Q 
q
49.61 565.04 368.5 -262.85 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.141 0.039 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS3 gs
226.461 476.04 m
227.578 476.04 228.493 476.954 228.493 478.072 c
228.493 484.167 l
228.493 485.285 227.578 486.2 226.461 486.2 c
215.285 486.2 l
214.168 486.2 213.254 485.285 213.254 484.167 c
213.254 478.072 l
213.254 476.954 214.168 476.04 215.285 476.04 c
226.461 476.04 l
h
B
226.771 477.042 m
227.192 477.042 227.533 477.384 227.533 477.805 c
B
214.989 485.331 m
214.568 485.331 214.227 484.99 214.227 484.569 c
B
299.162 476.04 m
300.279 476.04 301.194 476.954 301.194 478.072 c
301.194 484.167 l
301.194 485.285 300.279 486.2 299.162 486.2 c
287.987 486.2 l
286.869 486.2 285.955 485.285 285.955 484.167 c
285.955 478.072 l
285.955 476.954 286.869 476.04 287.987 476.04 c
299.162 476.04 l
h
B
299.472 477.042 m
299.893 477.042 300.235 477.384 300.235 477.805 c
B
287.691 485.331 m
287.27 485.331 286.928 484.99 286.928 484.569 c
B
317.337 476.04 m
318.455 476.04 319.369 476.954 319.369 478.072 c
319.369 484.167 l
319.369 485.285 318.455 486.2 317.337 486.2 c
306.162 486.2 l
305.044 486.2 304.13 485.285 304.13 484.167 c
304.13 478.072 l
304.13 476.954 305.044 476.04 306.162 476.04 c
317.337 476.04 l
h
B
317.648 477.042 m
318.069 477.042 318.41 477.384 318.41 477.805 c
B
305.866 485.331 m
305.445 485.331 305.104 484.99 305.104 484.569 c
B
353.688 476.04 m
354.805 476.04 355.719 476.954 355.719 478.072 c
355.719 484.167 l
355.719 485.285 354.805 486.2 353.688 486.2 c
342.512 486.2 l
341.395 486.2 340.481 485.285 340.481 484.167 c
340.481 478.072 l
340.481 476.954 341.395 476.04 342.512 476.04 c
353.688 476.04 l
h
B
353.998 477.042 m
354.419 477.042 354.76 477.384 354.76 477.805 c
B
342.216 485.331 m
341.795 485.331 341.454 484.99 341.454 484.569 c
B
0.129 0.063 0.035 0.004 k
208.285 476.04 m
209.403 476.04 210.317 476.954 210.317 478.072 c
210.317 484.167 l
210.317 485.285 209.403 486.2 208.285 486.2 c
197.11 486.2 l
195.992 486.2 195.078 485.285 195.078 484.167 c
195.078 478.072 l
195.078 476.954 195.992 476.04 197.11 476.04 c
208.285 476.04 l
h
B
208.596 477.042 m
209.017 477.042 209.358 477.384 209.358 477.805 c
B
196.814 485.331 m
196.393 485.331 196.052 484.99 196.052 484.569 c
B
244.636 476.04 m
245.754 476.04 246.668 476.954 246.668 478.072 c
246.668 484.167 l
246.668 485.285 245.754 486.2 244.636 486.2 c
233.461 486.2 l
232.343 486.2 231.429 485.285 231.429 484.167 c
231.429 478.072 l
231.429 476.954 232.343 476.04 233.461 476.04 c
244.636 476.04 l
h
B
244.946 477.042 m
245.367 477.042 245.709 477.384 245.709 477.805 c
B
233.165 485.331 m
232.744 485.331 232.403 484.99 232.403 484.569 c
B
262.811 476.04 m
263.929 476.04 264.843 476.954 264.843 478.072 c
264.843 484.167 l
264.843 485.285 263.929 486.2 262.811 486.2 c
251.636 486.2 l
250.518 486.2 249.604 485.285 249.604 484.167 c
249.604 478.072 l
249.604 476.954 250.518 476.04 251.636 476.04 c
262.811 476.04 l
h
B
263.122 477.042 m
263.543 477.042 263.884 477.384 263.884 477.805 c
B
251.34 485.331 m
250.919 485.331 250.578 484.99 250.578 484.569 c
B
280.987 476.04 m
282.104 476.04 283.019 476.954 283.019 478.072 c
283.019 484.167 l
283.019 485.285 282.104 486.2 280.987 486.2 c
269.811 486.2 l
268.694 486.2 267.779 485.285 267.779 484.167 c
267.779 478.072 l
267.779 476.954 268.694 476.04 269.811 476.04 c
280.987 476.04 l
h
B
281.297 477.042 m
281.718 477.042 282.059 477.384 282.059 477.805 c
B
269.515 485.331 m
269.094 485.331 268.753 484.99 268.753 484.569 c
B
335.512 476.04 m
336.63 476.04 337.545 476.954 337.545 478.072 c
337.545 484.167 l
337.545 485.285 336.63 486.2 335.512 486.2 c
324.337 486.2 l
323.219 486.2 322.305 485.285 322.305 484.167 c
322.305 478.072 l
322.305 476.954 323.219 476.04 324.337 476.04 c
335.512 476.04 l
h
B
335.823 477.042 m
336.244 477.042 336.585 477.384 336.585 477.805 c
B
324.041 485.331 m
323.62 485.331 323.279 484.99 323.279 484.569 c
B
0 g
BT
/T1_4 1 Tf
7 0 0 7 67.3659 542.54 Tm
(4)Tj
-0.005 Tc 6 0 0 6 398.7371 510.04 Tm
(360)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.9046 -2 Td
(1)Tj
-0.005 Tc 7 0 0 7 84.7072 459.3735 Tm
(Draw the graph)Tj
0 2.7857 TD
(Example: calculator keys for 150)Tj
/T1_5 1 Tf
0 Tc 14.2132 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
[(:)-24891(Answer: )]TJ
/T1_6 1 Tf
0 Tc 28.9576 0 Td
(\320)Tj
/T1_4 1 Tf
0.495 0 Td
(2)Tj
/T1_6 1 Tf
0.551 0 Td
(\341)Tj
/T1_4 1 Tf
-0.005 Tc 0.273 0 Td
(73)Tj
-14.254 -21.4405 Td
(Answer x = 105)Tj
/T1_5 1 Tf
0 Tc 6.8581 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( and 255)Tj
/T1_5 1 Tf
0 Tc 3.8701 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
[( appr)18(ox.)]TJ
-42.1968 30.4643 Td
[(Y)92(ou need a table of values. If you need a very accurate graph you should \
use 10)]TJ
/T1_5 1 Tf
0 Tc 35.1976 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
( intervals.)Tj
-35.5926 -1.7143 Td
(If not, intervals of 30)Tj
/T1_5 1 Tf
0 Tc 9.0002 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc 0.395 0 Td
[( will be satisfactory)92(. The question will nor)-18(mally indicate the level of accuracy)92(.)]TJ
ET
394.067 507.04 21.658 12 re
394.067 495.04 21.658 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 377.0794 510.04 Tm
(330)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-1.5921 -2 Td
(0)Tj
/T1_6 1 Tf
0.551 0 Td
(\341)Tj
/T1_4 1 Tf
-0.005 Tc 0.273 0 Td
(73)Tj
ET
372.41 507.04 21.657 12 re
372.41 495.04 21.657 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 355.4217 510.04 Tm
(300)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.9046 -2 Td
(0)Tj
ET
350.752 507.04 21.658 12 re
350.752 495.04 21.658 12 re
S
BT
/T1_4 1 Tf
-0.005 Tc 6 0 0 6 333.764 510.04 Tm
(270)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.0686 -2 Td
(-1)Tj
ET
329.094 507.04 21.658 12 re
329.094 495.04 21.658 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 312.1068 510.04 Tm
(240)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.0686 -2 Td
(-2)Tj
ET
307.437 507.04 21.657 12 re
307.437 495.04 21.657 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 290.449 510.04 Tm
(210)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.7561 -2 Td
(-2)Tj
/T1_6 1 Tf
0 Tc 0.8791 0 Td
(\341)Tj
/T1_4 1 Tf
-0.005 Tc 0.273 0 Td
(73)Tj
ET
285.779 507.04 21.658 12 re
285.779 495.04 21.658 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 268.7918 510.04 Tm
(180)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.0686 -2 Td
(-3)Tj
ET
264.122 507.04 21.658 12 re
264.122 495.04 21.658 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 247.1341 510.04 Tm
(150)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.7561 -2 Td
(-2)Tj
/T1_6 1 Tf
0 Tc 0.8791 0 Td
(\341)Tj
/T1_4 1 Tf
-0.005 Tc 0.273 0 Td
(73)Tj
ET
242.465 507.04 21.657 12 re
242.465 495.04 21.657 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 225.4764 510.04 Tm
(120)Tj
/T1_5 1 Tf
0 Tc 1.6531 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -1.0686 -2 Td
(-2)Tj
ET
220.807 507.04 21.658 12 re
220.807 495.04 21.658 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 205.4717 510.04 Tm
(90)Tj
/T1_5 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_4 1 Tf
-0.005 Tc -0.7931 -2 Td
(-1)Tj
ET
199.149 507.04 21.658 12 re
199.149 495.04 21.658 12 re
S
BT
/T1_4 1 Tf
6 0 0 6 183.8144 510.04 Tm
(60)Tj
/T1_5 1 Tf
0 Tc 1.1021 0 Td
(\006)Tj
/T1_4 1 Tf
-0.6291 -2 Td
(0)Tj
ET
177.492 507.04 21.657 12 re
177.492 495.04 21.657 12 re
S
BT
/T1_4 1 Tf
-0.005 Tc 6 0 0 6 162.1567 510.04 Tm
(30)Tj
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(Answers \(continued\))Tj
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(Advice:)Tj
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T*
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T*
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(Questions)Tj
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(Find x)Tj
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(1)Tj
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(4)Tj
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(find an angle)Tj
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(Use this to )Tj
T*
(find a side)Tj
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[(T)111(o find an angle:)]TJ
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[(Y)92(ou need thr)18(ee sides.)]TJ
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341.82 381.54 l
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(65)Tj
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(Easingwold School                               )Tj
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[(Pythagoras\325 theor)18(em and trigonometry)]TJ
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( )Tj
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317.11 457.04 l
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[(==)6995( 0)]TJ
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(047619)Tj
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(2 x 7 x 6)Tj
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BT
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(2)Tj
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( )Tj
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(\320)Tj
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(2)Tj
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(2)Tj
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( )Tj
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(\320)Tj
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( 2 x 6 x 7 cos70)Tj
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(a = x = 7)Tj
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194.61 497.54 m
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BT
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(sinB)Tj
ET
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BT
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(sin50)Tj
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(\006)Tj
ET
194.61 454.04 m
221.61 454.04 l
S
BT
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(a =)Tj
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(a = x = 9)Tj
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(\341)Tj
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(81 cm)Tj
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(a)Tj
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ET
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119.11 178.54 m
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(sinC)Tj
ET
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138.11 156.54 l
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BT
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(\006)Tj
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(sin100)Tj
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(\006)Tj
ET
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149.11 135.04 l
S
BT
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(a =)Tj
T*
(a = x = 9)Tj
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(\341)Tj
/T1_3 1 Tf
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(33 cm)Tj
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(sinA)Tj
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(a)Tj
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(sinB)Tj
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(b)Tj
ET
89.11 329.04 m
102.11 329.04 l
117.61 329.04 m
129.61 329.04 l
S
BT
/T1_3 1 Tf
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(=)Tj
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(a sinB)Tj
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(b)Tj
ET
116.61 306.54 m
132.61 306.54 l
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(18 x sin40)Tj
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(\006)Tj
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(12)Tj
ET
117.61 284.04 m
149.61 284.04 l
S
BT
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(70)Tj
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(\006)Tj
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(x)Tj
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(50)Tj
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(\006)Tj
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(6 cm)Tj
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(70)Tj
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(\006)Tj
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(12 m)Tj
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(x)Tj
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0.477 0 Td
(\006)Tj
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18.5926 -30.6875 Td
(A)Tj
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(A)Tj
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(A)Tj
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(A)Tj
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(B)Tj
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(B)Tj
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(B)Tj
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(B)Tj
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(C)Tj
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(C)Tj
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(C)Tj
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(C)Tj
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(a)Tj
-23.3333 -3 Td
(a)Tj
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(a)Tj
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(a)Tj
14.1667 -25.5 Td
(b)Tj
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(b)Tj
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(b)Tj
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(b)Tj
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(c)Tj
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(c)Tj
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(c)Tj
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(c)Tj
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(40)Tj
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(\006)Tj
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(18 m)Tj
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(100)Tj
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(\006)Tj
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(12 cm)Tj
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(30)Tj
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(\006)Tj
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(50)Tj
/T1_5 1 Tf
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(\006)Tj
/T1_3 1 Tf
-2.6354 5.8792 Td
(x)Tj
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(15 cm)Tj
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(17 cm)Tj
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(130)Tj
/T1_5 1 Tf
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(\006)Tj
/T1_3 1 Tf
0.5844 19.9718 Td
(x)Tj
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[(Ar)18(ea )]TJ
-27.6162 55 Td
[(W)18(e ar)18(e finding a side. W)18(e know one side )]TJ
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(and two angles. This suggests )Tj
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13.4992 0 Td
(sine rule)Tj
/T1_3 1 Tf
3.9001 0 Td
(. )Tj
-17.3993 -1.4286 Td
(Get into the habit of always labelling what )Tj
T*
[(we ar)18(e finding, ie side a or angle A.)]TJ
0.1766 -14.8571 Td
[(W)18(e ar)18(e finding an angle. W)18(e know two sides )]TJ
T*
(and one angle. This suggests )Tj
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13.1362 0 Td
(sine rule)Tj
/T1_3 1 Tf
3.9001 0 Td
(. )Tj
-17.0363 -1.4286 Td
(Label the triangle.)Tj
23.7503 22 Td
[(W)18(e ar)18(e finding an angle. W)18(e know thr)18(ee sides. This )]TJ
T*
(suggests )Tj
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4.1771 0 Td
(cosine rule)Tj
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4.9821 0 Td
(. Label the triangle.)Tj
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[(W)18(e ar)18(e finding a side. W)18(e know two sides and the )]TJ
T*
[(angle opposite the side we ar)18(e finding. This )]TJ
T*
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4.1771 0 Td
(cosine rule)Tj
/T1_3 1 Tf
4.9821 0 Td
(. Label the triangle.)Tj
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(Label the triangle.)Tj
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(= )Tj
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(1)Tj
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(/)Tj
0.365 -0.4 Td
(2)Tj
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( ab sin C)Tj
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(= )Tj
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(1)Tj
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(/)Tj
0.365 -0.4 Td
(2)Tj
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( x a x b x sin C)Tj
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(= )Tj
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(1)Tj
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(/)Tj
0.365 -0.4 Td
(2)Tj
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( x 17 x 15 x sin 130)Tj
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(\006)Tj
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(= 97)Tj
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(\341)Tj
/T1_3 1 Tf
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(7 cm)Tj
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(2)Tj
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(6 cm)Tj
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(7 cm)Tj
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(x)Tj
/T1_5 1 Tf
0.477 0 Td
(\006)Tj
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(9 cm)Tj
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(c)Tj
-28.9167 -12 Td
(c)Tj
33.6667 6.75 Td
(a)Tj
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(a)Tj
38.6667 4.3333 Td
(b)Tj
-32.25 -7.25 Td
(b)Tj
26 11.0833 Td
(A)Tj
-25 -14.25 Td
(A)Tj
16.8333 7.5 Td
(B)Tj
-31.1667 -6.25 Td
(B)Tj
49.4167 6 Td
(C)Tj
-39.1667 1.0833 Td
(C)Tj
0.172 0.89 0.796 0.047 k
/T1_0 1 Tf
-0.005 Tc 8 0 0 8 50.358 557.04 Tm
(Answers)Tj
0 g
/T1_3 1 Tf
23.3709 Tc 7 0 0 7 67.3659 543.04 Tm
(12)Tj
0 Tc 0 -19.1428 TD
(3)Tj
-0.005 Tc 2.6063 -25.4286 Td
[(At first glance we have insuf)18(ficient )]TJ
0 -1.4286 TD
[(infor)-18(mation. But, r)18(emember if we know )]TJ
T*
[(two angles we can easily find the thir)18(d )]TJ
T*
(angle. The missing angle is 50)Tj
/T1_5 1 Tf
0 Tc 13.2972 0 Td
(\006)Tj
/T1_3 1 Tf
0.395 0 Td
(.)Tj
-16.2985 4.2857 Td
(5)Tj
23.9269 25.4286 Td
(4)Tj
0 -24.9286 TD
(6)Tj
-0.005 Tc 17.0876 28.5714 Td
(A = x = 87)Tj
/T1_4 1 Tf
0 Tc 4.6741 0 Td
(\341)Tj
/T1_3 1 Tf
0.273 0 Td
(3)Tj
/T1_5 1 Tf
0.551 0 Td
(\006)Tj
/T1_3 1 Tf
-0.005 Tc -43.5607 -22.0714 Td
(sin A)Tj
10.634 -2.2143 Td
(A = x = 74)Tj
/T1_4 1 Tf
0 Tc 4.6741 0 Td
(\341)Tj
/T1_3 1 Tf
0.273 0 Td
(6)Tj
/T1_5 1 Tf
0.551 0 Td
(\006)Tj
/T1_3 1 Tf
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(sin A)Tj
ET
