ࡱ>   _U Pbjbj xxH ((kk''';;;8sG;~#****HHHG~I~I~I~I~I~I~>I~'nKVF\HnKnKI~kk**s^~"_"_"_nKXk*'*G~"_nKG~"_"_s6u* &;K4 ot3~t~0~tނT~ނ4uނ'uHRIr"_I\ JNHHHI~I~xYHHH~nKnKnKnKނHHHHHHHHH( 1: Honors Pre-Calculus Midterm Exam Review Name: January 2013 Chapter 1: Functions and Their Graphs 1. Evaluate the function at each specified value of the independent variable and simplify.  EMBED Equation.3  a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  1a.)_____________ 1b.)_____________ 1c.)_____________ 2. Evaluate the function at each specified value of the independent variable and simplify.  EMBED Equation.3  a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  2a.)_____________ 2b.)_____________ 2c.)_____________ 2d.)_____________ 3. Find the domain of the given function. Use interval notation! a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  3a.)_____________ 3b.)_____________ 3c.)_____________ 4. Use a graphing utility to graph the function and determine the open intervals on which the function is increasing, decreasing, or constant (use interval notation!). Identify any relative minimum or relative maximum values of the function. a.  EMBED Equation.3  b.  EMBED Equation.3  4a.) increasing:____________ decreasing:____________ constant:______________ rel. min.:______________ rel. max.:______________ 4b.) increasing:____________ decreasing:____________ constant:______________ rel. min.:______________ rel. max.:______________ 5. Determine algebraically if the function is even, odd, or neither. Verify using a graphing utility. a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  5a.)________________ 5b.)________________ 5c.)________________ 6. Given  EMBED Equation.3 ,  EMBED Equation.3  and  EMBED Equation.3 . Describe the sequence of transformations from  EMBED Equation.3 or  EMBED Equation.3 to  EMBED Equation.3 . a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  a.)________________________________________________________________________________________ b.)________________________________________________________________________________________ c.)________________________________________________________________________________________ 7. Given  EMBED Equation.3 ,  EMBED Equation.3  and  EMBED Equation.3 . Find the indicated values. a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  7a.)________________ 7b.)________________ 7c.)________________ d.  EMBED Equation.3  e.  EMBED Equation.3  f.  EMBED Equation.3  7d.)________________ 7e.)________________ 7f.)________________ 8. Find the inverse of the function algebraically. a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  8a.)________________ 8b.)________________ 8c.)________________ 9. Show that  EMBED Equation.3  and  EMBED Equation.3  are inverses.   EMBED Equation.3 ,  EMBED Equation.3  10. Given the graph  EMBED Equation.3  at the right, sketch the following:  a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  Chapter 2: Polynomials and Rational Functions 11. Express each complex number in standard form  EMBED Equation.3 . a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  11a.)_______________ 11b.)_______________ 11c.)_______________ d.  EMBED Equation.3  e.  EMBED Equation.3  f.  EMBED Equation.3  11d.)_______________ 11e.)_______________ 11f.)_______________ 12. Solve the following equations for x. a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  12a.)_______________ 12b.)_______________ 12c.)_______________ 13. If  EMBED Equation.3  use synthetic substitution to find: a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  13a.)_______________ 13b.)_______________ 13c.)_______________ 14. If -2 is a zero of the polynomial  EMBED Equation.3  find the value of k. 14.)________________ 15. A polynomial  EMBED Equation.3 is divided by  EMBED Equation.3 . The quotient is  EMBED Equation.3  and the remainder is -1. Find  EMBED Equation.3 . 15.)