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Underline important information if it helps. If you have time left at the end, check your answers. If you decide to change an answer, cross out the old answer. The methods that you need are listed below. You will have a calculator in the exam, so the examples show how to use a calculator to solve the problems, rather than other methods. Angles  Triangles Lines     Special Quadrilaterals        Polygons   Regular Polygons Regular polygons have equal sides and equal angles. SymmetryExamples  2 lines of symmetry 6 lines of symmetry no lines of symmetry rotational symmetry order 2 rotational symmetry order 6 rotational symmetry order 4 Units of Length Metric metres (m) centimetres (cm) millimetres (mm) kilometres (km) Learn 1 m = 100 cm 1 m = 1000 mm 1 cm = 10 mm 1 km = 1000 m (To convert from one unit to another multiply or divide by the conversion factor.) Imperial inches feet yards miles  PerimetersPerimeter = total length of outside edges. (You may need to find unknown edges)  Example Find the total length of coving needed to go around this ceiling. Unknown sides: AF = 3.6 + 1.5 = 5.1 m CD = 5.4  3 = 2.4 m Total length = 3 + 1.5 + 2.4 + 3.6 + 5.4 + 5.1 = 21 mCircumference of a circle = p ( diameter (You may need to double the radius.)  Example The radius of a circular flowerbed is 1.4 metres. What is its circumference? Diameter = 2 ( 1.4 = 2.8 Circumference = p ( 2.8 = 8.796& = 8.8 m (to 1 decimal place) Units of Area m2 cm2 mm2 km2 AreasArea of rectangle = length ( width Example Find the area of this rectangular lawn. Area = 6.4 ( 4.8 = 30.72 m2 Area of circle = p ( radius2 (You may need to halve the diameter.)  Example The diameter of a circular pond is 3 metres. What is its area? Radius = 3 ( 2 = 1.5 m Area = p ( 1.52 = 7.068& = 7.1 m2 (to 1 decimal place)  Area of triangle = ( base ( height Example Find the area of this triangular sign. Area = ( 36 ( 27 or 36 ( 27 ( 2 = 486 cm2 You may need to add or subtract areas and/or convert units.  Example Find the area of this window. Give the answer in m2. 80 cm = 0.8 m Area of rectangle = 0.8 ( 1 = 0.8 m2 Radius = 0.8 ( 2 = 0.4 m Area of full circle = p ( 0.42 = 0.5026& Area of semi-circle = 0.5026( 2 = 0.2513 Total area = 0.2513 + 0.8 = 1.051 = 1.05 m2 (to 2 decimal places) Units of Volume m3 cm3 mm3 litres (for liquids) Volumes     Prisms have a constant cross section.  Volume of cube = length ( width ( height Example Find the volume of this stock cube. Volume = 2 ( 2 ( 2 = 8 cm3  Volume of triangular prism = area of triangle ( length  Example Find the volume of this fudge bar. Area of triangle = ( 10 ( 8 or 10 ( 8 ( 2 = 40 cm2 Volume of bar = 40 ( 20 = 800 cm3  Volume of cuboid = length ( width ( height  Example Find the volume of this water tank. Give the answer in m3. 750 mm = 0.75 m 800 mm = 0.8 m Volume = 0.8 ( 1.2 ( 0.75 = 0.72 m3  Volume of cylinder = area of circle ( length  Example Find the volume of this can. Radius = 7 ( 2 = 3.5 cm Area of circle = p ( 3.52 = 38.4845& cm2 Volume of can = 38.4845& ( 10 = 384.845& = 385 cm3 (to nearest cm3)  MeasurementsLengths - you may need to measure to the nearest mm or cm. The arrow shows 3.8 cm or 38 mm to the nearest mm. This measurement is 4 cm to the nearest cm. Angles - make sure you use the right scale on your protractor. Follow the scale round from zero. Scale drawingsA scale of 1 : n means the real distances are n times more than those on the plan or map. Angles stay the same.  To find an actual distance, multiply by n Example The plan of a room has a scale of 1 : 50. The length of the room on the plan is 9.6 cm. What is the actual length of the room in metres? Actual length = 9.6 ( 50 = 480 cm Actual length = 480 ( 100 = 4.8 m  To find a distance for a plan or model, divide by n Example A model of a boat has a scale of 1 : 20. The length of the boat is 8.6 m. What is the length of the model in millimetres? Actual length = 8.6 m = 8.6 ( 1000 = 8600 mm Length of model = 8600 ( 20 = 430 mm Plans and ElevationsExample  Plan the view from above  Front elevation the view from the front   Side elevation the view from the side  Constructions To draw the perpendicular bisector of a line AB With compass point on A draw an arc. With compass point on B draw an arc. Join the points C and D (where the arcs meet). CD is the perpendicular bisector. E is the mid-point of AB  To draw a line perpendicular to AB through a point P on AB With compass point on P, draw arcs to cut AB at C and D. With compass point on C, then D, draw arcs above P to meet at E. PE is the perpendicular to AB at P.  To construct a regular hexagon or an equilateral triangle with vertices on a circle  Draw the circle. Keeping the radius the same, use the compass to 'step round' the circle. Join all the points for a regular hexagon.  Join alternate points for an equilateral triangle.  Constructions (continued) You may also be asked to construct a rectangle or a triangle with given sides or angles. To construct a triangle when given the length of its sides: eg with AB = 7.5 cm, AC = 6 cm and BC = 4.5 cm  Draw one side, AB = 7.5 cm. Open the compasses to the length of AC (6 cm) and with the point on A draw an arc. Open the compasses to the length of BC (4.5 cm) and with the point on B draw an arc. Where the arcs meet is the vertex C. Join AC and BC to give the traingle. If you measure the angles of triangle ABC, you should find: angle A = 37( angle B = 53( angle C = 90( ABC is a right-angled triangle.      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