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(Easingwold School                               )Tj
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(Easingwold School                               )Tj
ET
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[(V)55(ectors )]TJ
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(\320)Tj
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(1)Tj
ET
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B
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349.2 485.827 l
268.737 296.78 m
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263.45 299.879 l
282.725 290.326 m
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276.699 289.209 l
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367.518 474.275 m
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410.806 457.267 l
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0 g
411.987 457.78 m
411.16 458.03 410.623 458.26 409.96 458.526 c
409.96 456.004 l
410.197 456.116 411.16 456.5 411.987 456.749 c
412.871 457.017 413.673 457.199 414.194 457.265 c
413.673 457.33 412.871 457.513 411.987 457.78 c
f
333.557 457.267 m
333.34 534.738 l
S
332.828 535.919 m
332.578 535.092 332.348 534.555 332.082 533.891 c
334.604 533.891 l
334.491 534.129 334.108 535.092 333.859 535.919 c
333.591 536.803 333.408 537.605 333.343 538.126 c
333.278 537.605 333.095 536.803 332.828 535.919 c
f
BT
/T1_3 1 Tf
7 0 0 7 399.5879 447.7635 Tm
(4)Tj
-2.5006 0 Td
(3)Tj
-2.4297 0 Td
(2)Tj
-2.4297 0 Td
(1)Tj
-3.0266 0.4031 Td
(0)Tj
-0.3277 3.2403 Td
(1)Tj
0 2.4298 TD
(2)Tj
T*
(3)Tj
T*
(4)Tj
ET
0.25 w 
330.971 525.299 m
333.503 525.299 l
330.971 508.291 m
333.503 508.291 l
330.971 491.284 m
333.503 491.284 l
330.971 474.276 m
333.503 474.276 l
330.971 457.267 m
333.503 457.267 l
401.534 457.267 m
404.066 457.267 l
384.526 454.736 m
384.526 457.267 l
401.534 454.736 m
401.534 457.267 l
367.518 454.736 m
367.518 457.267 l
350.51 454.736 m
350.51 457.267 l
333.503 454.736 m
333.503 457.267 l
S
BT
/T1_0 1 Tf
9 0 0 9 259.7365 123.5301 Tm
(Note: )Tj
/T1_3 1 Tf
2.9609 0 Td
[(The arr)18(ows point )]TJ
-2.9609 -1.3333 Td
[(in the same dir)18(ection.)]TJ
0 -1.3333 TD
[(These would be wr)18(ong.)]TJ
-21.0734 48.0278 Td
(A vector can be written)Tj
0.7784 -18.4768 Td
[(Although technically incorr)18(ect you can assume )]TJ
/T1_0 1 Tf
20.8922 0 Td
(speed)Tj
/T1_3 1 Tf
2.8519 0 Td
( and )Tj
/T1_0 1 Tf
2.2419 0 Td
(velocity)Tj
/T1_3 1 Tf
3.6129 0 Td
( mean the )Tj
/T1_0 1 Tf
-29.5988 -1.3333 Td
(same thing)Tj
/T1_3 1 Tf
5.1478 0 Td
( in a GCSE Maths question.)Tj
5.6565 20.088 Td
(2)Tj
0 -1.1111 TD
(3)Tj
/T1_4 1 Tf
1.7407 0.7778 Td
[(or)-1964(or)]TJ
/T1_3 1 Tf
2.4254 Tc 1.7222 0 Td
[(aA)2425(B)]TJ
0 Tc 16.0186 -3.7222 Td
(a)Tj
3.4814 -1.4074 Td
(a)Tj
ET
0.5 w 
232.806 540.767 m
238.806 540.767 l
S
239.986 541.28 m
239.16 541.53 238.623 541.76 237.96 542.026 c
237.96 539.504 l
238.197 539.616 239.16 540 239.986 540.249 c
240.871 540.517 241.674 540.699 242.194 540.765 c
241.674 540.83 240.871 541.013 239.986 541.28 c
f
172.736 521.23 m
171.329 524.479 170.52 528.252 170.52 532.28 c
170.52 536.308 171.33 540.081 172.736 543.33 c
181.053 543.33 m
182.461 540.081 183.27 536.308 183.27 532.28 c
183.27 528.252 182.461 524.479 181.053 521.23 c
S
BT
/T1_3 1 Tf
9 0 0 9 135.2531 504.1634 Tm
(2)Tj
T*
(3)Tj
ET
133.67 491.114 m
132.263 494.363 131.453 498.135 131.453 502.163 c
131.453 506.192 132.263 509.964 133.67 513.214 c
141.986 513.214 m
143.394 509.964 144.203 506.192 144.203 502.163 c
144.203 498.135 143.394 494.363 141.986 491.114 c
S
BT
/T1_3 1 Tf
9 0 0 9 166.6535 427.1136 Tm
(2)Tj
T*
(3)Tj
ET
165.07 414.063 m
163.663 417.313 162.853 421.085 162.853 425.114 c
162.853 429.142 163.663 432.914 165.07 436.163 c
173.387 436.163 m
174.794 432.914 175.603 429.142 175.603 425.114 c
175.603 421.085 174.794 417.313 173.387 414.063 c
S
BT
/T1_3 1 Tf
9 0 0 9 70.0759 499.8216 Tm
(Let vector a =)Tj
6.5195 -4.0407 Td
(3)Tj
-0.1665 -1.1111 Td
(-5)Tj
ET
124.67 450.405 m
123.263 453.655 122.453 457.427 122.453 461.455 c
122.453 465.483 123.263 469.256 124.67 472.505 c
137.987 472.505 m
139.394 469.256 140.203 465.483 140.203 461.455 c
140.203 457.427 139.394 453.655 137.987 450.405 c
S
BT
/T1_3 1 Tf
9 0 0 9 204.1515 427.1136 Tm
(3)Tj
-0.1665 -1.1111 Td
(-5)Tj
ET
200.07 414.063 m
198.663 417.313 197.853 421.085 197.853 425.114 c
197.853 429.142 198.663 432.914 200.07 436.163 c
213.387 436.163 m
214.794 432.914 215.603 429.142 215.603 425.114 c
215.603 421.085 214.794 417.313 213.387 414.063 c
S
BT
/T1_3 1 Tf
9 0 0 9 332.1515 427.1136 Tm
(5)Tj
-0.1665 -1.1111 Td
(-2)Tj
ET
328.07 414.063 m
326.663 417.313 325.853 421.085 325.853 425.114 c
325.853 429.142 326.663 432.914 328.07 436.163 c
341.387 436.163 m
342.794 432.914 343.603 429.142 343.603 425.114 c
343.603 421.085 342.794 417.313 341.387 414.063 c
S
BT
/T1_3 1 Tf
9 0 0 9 203.9161 463.4554 Tm
(12)Tj
-0.1665 -1.1111 Td
(-20)Tj
ET
200.337 450.405 m
198.929 453.655 198.12 457.427 198.12 461.455 c
198.12 465.483 198.929 469.256 200.337 472.505 c
218.654 472.505 m
220.06 469.256 220.87 465.483 220.87 461.455 c
220.87 457.427 220.06 453.655 218.654 450.405 c
S
BT
/T1_3 1 Tf
9 0 0 9 298.9196 463.4554 Tm
(-3)Tj
0.1665 -1.1111 Td
(5)Tj
ET
296.337 450.405 m
294.929 453.655 294.12 457.427 294.12 461.455 c
294.12 465.483 294.929 469.256 296.337 472.505 c
309.654 472.505 m
311.06 469.256 311.87 465.483 311.87 461.455 c
311.87 457.427 311.06 453.655 309.654 450.405 c
S
BT
/T1_3 1 Tf
9 0 0 9 227.7424 459.1136 Tm
(and vector )Tj
/T1_5 1 Tf
5.0188 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
(c =)Tj
-14.4917 0 Td
(vector 4c =)Tj
-8.5456 0 Td
(If vector c =)Tj
0 -3.9954 TD
(vector a + vector c = )Tj
9.2864 9.1852 Td
(This means 2 along and 3 up.)Tj
0 -1.3333 TD
[(The two vectors shown ar)18(e both )]TJ
T*
(equal to vector a)Tj
3.3703 -6.8194 Td
(+)Tj
7 0 0 7 248.9993 428.1136 Tm
(add top line)Tj
-0.8885 -1.4286 Td
(add bottom line)Tj
ET
301.987 424.78 m
311.32 424.78 l
S
312.501 425.292 m
311.674 425.542 311.137 425.772 310.474 426.038 c
310.474 423.516 l
310.711 423.629 311.674 424.012 312.501 424.262 c
313.386 424.529 314.188 424.712 314.708 424.777 c
314.188 424.843 313.386 425.025 312.501 425.292 c
f
222.654 424.114 m
231.987 424.114 l
S
233.168 424.626 m
232.341 424.875 231.804 425.105 231.14 425.372 c
231.14 422.849 l
231.378 422.962 232.341 423.346 233.168 423.595 c
234.052 423.863 234.855 424.045 235.375 424.111 c
234.855 424.176 234.052 424.359 233.168 424.626 c
f
BT
/T1_0 1 Tf
9 0 0 9 77.0817 393.1551 Tm
(Speed)Tj
/T1_3 1 Tf
2.9819 0 Td
[( is distance travelled in a given time. It is not a vector)92(.)]TJ
/T1_0 1 Tf
-2.9819 -1.3333 Td
[(V)55(elocity)]TJ
/T1_3 1 Tf
3.7058 0 Td
[( is distance in a specified dir)18(ection travelled in a given time. It is a vector)92(.)]TJ
-4.4843 -5.3333 Td
[(If you have a question with for)18(ces or speed or velocity you must draw a triangle.)]TJ
7 0 0 7 76.0759 310.8216 Tm
[(These ar)18(e the for)18(ces or speeds or velocities that )]TJ
0 -1.4286 TD
[(pr)18(oduce the actual or r)18(esultant for)18(ce or velocity)92(. )]TJ
34.0349 1.375 Td
[(This is the r)18(esultant for)18(ce or )]TJ
0 -1.7143 TD
[(speed and the dir)18(ection, ie )]TJ
T*
(what actually happens. If it is )Tj
T*
(a plane or ship this is the actual )Tj
T*
[(dir)18(ection and speed or velocity)92(.)]TJ
/T1_0 1 Tf
9 0 0 9 70.0759 240.1136 Tm
(Remember: )Tj
/T1_3 1 Tf
5.7028 0 Td
[(If we ar)18(e trying to find the r)18(esult, arr)18(ows go in the same dir)18(ection.)]TJ
/T1_0 1 Tf
7 0 0 7 76.0759 283.4886 Tm
(Note:)Tj
/T1_3 1 Tf
2.665 0 Td
[( W)18(e add them together \(arr)18(ows in the same )]TJ
-2.665 -1.4286 Td
[(dir)18(ection\) to pr)18(oduce the actual or r)18(esultant for)18(ce )]TJ
0 -1.4286 TD
[(or speed or velocity)92(.)]TJ
ET
[0.5 2]0 d 
287.32 256.114 m
274.82 312.114 l
S
[]0 d 
274.82 312.114 m
252.32 277.114 l
287.32 256.114 l
384.695 235.197 m
397.82 246.259 l
409.32 238.447 l
72.508 220.322 m
92.07 228.884 l
92.758 214.197 l
254.32 291.114 m
233.32 279.114 l
254.32 268.614 l
S
255.61 268.545 m
254.983 269.138 254.605 269.584 254.13 270.118 c
253.003 267.863 l
253.265 267.857 254.298 267.769 255.149 267.623 c
256.06 267.467 256.86 267.271 257.354 267.097 c
256.918 267.388 256.282 267.91 255.61 268.545 c
f
255.09 292.149 m
254.248 291.956 253.668 291.889 252.96 291.791 c
254.211 289.601 l
254.362 289.817 255.008 290.628 255.601 291.254 c
256.237 291.925 256.842 292.482 257.262 292.797 c
256.778 292.595 255.99 292.356 255.09 292.149 c
f
307.82 287.114 m
289.32 284.676 l
S
288.221 283.998 m
289.075 283.868 289.64 283.717 290.334 283.547 c
289.977 286.044 l
289.758 285.899 288.859 285.383 288.076 285.019 c
287.238 284.629 286.469 284.335 285.964 284.197 c
286.488 284.205 287.308 284.138 288.221 283.998 c
f
94.067 225.182 m
92.07 228.884 l
90.47 224.995 l
396.007 242.465 m
397.82 246.259 l
393.735 245.259 l
405.163 239.088 m
409.32 238.447 l
407.183 242.069 l
89.285 225.732 m
92.07 228.884 l
87.867 229.043 l
S
BT
/T1_3 1 Tf
9 0 0 9 102.32 225.9466 Tm
[(If we know the actual or r)18(esultant for)18(ce or velocity and another )]TJ
0 -1.3333 TD
[(for)18(ce or velocity)92(, we join the arr)18(ows tip to tip.)]TJ
-3.5827 -5.4306 Td
[(What is the actual dir)18(ection and speed of the plane?)]TJ
0.925 0.725 0.075 0.012 k
/T1_0 1 Tf
10 0 0 10 50.6535 193.4466 Tm
(Example 1)Tj
ET
210.703 200.517 m
210.703 181.184 l
S
0 g
211.216 180.003 m
211.466 180.829 211.695 181.367 211.962 182.03 c
209.44 182.03 l
209.552 181.793 209.936 180.829 210.185 180.003 c
210.452 179.118 210.635 178.316 210.701 177.796 c
210.766 178.316 210.948 179.118 211.216 180.003 c
f
107.987 102.72 m
107.987 126.114 l
S
108.607 101.291 m
108.909 102.291 109.187 102.941 109.509 103.743 c
106.457 103.743 l
106.593 103.456 107.058 102.291 107.36 101.291 c
107.683 100.22 107.905 99.249 107.983 98.62 c
108.062 99.249 108.283 100.22 108.607 101.291 c
f
321.514 187.351 m
340.847 187.351 l
S
342.029 187.864 m
341.202 188.113 340.664 188.343 340.001 188.609 c
340.001 186.087 l
340.238 186.2 341.202 186.583 342.029 186.833 c
342.913 187.1 343.716 187.283 344.236 187.348 c
343.716 187.413 342.913 187.596 342.029 187.864 c
f
107.983 98.62 m
131.377 98.62 l
S
132.806 99.24 m
131.806 99.542 131.155 99.82 130.353 100.142 c
130.353 97.091 l
130.64 97.227 131.806 97.691 132.806 97.993 c
133.877 98.316 134.847 98.537 135.477 98.616 c
134.847 98.696 133.877 98.917 132.806 99.24 c
f
368.024 110.757 m
368.024 124.151 l
S
368.644 109.328 m
368.946 110.328 369.224 110.979 369.547 111.781 c
366.495 111.781 l
366.631 111.494 367.095 110.328 367.397 109.328 c
367.72 108.258 367.942 107.287 368.021 106.657 c
368.1 107.287 368.32 108.258 368.644 109.328 c
f
403.361 106.584 m
403.361 119.978 l
S
403.981 105.155 m
404.283 106.155 404.561 106.805 404.883 107.608 c
401.831 107.608 l
401.967 107.321 402.432 106.155 402.734 105.155 c
403.057 104.085 403.279 103.114 403.357 102.484 c
403.436 103.114 403.657 104.085 403.981 105.155 c
f
368.024 124.151 m
381.418 124.151 l
S
382.846 124.771 m
381.846 125.073 381.196 125.351 380.394 125.673 c
380.394 122.621 l
380.681 122.758 381.846 123.222 382.846 123.524 c
383.917 123.847 384.888 124.069 385.517 124.147 c
384.888 124.226 383.917 124.448 382.846 124.771 c
f
385.864 102.488 m
399.258 102.488 l
S
400.687 103.108 m
399.686 103.409 399.036 103.688 398.234 104.01 c
398.234 100.958 l
398.521 101.095 399.686 101.559 400.687 101.861 c
401.757 102.184 402.728 102.405 403.357 102.484 c
402.728 102.563 401.757 102.784 400.687 103.108 c
f
BT
/T1_3 1 Tf
9 0 0 9 126.7326 194.0716 Tm
(A plane is heading)Tj
T*
(south at 200 km/h)Tj
12.1393 1.3333 Td
(The wind is blowing)Tj
T*
(east at 50 km/h)Tj
-18.4345 -3.6991 Td
[(W)18(e ar)18(e finding the actual dir)18(ection and speed. V)55(ectors go in the same dir)18(ection. )]TJ
T*
(It will give the same answer if we do this:)Tj
8.0909 -3.6403 Td
(or this)Tj
26.6023 0.6921 Td
(or )Tj
ET
[0.5 1]0 d 
107.987 126.114 m
132.575 101.517 l
S
134.03 100.946 m
133.536 101.867 133.273 102.524 132.933 103.319 c
130.775 101.161 l
131.074 101.054 132.227 100.558 133.147 100.064 c
134.133 99.536 134.976 99.006 135.477 98.616 c
135.088 99.117 134.557 99.96 134.03 100.946 c
f
[]0 d 
202.476 95.456 m
202.476 118.85 l
S
203.096 94.027 m
203.398 95.028 203.676 95.678 203.999 96.48 c
200.947 96.48 l
201.083 96.193 201.548 95.028 201.849 94.027 c
202.173 92.957 202.394 91.986 202.473 91.356 c
202.551 91.986 202.773 92.957 203.096 94.027 c
f
174.983 118.853 m
198.376 118.853 l
S
199.805 119.473 m
198.805 119.775 198.155 120.053 197.352 120.376 c
197.352 117.324 l
197.64 117.46 198.805 117.925 199.805 118.226 c
200.876 118.55 201.846 118.771 202.476 118.85 c
201.846 118.929 200.876 119.15 199.805 119.473 c
f
[0.5 1]0 d 
174.983 118.853 m
199.57 94.257 l
S
201.025 93.686 m
200.532 94.607 200.269 95.263 199.929 96.059 c
197.771 93.901 l
198.07 93.794 199.222 93.298 200.143 92.804 c
201.129 92.276 201.972 91.746 202.473 91.356 c
202.083 91.857 201.553 92.7 201.025 93.686 c
f
BT
/T1_3 1 Tf
7 0 0 7 205.2243 104.3665 Tm
(200 km/h)Tj
-18.5006 0.779 Td
(200 km/h)Tj
4.8328 -2.9302 Td
(50 km/h)Tj
9.1385 4.8036 Td
(50 km/h)Tj
-0.02 Tc 9 0 0 9 70.0759 72.8216 Tm
[(W)18(e now use )]TJ
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(Pythagoras)Tj
/T1_6 1 Tf
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(\324)Tj
/T1_4 1 Tf
-0.02 Tc 0.24 0 Td
[( theor)18(em and trigonometry)]TJ
/T1_3 1 Tf
11.5895 0 Td
( \(pages 57-60\) and )Tj
/T1_4 1 Tf
8.2176 0 Td
(Bearings)Tj
/T1_3 1 Tf
3.7098 0 Td
( \(page 37\).)Tj
ET
210.32 529.78 m
210.05 529.402 209.681 528.943 209.095 528.943 c
208.717 528.943 208.6 528.961 208.159 529.204 c
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109.189 457.154 109.504 457.568 109.666 457.811 c
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f
184.32 457.447 m
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182.718 456.61 182.6 456.628 182.159 456.87 c
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282.32 457.447 m
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280.717 456.61 280.6 456.628 280.159 456.87 c
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354.32 496.114 m
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352.717 495.276 352.6 495.294 352.159 495.537 c
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f
385.654 483.447 m
385.383 483.069 385.014 482.61 384.429 482.61 c
384.051 482.61 383.934 482.628 383.493 482.87 c
383.195 483.033 382.862 483.294 382.53 483.294 c
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382.862 483.834 382.98 483.816 383.421 483.573 c
383.717 483.411 384.051 483.15 384.384 483.15 c
384.798 483.15 385.113 483.564 385.275 483.807 c
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f
116.654 498.114 m
116.383 497.735 116.014 497.276 115.429 497.276 c
115.051 497.276 114.934 497.294 114.493 497.537 c
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f
221.32 480.28 m
221.05 479.902 220.681 479.443 220.096 479.443 c
219.717 479.443 219.6 479.461 219.159 479.704 c
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219.385 480.244 219.717 479.983 220.051 479.983 c
220.465 479.983 220.78 480.397 220.942 480.641 c
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102.378 421.284 m
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100.442 421.248 100.775 420.987 101.108 420.987 c
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f
145.711 421.284 m
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144.109 420.447 143.991 420.465 143.551 420.708 c
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282.866 180.527 m
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(0)Tj
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T*
(3)Tj
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(4)Tj
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316.882 177.996 m
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282.866 180.527 l
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299.874 214.543 m
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336.192 237.512 m
338.193 241.355 l
334.349 243.356 l
314.672 204.057 m
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317.737 209.364 l
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BT
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(c)Tj
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0.031 0.243 0.502 0.004 k
357.61 113.54 m
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321.11 145.04 l
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335.61 82.04 m
277.11 82.04 l
299.11 113.54 l
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B
394.11 82.04 m
335.61 82.04 l
357.61 113.54 l
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BT
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(Example 3)Tj
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(Example 2)Tj
0 g
/T1_4 1 Tf
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[(A plane flies fr)18(om Acton Airport to Bour)-18(ne Airport. Bour)-18(ne Airport is 600 km due south )]TJ
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T*
[(Find the dir)18(ection in which the plane must fly and the airspeed \(ie speed in still \
air\).)]TJ
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(Method: )Tj
/T1_4 1 Tf
4.2948 0 Td
(600 km in 3 hours is an )Tj
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[(actual speed of 200 km/h. W)18(e have )]TJ
0 -1.3333 TD
[(an actual speed so vectors ar)18(e )]TJ
T*
(joined tip to tip.)Tj
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[(W)18(e now use Pythagoras)]TJ
/T1_5 1 Tf
10.6686 0 Td
(\324)Tj
/T1_4 1 Tf
0.26 0 Td
[( theor)18(em and trigonometry)92(.)]TJ
-10.9286 -1.3333 Td
[(Answer: Dir)18(ection 194)]TJ
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(\006)Tj
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(, airspeed 206 km/h.)Tj
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(Use Pythagoras)Tj
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(\324)Tj
/T1_4 1 Tf
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[( theor)18(em and trigonometry)92(. Answer: Dir)18(ection 117)]TJ
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(\006)Tj
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-0.015 Tc 0.385 0 Td
[(, r)18(esultant for)18(ce 11)]TJ
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(\341)Tj
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(2 N.)Tj
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(Note:)Tj
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s)Tj
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(\325)Tj
/T1_4 1 Tf
-31.6287 -1.3333 Td
[(theor)18(em and trigonometry \(see sine rules, cosine rules, pages 65 and 66\).)]TJ
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(200 km/h)Tj
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(This is the airspeed and )Tj
0 -1.2857 TD
[(dir)18(ection in which the )]TJ
T*
[(plane must fly)92(.)]TJ
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(50 km/h)Tj