______________________ 16. Two roots of the equation  EMBED Equation.3 are EMBED Equation.3  and  EMBED Equation.3 . Find the remaining roots. 16.)________________ 17. Find all real zeros of  EMBED Equation.3 . Use the rational root theorem and synthetic division. 17.)________________ 18. Sketch the graph of the equation (without a graphing calculator). Use the zeros of the function and the end behavior of the function.  EMBED Equation.3  19. A rectangular enclosure, sub-divided into three congruent pens as shown, is to be made using a barn as one side and 120 meters of fencing for the rest of the enclosure. Find the value of x that gives the maximum area for the enclosure. 19.)________________  SHAPE \* MERGEFORMAT  20. Solve for x.  EMBED Equation.3  20.)________________ 21. Find all real and imaginary roots of  EMBED Equation.3  21.)________________ 22. Find a cubic equation with integral coefficients having the solutions  EMBED Equation.3 . 22.)________________  23. Graph  EMBED Equation.3  24. Sketch the graph of the rational function by hand. Identify any x-intercepts, the y-intercept, horizontal asymptotes, vertical asymptotes, and slant asymptotes. a.  EMBED Equation.3  x-intercept(s) = _______ y-intercept = _________ H.A. = ______________ V.A. = ______________ S.A. = ______________ b.  EMBED Equation.3  x-intercept(s) = _______ y-intercept = _________ H.A. = ______________ V.A. = ______________ S.A. = ______________  c.  EMBED Equation.3  x-intercept(s) = _______ y-intercept = _________ H.A. = ______________ V.A. = ______________ S.A. = ______________ 25. Determine whether  EMBED Equation.3  has symmetry in: Circle the correct answer (s) a. the x-axis b. the y-axis c. the line y=x d. the origin  26. Sketch the graph of the quadratic function. Identify the vertex & intercept(s).  EMBED Equation.3  vertex = _________________ x-intercept(s) = ___________ y-intercept = _____________ Chapter 3 and Exponents Packet (Ch 5 from other textbook): Exponential Functions and Logarithmic Functions 27. Evaluate the following exponential expressions: a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  d.  EMBED Equation.3  27a.)_______________ 27b.)_______________ 27c.)_______________ 27d.)_______________ 28. Solve each exponential equation: a.  EMBED Equation.3  b.  EMBED Equation.3  28a.)_______________ 28b.)_______________ 29. A gallon of gasoline cost $3.09 two years ago. Now it costs $1.78. To the nearest percent, what has been the annual rate of decrease in cost? 29.)________________ 30. Graph  EMBED Equation.3  and  EMBED Equation.3 on the same set of axes. How are the graphs related? 31. Suppose $1,200 is invested at an interest rate of 9.6%. how much is the investment worth after 2 years if interest is compounded: a. Monthly? b. Continuously? 31a.)_______________ 31b.)_______________ 32. Given  EMBED Equation.3 , using rules of logarithms, find the value of: {without a calculator!} a.  EMBED Equation.3  b.  EMBED Equation.3  32a.)_______________ 32b.)_______________ 33. Find the exact value of: without a calculator! 33a.)_______________ a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  33b.)_______________ 33c.)_______________ 34. Express the following in terms of  EMBED Equation.3  a.  EMBED Equation.3  b.  EMBED Equation.3  34a.)__________________________________ 34b.)__________________________________ 35. Solve  EMBED Equation.3 . 35.)________________ 36. Solve  EMBED Equation.3 to the nearest hundredth. 36.)________________ 37. If 250 mg of ibuprofen has a half-life of 3 hours, then how much ibuprofen is in a persons bloodstream after (a) 7 hours? (b) after t hours? 37a.)_______________ 37b.)_______________ 38. Simplify: a.  EMBED Equation.3  38a.)_______________ b.  EMBED Equation.3  38b.)_______________ c.  EMBED Equation.3  38c.)_______________ 39. Solve for x: a.  EMBED Equation.3  39a.)_______________ b.  EMBED Equation.3  39b.)_______________ c.  EMBED Equation.3  39c.)_______________ d.  