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ET
273.61 403.04 m
273.61 381.221 l
S
274.122 380.04 m
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272.346 382.067 l
272.459 381.83 272.842 380.867 273.092 380.04 c
273.359 379.155 273.542 378.353 273.607 377.833 c
273.673 378.353 273.855 379.155 274.122 380.04 c
f
273.61 403.04 m
322.61 403.04 l
S
323.791 403.552 m
322.965 403.802 322.427 404.032 321.764 404.298 c
321.764 401.776 l
322.001 401.889 322.965 402.272 323.791 402.522 c
324.676 402.789 325.478 402.972 325.998 403.037 c
325.478 403.103 324.676 403.285 323.791 403.552 c
f
392.379 369.826 m
392.379 348.007 l
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392.891 346.826 m
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392.128 345.941 392.31 345.139 392.376 344.619 c
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f
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388.99 369.829 l
S
390.171 370.341 m
389.344 370.591 388.807 370.821 388.144 371.087 c
388.144 368.565 l
388.381 368.677 389.344 369.061 390.171 369.311 c
391.056 369.578 391.858 369.761 392.379 369.826 c
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f
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339.99 369.829 m
389.319 346.089 l
S
390.61 346.04 m
389.973 346.624 389.589 347.063 389.107 347.591 c
388.013 345.318 l
388.276 345.317 389.31 345.245 390.163 345.111 c
391.076 344.969 391.879 344.786 392.376 344.619 c
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f
[]0 d 
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S
369.325 445.323 m
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f
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371.535 449.221 l
S
372.047 448.04 m
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370.271 450.067 l
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371.284 447.155 371.467 446.353 371.532 445.833 c
371.597 446.353 371.78 447.155 372.047 448.04 c
f
[0.5 2]0 d 
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347.795 448.892 l
S
347.746 447.601 m
348.33 448.238 348.77 448.622 349.298 449.105 c
347.025 450.198 l
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346.675 447.135 346.492 446.333 346.325 445.835 c
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0.925 0.725 0.075 0.012 k
BT
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(Questions)Tj
0 g
/T1_4 1 Tf
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[(W)18(rite the following vectors in the for)-18(m)]TJ
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(1)Tj
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(2)Tj
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(a     a)Tj
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[(a     W)18(rite the following in ter)-18(ms of a and b)]TJ
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(b     b)Tj
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[(b     Pr)18(ove that DE is parallel to AC)]TJ
14.3333 16.7778 Td
(c     c)Tj
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[(d     3c)-4461(e     a )]TJ
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(\320)Tj
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0.5 0 Td
[( c)-2886(f     3a + 2b)]TJ
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(D is the midpoint of AB)Tj
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(E is the midpoint of BC)Tj
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(F is the midpoint of AC)Tj
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[(AC)-4999(BD)-4740(BE)]TJ
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(DC)Tj
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[(i)-6149(ii)-5631(iii)]TJ
T*
[(iv)-5667(v)-1074(DE)]TJ
ET
[]0 d 
115.429 104.027 m
122.429 104.027 l
S
123.61 104.54 m
122.783 104.79 122.246 105.02 121.583 105.286 c
121.583 102.764 l
121.82 102.876 122.783 103.26 123.61 103.509 c
124.495 103.777 125.297 103.959 125.818 104.025 c
125.297 104.09 124.495 104.273 123.61 104.54 c
f
172.929 104.027 m
179.929 104.027 l
S
181.11 104.54 m
180.283 104.79 179.746 105.02 179.083 105.286 c
179.083 102.764 l
179.32 102.876 180.283 103.26 181.11 103.509 c
181.995 103.777 182.797 103.959 183.318 104.025 c
182.797 104.09 181.995 104.273 181.11 104.54 c
f
115.429 87.043 m
122.429 87.043 l
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/T1_4 1 Tf
7 0 0 7 275.6084 363.04 Tm
(+           =)Tj
/T1_0 1 Tf
-27.2178 -3.8571 Td
(Remember:)Tj
/T1_4 1 Tf
5.4071 0 Td
[( All you have to do is use known r)18(outes)]TJ
/T1_0 1 Tf
23.9124 -0.8571 Td
(Note: )Tj
/T1_4 1 Tf
2.961 0 Td
[(When you find an answer)92(, )]TJ
-2.961 -1.7143 Td
(ie BE = )Tj
5 0 0 5 314.9534 321.04 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.37 -0.4 Td
(2)Tj
7 0 0 7 322.3643 318.04 Tm
( b in part iii, this becomes )Tj
-4.5778 -1.7143 Td
[(a known r)18(oute. This is used in part iv)74(.)]TJ
-29.3195 2.3571 Td
(a)Tj
0 -26.1429 TD
(b)Tj
1.9623 26.2143 Td
(i)Tj
0 -8.9286 TD
[(ii)-20806(iii)]TJ
1.9286 8.9286 Td
[(W)18(e know AB and BC. Find a way fr)18(om A to C )]TJ
0 -1.7143 TD
(along )Tj
/T1_0 1 Tf
2.7971 0 Td
(known)Tj
/T1_4 1 Tf
3.0911 0 Td
[( r)18(outes: A to B then B to C)]TJ
-5.8881 -2.1429 Td
(AC = AB + BC)Tj
0 -2 TD
(AC = a + b)Tj
0.0714 -3.0714 Td
(AB = a)Tj
T*
[(ther)18(efor)18(e BA = )]TJ
/T1_5 1 Tf
6.8891 0 Td
(\320)Tj
/T1_4 1 Tf
0.5 0 Td
[(a \(opposite dir)18(ection\))]TJ
-7.3891 -2 Td
(B to D is half of B to A)Tj
T*
[(ther)18(efor)18(e BD = )]TJ
/T1_5 1 Tf
6.9441 0 Td
(\320)Tj
/T1_4 1 Tf
5 0 0 5 164.9289 221.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 173.73 218.54 Tm
(a)Tj
12.9414 6 Td
(BE is half of BC)Tj
T*
(BC = b)Tj
T*
[(ther)18(efor)18(e BE = )]TJ
5 0 0 5 311.8928 235.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 320.6939 232.54 Tm
(b)Tj
-31.6963 -5 Td
[(iv)-20564(v)]TJ
2 0 Td
[(Find a way fr)18(om D to C along )]TJ
T*
[(known r)18(outes: D to B then B to C)]TJ
T*
(DC = DB + BC)Tj
T*
(DC = )Tj
5 0 0 5 131.4893 158.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 140.2904 155.54 Tm
(a +  b )Tj
-5.7815 -3 Td
(AC = a + b)Tj
23.5 9 Td
[(Find a way fr)18(om D to E along )]TJ
T*
[(known r)18(outes: D to B then B to E)]TJ
T*
(DE = DB + BE)Tj
T*
(DE = )Tj
5 0 0 5 282.2123 158.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 291.0134 155.54 Tm
(a + )Tj
5 0 0 5 303.2006 158.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 312.0016 155.54 Tm
(b )Tj
ET
144.275 329.93 m
149.475 329.93 l
S
150.42 330.34 m
149.759 330.54 149.329 330.724 148.798 330.937 c
148.798 328.919 l
148.988 329.009 149.759 329.316 150.42 329.516 c
151.128 329.73 151.77 329.875 152.186 329.928 c
151.77 329.98 151.128 330.126 150.42 330.34 c
f
169.175 329.93 m
174.375 329.93 l
S
175.32 330.34 m
174.659 330.54 174.229 330.724 173.698 330.937 c
173.698 328.919 l
173.888 329.009 174.659 329.316 175.32 329.516 c
176.028 329.73 176.67 329.875 177.086 329.928 c
176.67 329.98 176.028 330.126 175.32 330.34 c
f
298.675 325.13 m
303.875 325.13 l
S
304.82 325.54 m
304.159 325.74 303.729 325.924 303.198 326.137 c
303.198 324.119 l
303.388 324.209 304.159 324.516 304.82 324.715 c
305.528 324.93 306.17 325.076 306.586 325.128 c
306.17 325.18 305.528 325.326 304.82 325.54 c
f
114.675 303.13 m
119.875 303.13 l
S
120.82 303.54 m
120.159 303.74 119.729 303.924 119.198 304.137 c
119.198 302.119 l
119.388 302.209 120.159 302.516 120.82 302.715 c
121.528 302.93 122.17 303.076 122.586 303.128 c
122.17 303.18 121.528 303.326 120.82 303.54 c
f
114.675 288.63 m
119.875 288.63 l
S
120.82 289.04 m
120.159 289.24 119.729 289.424 119.198 289.637 c
119.198 287.619 l
119.388 287.709 120.159 288.016 120.82 288.215 c
121.528 288.43 122.17 288.576 122.586 288.628 c
122.17 288.68 121.528 288.826 120.82 289.04 c
f
113.675 268.13 m
118.875 268.13 l
S
119.82 268.54 m
119.159 268.74 118.729 268.924 118.198 269.137 c
118.198 267.119 l
118.388 267.209 119.159 267.516 119.82 267.715 c
120.528 267.93 121.17 268.076 121.586 268.128 c
121.17 268.18 120.528 268.326 119.82 268.54 c
f
143.675 253.63 m
148.875 253.63 l
S
149.82 254.04 m
149.159 254.24 148.729 254.424 148.198 254.637 c
148.198 252.619 l
148.388 252.709 149.159 253.016 149.82 253.215 c
150.528 253.43 151.17 253.576 151.586 253.628 c
151.17 253.68 150.528 253.826 149.82 254.04 c
f
143.175 225.13 m
148.375 225.13 l
S
149.32 225.54 m
148.659 225.74 148.229 225.924 147.698 226.137 c
147.698 224.119 l
147.888 224.209 148.659 224.516 149.32 224.715 c
150.028 224.93 150.67 225.076 151.086 225.128 c
150.67 225.18 150.028 225.326 149.32 225.54 c
f
295.175 240.13 m
300.375 240.13 l
S
301.32 240.54 m
300.659 240.74 300.229 240.924 299.698 241.137 c
299.698 239.119 l
299.888 239.209 300.659 239.516 301.32 239.715 c
302.028 239.93 302.67 240.076 303.086 240.128 c
302.67 240.18 302.028 240.326 301.32 240.54 c
f
265.175 253.13 m
270.375 253.13 l
S
271.32 253.54 m
270.659 253.74 270.229 253.924 269.698 254.137 c
269.698 252.119 l
269.888 252.209 270.659 252.516 271.32 252.715 c
272.028 252.93 272.67 253.076 273.086 253.128 c
272.67 253.18 272.028 253.326 271.32 253.54 c
f
132.175 176.63 m
137.375 176.63 l
S
138.32 177.04 m
137.659 177.24 137.229 177.424 136.698 177.637 c
136.698 175.619 l
136.888 175.709 137.659 176.016 138.32 176.215 c
139.028 176.43 139.67 176.576 140.086 176.628 c
139.67 176.68 139.028 176.826 138.32 177.04 c
f
114.175 176.63 m
119.375 176.63 l
S
120.32 177.04 m
119.659 177.24 119.229 177.424 118.698 177.637 c
118.698 175.619 l
118.888 175.709 119.659 176.016 120.32 176.215 c
121.028 176.43 121.67 176.576 122.086 176.628 c
121.67 176.68 121.028 176.826 120.32 177.04 c
f
150.175 176.63 m
155.375 176.63 l
S
156.32 177.04 m
155.659 177.24 155.229 177.424 154.698 177.637 c
154.698 175.619 l
154.888 175.709 155.659 176.016 156.32 176.215 c
157.028 176.43 157.67 176.576 158.086 176.628 c
157.67 176.68 157.028 176.826 156.32 177.04 c
f
113.675 162.63 m
118.875 162.63 l
S
119.82 163.04 m
119.159 163.24 118.729 163.424 118.198 163.637 c
118.198 161.619 l
118.388 161.709 119.159 162.016 119.82 162.215 c
120.528 162.43 121.17 162.576 121.586 162.628 c
121.17 162.68 120.528 162.826 119.82 163.04 c
f
265.175 162.63 m
270.375 162.63 l
S
271.32 163.04 m
270.659 163.24 270.229 163.424 269.698 163.637 c
269.698 161.619 l
269.888 161.709 270.659 162.016 271.32 162.215 c
272.028 162.43 272.67 162.576 273.086 162.628 c
272.67 162.68 272.028 162.826 271.32 163.04 c
f
265.175 176.13 m
270.375 176.13 l
S
271.32 176.54 m
270.659 176.74 270.229 176.924 269.698 177.137 c
269.698 175.119 l
269.888 175.209 270.659 175.516 271.32 175.715 c
272.028 175.93 272.67 176.076 273.086 176.128 c
272.67 176.18 272.028 176.326 271.32 176.54 c
f
282.675 176.13 m
287.875 176.13 l
S
288.82 176.54 m
288.159 176.74 287.729 176.924 287.198 177.137 c
287.198 175.119 l
287.388 175.209 288.159 175.516 288.82 175.715 c
289.528 175.93 290.17 176.076 290.586 176.128 c
290.17 176.18 289.528 176.326 288.82 176.54 c
f
300.675 176.13 m
305.875 176.13 l
S
306.82 176.54 m
306.159 176.74 305.729 176.924 305.198 177.137 c
305.198 175.119 l
305.388 175.209 306.159 175.516 306.82 175.715 c
307.528 175.93 308.17 176.076 308.586 176.128 c
308.17 176.18 307.528 176.326 306.82 176.54 c
f
101.175 141.63 m
106.375 141.63 l
S
107.32 142.04 m
106.659 142.24 106.229 142.424 105.698 142.637 c
105.698 140.619 l
105.888 140.709 106.659 141.016 107.32 141.215 c
108.028 141.43 108.67 141.576 109.086 141.628 c
108.67 141.68 108.028 141.826 107.32 142.04 c
f
156.675 141.63 m
161.875 141.63 l
S
162.82 142.04 m
162.159 142.24 161.729 142.424 161.198 142.637 c
161.198 140.619 l
161.388 140.709 162.159 141.016 162.82 141.215 c
163.528 141.43 164.17 141.576 164.586 141.628 c
164.17 141.68 163.528 141.826 162.82 142.04 c
f
162.675 127.13 m
167.875 127.13 l
S
168.82 127.54 m
168.159 127.74 167.729 127.924 167.198 128.137 c
167.198 126.119 l
167.388 126.209 168.159 126.516 168.82 126.715 c
169.528 126.93 170.17 127.076 170.586 127.128 c
170.17 127.18 169.528 127.326 168.82 127.54 c
f
132.175 303.13 m
137.375 303.13 l
S
138.32 303.54 m
137.659 303.74 137.229 303.924 136.698 304.137 c
136.698 302.119 l
136.888 302.209 137.659 302.516 138.32 302.715 c
139.028 302.93 139.67 303.076 140.086 303.128 c
139.67 303.18 139.028 303.326 138.32 303.54 c
f
148.175 303.13 m
153.375 303.13 l
S
154.32 303.54 m
153.659 303.74 153.229 303.924 152.698 304.137 c
152.698 302.119 l
152.888 302.209 153.659 302.516 154.32 302.715 c
155.028 302.93 155.67 303.076 156.086 303.128 c
155.67 303.18 155.028 303.326 154.32 303.54 c
f
BT
/T1_4 1 Tf
7 0 0 7 155.82 134.54 Tm
(DE = )Tj
5 0 0 5 173.7123 137.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 182.5134 134.54 Tm
(a + )Tj
5 0 0 5 194.7006 137.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 203.5017 134.54 Tm
(b)Tj
-6.8117 -2 Td
(2 DE = 2\( )Tj
5 0 0 5 187.2085 123.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 196.0096 120.54 Tm
(a + )Tj
5 0 0 5 208.1968 123.54 Tm
(1)Tj
0.5561 -0.4 Td
(/)Tj
0.0001 Tc 0.37 -0.4 Td
(2 )Tj
0 Tc 7 0 0 7 216.9979 120.54 Tm
(b \) = a + b)Tj
6.8317 0.0714 Td
[(Ther)18(efor)18(e DE is parallel to AC)]TJ
ET
328.654 316.374 m
328.383 315.995 328.014 315.536 327.429 315.536 c
327.051 315.536 326.934 315.554 326.493 315.797 c
326.195 315.959 325.862 316.22 325.53 316.22 c
325.115 316.22 324.8 315.806 324.638 315.563 c
324.26 315.923 l
324.53 316.301 324.899 316.76 325.485 316.76 c
325.862 316.76 325.98 316.742 326.421 316.5 c
326.717 316.337 327.051 316.076 327.384 316.076 c
327.798 316.076 328.113 316.49 328.275 316.733 c
328.654 316.374 l
f
134.32 280.374 m
134.05 279.995 133.681 279.536 133.095 279.536 c
132.717 279.536 132.6 279.554 132.159 279.797 c
131.862 279.959 131.529 280.22 131.196 280.22 c
130.782 280.22 130.467 279.806 130.305 279.563 c
129.927 279.923 l
130.197 280.301 130.566 280.76 131.151 280.76 c
131.529 280.76 131.646 280.742 132.087 280.5 c
132.384 280.337 132.717 280.076 133.051 280.076 c
133.464 280.076 133.78 280.49 133.942 280.733 c
134.32 280.374 l
f
146.986 280.374 m
146.716 279.995 146.347 279.536 145.762 279.536 c
145.384 279.536 145.267 279.554 144.826 279.797 c
144.529 279.959 144.196 280.22 143.863 280.22 c
143.448 280.22 143.133 279.806 142.971 279.563 c
142.593 279.923 l
142.863 280.301 143.233 280.76 143.818 280.76 c
144.196 280.76 144.313 280.742 144.754 280.5 c
145.051 280.337 145.384 280.076 145.717 280.076 c
146.131 280.076 146.447 280.49 146.609 280.733 c
146.986 280.374 l
f
134.878 258.877 m
134.608 258.499 134.238 258.04 133.653 258.04 c
133.275 258.04 133.158 258.058 132.717 258.301 c
132.42 258.463 132.087 258.724 131.754 258.724 c
131.339 258.724 131.025 258.31 130.862 258.067 c
130.485 258.427 l
130.755 258.805 131.124 259.265 131.709 259.265 c
132.087 259.265 132.204 259.247 132.645 259.003 c
132.942 258.841 133.275 258.58 133.608 258.58 c
134.022 258.58 134.338 258.994 134.5 259.237 c
134.878 258.877 l
f
168.32 244.707 m
168.05 244.329 167.681 243.87 167.095 243.87 c
166.717 243.87 166.6 243.888 166.159 244.13 c
165.862 244.292 165.529 244.554 165.196 244.554 c
164.782 244.554 164.467 244.14 164.305 243.896 c
163.927 244.257 l
164.197 244.635 164.566 245.094 165.151 245.094 c
165.529 245.094 165.646 245.076 166.087 244.833 c
166.384 244.671 166.717 244.41 167.05 244.41 c
167.465 244.41 167.78 244.824 167.942 245.067 c
168.32 244.707 l
f
177.986 216.374 m
177.716 215.995 177.347 215.536 176.762 215.536 c
176.384 215.536 176.267 215.554 175.826 215.797 c
175.529 215.959 175.196 216.22 174.863 216.22 c
174.448 216.22 174.133 215.806 173.971 215.563 c
173.593 215.923 l
173.863 216.301 174.233 216.76 174.818 216.76 c
175.196 216.76 175.313 216.742 175.754 216.5 c
176.051 216.337 176.384 216.076 176.717 216.076 c
177.131 216.076 177.446 216.49 177.609 216.733 c
177.986 216.374 l
f
144.653 153.707 m
144.383 153.329 144.014 152.87 143.429 152.87 c
143.051 152.87 142.934 152.888 142.493 153.13 c
142.195 153.292 141.862 153.554 141.529 153.554 c
141.115 153.554 140.8 153.14 140.638 152.896 c
140.26 153.257 l
140.53 153.635 140.899 154.094 141.485 154.094 c
141.862 154.094 141.98 154.076 142.421 153.833 c
142.717 153.671 143.051 153.41 143.384 153.41 c
143.798 153.41 144.113 153.824 144.275 154.067 c
144.653 153.707 l
f
158.986 153.707 m
158.716 153.329 158.347 152.87 157.762 152.87 c
157.384 152.87 157.267 152.888 156.826 153.13 c
156.529 153.292 156.196 153.554 155.863 153.554 c
155.448 153.554 155.133 153.14 154.971 152.896 c
154.593 153.257 l
154.863 153.635 155.233 154.094 155.818 154.094 c
156.196 154.094 156.313 154.076 156.754 153.833 c
157.051 153.671 157.384 153.41 157.717 153.41 c
158.131 153.41 158.446 153.824 158.609 154.067 c
158.986 153.707 l
f
122.211 132.877 m
121.941 132.499 121.572 132.04 120.986 132.04 c
120.609 132.04 120.491 132.058 120.05 132.301 c
119.754 132.463 119.42 132.724 119.087 132.724 c
118.673 132.724 118.358 132.31 118.196 132.067 c
117.818 132.427 l
118.088 132.805 118.457 133.265 119.042 133.265 c
119.42 133.265 119.537 133.247 119.978 133.003 c
120.276 132.841 120.609 132.58 120.942 132.58 c
121.356 132.58 121.671 132.994 121.833 133.237 c
122.211 132.877 l
f
134.32 132.877 m
134.05 132.499 133.681 132.04 133.095 132.04 c
132.717 132.04 132.6 132.058 132.159 132.301 c
131.862 132.463 131.529 132.724 131.196 132.724 c
130.782 132.724 130.467 132.31 130.305 132.067 c
129.927 132.427 l
130.197 132.805 130.566 133.265 131.151 133.265 c
131.529 133.265 131.646 133.247 132.087 133.003 c
132.384 132.841 132.717 132.58 133.051 132.58 c
133.464 132.58 133.78 132.994 133.942 133.237 c
134.32 132.877 l
f
186.986 132.877 m
186.717 132.499 186.347 132.04 185.762 132.04 c
185.385 132.04 185.267 132.058 184.826 132.301 c
184.529 132.463 184.196 132.724 183.863 132.724 c
183.448 132.724 183.134 132.31 182.971 132.067 c
182.593 132.427 l
182.864 132.805 183.233 133.265 183.818 133.265 c
184.196 133.265 184.313 133.247 184.754 133.003 c
185.051 132.841 185.385 132.58 185.717 132.58 c
186.131 132.58 186.446 132.994 186.609 133.237 c
186.986 132.877 l
f
207.986 132.877 m
207.717 132.499 207.347 132.04 206.762 132.04 c
206.385 132.04 206.267 132.058 205.826 132.301 c
205.529 132.463 205.196 132.724 204.863 132.724 c
204.448 132.724 204.134 132.31 203.971 132.067 c
203.593 132.427 l
203.863 132.805 204.233 133.265 204.818 133.265 c
205.196 133.265 205.313 133.247 205.754 133.003 c
206.051 132.841 206.385 132.58 206.717 132.58 c
207.131 132.58 207.446 132.994 207.609 133.237 c
207.986 132.877 l
f
199.987 118.707 m
199.717 118.329 199.347 117.87 198.762 117.87 c
198.384 117.87 198.267 117.888 197.826 118.13 c
197.529 118.292 197.196 118.554 196.863 118.554 c
196.448 118.554 196.133 118.14 195.971 117.896 c
195.593 118.257 l
195.863 118.635 196.233 119.094 196.818 119.094 c
197.196 119.094 197.313 119.076 197.754 118.833 c
198.051 118.671 198.384 118.41 198.717 118.41 c
199.131 118.41 199.446 118.824 199.609 119.067 c
199.987 118.707 l
f
221.986 118.707 m
221.716 118.329 221.347 117.87 220.762 117.87 c
220.385 117.87 220.267 117.888 219.826 118.13 c
219.529 118.292 219.196 118.554 218.863 118.554 c
218.448 118.554 218.133 118.14 217.971 117.896 c
217.593 118.257 l
217.863 118.635 218.233 119.094 218.818 119.094 c
219.196 119.094 219.313 119.076 219.754 118.833 c
220.051 118.671 220.385 118.41 220.717 118.41 c
221.132 118.41 221.447 118.824 221.609 119.067 c
221.986 118.707 l
f
237.986 118.374 m
237.717 117.995 237.347 117.536 236.762 117.536 c
236.385 117.536 236.267 117.554 235.826 117.797 c
235.529 117.959 235.196 118.22 234.863 118.22 c
234.448 118.22 234.134 117.806 233.971 117.563 c
233.593 117.923 l
233.863 118.301 234.233 118.76 234.818 118.76 c
235.196 118.76 235.313 118.742 235.754 118.5 c
236.051 118.337 236.385 118.076 236.717 118.076 c
237.131 118.076 237.446 118.49 237.609 118.733 c
237.986 118.374 l
f
250.653 118.374 m
250.383 117.995 250.014 117.536 249.429 117.536 c
249.051 117.536 248.934 117.554 248.493 117.797 c
248.195 117.959 247.862 118.22 247.53 118.22 c
247.115 118.22 246.8 117.806 246.638 117.563 c
246.26 117.923 l
246.53 118.301 246.899 118.76 247.485 118.76 c
247.862 118.76 247.98 118.742 248.421 118.5 c
248.717 118.337 249.051 118.076 249.384 118.076 c
249.798 118.076 250.113 118.49 250.275 118.733 c
250.653 118.374 l
f
295.545 153.877 m
295.274 153.499 294.905 153.04 294.32 153.04 c
293.942 153.04 293.825 153.058 293.384 153.301 c
293.087 153.463 292.754 153.724 292.421 153.724 c
292.006 153.724 291.691 153.31 291.529 153.067 c
291.151 153.427 l
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(Note:)Tj
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[(ar)18(ea)]TJ
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(a)Tj
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(b)Tj
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[(T)111(ables and graphs)]TJ
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(This table shows the number of cars using a car park over a period of 10\
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[(1)-1334(What is the modal class?)]TJ
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[(2)-1334(Estimate the median.)]TJ
T*
[(3)-1334(Estimate the mean.)]TJ
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(Answers)Tj
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/T1_3 1 Tf
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(\320)Tj
/T1_3 1 Tf
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( 299 cars.)Tj
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T*
[(5 + 18 + 30 = 53. Ther)18(efor)18(e ther)18(e ar)18(e 53 days with less than 300 cars.)]TJ
T*
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(\320)Tj
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( 299 class.)Tj
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(A good estimate of the median would be about 290 cars.)Tj
-0.0001 Tc -1.6198 -1.7143 Td
[(3)-1064(The mean is found by first multiplying the mid-value of each class by th\
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(100)Tj
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(Easingwold School                               )Tj
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[(Cumulative fr)18(equency)]TJ
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[(1)-1334(What is the range of the marks?)]TJ
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[(2)-1334(Draw a cumulative fr)18(equency diagram.)]TJ
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[(3)-1334(What is the median mark?)]TJ
T*
[(4)-1334(What is the upper quartile?)]TJ
T*
[(5)-1334(What is the lower quartile?)]TJ
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[(6)-1334(What is the inter)18(quartile range?)]TJ
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[(1)-1064(The range is 65 )]TJ
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(\320)Tj
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259.163 231.266 m
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205.175 103.076 l
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296.542 282.497 l
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298.326 283.093 l
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261.251 234.344 l
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262.708 234.185 l
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T*
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(\320)Tj
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T*
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T*
(13 )Tj
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(\324)Tj
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(A)Tj
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[(Cumulative fr)18(equency)]TJ
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(diagrams show the number of hours the bulbs lasted.)Tj
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353.61 427.757 m
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338.61 330.757 m
352.944 330.757 l
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116.61 410.09 m
118.017 406.841 118.827 403.068 118.827 399.04 c
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102.61 421.924 m
115.11 421.924 l
104.11 325.59 m
116.61 325.59 l
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BT
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(\b)Tj
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0.713 0 Td
(x)Tj
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(2)Tj
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(n)Tj
ET
89.11 301.19 m
101.61 301.19 l
102.61 397.09 m
115.11 397.09 l
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BT
/T1_2 1 Tf
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(2)Tj
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(\b)Tj
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0.713 0 Td
(x)Tj
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(n)Tj
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118.793 292.09 m
117.386 295.34 116.576 299.112 116.576 303.14 c
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133.11 314.19 m
134.517 310.941 135.327 307.168 135.327 303.14 c
135.327 299.112 134.517 295.34 133.11 292.09 c
119.11 301.19 m
131.61 301.19 l
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BT
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(\320)Tj
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(\b)Tj
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0.713 0 Td
(x)Tj
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(2)Tj
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(n)Tj
ET
89.11 274.69 m
101.61 274.69 l
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BT
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(2)Tj
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(\b)Tj
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0.713 0 Td
(x)Tj
-0.3935 -1.2222 Td
(n)Tj
ET
118.793 265.59 m
117.386 268.84 116.576 272.612 116.576 276.64 c
116.576 280.668 117.386 284.441 118.793 287.69 c
133.11 287.69 m
134.517 284.441 135.327 280.668 135.327 276.64 c
135.327 272.612 134.517 268.84 133.11 265.59 c
119.11 274.69 m
131.61 274.69 l
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BT
/T1_4 1 Tf
9 0 0 9 107.11 272.6902 Tm
(\320)Tj
ET
75.61 271.465 m
77.235 273.965 l
78.61 267.59 l
84.61 288.84 l
139.61 288.84 l
344.61 280.757 m
345.422 282.007 l
346.11 278.819 l
349.11 289.444 l
363.61 289.444 l
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BT
/T1_2 1 Tf
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(Count how many numbers we have)Tj
T*
(Add the numbers )Tj
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(\()Tj
/T1_3 1 Tf
0.26 0 Td
(\b)Tj
/T1_2 1 Tf
0.713 0 Td
( means add\))Tj
7.02 0 0 7.02 142.2164 180.6916 Tm
(Divide by n)Tj
5.46 0 0 5.46 142.2164 174.4516 Tm
(\(all we have done so far is find the mean!\))Tj
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(  )Tj
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[(Squar)18(e the mean)-85( )]TJ
T*
(Put 40)Tj
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2.8521 0 Td
(\341)Tj
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0.278 0 Td
(6406 into your calculator memory)Tj
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[(Add the numbers squar)18(ed)]TJ
T*
(Divide by n)Tj
T*
[(Subtract the mean squar)18(ed)]TJ
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(\(this number is in calculator memory\))Tj
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[(Squar)18(e r)18(oot)]TJ
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(1)Tj
T*
(2)Tj
T*
(3)Tj
T*
(4)Tj
T*
(5)Tj
T*
(6)Tj
T*
(7)Tj
T*
(8)Tj
T*
(9)Tj
5.1943 21.3333 Td
(n)Tj
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T*
(\b)Tj
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0.713 0 Td
(x)Tj
/T1_3 1 Tf
-0.713 -10.6667 Td
(\b)Tj
/T1_2 1 Tf
0.713 0 Td
(x)Tj
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(2)Tj
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(2)Tj
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(=)Tj
T*
(=)Tj
T*
(=)Tj
0 -5.3333 TD
(=)Tj
0 -2.6667 TD
(=)Tj
T*
(=)Tj
T*
(=)Tj
4.6672 21.3333 Td
(8)Tj
-0.556 -2.6667 Td
(51)Tj
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(6)Tj
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(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(375)Tj
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(40)Tj
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1.112 0 Td
(\341)Tj
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0.278 0 Td
(6406)Tj
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(395)Tj
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(49)Tj
/T1_4 1 Tf
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(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(375)Tj
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(8)Tj
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0.556 0 Td
(\341)Tj
/T1_2 1 Tf
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(73437)Tj
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(2)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(955)Tj
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(5 + 7 + 3 + 10 + 4 + 6 + 12 + 4)Tj
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(6)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(375)Tj
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(2)Tj
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(5)Tj
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(2)Tj
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( + 7)Tj
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(2)Tj
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( + 3)Tj
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(2)Tj
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( + 10)Tj
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(2)Tj
7.02 0 0 7.02 302.6075 124.5317 Tm
( + 4)Tj
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(2)Tj
7.02 0 0 7.02 317.6917 124.5317 Tm
( + 6)Tj
4.68 0 0 4.68 330.1738 127.6517 Tm
(2)Tj
7.02 0 0 7.02 332.776 124.5317 Tm
( + 12)Tj
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(2)Tj
7.02 0 0 7.02 351.7634 124.5317 Tm
( + 4)Tj
4.68 0 0 4.68 364.2455 127.6517 Tm
(2)Tj
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(49)Tj
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1.112 0 Td
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W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
49.61 42.05 368.5 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 50.6063 35.0006 Tm
(82)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 265.7926 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
49.61 565.04 368.5 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0296 Tw 14 0 0 14 185.5459 553.4575 Tm
(Line of best fit)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0113 Tc 0.0278 Tw 9 0 0 9 67.6142 532.3864 Tm
[(Scatter diagrams ar)18(e used to find r)18(elationships \(or corr)18(elation\) between two sets of data.)]TJ
-0.0057 Tc 0 -17.5099 TD
[(A line of best fit is drawn by looking at the cr)18(osses on a scatter diagram and then)]TJ
0 -1.3333 TD
[(drawing a line. Nor)-18(mally ther)18(e would be a similar number of cr)18(osses above the line as)]TJ
T*
(below the line.)Tj
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 50.6063 327.4583 Tm
(Questions)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 67.6142 312.6237 Tm
[(1)-1332(Draw a line of best fit on this scatter diagram. This scatter diagram sh\
ows the)]TJ
1.888 -1.3333 Td
(masses of 16 pupils against their ages.)Tj
-1.888 -21.6317 Td
[(2)-1334(Use your line of best fit to estimate the mass of a 13 year old pupil.)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 50.6063 85.4344 Tm
(Answers)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 7 0 0 7 67.6142 73.4344 Tm
[(1)-1064(The line should be drawn so that ther)18(e ar)18(e a similar number of cr)18(osses above the line as below the line.)]TJ
0 Tc 0 Tw 0 -1.7143 TD
(2)Tj
/T1_0 1 Tf
-0.006 Tc 1.6198 0 Td
(Method:)Tj
/T1_2 1 Tf
-0.0057 Tc 0.0278 Tw 4.257 0 Td
[(Draw a line fr)18(om 13 years to the line of best fit. Read the mass. The answer should be\
 about 60 kg.)]TJ
ET
0 0 0 0 k
65.86 292.32 336 -171.55 re
f*
Q Q 
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
129.65 285.704 m
129.65 158.204 l
320.988 158.204 l
S
0 g
BT
/T1_2 1 Tf
7 0 0 7 113.9 176.5885 Tm
(30)Tj
0 3.1443 TD
(40)Tj
0 3.0371 TD
(50)Tj
T*
(60)Tj
0 2.93 TD
(70)Tj
0 3.1978 TD
(80)Tj
7.9184 -20.0084 Td
(9)Tj
8.1537 Tc -2.9107 0 Td
[(81)8154(1)]TJ
0 Tc 5.7934 0 Td
[(10)-7879(13)]TJ
6.1513 0 Td
[(12)-7738(15)]TJ
5.9572 0 Td
(14)Tj
ET
129.65 158.204 m
129.65 153.704 l
129.65 158.204 m
125.15 158.204 l
129.65 179.464 m
125.15 179.464 l
129.65 200.723 m
125.15 200.723 l
129.65 221.983 m
125.15 221.983 l
129.65 243.243 m
125.15 243.243 l
129.65 264.503 m
125.15 264.503 l
129.65 285.763 m
125.15 285.763 l
172.169 158.204 m
172.169 153.704 l
150.9 158.204 m
150.9 153.704 l
214.689 158.204 m
214.689 153.704 l
193.4 158.204 m
193.4 153.704 l
257.209 158.204 m
257.209 153.704 l
235.9 158.204 m
235.9 153.704 l
299.729 158.204 m
299.729 153.704 l
278.4 158.204 m
278.4 153.704 l
S
BT
/T1_2 1 Tf
0 7 -7 0 104.275 211.1719 Tm
(Mass \(kg\))Tj
7 0 0 7 207.8942 127.3288 Tm
(Age \(years\))Tj
-8.383 7.0893 Td
(x)Tj
0 1.5185 TD
(x)Tj
T*
(x)Tj
3.0179 -1.5186 Td
(x)Tj
2.5716 Tc 0 1.5186 TD
(xx)Tj
2.5537 Tc 3.0536 1.5186 Td
(xx)Tj
0 Tc 3.0357 1.5515 Td
(x)Tj
3.0357 1.5185 Td
(x)Tj
2.5537 Tc 3.0357 3.1071 Td
[(xx)36(x)]TJ
2.518 Tc 3.0357 1.4279 Td
(xx)Tj
0 Tc 3 1.5185 Td
(x)Tj
ET
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
/GS6 gs
52.58 524.08 362.56 -134.45 re
f*
Q Q 
68.206 518.298 m
68.206 439.26 l
158.915 439.26 l
S
159.86 439.67 m
159.199 439.869 158.769 440.053 158.239 440.266 c
158.239 438.249 l
158.429 438.339 159.199 438.646 159.86 438.845 c
160.568 439.059 161.21 439.205 161.626 439.258 c
161.21 439.31 160.568 439.456 159.86 439.67 c
f
67.796 519.243 m
67.597 518.582 67.413 518.152 67.2 517.621 c
69.218 517.621 l
69.127 517.811 68.821 518.582 68.621 519.243 c
68.407 519.951 68.261 520.592 68.209 521.009 c
68.157 520.592 68.01 519.951 67.796 519.243 c
f
BT
/T1_3 1 Tf
0 7 -7 0 60.9291 468.4597 Tm
(Height)Tj
7 0 0 7 105.0278 428.6096 Tm
(Mass)Tj
9 0 0 9 67.4272 405.4622 Tm
(This diagram shows a)Tj
/T1_0 1 Tf
0 -1.2222 TD
(positive correlation)Tj
/T1_3 1 Tf
13.3003 1.2222 Td
(This diagram shows a)Tj
/T1_0 1 Tf
T*
(negative correlation)Tj
ET
188.207 518.298 m
188.207 439.26 l
278.916 439.26 l
S
279.861 439.67 m
279.199 439.869 278.77 440.053 278.239 440.266 c
278.239 438.249 l
278.429 438.339 279.199 438.646 279.861 438.845 c
280.568 439.059 281.21 439.205 281.626 439.258 c
281.21 439.31 280.568 439.456 279.861 439.67 c
f
187.797 519.243 m
187.597 518.582 187.413 518.152 187.2 517.621 c
189.218 517.621 l
189.128 517.811 188.821 518.582 188.622 519.243 c
188.408 519.951 188.261 520.592 188.209 521.009 c
188.157 520.592 188.011 519.951 187.797 519.243 c
f
BT
/T1_3 1 Tf
0 7 -7 0 181.8593 450.9265 Tm
(Time spent at work)Tj
7 0 0 7 194.3613 428.6096 Tm
(Time spent at home)Tj
9 0 0 9 307.5336 405.4622 Tm
(This diagram shows)Tj
/T1_0 1 Tf
T*
(no correlation)Tj
ET
308.61 518.298 m
308.61 439.26 l
399.319 439.26 l
S
400.264 439.67 m
399.603 439.869 399.173 440.053 398.643 440.266 c
398.643 438.249 l
398.832 438.339 399.603 438.646 400.264 438.845 c
400.972 439.059 401.614 439.205 402.03 439.258 c
401.614 439.31 400.972 439.456 400.264 439.67 c
f
308.201 519.243 m
308.001 518.582 307.817 518.152 307.604 517.621 c
309.622 517.621 l
309.532 517.811 309.225 518.582 309.025 519.243 c
308.811 519.951 308.665 520.592 308.613 521.009 c
308.56 520.592 308.415 519.951 308.201 519.243 c
f
BT
/T1_3 1 Tf
0 7 -7 0 302.2631 447.5266 Tm
(House number)Tj
7 0 0 7 324.0981 428.6096 Tm
(Classroom number)Tj
-35.1766 2.1553 Td
(x)Tj
17.1033 9.714 Td
(x)Tj
0.9719 -0.9719 Td
(x)Tj
1.6198 0.324 Td
(x)Tj
1.1388 Tc -0.3239 -1.6198 Td
(xx)Tj
0 Tc 1.2958 -1.6198 Td
(x)Tj
1.2958 0.324 Td
(x)Tj
0 -1.2959 TD
(x)Tj
-0.3239 -0.9718 Td
(x)Tj
2.2677 0.6479 Td
(x)Tj
0 -1.6198 TD
(x)Tj
0.9719 -0.6479 Td
(x)Tj
0.9719 -0.3239 Td
(x)Tj
0.3239 -1.2958 Td
(x)Tj
7.4812 0.9719 Td
(x)Tj
1.2959 -0.9719 Td
(x)Tj
0.9719 1.2958 Td
(x)Tj
-1.9438 1.2958 Td
(x)Tj
0.9719 1.6198 Td
(x)Tj
0.9719 1.9438 Td
(x)Tj
3.0825 Tc -1.6198 2.2678 Td
[(xx)972(x)]TJ
0 Tc 5.1834 -1.2959 Td
(x)Tj
-0.648 -1.9438 Td
(x)Tj
5.2198 2.9157 Td
(x)Tj
0 -3.2396 TD
(x)Tj
-2.2677 0.6479 Td
(x)Tj
-1.2958 -1.9438 Td
(x)Tj
-0.3239 -1.2958 Td
(x)Tj
-0.6479 -1.9438 Td
(x)Tj
0.4909 Tc 3.8876 -0.3239 Td
(xx)Tj
0 Tc 0.6479 2.9157 Td
(x)Tj
-7.1636 0.3239 Td
(x)Tj
-36.2471 -2.9109 Td
(x)Tj
0.3239 1.6198 Td
(x)Tj
1.6198 -0.6289 Td
(x)Tj
7.1271 7.4321 Td
(x)Tj
0.9719 -0.6479 Td
(x)Tj
-2.2677 -0.6479 Td
(x)Tj
-0.6479 -2.2677 Td
(x)Tj
-1.2959 1.2958 Td
(x)Tj
-2.9156 -0.648 Td
(x)Tj
1.2958 -2.5917 Td
(x)Tj
0 -1.9438 TD
(x)Tj
ET
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS3 cs 1  scn
/GS7 gs
BT
/T1_4 1 Tf
-0.0001 Tc 0.0296 Tw 18 0 0 18 50.6063 598.6229 Tm
(Scatter diagrams)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 50.6063 579.9141 Tm
[(These ar)18(e used to find connections between two sets of data.)]TJ
ET
0 0 0 1 K
0.125 w 10 M 
49.61 572.61 m
418.11 572.61 l
S
0.042 w 
49.61 572.44 m
418.11 572.44 l
S
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1 g
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/RelativeColorimetric ri
/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(83)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 554.95 368.51 -22.67 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0295 Tw 14 0 0 14 102.838 543.3708 Tm
[(Estimation of pr)18(obability by experiment)]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 523.4059 Tm
[(W)18(e can carry out an experiment to help us to estimate pr)18(obability)92(, eg we could thr)18(ow)]TJ
-0.0001 Tc 0 -1.3333 TD
(a thousand drawing-pins and count how many times they landed point up. T\
his would)Tj
T*
[(allow us to use the pr)18(obability to estimate how many would land point up if a million)]TJ