EMBED Equation.3  39d.)_______________ 40. Solve for x: a.  EMBED Equation.3  40a.)_______________ b.  EMBED Equation.3  40b.)_______________ c.  EMBED Equation.3  40c.)_______________ d.  EMBED Equation.3  40d.)_______________ Chapter 4 [4.1-4.6]: Trigonometry 41. A circle has a radius of 7 inches. Find the length of the arc intercepted by a central angle of  EMBED Equation.3 . 41.)________________ 42. The circular blade on a saw rotates at 2400 revolutions per minute. a. Find the angular speed in radians per second. 42a.)_______________ b. The blade has a radius of 4 inches. Find the linear speed of a blade tip in inches per second. 42b.)_______________ 43. A satellite in circular orbit 1125 km above a planet makes one complete revolution every 120 minutes. Assuming that he planet is a sphere of radius 6400 km, find the linear speed of the satellite in kilometers per minute. Round your answer to the nearest whole number. 43.)________________ 44. A truck is moving at a rate of 90 km per hour and the diameter of its wheels is 1.25 meters. Find the angular speed of the wheels in radians per minute. 44.)________________ 45. Evaluate (if possible) the six trigonometric functions if  EMBED Equation.3 . 45.  EMBED Equation.3  46. Evaluate the trigonometric function. a.  EMBED Equation.3  b.  EMBED Equation.3  c.  EMBED Equation.3  46a.)_______________ 46b.)_______________ 46c.)_______________ d.  EMBED Equation.3  e.  EMBED Equation.3  f.  EMBED Equation.3  46d.)_______________ 46e.)_______________ 46f.)_______________ 47. Find the exact values of the six trigonometric functions of the angle  EMBED Equation.3  shown in the figure.  SHAPE \* MERGEFORMAT  47.  EMBED Equation.3  48. Simplify each expression. a.  EMBED Equation.3  b.  EMBED Equation.3  48a.)_______________ 48b.)_______________ c.  EMBED Equation.3  d.  EMBED Equation.3  48c.)_______________ 48d.)_______________ 49. Find two solutions of the equation. Give your answers in degrees  EMBED Equation.3  and radians  EMBED Equation.3  without using a calculator. a.  EMBED Equation.3  b.  EMBED Equation.3  49a.)_____________________ 49b.)_____________________ 50. John stands 150 meters from a water tower and sights the top at an angle of elevation of  EMBED Equation.3 . How tall is the tower? 50.)________________ 51. The Aerial run in Snowbird, Utah has an angle of elevation of  EMBED Equation.3 . Its vertical drop is 2900 feet. Estimate the length of the run. 51.)________________ 52. In a sightseeing boat near the base of the Horseshoe Falls at Niagara Falls, a passenger estimates the angle of elevation to the top of the falls to be  EMBED Equation.3 . If the Horseshoe Falls are 173 feet high, what is the distance from the boat to the base of the falls? 52.)________________ 53. Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle.  EMBED Equation.3  53.  EMBED Equation.3  54. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle.  EMBED Equation.3  54.  EMBED Equation.3  Answer the questions regarding the amplitude, period, phase shift and vertical shift of each trigonometric function  EMBED Equation.3 or  EMBED Equation.3 . Then graph two full periods of the trigonometric function. Be sure to label your axes accurately! 55.  EMBED Equation.3  a = b = c = d = amplitude = period = phase shift = vertical shift =  SHAPE \* MERGEFORMAT  56.  EMBED Equation.3  a = b = c = d = amplitude = period = phase shift = vertical shift =  SHAPE \* MERGEFORMAT  57.  EMBED Equation.3  a = b = c = d = amplitude = period = phase shift = vertical shift =  SHAPE \* MERGEFORMAT  58.  EMBED Equation.3  a = b = c = d = amplitude = period = phase shift = vertical shift =  SHAPE \* MERGEFORMAT  Graph two periods of the trigonometric function. 59.  EMBED Equation.3  a = b = c = d = amplitude = period = phase shift = vertical shift =  SHAPE \* MERGEFORMAT  60.  EMBED Equation.3  a = b = c = d = amplitude = period = phase shift = vertical shift =  SHAPE \* MERGEFORMAT  Answer Key Midterm Review Packet January 2013 1a. 10 1b.  