T*
[(drawing-pins wer)18(e thr)18(own.)]TJ
-0.0224 Tc 0 -1.9633 TD
[(The mor)18(e times an experiment is carried out, the mor)18(e likely the data obtained is accurate.)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0002 Tc 0 Tw 10 0 0 10 51.3228 452.0674 Tm
(Example)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0278 Tw 9 0 0 9 68.3307 437.2327 Tm
[(A six-sided die is thr)18(own. Her)18(e ar)18(e the r)18(esults:)]TJ
-0.0001 Tc 0 -8.3866 TD
[(John thr)18(ew the die 30 times. Andr)18(ea thr)18(ew the die 300 times.)]TJ
0 -1.9633 TD
[(Andr)18(ea is mor)18(e likely to obtain the better estimate because she has thr)18(own the die)]TJ
-0.0002 Tc 0 -1.3333 TD
[(mor)18(e times than John.)]TJ
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 10 0 0 10 51.3228 314.4144 Tm
(Questions)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 299.5799 Tm
[(A die is thr)18(own 600 times. These r)18(esults ar)18(e obtained.)]TJ
-0.0001 Tc 0 -6.3526 TD
[(1)-1334(Do the r)18(esults indicate the die is biased? )]TJ
0 -1.9633 TD
[(2)-1334(Justify your answer)92(. )]TJ
T*
[(3)-1334(Use the data to work out the pr)18(obability of the die landing on:)]TJ
-0.0002 Tc 1.8898 -1.3333 Td
[(a)-741(1,   b  3,   c  4,   d  6)]TJ
-0.0001 Tc -1.8898 -1.9633 Td
[(4)-1332(If the die wer)18(e fair how many times would you expect it to land on each )]TJ
1.888 -1.3333 Td
[(number if it wer)18(e thr)18(own 600 times?)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
0 Tw 8 0 0 8 51.3228 144.8943 Tm
(Answers)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 7 0 0 7 68.3307 132.8943 Tm
(1    The die seems to be biased.)Tj
0 -1.7143 TD
[(2)-1050(Mor)18(e 3s wer)18(e obtained than would be expected by chance. Fewer 4s wer)18(e obtained than would be )]TJ
1.6198 -1.7143 Td
(expected by chance.)Tj
1.0638 Tc -1.0363 Tw -1.6198 -1.7143 Td
[(3a)1064(  )]TJ
-0.0001 Tc 0 Tw 4.9 0 0 4.9 87.5795 99.6943 Tm
(102)Tj
0 Tc 7 0 0 7 95.7513 96.8943 Tm
(/)Tj
-0.0001 Tc 4.9 0 0 4.9 98.3404 95.4944 Tm
(600)Tj
-0.0004 Tc 7 0 0 7 108.6515 96.8943 Tm
(= )Tj
-0.0002 Tc 4.9 0 0 4.9 115.4513 99.6943 Tm
(51)Tj
0 Tc 7 0 0 7 120.8991 96.8943 Tm
(/)Tj
-0.0001 Tc 4.9 0 0 4.9 123.4882 95.4944 Tm
(300)Tj
-0.0004 Tc 7 0 0 7 133.7994 96.8943 Tm
(= )Tj
-0.0002 Tc 4.9 0 0 4.9 140.5991 99.6943 Tm
(17)Tj
0 Tc 7 0 0 7 146.047 96.8943 Tm
(/)Tj
-0.0001 Tc 4.9 0 0 4.9 148.6361 95.4944 Tm
(100)Tj
-0.0002 Tc 0.0277 Tw 7 0 0 7 176.0472 96.8943 Tm
(b  )Tj
-0.0001 Tc 0 Tw 4.9 0 0 4.9 184.6017 99.6943 Tm
(181)Tj
0 Tc 7 0 0 7 192.7735 96.8943 Tm
(/)Tj
-0.0001 Tc 4.9 0 0 4.9 195.3626 95.4944 Tm
(600)Tj
-0.0002 Tc 0.0278 Tw 7 0 0 7 79.6693 84.8943 Tm
(c  )Tj
0 Tw 4.9 0 0 4.9 87.3214 87.6943 Tm
(31)Tj
0 Tc 7 0 0 7 92.7693 84.8943 Tm
(/)Tj
-0.0001 Tc 4.9 0 0 4.9 95.3584 83.4944 Tm
(600)Tj
-0.0002 Tc 0.0277 Tw 7 0 0 7 176.0472 84.8943 Tm
(d  )Tj
0 Tw 4.9 0 0 4.9 184.6017 87.6943 Tm
(92)Tj
0 Tc 7 0 0 7 190.0496 84.8943 Tm
(/)Tj
-0.0001 Tc 4.9 0 0 4.9 192.6387 83.4944 Tm
(600)Tj
-0.0004 Tc 7 0 0 7 202.9498 84.8943 Tm
(= )Tj
-0.0002 Tc 4.9 0 0 4.9 209.7495 87.6943 Tm
(23)Tj
0 Tc 7 0 0 7 215.1974 84.8943 Tm
(/)Tj
-0.0001 Tc 4.9 0 0 4.9 217.7865 83.4944 Tm
(150)Tj
0.0277 Tw 7 0 0 7 68.3307 72.8943 Tm
[(4)-1050(W)18(e would expect the die to land on each number a similar amount of times.\
 The chance of each number is)]TJ
0 Tc 0 Tw 4.9 0 0 4.9 79.6693 63.6943 Tm
(1)Tj
7 0 0 7 82.3932 60.8943 Tm
(/)Tj
4.9 0 0 4.9 84.9823 59.4944 Tm
(6)Tj
-0.0001 Tc 0.0277 Tw 7 0 0 7 87.7063 60.8943 Tm
[(. Ther)18(efor)18(e we would expect each number to occur about 100 times.)]TJ
ET
0 0 0 0 k
160.37 291.28 184.41 -34.04 re
f*
Q Q 
0 g
/GS5 gs
BT
/T1_2 1 Tf
2.344 Tc 7 0 0 7 190.074 278.9599 Tm
[(1)-133(2)-17(3456)]TJ
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
182.57 274.629 122.5 13.65 re
203.22 288.06 m
203.22 274.629 l
224.133 288.06 m
224.133 274.629 l
S
BT
/T1_2 1 Tf
0 Tc 7 0 0 7 186.182 264.3769 Tm
[(102)-1365(112)-1249(181)-1510(31)-1788(82)-1788(92)]TJ
ET
182.57 288.279 m
182.57 259.696 l
305.07 259.696 l
305.07 288.279 l
203.22 288.06 m
203.22 259.696 l
224.133 288.06 m
224.133 259.696 l
244.185 288.06 m
244.185 259.696 l
264.82 288.06 m
264.82 259.696 l
284.77 288.06 m
284.77 259.696 l
S
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
/GS6 gs
112.5 428.93 244.14 -52.34 re
f*
Q Q 
BT
/T1_2 1 Tf
7 0 0 7 193.2742 417.0799 Tm
(1)Tj
0 -2.4 TD
(2)Tj
3.0333 2.4 Td
(2)Tj
T*
(7)Tj
2.9166 2.4 Td
(3)Tj
T*
(3)Tj
2.75 2.4 Td
(4)Tj
T*
(8)Tj
2.8666 2.4 Td
(5)Tj
T*
(4)Tj
2.9166 2.4 Td
(6)Tj
T*
(6)Tj
ET
138.521 395.599 168.349 30.8 re
138.506 410.78 m
306.651 410.78 l
206.42 426.18 m
206.42 395.599 l
227.333 426.18 m
227.333 395.599 l
246.903 426.18 m
246.903 395.599 l
266.97 426.18 m
266.97 395.599 l
287.139 426.18 m
287.139 395.599 l
S
BT
/T1_2 1 Tf
7 0 0 7 191.3282 385.347 Tm
(46)Tj
-6.4514 4.5333 Td
(Side of die)Tj
1.314 -2.4 Td
(John)Tj
-0.5365 -2.1333 Td
[(Andrea)-5447(51)-1805(53)-1638(47)-1755(46)-1805(57)]TJ
ET
138.521 426.399 m
138.521 380.665 l
306.87 380.665 l
306.87 426.399 l
206.42 426.18 m
206.42 380.665 l
185.77 426.18 m
185.77 380.665 l
227.333 426.18 m
227.333 380.665 l
246.903 426.18 m
246.903 380.665 l
266.97 426.18 m
266.97 380.665 l
287.139 426.18 m
287.139 380.665 l
S
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS3 cs 1  scn
/GS7 gs
BT
/T1_3 1 Tf
-0.0002 Tc 18 0 0 18 326.4689 598.6229 Tm
[(Pr)18(obability)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0054 Tc 0.0278 Tw 9 0 0 9 51.3228 579.9141 Tm
[(Y)92(ou need to understand when to multiply pr)18(obabilities, when to add pr)18(obabilities and)]TJ
0 -1.3333 TD
[(tr)18(ee diagrams.)]TJ
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-0.278 -1.2222 Td
(11)Tj
4.9816 Tc -2.5739 0.6667 Td
(x=)Tj
ET
161.61 264.04 m
172.61 264.04 l
212.11 264.04 m
223.11 264.04 l
260.61 264.04 m
271.61 264.04 l
243.61 301.54 m
254.61 301.54 l
181.61 301.54 m
192.61 301.54 l
S
BT
/T1_3 1 Tf
0 Tc 9 0 0 9 264.108 266.04 Tm
(1)Tj
-0.278 -1.2222 Td
(11)Tj
-21.5822 21.2222 Td
[(A boy is blindfolded. What is the pr)18(obability )]TJ
0 -1.3333 TD
(he chooses a blue sweet, eats it, then chooses )Tj
T*
[(a r)18(ed sweet?)]TJ
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/T1_0 1 Tf
10 0 0 10 50.358 496.04 Tm
(Example)Tj
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(Method)Tj
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(Questions)Tj
0 g
/T1_3 1 Tf
9 0 0 9 84.8771 328.54 Tm
(The boy needs)Tj
-1.9457 -12 Td
(1)Tj
0 -1.8333 TD
(2)Tj
ET
0.055 0.024 0.482 0 k
152.61 504.04 115 40.5 re
B
0 g
BT
/T1_0 1 Tf
9 0 0 9 163.6779 528.04 Tm
(AND)Tj
/T1_3 1 Tf
2.2769 0 Td
( means )Tj
/T1_0 1 Tf
3.4649 0 Td
[(MUL)92(TIPL)111(Y)]TJ
-4.1666 -1.5555 Td
(OR)Tj
/T1_3 1 Tf
1.4629 0 Td
( means )Tj
/T1_0 1 Tf
3.4649 0 Td
(ADD)Tj
0 0 0 0 k
/T1_3 1 Tf
-0.0001 Tc 0.0001 Tw 6.6 0 0 6.6 71.1981 355.29 Tm
(BLUE SWEET)Tj
1 g
0 Tc 0 Tw 8 0 0 8 328.4044 453.4365 Tm
(R)Tj
-0.7682 -1.7559 Td
(B)Tj
4.1771 2.0002 Td
(B)Tj
0 g
-1.7881 -0.8103 Td
(W)Tj
1.9716 -1.9175 Td
(W)Tj
2.3441 0.2285 Td
(W)Tj
-4.6919 -2.3438 Td
(W)Tj
-1.7412 0.8077 Td
(W)Tj
1 g
5.6915 -0.103 Td
(B)Tj
-1.999 -0.7954 Td
(B)Tj
-1.6525 2.1619 Td
(R)Tj
3.6689 1.9597 Td
(R)Tj
ET
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1 g
1 i 
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0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0004 Tc 8 0 0 8 408.358 35.0006 Tm
(87)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
0 0 0 0 k
50.32 593.39 368.51 -22.68 re
f*
/CS2 cs 1  scn
BT
/T1_0 1 Tf
0.0295 Tw 14 0 0 14 168.4432 581.8038 Tm
[(Pr)18(obability \(at least\))]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0 Tw 10 0 0 10 369.6773 604.6698 Tm
[(Pr)18(obability)]TJ
/T1_3 1 Tf
0.0278 Tw 9 0 0 9 68.3307 557.2368 Tm
[(This page shows you a shortcut. This is used when a question asks for th\
e pr)18(obability)]TJ
0 Tw 0 -1.3333 TD
(of )Tj
/T1_4 1 Tf
0 Tc 1.1943 0 Td
(\322)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.5188 0 Td
(at least)Tj
/T1_4 1 Tf
0 Tc 0 Tw 3.2284 0 Td
(\323)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.5188 0 Td
( or the )Tj
/T1_4 1 Tf
0 Tc 0 Tw 3.2849 0 Td
(\322)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.5188 0 Td
[(pr)18(obability of not getting)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 11.3148 0 Td
(\323)Tj
/T1_3 1 Tf
0.5189 0 Td
(.)Tj
/CS3 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 10 0 0 10 51.3228 521.8981 Tm
(Questions)Tj
0 0 0 1 k
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 9 0 0 9 68.3307 507.0635 Tm
[(Thr)18(ee coins ar)18(e tossed. )]TJ
0 -1.9633 TD
[(What is the pr)18(obability of:)]TJ
-0.0001 Tc T*
[(1)-1334(Exactly one head?)]TJ
-0.0002 Tc T*
[(2)-1334(At least one head?)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0 Tw 8 0 0 8 51.3228 433.5518 Tm
(Answers)Tj
0 0 0 1 k
/T1_3 1 Tf
0.0277 Tw 7 0 0 7 68.3307 421.5518 Tm
[(1)-1064(W)18(e need:)]TJ
-0.0002 Tc 1.6198 -8.5714 Td
[(\(Or you could use a tr)18(ee diagram, see page 84.\))]TJ
-0.0001 Tc -1.6198 -1.7143 Td
[(2)-1064(Remember)92(, the total pr)18(obability for all of the possible ways thr)18(ee coins can land is 1.  W)18(e could say:)]TJ
1.6198 -6.8571 Td
(This will work but it takes a long time!)Tj
/T1_0 1 Tf
0.0296 Tw 0 -1.7143 TD
[(Think car)18(efully)]TJ
/T1_3 1 Tf
0.0277 Tw T*
[(Sometimes it is quicker to work out the pr)18(obability of what we do not want.)]TJ
/T1_0 1 Tf
0.0296 Tw T*
(What don)Tj
/T1_5 1 Tf
0 Tc 0 Tw 4.6198 0 Td
(\325)Tj
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 0.2782 0 Td
(t we want?)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw -4.898 -1.7143 Td
[(W)18(e don)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 3.5468 0 Td
(\325)Tj
/T1_3 1 Tf
-0.0001 Tc 0.0277 Tw 0.2422 0 Td
[(t want thr)18(ee tails. Any other outcome will contain at least one head.)]TJ
-3.789 -1.7143 Td
[(The pr)18(obability of thr)18(ee tails is:)]TJ
ET
0 0 0 0 k
69.33 341.84 345.54 -32.55 re
f*
Q Q 
0.114 0.082 0.063 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS5 gs
92.297 338.447 m
98.788 338.447 104.051 333.185 104.051 326.693 c
104.051 320.202 98.788 314.939 92.297 314.939 c
85.805 314.939 80.543 320.202 80.543 326.693 c
80.543 333.185 85.805 338.447 92.297 338.447 c
h
B
136.929 338.447 m
143.421 338.447 148.683 333.185 148.683 326.693 c
148.683 320.202 143.421 314.939 136.929 314.939 c
130.438 314.939 125.175 320.202 125.175 326.693 c
125.175 333.185 130.438 338.447 136.929 338.447 c
h
B
181.332 338.447 m
187.823 338.447 193.086 333.185 193.086 326.693 c
193.086 320.202 187.823 314.939 181.332 314.939 c
174.84 314.939 169.578 320.202 169.578 326.693 c
169.578 333.185 174.84 338.447 181.332 338.447 c
h
B
225.061 338.447 m
231.553 338.447 236.815 333.185 236.815 326.693 c
236.815 320.202 231.553 314.939 225.061 314.939 c
218.57 314.939 213.307 320.202 213.307 326.693 c
213.307 333.185 218.57 338.447 225.061 338.447 c
h
B
270.694 338.447 m
277.185 338.447 282.448 333.185 282.448 326.693 c
282.448 320.202 277.185 314.939 270.694 314.939 c
264.203 314.939 258.94 320.202 258.94 326.693 c
258.94 333.185 264.203 338.447 270.694 338.447 c
h
B
315.096 338.447 m
321.588 338.447 326.85 333.185 326.85 326.693 c
326.85 320.202 321.588 314.939 315.096 314.939 c
308.605 314.939 303.342 320.202 303.342 326.693 c
303.342 333.185 308.605 338.447 315.096 338.447 c
h
B
0.039 0.02 0.486 0 k
106.26 321.06 17.5 11.5 re
B
150.26 321.06 17.5 11.5 re
B
194.26 321.06 17.5 11.5 re
B
239.26 321.06 17.5 11.5 re
B
284.26 321.06 17.5 11.5 re
B
328.26 321.06 17.5 11.5 re
B
0 g
BT
/T1_3 1 Tf
6 0 0 6 83.9755 324.2896 Tm
(HEAD)Tj
/T1_0 1 Tf
0.0001 Tc 3.9904 0 Td
(AND)Tj
/T1_3 1 Tf
0 Tc 3.4485 0 Td
(HEAD)Tj
/T1_0 1 Tf
3.9519 0 Td
(AND)Tj
/T1_3 1 Tf
3.4484 0 Td
(HEAD)Tj
/T1_0 1 Tf
4.3204 0 Td
[(OR)-20697(OR    )]TJ
/T1_3 1 Tf
9 0 0 9 349.9332 324.2896 Tm
(. . .)Tj
6 0 0 6 216.7402 324.2896 Tm
(HEAD)Tj
/T1_0 1 Tf
3.9904 0 Td
(AND)Tj
/T1_3 1 Tf
3.6151 0 Td
(HEAD)Tj
/T1_0 1 Tf
3.9519 0 Td
(AND)Tj
/T1_3 1 Tf
3.8075 0 Td
(TAIL)Tj
ET
0.114 0.082 0.063 0.004 k
111.343 411.27 m
116.943 411.27 121.483 406.73 121.483 401.13 c
121.483 395.53 116.943 390.99 111.343 390.99 c
105.743 390.99 101.203 395.53 101.203 401.13 c
101.203 406.73 105.743 411.27 111.343 411.27 c
h
B
150.197 411.27 m
155.798 411.27 160.337 406.73 160.337 401.13 c
160.337 395.53 155.798 390.99 150.197 390.99 c
144.597 390.99 140.058 395.53 140.058 401.13 c
140.058 406.73 144.597 411.27 150.197 411.27 c
h
B
188.165 411.27 m
193.765 411.27 198.305 406.73 198.305 401.13 c
198.305 395.53 193.765 390.99 188.165 390.99 c
182.565 390.99 178.025 395.53 178.025 401.13 c
178.025 406.73 182.565 411.27 188.165 411.27 c
h
B
227.218 411.27 m
232.818 411.27 237.358 406.73 237.358 401.13 c
237.358 395.53 232.818 390.99 227.218 390.99 c
221.618 390.99 217.078 395.53 217.078 401.13 c
217.078 406.73 221.618 411.27 227.218 411.27 c
h
B
266.072 411.27 m
271.672 411.27 276.212 406.73 276.212 401.13 c
276.212 395.53 271.672 390.99 266.072 390.99 c
260.472 390.99 255.932 395.53 255.932 401.13 c
255.932 406.73 260.472 411.27 266.072 411.27 c
h
B
303.965 411.27 m
309.565 411.27 314.105 406.73 314.105 401.13 c
314.105 395.53 309.565 390.99 303.965 390.99 c
298.365 390.99 293.825 395.53 293.825 401.13 c
293.825 406.73 298.365 411.27 303.965 411.27 c
h
B
343.018 411.27 m
348.618 411.27 353.158 406.73 353.158 401.13 c
353.158 395.53 348.618 390.99 343.018 390.99 c
337.419 390.99 332.878 395.53 332.878 401.13 c
332.878 406.73 337.419 411.27 343.018 411.27 c
h
B
382.873 411.27 m
388.473 411.27 393.012 406.73 393.012 401.13 c
393.012 395.53 388.473 390.99 382.873 390.99 c
377.273 390.99 372.732 395.53 372.732 401.13 c
372.732 406.73 377.273 411.27 382.873 411.27 c
h
B
72.29 411.27 m
77.89 411.27 82.43 406.73 82.43 401.13 c
82.43 395.53 77.89 390.99 72.29 390.99 c
66.69 390.99 62.15 395.53 62.15 401.13 c
62.15 406.73 66.69 411.27 72.29 411.27 c
h
B
0.039 0.02 0.486 0 k
83.65 396.13 16.5 11 re
B
122.65 396.13 16.5 11 re
B
161.15 396.13 16.5 11 re
B
199.65 396.13 16.5 11 re
B
238.15 396.13 16.5 11 re
B
276.65 396.13 16.5 11 re
B
315.15 396.13 16.5 11 re
B
354.65 396.13 16.5 11 re
B
0 g
BT
/T1_3 1 Tf
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(HEAD)Tj
/T1_0 1 Tf
3.5201 0 Td
(AND)Tj
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3.3478 0 Td
(TAIL)Tj
/T1_0 1 Tf
3.1279 0 Td
(AND)Tj
/T1_3 1 Tf
3.3478 0 Td
(TAIL)Tj
/T1_0 1 Tf
0.0001 Tc 3.5093 0 Td
(OR)Tj
/T1_3 1 Tf
0 Tc 2.8186 0 Td
(TAIL)Tj
/T1_0 1 Tf
3.1612 0 Td
(AND)Tj
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2.9887 0 Td
(HEAD)Tj
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3.487 0 Td
(AND)Tj
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(TAIL)Tj
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(OR)Tj
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(TAIL)Tj
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(AND)Tj
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3.3478 0 Td
(TAIL)Tj
/T1_0 1 Tf
3.1279 0 Td
(AND)Tj
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(HEAD)Tj
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(1)Tj
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(  2)Tj
ET
69.316 380.464 m
75.983 383.464 l
108.65 380.464 m
115.317 383.464 l
146.775 380.464 m
153.441 383.464 l
185.066 380.464 m
191.734 383.464 l
223.816 380.464 m
230.484 383.464 l
262.963 380.464 m
269.629 383.464 l
301.379 380.38 m
308.046 383.38 l
340.734 380.38 m
347.4 383.38 l
379.691 380.38 m
386.358 383.38 l
407.296 379.839 m
413.963 382.839 l
S
BT
/T1_3 1 Tf
7 0 0 7 110.1244 383.5569 Tm
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
5.6892 1.2143 Td
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
37.3544 1.2143 Td
(3)Tj
-0.278 -1.2143 Td
(  8)Tj
4.8751 Tc -44.8041 0.609 Td
[(xx)-122(+)]TJ
0 Tc 13.5137 0.6053 Td
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
5.7873 1.2143 Td
(1)Tj
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(  2)Tj
5.8321 1.2143 Td
(1)Tj
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(  2)Tj
4.9466 Tc -7.8705 0.609 Td
[(xx)-194(+)]TJ
0 Tc 13.6566 0.6053 Td
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
5.8588 1.2143 Td
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
5.9035 1.2143 Td
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
5.1609 Tc -8.0848 0.609 Td
(xx)Tj
0 Tc 10.6223 0.0443 Td
(=)Tj
10.2873 Tc 11 0 0 11 64.866 378.4636 Tm
(\(\()Tj
10.2551 Tc 8.3049 0 Td
[(\)\))8212(\()2212(\))]TJ
ET
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
/GS6 gs
68.53 236.58 298.67 -97.23 re
f*
Q Q 
0.114 0.082 0.063 0.004 k
111.555 233.385 m
117.155 233.385 121.695 228.845 121.695 223.245 c
121.695 217.645 117.155 213.105 111.555 213.105 c
105.955 213.105 101.415 217.645 101.415 223.245 c
101.415 228.845 105.955 233.385 111.555 233.385 c
h
B
150.608 233.385 m
156.208 233.385 160.748 228.845 160.748 223.245 c
160.748 217.645 156.208 213.105 150.608 213.105 c
145.008 213.105 140.468 217.645 140.468 223.245 c
140.468 228.845 145.008 233.385 150.608 233.385 c
h
B
190.462 233.385 m
196.062 233.385 200.602 228.845 200.602 223.245 c
200.602 217.645 196.062 213.105 190.462 213.105 c
184.862 213.105 180.323 217.645 180.323 223.245 c
180.323 228.845 184.862 233.385 190.462 233.385 c
h
B
0.039 0.02 0.486 0 k
122.71 217.43 17.5 11.5 re
B
161.71 217.43 17.5 11.5 re
B
0 g
BT
/T1_3 1 Tf
0 Tc 6 0 0 6 105.4013 221.1713 Tm
(TAIL)Tj
/T1_0 1 Tf
3.1611 0 Td
(AND)Tj
/T1_3 1 Tf
3.3478 0 Td
(TAIL)Tj
/T1_0 1 Tf
3.1279 0 Td
(AND)Tj
/T1_3 1 Tf
3.5144 0 Td
(TAIL)Tj
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(1)Tj
-0.278 -1.2143 Td
(  2)Tj
6.1445 1.2143 Td
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
5.8321 1.2143 Td
(1)Tj
-0.278 -1.2143 Td
(  2)Tj
0.7149 -4.2094 Td
(1)Tj
-0.278 -1.2143 Td
(  8)Tj
4.3247 6.638 Td
(1)Tj
-0.278 -1.2143 Td
(  8)Tj
8.7313 -4.1558 Td
(7)Tj
-0.278 -1.2143 Td
(  8)Tj
5.3578 Tc -21.1984 5.9791 Td
(xx)Tj
0 Tc 10.9628 -0.0533 Td
(=)Tj
-16.1166 -3.0453 Td
(Total probability )Tj
/T1_4 1 Tf
7.6251 0 Td
(\320)Tj
/T1_3 1 Tf
0.5 0 Td
( Probability of three tails = Probability of at least one head)Tj
-4.1251 -2.3522 Td
(1)Tj
/T1_4 1 Tf
3.5714 0 Td
(\320)Tj
/T1_3 1 Tf
11.6429 0 Td
(=)Tj
ET
113.876 200.93 m
106.876 196.597 l
154.876 200.93 m
147.876 196.597 l
193.751 200.93 m
186.751 196.597 l
224.96 200.93 m
217.96 196.597 l
196.71 162.909 m
189.71 158.576 l
283.856 163.159 m
276.856 158.826 l
S
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS4 cs 1  scn
/GS7 gs
85.21 130.34 294.96 -39.83 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0001 Tc 9 0 0 9 91.4616 117.2915 Tm
(Note:)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 2.9702 0 Td
(When a question states )Tj
/T1_4 1 Tf
0 Tc 0 Tw 10.8115 0 Td
(\322)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.5188 0 Td
(at least)Tj
/T1_4 1 Tf
0 Tc 0 Tw 3.2285 0 Td
(\323)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.5188 0 Td
( always consider the short cut)Tj
-18.0479 -1.9633 Td
[(T)111(otal pr)18(obability )]TJ
/T1_4 1 Tf
0 Tc 0 Tw 7.5492 0 Td
(\320)Tj
/T1_3 1 Tf
-0.0002 Tc 0.0278 Tw 0.4999 0 Td
( what we do not want = what we do want)Tj
ET
0 0 0 1 K
10 M 
85.21 130.34 294.96 -39.83 re
S
Q Q 
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(100 centimetres \(cm\) = 1 metre \(m\))Tj
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(1000 millilitres \(ml\) = 1 litre \(l\))Tj
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(. You are expected )Tj
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0.0278 Tw T*
[(1)-1332(A cube has a volume of 216 cm)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 212.5633 350.6781 Tm
(3)Tj
9 0 0 9 216.0655 347.0782 Tm
(.)Tj
-0.0001 Tc 0.0278 Tw -14.6066 -1.3333 Td
(What is the length of each side?)Tj
-1.888 -1.6483 Td
[(2)-1334(What is the value of 5)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 172.6863 323.8435 Tm
(4)Tj
9 0 0 9 176.1885 320.2436 Tm
(?)Tj
-0.0001 Tc 0.0278 Tw -12.0638 -1.6483 Td
[(3)-1334(Calculate the value of:)]TJ
0 Tw 1.8898 -1.6483 Td
[(a)-741(2401)]TJ
-0.0002 Tc 6.3 0 0 6.3 115.9732 294.1741 Tm
(3/4)Tj
0 Tc 9 0 0 9 147.3122 290.5742 Tm
(b)Tj
6.3 0 0 6.3 158.3227 294.1741 Tm
(5)Tj
/T1_3 1 Tf
9 0 0 9 161.8249 290.5742 Tm
(\002)Tj
/T1_2 1 Tf
-0.0001 Tc 0.5488 0 Td
(243)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
0.0295 Tw -12.9065 -2.4357 Td
[(4)-1298(Standar)18(d for)-18(m)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0278 Tw 1.8898 -1.4908 Td
[(1)-1332(W)18(rite 6)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 5.135 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(32 x 10)Tj
/T1_4 1 Tf
0 Tc 0 Tw 6.3 0 0 6.3 146.1812 258.8355 Tm
(\320)Tj
/T1_2 1 Tf
0.4998 0 Td
(4)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 155.5839 255.2356 Tm
[(as an or)18(dinary)]TJ
0 Tw -7.8864 -1.3333 Td
[(number)92(.)]TJ
-0.0001 Tc 0.0277 Tw -1.888 -1.6483 Td
[(2)-1334(W)18(rite 273 000 in standar)18(d for)-18(m.)]TJ
0 -1.6483 TD
[(3)-1334(W)18(rite 0)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 5.1367 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2779 0 Td
[(0072 in standar)18(d for)-18(m.)]TJ
1.3338 Tc 0 Tw -5.4146 -1.6483 Td
(48)Tj
/T1_4 1 Tf
0 Tc 2.4456 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(42 x 10)Tj
/T1_4 1 Tf
0 Tc 0 Tw 6.3 0 0 6.3 121.9769 202.3316 Tm
(\320)Tj
/T1_2 1 Tf
0.4998 0 Td
(6)Tj
/T1_4 1 Tf
9 0 0 9 131.3796 198.7316 Tm
(\326)Tj
/T1_2 1 Tf
0.9714 0 Td
(3)Tj
/T1_4 1 Tf
0.5559 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(4 x 10)Tj
/T1_4 1 Tf
0 Tc 0 Tw 6.3 0 0 6.3 172.4738 202.3316 Tm
(\320)Tj
/T1_2 1 Tf
0.4998 0 Td
(2)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 9 0 0 9 50.6063 176.8103 Tm
[(5)-1298(Per)18(centages and fractions)]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0279 Tc 0.0278 Tw 1.8898 -1.4908 Td
[(1)-1360(A cinema holds 3200 people.)]TJ
1.888 -1.3333 Td
[(Safety r)18(egulations r)18(equir)18(e the)]TJ
0 -1.3333 TD
[(capacity to be r)18(educed by )]TJ
0 Tc 0 Tw 6.3 0 0 6.3 186.6753 142.993 Tm
(3)Tj
9 0 0 9 190.0024 139.393 Tm
(/)Tj
6.3 0 0 6.3 193.0812 137.5931 Tm
(8)Tj
-0.028 Tc 0.0278 Tw 9 0 0 9 196.4083 139.393 Tm
(. What)Tj
-0.0279 Tc -12.4224 -1.3333 Td
[(is the capacity after the r)18(eduction?)]TJ
-0.0002 Tc -1.888 -1.6483 Td
[(2)-1332(Mrs Saunders ear)-18(ned \243240 per)]TJ
-0.0001 Tc 1.888 -1.3333 Td
[(week. She r)18(eceived a 6%)]TJ
-0.0002 Tc T*
[(incr)18(ease. What was her wage)]TJ
T*
[(after the incr)18(ease?)]TJ
-0.0001 Tc 19.7332 52.6614 Td
[(3)-1332(Mr W)-24(illiams ear)-18(ned \243180 per)]TJ
1.888 -1.3333 Td
[(week in 1990. He r)18(eceived a 4%)]TJ
T*
(rise each year for five years.)Tj
T*
(Calculate his wage in 1995.)Tj
-0.0002 Tc -1.888 -1.6483 Td
[(4)-1332(Miss Soames bought a car for )]TJ
-0.0001 Tc 1.888 -1.3333 Td
[(\24310 000. The car depr)18(eciated by)]TJ
T*
[(10% each year)92(. How much was it)]TJ
-0.0002 Tc T*
(worth after four years?)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw -3.7778 -2.4357 Td
[(6)-1298(Calculating gr)18(owth and decay rates)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0278 Tw 1.8889 -1.4908 Td
(The value of an antique vase)Tj
0.0009 -1.3333 Td
[(incr)18(eases by 4% each year)92(. Its value in)]TJ
T*
(1990 was \2432704.)Tj
0 -1.6483 TD
[(a)-1369(Calculate its value in 1996 to the)]TJ
-0.0002 Tc 1.888 -1.3333 Td
[(near)18(est pound.)]TJ
-0.0001 Tc -1.888 -1.6483 Td
[(b)-1279(Calculate its value in 1988.)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
0.0296 Tw -1.8898 -2.4357 Td
[(7)-1298(Patter)-18(ns you must r)18(ecognise)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 1.8898 -1.4908 Td
[(1)-1332(What ar)18(e the special names given)]TJ
-0.0002 Tc 1.888 -1.3333 Td
(to these numbers?)Tj
-0.0001 Tc 0.0018 -1.6483 Td
[(a)-741(1, 4, 9, 16, 25, 36...)]TJ
T*
[(b)-649(1, 8, 27, 64, 125, 216...)]TJ
T*
[(c)-778(1, 3, 6, 10, 15, 21...)]TJ
-0.0002 Tc -1.8898 -1.6483 Td
[(2)-1334(List the factors of 30.)]TJ
T*
[(3)-1332(Complete the next thr)18(ee prime)]TJ
0 Tw 1.888 -1.3333 Td
(numbers:)Tj
0.0278 Tw 0.0018 -1.6483 Td
(2, 3, 5, 7...)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw -3.7795 -2.4357 Td
[(8)-1298(Pr)18(oduct of primes, highest common)]TJ
1.8898 -1.3333 Td
[(factor)92(, lowest common multiple and)]TJ
-0.0002 Tc 0 Tw 0 -1.3333 TD
[(r)18(ecipr)18(ocals)]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0113 Tc 0.0278 Tw 0 -1.4908 TD
[(1)-1343(W)18(rite 1960 as a pr)18(oduct of primes.)]TJ
-0.0001 Tc 0 -1.6483 TD
[(2)-1332(Find the HCF and LCM of 36 )]TJ
-0.0002 Tc 1.888 -1.3333 Td
(and 90.)Tj
0.0054 Tc -1.888 -1.6483 Td
[(3)-1328(Find the r)18(ecipr)18(ocal of -8.)]TJ
ET
Q Q 
q
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-1 661 470 -662 re
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/GS3 gs
BT
/T1_2 1 Tf
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(0)Tj
/T1_4 1 Tf
0.556 0 Td
(\341)Tj
/T1_2 1 Tf
0.278 0 Td
(217)Tj
ET
95.995 506.67 m
95.726 506.67 95.541 506.889 95.541 507.124 c
95.541 507.359 95.726 507.578 95.995 507.578 c
96.264 507.578 96.449 507.359 96.449 507.124 c
96.449 506.889 96.264 506.67 95.995 506.67 c
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106.295 506.67 m
106.026 506.67 105.841 506.889 105.841 507.124 c
105.841 507.359 106.026 507.578 106.295 507.578 c
106.564 507.578 106.749 507.359 106.749 507.124 c
106.749 506.889 106.564 506.67 106.295 506.67 c
f
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS3 cs 1  scn
BT
/T1_5 1 Tf
-0.0001 Tc 0.0296 Tw 18 0 0 18 50.6063 599.7852 Tm
(Diagnostic tests)Tj
0 0 0 1 k
/T1_2 1 Tf
-0.0224 Tc 0.0278 Tw 8.73 0 0 9 49.6063 584.2314 Tm
[(These tests will help you check how good you ar)18(e at questions on each topic. If you have dif)18(ficulty)92(,)]TJ
0 -1.3333 TD
[(r)18(evise the topic again.)]TJ
ET
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0.125 w 10 M 0 j 0 J []0 d 
49.61 565.6 m
418.11 565.6 l
S
0.042 w 
49.61 565.44 m
418.11 565.44 l
S
Q Q 
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/RelativeColorimetric ri
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0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
/CS1 cs 1  scn
BT
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 9 0 0 9 51.3228 574.2445 Tm
[(9)-1298(T)92(rial and impr)18(ovement)]TJ
0 0 0 1 k
/T1_1 1 Tf
0.0277 Tw 1.8889 -1.4908 Td
[(Find the value of x corr)18(ect to one)]TJ
0.0009 -1.3333 Td
(decimal place using trial and)Tj
-0.0002 Tc 0 -1.3333 TD
[(impr)18(ovement. Y)92(ou must show all of)]TJ
-0.0001 Tc T*
(your working.)Tj
0 Tc 0 Tw 1.8898 -1.6483 Td
(x)Tj
6.3 0 0 6.3 89.676 513.5925 Tm
(3)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 95.9287 509.9926 Tm
(+ x = 108)Tj
/CS1 cs 1  scn
/T1_0 1 Tf
0 Tw -4.9562 -2.4357 Td
[(10)-706(Equations)]TJ
0 0 0 1 k
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 1.8898 -1.4908 Td
(Solve these equations. Give the)Tj
-0.0002 Tc T*
[(answer corr)18(ect to thr)18(ee significant)]TJ
T*
[(figur)18(es wher)18(e appr)18(opriate.)]TJ
1.3338 Tc 0 Tw 0 -1.6483 TD
(1y)Tj
0 Tc 6.3 0 0 6.3 89.676 439.4193 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 95.9287 435.8193 Tm
(= 10)Tj
0 Tc 0 Tw -3.0664 -1.6483 Td
(2)Tj
/T1_2 1 Tf
1.8898 0 Td
(\002)Tj
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 0.5488 0 Td
(y = 17)Tj
0 Tc 0 Tw -2.4386 -1.6483 Td
(3)Tj
6.3 0 0 6.3 85.3386 409.7499 Tm
(5)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 88.8408 406.15 Tm
(/y = 8)Tj
-2.2789 -1.6483 Td
[(4)-1334(3\(y + 6\) )]TJ
/T1_3 1 Tf
0 Tc 0 Tw 5.5858 0 Td
(\320)Tj
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 2\(4y )Tj
/T1_3 1 Tf
0 Tc 0 Tw 2.4647 0 Td
(\320)Tj
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
( 1\) = 8)Tj
/CS1 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw -10.94 -2.4357 Td
[(11)-706(Rewriting for)-18(mulae)]TJ
0 0 0 1 k
/T1_1 1 Tf
0.0278 Tw 1.8898 -1.4908 Td
(Make y the subject:)Tj
0 Tc 0 Tw T*
(1)Tj
/T1_2 1 Tf
1.8898 0 Td
(\002)Tj
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 0.5488 0 Td
(y = 4c)Tj
1.3338 Tc 0 Tw -2.4386 -1.6483 Td
(2y)Tj
0 Tc 6.3 0 0 6.3 89.676 329.9074 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 95.9287 326.3075 Tm
(= 25x)Tj
0 Tc 0 Tw 6.3 0 0 6.3 119.015 329.9074 Tm
(2)Tj
9 0 0 9 68.3307 311.4729 Tm
(3)Tj
6.3 0 0 6.3 85.3386 315.0728 Tm
(A)Tj
9 0 0 9 89.659 311.4729 Tm
(/)Tj
6.3 0 0 6.3 92.9879 309.6728 Tm
(y)Tj
-0.0003 Tc 0.0279 Tw 9 0 0 9 98.7746 311.4729 Tm
(= B)Tj
/CS1 cs 1  scn
/T1_0 1 Tf
-0.0002 Tc 0 Tw -5.2724 -2.4357 Td
[(12)-706(Iteration)]TJ
0 0 0 1 k
/T1_1 1 Tf
0.0278 Tw 1.8898 -1.4908 Td
[(1)-1332(Pr)18(oduce two iterative for)-18(mulae)]TJ
1.888 -1.3333 Td
(for x)Tj
-0.0003 Tc 0 Tw 6.3 0 0 6.3 103.3949 267.7341 Tm
(2 )Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 108.8225 264.1342 Tm
(+ 7x + 13 = 0)Tj
-0.0001 Tc -4.4991 -1.6483 Td
[(2)-1332(The iterative for)-18(mula)]TJ
-0.0002 Tc 1.888 -4.9449 Td
(can be used to solve the)Tj
-0.0001 Tc 0 -1.3333 TD
(equation x)Tj
0 Tc 0 Tw 6.3 0 0 6.3 128.068 196.3956 Tm
(2)Tj
/T1_3 1 Tf
9 0 0 9 134.3208 192.7956 Tm
(\320)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 2x )Tj
/T1_3 1 Tf
0 Tc 0 Tw 1.649 0 Td
(\320)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 15 = 0. Use)Tj
-0.0002 Tc -8.093 -1.3333 Td
[(the iterative for)-18(mula to find a)]TJ
T*
(solution to the equation. Start)Tj
-0.0001 Tc T*
(with x)Tj
0 Tc 0 Tw 6.3 0 0 6.3 109.0573 154.9957 Tm
(1)Tj
-0.0002 Tc 9 0 0 9 112.5595 156.7956 Tm
(=7.)Tj
/CS1 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0295 Tw -6.8041 -2.4357 Td
[(13  Dir)18(ect and inverse variation)]TJ
0 0 0 1 k
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 1.8898 -1.4908 Td
[(a is pr)18(oportional to c)]TJ
0 Tc 0 Tw 6.3 0 0 6.3 152.4425 125.057 Tm
(3)Tj
-0.0001 Tc 0.0277 Tw 9 0 0 9 68.3307 106.6224 Tm
(a = 50 when c = 2)Tj
0 -1.6483 TD
[(1)-1334(Find a when c = 10)]TJ
0 -1.4908 TD
[(2)-1334(Find c when a = 400)]TJ
/CS1 cs 1  scn
/T1_0 1 Tf
0.0296 Tw 19.7314 55.0971 Td
[(14)-706(Using algebraic for)-18(mulae)]TJ
0 0 0 1 k
/T1_1 1 Tf
-0.0003 Tc 0.0278 Tw 1.8898 -1.4908 Td
(a = )Tj
0 Tc 0 Tw 6.3 0 0 6.3 279.0835 564.4272 Tm
(1)Tj
9 0 0 9 282.5857 560.8273 Tm
(/)Tj
6.3 0 0 6.3 285.9145 559.0272 Tm
(5)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 289.4168 560.8273 Tm
(, b = 2)Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.0272 0 Td
(\341)Tj
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 0.2778 0 Td
(3, c = -3)Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.7868 0 Td
(\341)Tj
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 0.2778 0 Td
(7, d = -)Tj
0 Tc 0 Tw 6.3 0 0 6.3 385.9849 564.4272 Tm
(4)Tj
9 0 0 9 389.4871 560.8273 Tm
(/)Tj
6.3 0 0 6.3 392.816 559.0272 Tm
(5)Tj
-0.0001 Tc 0.0278 Tw 9 0 0 9 262.9212 545.9927 Tm
(Find the value of: )Tj
-0.0002 Tc 0 -1.6483 TD
[(1)-1334(6\(4a - 3d\))]TJ
0 Tc 0 Tw T*
(2)Tj
0 -3.2966 TD
(3)Tj
T*
(4)Tj
-0.0001 Tc 0.0278 Tw 1.8898 -1.6483 Td
[(a)-729(Calculate v when r = 3, h = 4)]TJ
0 -1.6483 TD
[(b)-637(Calculate h when r = 10, )]TJ
-0.0002 Tc 1.2483 -1.3333 Td
(v = 400)Tj
-0.0001 Tc -1.2483 -1.6483 Td
[(c)-766(Calculate r when h = 5,)]TJ
-0.0002 Tc 1.2483 -1.3333 Td
(v = 300)Tj
/CS1 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw -5.0278 -2.4357 Td
[(15)-706(Rules for indices \(powers\))]TJ
0 -10.5197 TD
[(16)-706(Expansion of brackets)]TJ
0 0 0 1 k
/T1_1 1 Tf
0 Tw 1.8898 -1.4908 Td
(Simplify:)Tj
1.3338 Tc 0 -1.6483 TD
(1a)Tj
0 Tc 6.3 0 0 6.3 284.5983 247.2301 Tm
(5)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 290.8511 243.6302 Tm
(x a)Tj
0 Tc 0 Tw 6.3 0 0 6.3 302.6082 247.2301 Tm
(3)Tj
1.3338 Tc 9 0 0 9 262.9212 228.7956 Tm
[(24)1334(a)]TJ
0 Tc 6.3 0 0 6.3 289.6015 232.3956 Tm
(4)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 295.8542 228.7956 Tm
(x 3a)Tj
1.3338 Tc 0 Tw -3.6592 -1.6483 Td
[(38)1334(a)]TJ
0 Tc 6.3 0 0 6.3 289.6015 217.5609 Tm
(6)Tj
/T1_3 1 Tf
9 0 0 9 295.8542 213.961 Tm
(\326)Tj
/T1_1 1 Tf
-0.0003 Tc 0.9714 0 Td
(2a)Tj
6.3 0 0 6.3 314.2691 217.5609 Tm
(-4)Tj
-0.0002 Tc 9 0 0 9 262.9212 199.1262 Tm
(Expand:)Tj
T*
[(4)-1334(5a\(4a)]TJ
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(2)Tj
-0.0001 Tc 9 0 0 9 305.1139 184.2916 Tm
(x )Tj
/T1_3 1 Tf
0 Tc 0.7875 0 Td
(\320)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 0.4999 0 Td
( 3ac\))Tj
1.3338 Tc 0 Tw -5.9754 -1.6483 Td
[(52)1334(a)]TJ
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(2)Tj
9 0 0 9 293.1037 169.457 Tm
(c)Tj
6.3 0 0 6.3 297.4411 173.0569 Tm
(3)Tj
-0.0002 Tc 9 0 0 9 300.9433 169.457 Tm
(\(3ad)Tj
0 Tc 6.3 0 0 6.3 318.4511 173.0569 Tm
(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 324.7039 169.457 Tm
(+ 4a)Tj
0 Tc 0 Tw 6.3 0 0 6.3 343.1187 173.0569 Tm
(2)Tj
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(c\))Tj
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(Easingwold School                               )Tj
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89.392 397.453 89.126 398.623 89.03 399.382 c
88.935 398.623 88.669 397.453 88.279 396.163 c
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BT
/T1_2 1 Tf
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(20)Tj
0.7711 -4.1605 Td
[(1100)-1177(1200)]TJ
ET
109.493 303.167 m
109.493 299.947 l
89.084 303.167 m
89.084 299.947 l
85.864 320.174 m
89.084 320.174 l
S
BT
/T1_2 1 Tf
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(Time)Tj
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(Poole)Tj
-2.814 14.2761 Td
(Basingstoke)Tj
6.7535 -14.2761 Td
(0)Tj
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(Distance in kilometres)Tj
ET
145.208 388.206 m
134.732 388.206 l
104.393 320.174 l
89.084 303.167 l
S
BT
/T1_2 1 Tf
6 0 0 6 77.7863 334.9761 Tm
(40)Tj
ET
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89.084 337.182 l
S
BT
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(60)Tj
ET
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89.084 354.19 l
S
BT
/T1_2 1 Tf
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(80)Tj
ET
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89.084 371.198 l
S
BT
/T1_2 1 Tf
6 0 0 6 74.4509 385.9996 Tm
(100)Tj
ET
85.864 388.206 m
89.084 388.206 l
S
BT
/T1_2 1 Tf
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(1300)Tj
ET
129.902 303.167 m
129.902 299.947 l
S
BT
/T1_2 1 Tf
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(1400)Tj
ET
150.311 303.167 m
150.311 299.947 l
S
BT
/T1_2 1 Tf
6 0 0 6 164.049 293.0054 Tm
(1500)Tj
ET
170.72 303.167 m
170.72 299.947 l
S
BT
/T1_2 1 Tf
6 0 0 6 184.458 293.0054 Tm
(1600)Tj
ET
191.129 303.167 m
191.129 299.947 l
S
BT
/T1_2 1 Tf
6 0 0 6 204.8671 293.0054 Tm
(1700)Tj
ET
211.538 303.167 m
211.538 299.947 l
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q
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0 660.06 467.04 -660 re
W n
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/GS7 gs
245.2 482.13 172.91 -117.9 re
f*
Q Q 
258.849 451.209 m
392.77 451.209 l
273.833 449.998 m
274.061 450.107 274.986 450.475 275.779 450.714 c
276.628 450.971 277.399 451.146 277.898 451.209 c
277.399 451.272 276.628 451.447 275.779 451.704 c
274.986 451.943 274.47 452.164 273.833 452.42 c
268.391 449.998 m
268.618 450.107 269.543 450.475 270.337 450.714 c
271.186 450.971 271.956 451.146 272.456 451.209 c
271.956 451.272 271.186 451.447 270.337 451.704 c
269.543 451.943 269.027 452.164 268.391 452.42 c
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BT
/T1_2 1 Tf
2.695 Tc 6 0 0 6 302.4131 455.0491 Tm
(ab)Tj
ET
q
245.2 482.13 172.91 -117.9 re
W* n
349.627 357.937 m
303.825 483.781 l
308.289 471.815 m
299.815 468.804 293.748 460.715 293.748 451.209 c
296.178 451.209 m
296.178 440.478 304.878 431.778 315.609 431.778 c
317.971 431.778 320.235 432.199 322.329 432.971 c
323.169 430.69 m
331.518 433.766 337.471 441.793 337.471 451.209 c
335.041 451.209 m
335.041 461.94 326.341 470.64 315.609 470.64 c
313.327 470.64 311.137 470.247 309.103 469.524 c
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Q 
BT
/T1_2 1 Tf
2.2631 Tc 6 0 0 6 306.4837 440.6489 Tm
[(c7)2263(0)]TJ
/T1_3 1 Tf
0 Tc 3.8571 0 Td
(\006)Tj
ET
258.849 391.323 m
392.77 391.323 l
273.833 390.112 m
274.061 390.22 274.986 390.589 275.779 390.828 c
276.628 391.085 277.399 391.26 277.898 391.323 c
277.399 391.385 276.628 391.561 275.779 391.817 c
274.986 392.057 274.47 392.278 273.833 392.534 c
268.391 390.112 m
268.618 390.22 269.543 390.589 270.337 390.828 c
271.186 391.085 271.956 391.26 272.456 391.323 c
271.956 391.385 271.186 391.561 270.337 391.817 c
269.543 392.057 269.027 392.278 268.391 392.534 c
S
BT
/T1_2 1 Tf
2.6765 Tc 6 0 0 6 323.9334 395.1628 Tm
(de)Tj
ET
330.085 411.929 m
321.612 408.918 315.544 400.829 315.544 391.323 c
317.975 391.323 m
317.975 380.591 326.674 371.892 337.406 371.892 c
339.768 371.892 342.031 372.313 344.125 373.085 c
344.966 370.803 m
353.314 373.88 359.268 381.906 359.268 391.323 c
356.837 391.323 m
356.837 402.054 348.137 410.754 337.406 410.754 c
335.124 410.754 332.934 410.361 330.899 409.638 c
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BT
/T1_2 1 Tf
2.8065 Tc 6 0 0 6 327.8934 380.7627 Tm
(gf)Tj
ET
q
-1 661 470 -662 re
W n
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W n
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245.2 265.7 172.91 -135.78 re
f*
Q Q 
BT
/T1_2 1 Tf
0 Tc 9 0 0 9 253.6195 243.9197 Tm
(A)Tj
ET
1.5 w 1 J 
263.725 247.43 m
263.725 247.43 l
S
BT
/T1_2 1 Tf
9 0 0 9 406.1496 204.5001 Tm
(B)Tj
ET
401.424 208.01 m
401.424 208.01 l
S
BT
/T1_2 1 Tf
9 0 0 9 337.2374 153.7406 Tm
(C)Tj
ET
335.545 163.191 m
335.545 163.191 l
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0.5 w 0 J 
255.069 166.542 m
255.069 197.567 l
S
254.459 198.647 m
254.192 197.764 253.946 197.189 253.661 196.48 c
256.358 196.48 l
256.238 196.734 255.827 197.764 255.561 198.647 c
255.275 199.593 255.079 200.451 255.01 201.008 c
254.94 200.451 254.745 199.593 254.459 198.647 c
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BT
/T1_2 1 Tf
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(N)Tj
ET
q
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W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