EMBED Equation.3  1c.  EMBED Equation.3  2a. -3 2b. -1 2c. 2 2d. 6 3a.  EMBED Equation.3  3b.  EMBED Equation.3  3c.  EMBED Equation.3  4a. increasing:  EMBED Equation.3  4a. decreasing:  EMBED Equation.3  4a. constant: none 4a. rel. min.:  EMBED Equation.3  4a. rel. max.:  EMBED Equation.3  4b. increasing:  EMBED Equation.3  4b. decreasing:  EMBED Equation.3  4b. constant: none 4b. rel. min.:  EMBED Equation.3  4b. rel. max.: none 5a. even 5b. neither 5c. odd 6a.  EMBED Equation.3  has a horizontal shift 2 units left, reflects over the x-axis and has a vertical shift 6 units down 6b.  EMBED Equation.3  has a vertical stretch of 2 and a vertical shift up 3 units 6c.  EMBED Equation.3  has a horiz. shift 5 units right, reflects over the x-axis, a vertical shrink of and a vertical shift 7 units down 7a. -7 7b. 70 7c. 5 7d.  EMBED Equation.3  7e.  EMBED Equation.3  7f. -97 8a.  EMBED Equation.3  8b.  EMBED Equation.3  8c.  EMBED Equation.3  9. show that  EMBED Equation.3  10. See graphs 11a.  EMBED Equation.3  11b.  EMBED Equation.3  11c.  EMBED Equation.3  11d.  EMBED Equation.3  11e.  EMBED Equation.3  11f.  EMBED Equation.3  12a.  EMBED Equation.3  12b.  EMBED Equation.3  12c.  EMBED Equation.3  13a. 13 13b.  EMBED Equation.3  13c.  EMBED Equation.3  14. 18 15.  EMBED Equation.3  16.  EMBED Equation.3  17.  EMBED Equation.3  18. See graph 19. 15 meters 20.  EMBED Equation.3  21.  EMBED Equation.3  22.  EMBED Equation.3  23. See graph 24a. x-intercept:  EMBED Equation.3 ; y-intercept:  EMBED Equation.3 ; H.A.: y = 1; V.A.: x = 2; S.A.: none 24b. x-intercept:  EMBED Equation.3 ; y-intercept:  EMBED Equation.3 ; H.A.: y = 2; V.A.: x = 2 and x = -2; S.A.: none 24c. x-intercept: none; y-intercept:  EMBED Equation.3 ; H.A.: none; V.A.: x = 3; S.A.: x + 2 25. c and d 26. vertex:  EMBED Equation.3 ; x-intercept:  EMBED Equation.3 ; y-intercept:  EMBED Equation.3  27a. 27 27b.  EMBED Equation.3  27c. 729 27d.  EMBED Equation.3  28a. -1 28b.  EMBED Equation.3  29. 24.1% 30. See graph 31a. $1452.89 31b. $1454.00 32a. 0.6021 32b. -0.6021 33a. 4 33b.  EMBED Equation.3  33c. 125 34a.  EMBED Equation.3  34b.  EMBED Equation.3  35.  EMBED Equation.3  36. 3.13 37a.  EMBED Equation.3  37b.  EMBED Equation.3  38a. 81 38b. 64 38c.  EMBED Equation.3  39a.  EMBED Equation.3  39b.  EMBED Equation.3  39c.  EMBED Equation.3  39d. 1 40a. -0.483 40b.  EMBED Equation.3  40c.  EMBED Equation.3  40d. -2 41.  EMBED Equation.3  inches 42a.  EMBED Equation.3  rad/sec 42b.  EMBED Equation.3 in/sec 43. 394 km/min 44. 2400 rad/min 45.  EMBED Equation.3  46a.  EMBED Equation.3  46b. -2 46c.  EMBED Equation.3  46d. 1 46e. 0 46f.  EMBED Equation.3  47.  EMBED Equation.3  48a.  EMBED Equation.3  48b. 2 48c.  EMBED Equation.3  48d.  EMBED Equation.3  49a.  EMBED Equation.3  49b.  EMBED Equation.3  50. 108.98 meters 51. 8398.54 feet 52. 299.64 feet 53.  EMBED Equation.3  54.  EMBED Equation.3  55. 60. See graphs 55. a = 1 b = 4 c = 0 d = -2 Amp = 1 Per =  EMBED Equation.3  Phase Shift = 0 Vert. Shift = -2 56. a = -3 b =  EMBED Equation.3  c = 0 d = 1 Amp = 3 Per =  EMBED Equation.3  Phase Shift = 0 Vert. Shift = 1 57. a = 3 b =1 c = EMBED Equation.3  d = 4 Amp = 3 Per =  EMBED Equation.3  Phase Shift =  EMBED Equation.3  Vert. Shift = 4 58. a = 4 b =  EMBED Equation.3  c = -1 d = -3 Amp = 4 Per = 4 Phase Shift = -1 Vert. Shift = -3 59. a = -3 b = 2 c = 0 d = 0 Amp = none Per =  EMBED Equation.3  Phase Shift = none Vert. Shift = none 60. a =  EMBED Equation.3  b = 1 c = 0 d = 1 Amp = none Per =  EMBED Equation.3  Phase Shift = none Vert. Shift = 1     BARN ( 12 18 (*,12;<FGHIRopqr̫̙̽~fTC1#hh*)5CJOJQJ^JaJ hh*)CJOJQJ^JaJ#hhI.5CJOJQJ^JaJ.hUP5CJOJQJ^JaJeh r 4hh*)5CJOJQJ^JaJeh r #hh*)5CJOJQJ^JaJ#hhi5CJOJQJ^JaJh5CJOJQJ^JaJ#hh5CJOJQJ^JaJh5CJOJQJ^JaJ#hh+T5CJOJQJ^JaJ2IpqN P n o   1 gd}gdihgdr            ! 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