/GS9 gs
34.33 204.11 195.59 -149.31 re
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Q Q 
77.381 68.351 m
211.927 68.351 l
S
213.627 69.089 m
212.437 69.449 211.663 69.78 210.708 70.163 c
210.708 66.531 l
211.05 66.693 212.437 67.246 213.627 67.605 c
214.901 67.99 216.057 68.253 216.806 68.347 c
216.057 68.441 214.901 68.704 213.627 69.089 c
f
77.404 68.351 m
77.404 195.456 l
S
76.61 197.355 m
76.25 196.164 75.919 195.391 75.536 194.436 c
79.168 194.436 l
79.006 194.778 78.453 196.164 78.094 197.355 c
77.709 198.629 77.446 199.784 77.352 200.533 c
77.258 199.784 76.995 198.629 76.61 197.355 c
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BT
/T1_2 1 Tf
2.7095 Tc 6 0 0 6 95.3138 58.8111 Tm
(123456)Tj
0 Tc 7.2 0 0 7.2 65.808 182.43 Tm
(30)Tj
0.6149 2.282 Td
(y)Tj
19.5833 -19.2361 Td
(x)Tj
-20.1982 8.7905 Td
(15)Tj
0 2.7212 TD
(20)Tj
T*
(25)Tj
0.4168 -10.885 Td
(5)Tj
-0.4168 2.7213 Td
(10)Tj
ET
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BT
/T1_0 1 Tf
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[(38)-706(Similarity)]TJ
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/T1_1 1 Tf
0.0278 Tw 1.8898 -1.4908 Td
[(AC = 10 cm)-4661(BC = 12 cm)]TJ
0 -1.4908 TD
[(AD = 6 cm)-5180(DE = 9 cm)]TJ
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(Find the length of:)Tj
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[(1A)1334(E)]TJ
T*
[(2A)1334(B)]TJ
T*
[(3B)1334(D)]TJ
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[(41)-706(Combined and inverse)]TJ
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[(transfor)-18(mations)]TJ
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[(1)-1338(A shape X is translated by the)]TJ
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[(vector to )2701(pr)18(oduce )2701(X)]TJ
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(\325)Tj
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(.)Tj
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[(Describe the transfor)-18(mation to)]TJ
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[(re)-18(t)-18(u)-18(r)-36(n)-18( X)]TJ
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(\325)Tj
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( to X.)Tj
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[(2)-1332(A shape H is r)18(eflected in the line)]TJ
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[(x = 3 to pr)18(oduce H)]TJ
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(\325)Tj
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(. Describe the)Tj
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[(transfor)-18(mation to r)18(etur)-18(n H)]TJ
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(\325)Tj
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( to H.)Tj
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[(42-43  Enlar)18(gement by a fractional scale)]TJ
1.8898 -1.3333 Td
(factor and a negative scale factor)Tj
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0.0277 Tw 0 -1.4908 TD
[(1)-1332(Enlar)18(ge the triangle A by a scale)]TJ
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(factor of )Tj
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(1)Tj
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(/)Tj
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(2)Tj
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[(. Centr)18(e of)]TJ
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[(enlar)18(gement is the point \(7,3\).)]TJ
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[(2)-1332(Enlar)18(ge the triangle A by a scale)]TJ
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(factor of )Tj
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(\320)Tj
/T1_1 1 Tf
-0.0002 Tc 0.0278 Tw 0.4998 0 Td
[(2, centr)18(e of)]TJ
-4.5529 -1.3333 Td
[(enlar)18(gement is the point \(1, 0\).)]TJ
/CS1 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw -3.7778 -21.2118 Td
[(44)-706(Compound measur)18(es)]TJ
0 0 0 1 k
/T1_1 1 Tf
0.0277 Tw 1.8898 -1.4908 Td
[(1)-1332(A car travels 324 kilometr)18(es in )]TJ
1.888 -1.3333 Td
(3 hours 52 minutes. Calculate the)Tj
0 -1.3333 TD
[(speed in kilometr)18(es per hour)92(.)]TJ
-0.0002 Tc -1.888 -1.6483 Td
[(2)-1332(A car travels at 25 metr)18(es per)]TJ
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(second. What is this speed in)Tj
-0.0002 Tc T*
[(kilometr)18(es per hour?)]TJ
ET
Q Q 
q
246.91 433.18 164.15 -163.51 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS6 gs
273.041 278.554 m
273.041 426.287 l
273.041 366.594 m
403.11 366.594 l
S
0.25 w 
270.206 409.113 m
273.041 409.113 l
270.206 423.287 m
273.041 423.287 l
270.206 394.94 m
273.041 394.94 l
270.206 380.767 m
273.041 380.767 l
301.387 363.759 m
301.387 366.594 l
287.214 363.759 m
287.214 366.594 l
315.561 363.759 m
315.561 366.594 l
329.734 363.759 m
329.734 366.594 l
343.907 363.759 m
343.907 366.594 l
358.08 363.759 m
358.08 366.594 l
372.254 363.759 m
372.254 366.594 l
S
0 g
BT
/T1_1 1 Tf
7 0 0 7 264.8142 420.7868 Tm
(4)Tj
0 -2.0248 TD
(3)Tj
T*
(2)Tj
T*
(1)Tj
ET
270.206 352.421 m
273.041 352.421 l
S
BT
/T1_1 1 Tf
7 0 0 7 262.4833 349.9205 Tm
(-1)Tj
ET
270.206 338.247 m
273.041 338.247 l
S
BT
/T1_1 1 Tf
7 0 0 7 262.4833 335.7472 Tm
(-2)Tj
ET
270.206 324.074 m
273.041 324.074 l
S
BT
/T1_1 1 Tf
7 0 0 7 262.4833 321.5739 Tm
(-3)Tj
ET
270.206 309.9 m
273.041 309.9 l
S
BT
/T1_1 1 Tf
7 0 0 7 262.4833 307.4005 Tm
(-4)Tj
ET
270.206 295.727 m
273.041 295.727 l
S
BT
/T1_1 1 Tf
7 0 0 7 262.4833 293.2272 Tm
(-5)Tj
ET
270.206 281.554 m
273.041 281.554 l
S
BT
/T1_1 1 Tf
7 0 0 7 262.4833 279.0539 Tm
(-6)Tj
15.4035 11.0046 Td
(7)Tj
ET
386.427 363.759 m
386.427 366.594 l
S
BT
/T1_1 1 Tf
7 0 0 7 384.4809 356.0861 Tm
(8)Tj
ET
400.601 363.759 m
400.601 366.594 l
S
BT
/T1_1 1 Tf
7 0 0 7 398.6547 356.0861 Tm
(9)Tj
-6.0744 0 Td
(6)Tj
-2.0248 0 Td
(5)Tj
-2.0248 0 Td
(4)Tj
-2.0247 0 Td
(3)Tj
-2.0248 0 Td
(2)Tj
-2.0248 0 Td
(1)Tj
-2.5248 0.7857 Td
(0)Tj
ET
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0.5 w 1 J 
287.214 380.767 m
343.907 380.767 l
315.561 409.113 l
287.214 380.767 l
h
B
0 g
BT
/T1_1 1 Tf
7 0 0 7 314.0581 390.4601 Tm
(A)Tj
ET
Q Q Q 
q
113.71 115.03 22.3 -23.87 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS7 gs
BT
/T1_1 1 Tf
9 0 0 9 122.1068 105.5901 Tm
(3)Tj
0 -1.2222 TD
(7)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
119.692 112.312 m
117.703 109.594 116.527 106.244 116.527 102.618 c
116.527 98.992 117.703 95.642 119.692 92.923 c
129.692 112.312 m
131.681 109.594 132.857 106.244 132.857 102.618 c
132.857 98.992 131.681 95.642 129.692 92.923 c
S
Q Q Q 
q
52.32 345.92 159.66 -169.84 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0.25 0.5 0 k
0 G
0.25 w 4 M 0 j 0 J []0 d 
/GS8 gs
112.48 334.138 m
80.513 278.842 l
134.08 276.79 l
112.48 334.138 l
B
163.996 270.886 m
205.08 319.79 l
152.683 331.112 l
163.996 270.886 l
B
0 g
BT
/T1_1 1 Tf
7 0 0 7 86.6674 280.417 Tm
(70)Tj
/T1_3 1 Tf
1.112 0 Td
(\006)Tj
/T1_1 1 Tf
13.4067 4.772 Td
(70)Tj
/T1_3 1 Tf
1.112 0 Td
(\006)Tj
/T1_1 1 Tf
-11.1164 -4.8291 Td
(80)Tj
/T1_3 1 Tf
1.112 0 Td
(\006)Tj
/T1_1 1 Tf
4.4923 5.7434 Td
(80)Tj
/T1_3 1 Tf
1.112 0 Td
(\006)Tj
/T1_1 1 Tf
4.1265 5.6546 -5.6546 4.1265 186.3921 283.7914 Tm
(8 cm)Tj
7 0 0 7 101.1718 270.0172 Tm
(8 cm)Tj
-3.3923 -8.3468 Td
(6 cm)Tj
5.6084 -4.1881 4.1881 5.6084 121.1245 220.5439 Tm
(10 cm)Tj
0.0001 Tc -0.0001 Tw 4.3211 5.5069 -5.5069 4.3211 173.5282 229.6896 Tm
(10 cm)Tj
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(6 cm)Tj
ET
0 0.25 0.5 0 k
97.413 235.59 m
97.413 192.79 l
153.413 192.79 l
97.413 235.59 l
h
B
97.413 192.79 7.6 7.6 re
S
162.613 208.79 m
205.413 208.79 l
205.413 264.79 l
162.613 208.79 l
h
B
197.813 208.79 7.6 7.6 re
S
0 g
BT
/T1_1 1 Tf
9 0 0 9 70.0384 328.144 Tm
(1)Tj
0 -10.1481 TD
(2)Tj
ET
Q Q Q 
q
52.32 541.94 167.25 -83.87 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS9 gs
BT
/T1_1 1 Tf
7 0 0 7 130.6514 535.1119 Tm
(A)Tj
ET
0.031 0.243 0.502 0.004 k
0 G
0.5 w 4 M 0 j 1 J []0 d 
208.361 467.445 m
133.799 532.823 l
59.237 467.445 l
208.361 467.445 l
h
B
77.878 483.79 m
189.72 483.79 l
S
0 J 
114.017 466.296 m
114.234 466.398 115.112 466.748 115.866 466.976 c
116.673 467.219 117.405 467.386 117.879 467.445 c
117.405 467.505 116.673 467.671 115.866 467.916 c
115.112 468.143 114.622 468.353 114.017 468.596 c
108.847 466.296 m
109.063 466.398 109.942 466.748 110.696 466.976 c
111.503 467.219 112.234 467.386 112.709 467.445 c
112.234 467.505 111.503 467.671 110.696 467.916 c
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0.0277 Tw 1.8898 -1.4908 Td
[(1)-1332(The ratio of the volume of cube A)]TJ
1.888 -1.3333 Td
(to cube B is 512 : 343.)Tj
-0.0002 Tc T*
(What is the ratio of the side of)Tj
-0.0001 Tc 0 -1.3333 TD
(cube A to cube B?)Tj
-0.0002 Tc -1.888 -1.6483 Td
[(2)-1334(Convert 0)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 6.3052 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 0.2778 0 Td
(3 m)Tj
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(2)Tj
-0.0002 Tc 0.0278 Tw 9 0 0 9 343.8417 507.158 Tm
(into cm)Tj
0 Tc 0 Tw 6.3 0 0 6.3 374.08 510.7578 Tm
(2)Tj
/CS1 cs 1  scn
/T1_0 1 Tf
-0.0002 Tc 9 0 0 9 245.9134 485.2366 Tm
[(57)-706(Pythagoras)]TJ
/T1_1 1 Tf
0 Tc 7.1286 0 Td
(\325)Tj
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 0.2959 0 Td
[( theor)18(em )]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0278 Tw -5.5348 -1.4908 Td
[(1)-1334(Find x)]TJ
0 -10.1575 TD
[(2)-1334(Find y)]TJ
/CS1 cs 1  scn
/T1_0 1 Tf
0.0296 Tw -1.8898 -10.9254 Td
[(58)-706(T)92(rigonometry: Finding an angle)]TJ
ET
Q Q 
q
246.91 279.02 147.92 -104.89 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.031 0.243 0.502 0.004 k
0 G
0.5 w 4 M 0 j 1 J []0 d 
/GS7 gs
275.685 185.887 m
366.394 185.887 l
366.394 271.493 l
275.685 185.887 l
h
B
0 J 
360.071 185.876 m
360.071 192.199 l
366.394 192.199 l
S
0 g
BT
/T1_2 1 Tf
-0.0001 Tc 0.0001 Tw 7.0009 0 0 7.0009 316.08 178.5386 Tm
(8 cm)Tj
-1.8492 7.6418 Td
(11 cm)Tj
0 Tc 0 Tw 8.1201 3.5781 Td
(x)Tj
ET
1 J 
351.585 257.49 m
355.301 253.562 360.561 251.112 366.394 251.112 c
S
Q Q Q 
q
263.92 374.93 128.08 -72.35 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.031 0.243 0.502 0.004 k
0 G
0.5 w 4 M 0 j 1 J []0 d 
/GS8 gs
362.756 308.411 m
362.756 361.985 l
280.435 361.985 l
362.756 308.411 l
h
B
0 J 
356.469 361.8 m
356.469 355.477 l
362.792 355.477 l
S
0 g
BT
/T1_2 1 Tf
-0.0001 Tc 0.0001 Tw 7.0009 0 0 7.0009 306.8341 326.7992 Tm
(11 cm)Tj
8.2483 0.957 Td
(6 cm)Tj
0 Tc 0 Tw -5.9346 4.6851 Td
(y)Tj
ET
Q Q Q 
q
246.91 481.45 145.09 -85.05 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS9 gs
354.949 408.103 m
354.949 414.426 l
361.273 414.426 l
S
0 0.25 0.5 0 k
1 J 
271.982 408.036 m
361.273 408.036 l
361.273 479.469 l
271.982 408.036 l
h
B
0 g
BT
/T1_2 1 Tf
-0.0001 Tc 0.0001 Tw 7.0009 0 0 7.0009 363.2599 439.6386 Tm
(8 cm)Tj
-7.5341 -5.6063 Td
(10 cm)Tj
0 Tc 0 Tw 0.0212 6.2563 Td
(x)Tj
ET
Q Q Q 
q
52.32 267.2 164.41 -75.38 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.031 0.243 0.502 0.004 k
0 G
0.5 w 4 M 0 j 1 J []0 d 
/GS10 gs
162.435 235.826 m
113.325 235.826 l
113.325 214.779 l
64.215 214.779 l
64.215 256.873 l
204.53 256.873 l
204.53 200.747 l
162.435 200.747 l
162.435 235.826 l
h
B
0 g
BT
/T1_2 1 Tf
7.0002 0 0 7.0002 122.1897 258.6879 Tm
(20 cm)Tj
-8.0645 -3.3284 Td
(6 cm)Tj
2.1713 -3.9998 Td
(7 cm)Tj
2.3785 2.1856 Td
(3 cm)Tj
11.4424 -3.9856 Td
(6 cm)Tj
-1.9927 2.957 Td
(5 cm)Tj
3.3999 2.7927 Td
(8 cm)Tj
ET
Q Q Q 
q
52.32 541.94 166.91 -196.52 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.028 0.373 0.753 0.004 k
/GS11 gs
86.876 408.7 m
129.21 408.7 l
187.21 448.033 l
144.543 448.033 l
86.876 408.7 l
f
0.031 0.243 0.502 0.004 k
86.876 408.7 m
65.876 380.7 l
150.543 380.033 l
129.21 408.7 l
86.876 408.7 l
f
208.543 419.7 m
187.21 448.033 l
129.21 408.7 l
150.543 380.7 l
208.543 419.7 l
f
0 G
0.5 w 4 M 0 j 1 J [0.1 2]0 d 
132.417 497.7 m
74.239 459.173 l
S
0 J []0 d 
74.239 498.848 m
74.239 459.173 l
140.365 459.173 l
74.239 498.848 l
h
B
0 g
BT
/T1_2 1 Tf
6.9996 0 0 6.9996 96.8358 451.782 Tm
(5 cm)Tj
-5.7895 3.6578 Td
(3 cm)Tj
ET
0.028 0.373 0.753 0.004 k
198.543 497.7 m
132.417 537.375 l
74.239 498.848 l
140.365 459.173 l
198.543 497.7 l
h
B
0 g
BT
/T1_2 1 Tf
6.9996 0 0 6.9996 175.784 473.1741 Tm
(8 cm)Tj
ET
74.239 467.303 m
82.369 467.303 l
82.369 459.173 l
S
1 J [0.1 2]0 d 
132.417 537.375 m
132.417 497.7 l
198.543 497.7 l
S
[]0 d 
150.739 380.431 m
129.479 408.777 l
86.96 408.777 l
65.7 380.431 l
150.739 380.431 l
h
S
BT
/T1_2 1 Tf
7 0 0 7 97.118 373.3514 Tm
(12 cm)Tj
ET
0 J [2 2]0 d 
121.479 408.777 m
121.479 380.431 l
S
[]0 d 
121.456 389.464 m
130.489 389.464 l
130.489 380.431 l
S
BT
/T1_2 1 Tf
7 0 0 7 104.726 394.1014 Tm
(4 cm)Tj
ET
1 J 
208.803 419.687 m
187.543 448.034 l
145.023 448.034 l
86.96 408.777 m
145.023 448.034 l
129.479 408.777 m
187.543 448.034 l
150.739 380.431 m
208.803 419.687 l
S
[0.1 2]0 d 
123.764 419.687 m
65.7 380.431 l
145.023 448.034 m
123.764 419.687 l
208.803 419.687 l
S
BT
/T1_2 1 Tf
7 0 0 7 183.4984 395.3514 Tm
(0.8 m)Tj
-1.7035 -4.0091 Td
(\(Not to scale\))Tj
-1.671 11.7958 Td
(6 cm)Tj
ET
Q Q Q 
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 1 k
BT
/T1_5 1 Tf
-0.0001 Tc 0.0278 Tw 10 0 0 10 346.0597 604.6698 Tm
(Diagnostic tests)Tj
ET
0 0 0 1 K
0.5 w 10 M 0 j 0 J []0 d 
84.65 94.79 m
99.65 94.79 l
152.46 93.87 m
170.8 93.87 l
S
0 0 0 0 k
50.32 42.05 368.51 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0003 Tc 0 Tw 8 0 0 8 403.6236 35.0006 Tm
(105)Tj
/T1_6 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 51.3228 35.5258 Tm
(Easingwold School                               )Tj
ET
Q Q 
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1 g
1 i 
/RelativeColorimetric ri
/GS0 gs
0 660 m
0 660 l
f
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0 0 0 k
49.61 42.05 368.5 -13.76 re
f*
0 0 0 1 k
BT
/T1_0 1 Tf
-0.0003 Tc 8 0 0 8 50.6063 35.0006 Tm
(106)Tj
/T1_1 1 Tf
-0.0001 Tc 0.0278 Tw 7 0 0 7 265.7926 35.5258 Tm
(Easingwold School                               )Tj
/CS2 cs 1  scn
/T1_0 1 Tf
0.0296 Tw 9 0 0 9 50.6063 574.2445 Tm
[(59)-706(T)92(rigonometry: Finding a side)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0278 Tw 1.8898 -1.4908 Td
[(1)-1334(Find x)]TJ
0 -20.267 TD
[(2)-1334(Find y)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
0.0296 Tw -1.8898 -2.4357 Td
[(60)-706(T)92(rigonometry: Solving pr)18(oblems)]TJ
0 0 0 1 k
/T1_2 1 Tf
-0.0002 Tc 0.0278 Tw 1.8889 -1.4908 Td
(A ship sails 300 km on a bearing of)Tj
-0.0001 Tc 0 Tw 0.0009 -1.3333 Td
(078)Tj
/T1_3 1 Tf
0 Tc 1.6677 0 Td
(\241)Tj
/T1_2 1 Tf
0.3999 0 Td
(.)Tj
-0.0001 Tc 0.0277 Tw -2.0676 -1.6483 Td
[(1)-1334(How far north has the ship sailed?)]TJ
-0.0224 Tc 0 -1.6483 TD
[(2)-1354(How far east has the ship sailed?)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw -1.8898 -2.4357 Td
[(61)-706(T)92(rigonometry and Pythagoras)]TJ
/T1_4 1 Tf
0 Tc 0 Tw 15.8151 0 Td
(\325)Tj
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw -13.9253 -1.3333 Td
[(theor)18(em for 3-D shapes)]TJ
0 0 0 1 k
/T1_2 1 Tf
0.0277 Tw 0 -1.4908 TD
[(1)-1334(Find the distance fr)18(om B to H)]TJ
0 -1.6483 TD
[(2)-1334(Find the angle BHF)]TJ
/CS2 cs 1  scn
/T1_0 1 Tf
0.0296 Tw -1.8898 -14.8901 Td
(62-64  Sine, cosine and tangent of any)Tj
0 Tw 1.8898 -1.3333 Td
(angle)Tj
0 0 0 1 k
/T1_2 1 Tf
0.0278 Tw 0 -1.4908 TD
(Cosx = -0)Tj
/T1_3 1 Tf
0 Tc 0 Tw 4.3703 0 Td
(\341)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.2779 0 Td
(7313537. Find the values of)Tj
-4.6482 -1.3333 Td
(x between 0)Tj
/T1_3 1 Tf
0 Tc 0 Tw 5.5373 0 Td
(\241)Tj
/T1_2 1 Tf
-0.0001 Tc 0.0278 Tw 0.7055 0 Td
(and 360)Tj
/T1_3 1 Tf
0 Tc 0 Tw 3.6589 0 Td
(\241)Tj
/CS2 cs 1  scn
/T1_0 1 Tf
-0.0001 Tc 0.0296 Tw 9.8297 56.27 Td
[(65-66  Sine rule, cosine rule, ar)18(ea of a)]TJ
0 Tw 1.8898 -1.3333 Td
(triangle)Tj
0.0295 Tw -1.8898 -22.5371 Td
[(67-70  V)55(ectors)]TJ
ET
Q Q 
q
263.2 356.36 151.66 -203.76 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 g
/GS6 gs
BT
/T1_2 1 Tf
6 0 0 6 289.792 254.0265 Tm
(0)Tj
-1.125 1.1389 Td
(0)Tj
3.9596 -1.1389 Td
(1)Tj
-3.9596 3.9736 Td
(1)Tj
6.7943 -3.9736 Td
(2)Tj
-6.7943 6.8082 Td
(2)Tj
0 2.8346 TD
(3)Tj
T*
(4)Tj
9.5185 -3.2969 Td
(a)Tj
-9.5185 6.1316 Td
(5)Tj
2.2787 Tc 9.6289 -15.3122 Td
(3456)Tj
ET
0 G
0.5 w 4 M 0 j 0 J []0 d 
291.46 352.485 m
291.46 262.61 l
400.335 262.61 l
S
401.516 263.122 m
400.689 263.372 400.152 263.602 399.489 263.868 c
399.489 261.346 l
399.726 261.459 400.689 261.842 401.516 262.092 c
402.401 262.359 403.203 262.542 403.723 262.607 c
403.203 262.673 402.401 262.855 401.516 263.122 c
f
290.947 353.666 m
290.698 352.84 290.468 352.302 290.202 351.639 c
292.724 351.639 l
292.611 351.876 292.228 352.84 291.978 353.666 c
291.711 354.551 291.528 355.353 291.463 355.873 c
291.397 355.353 291.215 354.551 290.947 353.666 c
f
0.25 w 
288.718 347.65 m
291.46 347.65 l
288.718 330.641 m
291.46 330.641 l
288.718 313.633 m
291.46 313.633 l
288.718 296.626 m
291.46 296.626 l
288.718 279.618 m
291.46 279.618 l
288.718 262.61 m
291.46 262.61 l
291.46 259.868 m
291.46 262.61 l
308.468 259.868 m
308.468 262.61 l
325.476 259.868 m
325.476 262.61 l
342.483 259.868 m
342.483 262.61 l
359.491 259.868 m
359.491 262.61 l
376.5 259.868 m
376.5 262.61 l
393.507 259.868 m
393.507 262.61 l
S
0.5 w 
308.468 313.633 m
359.491 296.626 l
332.71 308.527 m
333.979 305.13 l
331.043 303.194 l
S
BT
/T1_2 1 Tf
0 Tc 9 0 0 9 403.8525 237.5265 Tm
(x)Tj
0 -1.2222 TD
(y)Tj
ET
401.439 244.249 m
399.451 241.531 399.274 238.181 399.274 234.555 c
399.274 230.928 399.451 227.579 401.439 224.86 c
410.46 244.249 m
412.449 241.53 412.625 238.181 412.625 234.555 c
412.625 230.928 412.449 227.579 410.46 224.86 c
S
BT
/T1_2 1 Tf
9 0 0 9 332.3525 199.7765 Tm
(x)Tj
T*
(y)Tj
ET
329.939 206.499 m
327.951 203.781 327.774 200.431 327.774 196.805 c
327.774 193.178 327.951 189.829 329.939 187.11 c
338.96 206.499 m
340.949 203.78 341.125 200.431 341.125 196.805 c
341.125 193.178 340.949 189.829 338.96 187.11 c
S
BT
/T1_2 1 Tf
9 0 0 9 371.7714 177.0822 Tm
(5)Tj
T*
(4)Tj
ET
370.024 183.804 m
368.035 181.086 367.859 177.736 367.859 174.11 c
367.859 170.484 368.035 167.134 370.024 164.415 c
379.045 183.804 m
381.033 181.086 381.21 177.736 381.21 174.11 c
381.21 170.484 381.033 167.134 379.045 164.415 c
S
BT
/T1_2 1 Tf
9 0 0 9 278.46 232.86 Tm
[(W)18(rite the vector a in the for)-18(m )]TJ
0 -8.5 TD
(Find vector b.)Tj
0 1.7222 TD
[(V)55(ector a + vector b = )]TJ
0.0833 4.4444 Td
[(W)18(rite the vector -3a )]TJ
0 -1.3333 TD
[(in the for)-18(m )]TJ
-1.75 3.6667 Td
(1)Tj
0 -2.3333 TD
(2)Tj
0 -4.4444 TD
(3)Tj
ET
354.934 169.697 m
354.664 169.319 354.295 168.86 353.71 168.86 c
353.332 168.86 353.215 168.878 352.773 169.121 c
352.477 169.283 352.144 169.544 351.811 169.544 c
351.396 169.544 351.081 169.13 350.919 168.887 c
350.541 169.247 l
350.811 169.625 351.18 170.084 351.765 170.084 c
352.144 170.084 352.26 170.066 352.702 169.823 c
352.999 169.661 353.332 169.4 353.665 169.4 c
354.079 169.4 354.394 169.814 354.556 170.057 c
354.934 169.697 l
f
311.184 169.697 m
310.914 169.319 310.545 168.86 309.96 168.86 c
309.582 168.86 309.465 168.878 309.023 169.121 c
308.727 169.283 308.394 169.544 308.061 169.544 c
307.646 169.544 307.331 169.13 307.169 168.887 c
306.791 169.247 l
307.061 169.625 307.43 170.084 308.015 170.084 c
308.394 170.084 308.51 170.066 308.952 169.823 c
309.249 169.661 309.582 169.4 309.915 169.4 c
310.329 169.4 310.644 169.814 310.806 170.057 c
311.184 169.697 l
f
331.184 154.197 m
330.914 153.819 330.545 153.36 329.96 153.36 c
329.582 153.36 329.465 153.378 329.023 153.621 c
328.727 153.783 328.394 154.044 328.061 154.044 c
327.646 154.044 327.331 153.63 327.169 153.387 c
326.791 153.747 l
327.061 154.125 327.43 154.584 328.015 154.584 c
328.394 154.584 328.51 154.566 328.952 154.323 c
329.249 154.161 329.582 153.9 329.915 153.9 c
330.329 153.9 330.644 154.314 330.806 154.557 c
331.184 154.197 l
f
360.21 209.86 m
359.94 209.482 359.571 209.023 358.986 209.023 c
358.607 209.023 358.49 209.041 358.049 209.284 c
357.753 209.446 357.419 209.707 357.086 209.707 c
356.672 209.707 356.357 209.293 356.195 209.05 c
355.816 209.41 l
356.087 209.788 356.456 210.247 357.041 210.247 c
357.419 210.247 357.536 210.229 357.978 209.986 c
358.275 209.824 358.607 209.563 358.94 209.563 c
359.355 209.563 359.67 209.977 359.832 210.22 c
360.21 209.86 l
f
349.934 230.697 m
349.664 230.319 349.295 229.86 348.71 229.86 c
348.332 229.86 348.215 229.878 347.773 230.121 c
347.477 230.283 347.144 230.544 346.811 230.544 c
346.396 230.544 346.081 230.13 345.919 229.887 c
345.541 230.247 l
345.811 230.625 346.18 231.084 346.765 231.084 c
347.144 231.084 347.26 231.066 347.702 230.823 c
347.999 230.661 348.332 230.4 348.665 230.4 c
349.079 230.4 349.394 230.814 349.556 231.057 c
349.934 230.697 l
f
343.463 307.78 m
343.247 307.477 342.952 307.11 342.483 307.11 c
342.181 307.11 342.087 307.125 341.734 307.319 c
341.497 307.448 341.231 307.657 340.964 307.657 c
340.633 307.657 340.38 307.326 340.251 307.132 c
339.948 307.42 l
340.165 307.722 340.46 308.09 340.928 308.09 c
341.231 308.09 341.324 308.075 341.677 307.881 c
341.915 307.751 342.181 307.542 342.447 307.542 c
342.779 307.542 343.031 307.873 343.161 308.068 c
343.463 307.78 l
f
Q Q Q 
q
263.2 559.19 148.64 -179.28 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0 0.25 0.5 0 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS7 gs
319.7 430.574 m
383.034 470.907 l
383.367 400.22 l
319.7 430.574 l
h
B
291.034 526.553 m
387.534 526.553 l
328.7 470.553 l
291.034 526.553 l
h
B
0 g
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(Easingwold School                               )Tj
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T*
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(Supplementary material)Tj
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[(Chance \(pr)18(obability\))-268(..................................83-87)]TJ
T*
[(Cir)18(cles)-155(..................................................48-51, 94)]TJ
T*
[(Cir)18(cumfer)18(ence)-43(...........................................48, 94)]TJ
T*
[(Class interval)-103(...................................................75)]TJ
T*
[(Combined transfor)-18(mations)-144(.............................41)]TJ
T*
[(Comparing data)-37(........................................75, 78)]TJ
T*
[(Comparing distributions)-164(.................................79)]TJ
0 Tw T*
[(Compasses)-34(......................................................71)]TJ
0.0278 Tw T*
[(Compound measur)18(es)-6(......................................44)]TJ
T*
[(Conditional pr)18(obability)-89(..............................85-87)]TJ
0 Tw T*
[(Cone)-236(...............................................................48)]TJ
0.0279 Tw T*
[(Congruence)-115(..................................39, 40, 50, 51)]TJ
-0.0001 Tc 0.0277 Tw T*
[(Congruent triangles)-39(......................39, 40, 50, 51)]TJ
-0.0002 Tc 0 Tw T*
[(Constructions)-131(..................................................71)]TJ
0.0278 Tw T*
[(Continuous data)-249(.............................................94)]TJ
-0.0001 Tc T*
[(Conver)18(ging/diver)18(ging sequences)-28(...................12)]TJ
-0.0002 Tc T*
[(Conversion \(metric units\))-159(..........................56, 94)]TJ
T*
[(Co-or)18(dinates \(3-D\))-249(..........................................88)]TJ
0 Tw T*
[(Corr)18(elation)-168(......................................................82)]TJ
0.0278 Tw T*
[(Corr)18(esponding angles)-232(....................................36)]TJ
T*
[(Cosine \(cos\))-246(...............................................58-66)]TJ
ET
Q Q 
q
307.05 425.04 37.78 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS17 gs
322.177 414.55 m
323.295 414.55 324.209 415.464 324.209 416.582 c
324.209 422.677 l
324.209 423.795 323.295 424.71 322.177 424.71 c
311.002 424.71 l
309.885 424.71 308.97 423.795 308.97 422.677 c
308.97 416.582 l
308.97 415.464 309.885 414.55 311.002 414.55 c
322.177 414.55 l
h
B
322.488 415.552 m
322.909 415.552 323.25 415.894 323.25 416.315 c
B
310.706 423.841 m
310.285 423.841 309.944 423.5 309.944 423.079 c
B
340.395 414.55 m
341.513 414.55 342.427 415.464 342.427 416.582 c
342.427 422.677 l
342.427 423.795 341.513 424.71 340.395 424.71 c
329.22 424.71 l
328.102 424.71 327.188 423.795 327.188 422.677 c
327.188 416.582 l
327.188 415.464 328.102 414.55 329.22 414.55 c
340.395 414.55 l
h
B
340.706 415.552 m
341.127 415.552 341.468 415.894 341.468 416.315 c
B
328.924 423.841 m
328.503 423.841 328.162 423.5 328.162 423.079 c
B
0 g
BT
/T1_0 1 Tf
1.8657 Tc 6 0 0 6 313.637 417.2292 Tm
[(MM)1866(R)]TJ
ET
Q Q Q 
q
307.05 438.84 56.57 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS18 gs
322.177 428.131 m
323.295 428.131 324.209 429.045 324.209 430.163 c
324.209 436.258 l
324.209 437.376 323.295 438.29 322.177 438.29 c
311.002 438.29 l
309.885 438.29 308.97 437.376 308.97 436.258 c
308.97 430.163 l
308.97 429.045 309.885 428.131 311.002 428.131 c
322.177 428.131 l
h
B
322.488 429.133 m
322.909 429.133 323.25 429.475 323.25 429.895 c
B
310.706 437.421 m
310.285 437.421 309.944 437.081 309.944 436.66 c
B
340.395 428.131 m
341.513 428.131 342.427 429.045 342.427 430.163 c
342.427 436.258 l
342.427 437.376 341.513 438.29 340.395 438.29 c
329.22 438.29 l
328.102 438.29 327.188 437.376 327.188 436.258 c
327.188 430.163 l
327.188 429.045 328.102 428.131 329.22 428.131 c
340.395 428.131 l
h
B
340.706 429.133 m
341.127 429.133 341.468 429.475 341.468 429.895 c
B
328.924 437.421 m
328.503 437.421 328.162 437.081 328.162 436.66 c
B
358.614 428.131 m
359.731 428.131 360.645 429.045 360.645 430.163 c
360.645 436.258 l
360.645 437.376 359.731 438.29 358.614 438.29 c
347.438 438.29 l
346.321 438.29 345.406 437.376 345.406 436.258 c
345.406 430.163 l
345.406 429.045 346.321 428.131 347.438 428.131 c
358.614 428.131 l
h
B
358.924 429.133 m
359.345 429.133 359.686 429.475 359.686 429.895 c
B
347.142 437.421 m
346.721 437.421 346.38 437.081 346.38 436.66 c
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 311.137 430.8095 Tm
[(SIN)-1269(COS)-963(TAN)]TJ
ET
Q Q Q 
q
307.05 452.64 73.07 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS19 gs
322.177 441.993 m
323.295 441.993 324.209 442.907 324.209 444.025 c
324.209 450.121 l
324.209 451.238 323.295 452.152 322.177 452.152 c
311.002 452.152 l
309.885 452.152 308.97 451.238 308.97 450.121 c
308.97 444.025 l
308.97 442.907 309.885 441.993 311.002 441.993 c
322.177 441.993 l
h
B
322.488 442.996 m
322.909 442.996 323.25 443.337 323.25 443.757 c
B
310.706 451.284 m
310.285 451.284 309.944 450.943 309.944 450.522 c
B
340.145 441.993 m
341.263 441.993 342.177 442.907 342.177 444.025 c
342.177 450.121 l
342.177 451.238 341.263 452.152 340.145 452.152 c
328.97 452.152 l
327.852 452.152 326.938 451.238 326.938 450.121 c
326.938 444.025 l
326.938 442.907 327.852 441.993 328.97 441.993 c
340.145 441.993 l
h
B
340.456 442.996 m
340.877 442.996 341.218 443.337 341.218 443.757 c
B
328.674 451.284 m
328.253 451.284 327.912 450.943 327.912 450.522 c
B
358.177 441.993 m
359.295 441.993 360.209 442.907 360.209 444.025 c
360.209 450.121 l
360.209 451.238 359.295 452.152 358.177 452.152 c
347.002 452.152 l
345.885 452.152 344.97 451.238 344.97 450.121 c
344.97 444.025 l
344.97 442.907 345.885 441.993 347.002 441.993 c
358.177 441.993 l
h
B
358.488 442.996 m
358.909 442.996 359.25 443.337 359.25 443.757 c
B
346.706 451.284 m
346.285 451.284 345.944 450.943 345.944 450.522 c
B
376.145 441.993 m
377.263 441.993 378.177 442.907 378.177 444.025 c
378.177 450.121 l
378.177 451.238 377.263 452.152 376.145 452.152 c
364.97 452.152 l
363.852 452.152 362.938 451.238 362.938 450.121 c
362.938 444.025 l
362.938 442.907 363.852 441.993 364.97 441.993 c
376.145 441.993 l
h
B
376.456 442.996 m
376.877 442.996 377.218 443.337 377.218 443.757 c
B
364.674 451.284 m
364.253 451.284 363.912 450.943 363.912 450.522 c
B
0 g
BT
/T1_0 1 Tf
0.0001 Tc 6 0 0 6 345.845 444.6721 Tm
(DMS)Tj
0 Tc 4 0 0 5 309.5823 445.1915 Tm
(D)Tj
/T1_3 1 Tf
0.7592 0 Td
(\006)Tj
/T1_0 1 Tf
0.0002 Tc -0.0001 Tw 0.4001 0 Td
(M S )Tj
/T1_3 1 Tf
0 Tc 0 Tw 8 0 0 8 328.9119 442.6705 Tm
(\006)Tj
ET
369.344 448.26 m
368.84 448.076 368.56 447.78 368.56 447.413 c
368.56 447.221 368.64 447.093 368.776 447.093 c
368.823 447.093 368.911 447.109 368.968 447.109 c
369.231 447.109 369.367 446.925 369.367 446.741 c
369.367 446.493 369.183 446.325 368.911 446.325 c
368.496 446.325 368.16 446.709 368.16 447.173 c
368.16 447.724 368.592 448.228 369.271 448.46 c
369.344 448.26 l
h
367.385 448.26 m
366.881 448.076 366.601 447.78 366.601 447.413 c
366.601 447.221 366.681 447.093 366.817 447.093 c
366.865 447.093 366.953 447.109 367.009 447.109 c
367.273 447.109 367.409 446.925 367.409 446.741 c
367.409 446.493 367.224 446.325 366.953 446.325 c
366.537 446.325 366.201 446.709 366.201 447.173 c
366.201 447.724 366.633 448.228 367.312 448.46 c
367.385 448.26 l
f
374.304 446.525 m
374.808 446.709 375.088 447.005 375.088 447.373 c
375.088 447.565 375.008 447.693 374.871 447.693 c
374.823 447.693 374.736 447.676 374.68 447.676 c
374.416 447.676 374.28 447.86 374.28 448.044 c
374.28 448.292 374.464 448.46 374.736 448.46 c
375.152 448.46 375.487 448.076 375.487 447.612 c
375.487 447.061 375.055 446.557 374.376 446.325 c
374.304 446.525 l
h
372.345 446.525 m
372.849 446.709 373.129 447.005 373.129 447.373 c
373.129 447.565 373.049 447.693 372.913 447.693 c
372.865 447.693 372.777 447.676 372.721 447.676 c
372.457 447.676 372.321 447.86 372.321 448.044 c
372.321 448.292 372.505 448.46 372.777 448.46 c
373.193 448.46 373.529 448.076 373.529 447.612 c
373.529 447.061 373.096 446.557 372.417 446.325 c
372.345 446.525 l
f
338.47 446.525 m
338.974 446.709 339.254 447.005 339.254 447.373 c
339.254 447.565 339.174 447.693 339.038 447.693 c
338.99 447.693 338.902 447.676 338.846 447.676 c
338.582 447.676 338.446 447.86 338.446 448.044 c
338.446 448.292 338.63 448.46 338.902 448.46 c
339.318 448.46 339.654 448.076 339.654 447.612 c
339.654 447.061 339.221 446.557 338.542 446.325 c
338.47 446.525 l
h
336.511 446.525 m
337.015 446.709 337.295 447.005 337.295 447.373 c
337.295 447.565 337.215 447.693 337.079 447.693 c
337.03 447.693 336.943 447.676 336.887 447.676 c
336.623 447.676 336.487 447.86 336.487 448.044 c
336.487 448.292 336.671 448.46 336.943 448.46 c
337.359 448.46 337.695 448.076 337.695 447.612 c
337.695 447.061 337.263 446.557 336.583 446.325 c
336.511 446.525 l
h
333.345 446.525 m
333.849 446.709 334.129 447.005 334.129 447.373 c
334.129 447.565 334.049 447.693 333.913 447.693 c
333.865 447.693 333.777 447.676 333.721 447.676 c
333.457 447.676 333.321 447.86 333.321 448.044 c
333.321 448.292 333.505 448.46 333.777 448.46 c
334.193 448.46 334.529 448.076 334.529 447.612 c
334.529 447.061 334.096 446.557 333.417 446.325 c
333.345 446.525 l
h
318.095 447.525 m
318.599 447.709 318.879 448.005 318.879 448.373 c
318.879 448.565 318.799 448.693 318.663 448.693 c
318.615 448.693 318.527 448.676 318.471 448.676 c
318.207 448.676 318.071 448.86 318.071 449.044 c
318.071 449.292 318.255 449.46 318.527 449.46 c
318.943 449.46 319.279 449.076 319.279 448.612 c
319.279 448.061 318.846 447.557 318.167 447.325 c
318.095 447.525 l
h
321.47 447.525 m
321.974 447.709 322.254 448.005 322.254 448.373 c
322.254 448.565 322.174 448.693 322.038 448.693 c
321.99 448.693 321.902 448.676 321.846 448.676 c
321.582 448.676 321.446 448.86 321.446 449.044 c
321.446 449.292 321.63 449.46 321.902 449.46 c
322.318 449.46 322.654 449.076 322.654 448.612 c
322.654 448.061 322.221 447.557 321.542 447.325 c
321.47 447.525 l
h
322.72 447.525 m
323.224 447.709 323.504 448.005 323.504 448.373 c
323.504 448.565 323.424 448.693 323.288 448.693 c
323.24 448.693 323.152 448.676 323.096 448.676 c
322.832 448.676 322.696 448.86 322.696 449.044 c
322.696 449.292 322.88 449.46 323.152 449.46 c
323.568 449.46 323.904 449.076 323.904 448.612 c
323.904 448.061 323.471 447.557 322.792 447.325 c
322.72 447.525 l
f
Q Q Q 
q
307.05 466.44 38.32 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS20 gs
322.177 455.856 m
323.295 455.856 324.209 456.77 324.209 457.888 c
324.209 463.983 l
324.209 465.101 323.295 466.015 322.177 466.015 c
311.002 466.015 l
309.885 466.015 308.97 465.101 308.97 463.983 c
308.97 457.888 l
308.97 456.77 309.885 455.856 311.002 455.856 c
322.177 455.856 l
h
B
322.488 456.858 m
322.909 456.858 323.25 457.2 323.25 457.62 c
B
310.706 465.147 m
310.285 465.147 309.944 464.806 309.944 464.385 c
B
340.115 455.856 m
341.232 455.856 342.147 456.77 342.147 457.888 c
342.147 463.983 l
342.147 465.101 341.232 466.015 340.115 466.015 c
328.939 466.015 l
327.822 466.015 326.908 465.101 326.908 463.983 c
326.908 457.888 l
326.908 456.77 327.822 455.856 328.939 455.856 c
340.115 455.856 l
h
B
340.426 456.858 m
340.846 456.858 341.187 457.2 341.187 457.62 c
B
328.643 465.147 m
328.222 465.147 327.882 464.806 327.882 464.385 c
B
0 g
BT
/T1_0 1 Tf
6 0 0 6 310.887 458.1595 Tm
[(EXP)-1482(EE)]TJ
ET
Q Q Q 
q
307.05 480.24 19.57 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS21 gs
322.177 469.718 m
323.295 469.718 324.209 470.632 324.209 471.75 c
324.209 477.846 l
324.209 478.963 323.295 479.878 322.177 479.878 c
311.002 479.878 l
309.885 479.878 308.97 478.963 308.97 477.846 c
308.97 471.75 l
308.97 470.632 309.885 469.718 311.002 469.718 c
322.177 469.718 l
h
B
322.488 470.721 m
322.909 470.721 323.25 471.062 323.25 471.483 c
B
310.706 479.009 m
310.285 479.009 309.944 478.668 309.944 478.247 c
B
0 g
BT
/T1_0 1 Tf
7.2001 0 0 7.2001 311.5226 474.0752 Tm
(+)Tj
/T1_4 1 Tf
0.8885 -0.4445 Td
(\320)Tj
ET
319.52 477.875 m
314.72 471.075 l
S
Q Q Q 
q
307.05 494.04 19.82 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS22 gs
322.177 483.018 m
323.295 483.018 324.209 483.932 324.209 485.05 c
324.209 491.146 l
324.209 492.263 323.295 493.178 322.177 493.178 c
311.002 493.178 l
309.885 493.178 308.97 492.263 308.97 491.146 c
308.97 485.05 l
308.97 483.932 309.885 483.018 311.002 483.018 c
322.177 483.018 l
h
B
322.488 484.021 m
322.909 484.021 323.25 484.362 323.25 484.783 c
B
310.706 492.309 m
310.285 492.309 309.944 491.968 309.944 491.547 c
B
0 g
BT
/T1_0 1 Tf
7.5599 0 0 7.5599 311.4744 485.2996 Tm
(a)Tj
5.04 0 0 5.04 315.7769 487.9134 Tm
(b)Tj
0.624 -0.75 Td
(c)Tj
ET
317.365 486.149 m
320.893 489.173 l
S
Q Q Q 
q
307.05 507.84 20.07 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS23 gs
322.177 497.318 m
323.295 497.318 324.209 498.232 324.209 499.35 c
324.209 505.446 l
324.209 506.563 323.295 507.478 322.177 507.478 c
311.002 507.478 l
309.885 507.478 308.97 506.563 308.97 505.446 c
308.97 499.35 l
308.97 498.232 309.885 497.318 311.002 497.318 c
322.177 497.318 l
h
B
322.488 498.321 m
322.909 498.321 323.25 498.662 323.25 499.083 c
B
310.706 506.609 m
310.285 506.609 309.944 506.268 309.944 505.847 c
B
0 g
BT
/T1_5 1 Tf
4 0 0 4 314.345 503.725 Tm
(\005)Tj
ET
0.75 w 1 J 
319.095 505.6 m
315.72 499.6 l
314.696 501.904 l
314.408 501.776 314.152 501.808 v
S
Q Q Q 
q
307.05 521.64 19.35 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.137 0.063 0.008 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS24 gs
322.007 510.618 m
323.125 510.618 324.039 511.532 324.039 512.65 c
324.039 518.746 l
324.039 519.863 323.125 520.778 322.007 520.778 c
310.832 520.778 l
309.715 520.778 308.8 519.863 308.8 518.746 c
308.8 512.65 l
308.8 511.532 309.715 510.618 310.832 510.618 c
322.007 510.618 l
h
B
322.318 511.621 m
322.739 511.621 323.08 511.962 323.08 512.383 c
B
310.536 519.909 m
310.115 519.909 309.774 519.568 309.774 519.147 c
B
0.75 w 1 J 
318.925 519.15 m
315.55 513.15 l
314.526 515.454 l
314.238 515.326 313.982 515.358 v
S
Q Q Q 
q
307.05 535.44 20.32 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.141 0.039 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS25 gs
322.55 524.668 m
323.668 524.668 324.582 525.582 324.582 526.7 c
324.582 532.796 l
324.582 533.913 323.668 534.828 322.55 534.828 c
311.375 534.828 l
310.257 534.828 309.343 533.913 309.343 532.796 c
309.343 526.7 l
309.343 525.582 310.257 524.668 311.375 524.668 c
322.55 524.668 l
h
B
322.86 525.671 m
323.281 525.671 323.623 526.012 323.623 526.433 c
B
311.079 533.959 m
310.658 533.959 310.317 533.618 310.317 533.197 c
B
0 g
BT
/T1_5 1 Tf
4 0 0 4 314.718 531.0751 Tm
(\006)Tj
ET
0.75 w 1 J 
319.468 532.95 m
316.093 526.95 l
315.069 529.254 l
314.781 529.126 314.525 529.158 v
S
Q Q Q 
q
307.05 549.24 20.32 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.141 0.039 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS26 gs
322.007 538.968 m
323.125 538.968 324.039 539.882 324.039 541 c
324.039 547.096 l
324.039 548.213 323.125 549.128 322.007 549.128 c
310.832 549.128 l
309.715 549.128 308.8 548.213 308.8 547.096 c
308.8 541 l
308.8 539.882 309.715 538.968 310.832 538.968 c
322.007 538.968 l
h
B
322.318 539.971 m
322.739 539.971 323.08 540.312 323.08 540.733 c
B
310.536 548.259 m
310.115 548.259 309.774 547.918 309.774 547.497 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 313.717 541.272 Tm
(x)Tj
/T1_5 1 Tf
3 0 0 3 318.8 542.875 Tm
(\003)Tj
-0.0417 0.9583 Td
(\004)Tj
ET
0.25 w 
318.425 545.125 m
320.675 545.125 l
S
Q Q Q 
q
307.05 563.04 20.32 -11.34 re
W* n
q
-1 661 470 -662 re
W n
q
0 660.06 467.04 -660 re
W n
0.188 0.141 0.039 0.004 k
0 G
0.5 w 4 M 0 j 0 J []0 d 
/GS27 gs
322.216 552.268 m
323.334 552.268 324.249 553.182 324.249 554.3 c
324.249 560.396 l
324.249 561.513 323.334 562.428 322.216 562.428 c
311.041 562.428 l
309.924 562.428 309.009 561.513 309.009 560.396 c
309.009 554.3 l
309.009 553.182 309.924 552.268 311.041 552.268 c
322.216 552.268 l
h
B
322.527 553.271 m
322.948 553.271 323.289 553.612 323.289 554.033 c
B
310.745 561.559 m
310.324 561.559 309.984 561.218 309.984 560.797 c
B
0 g
BT
/T1_0 1 Tf
7.6799 0 0 7.6799 313.9265 554.572 Tm
(y)Tj
/T1_5 1 Tf
4 0 0 4 319.1008 557.6101 Tm
(\006)Tj
ET
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/ID[<1f791069f0b8b7ee6884e8f086c893e4><b8052a984c8de7e30b2742b48cd5b0ef>]
>>
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