Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 51 4 The first six triangle numbers are 1, 3, 6, 10, 15, 21. a What are the next two numbers in the sequence? [1] b Explain in words the term-to-term rule for the sequence. [2] c The rule for the nth triangle number is 1 2 ( + 1). Use this rule to calculate the 50th triangle number. [1] 5 For each sequence, consider its relation to the sequences of square, cube or triangular numbers, then: i write down the next two terms; ii write down the expression for the nth term. a –1, 2, 7, 14, 23 i [2] ii [2] b 0, 2, 5, 9, 14 i [2] ii [2] c 1 4 , 2, 6 3 4 , 16, 31 1 4 i [2] ii [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 52 15 Graphs in practical situations Estimated time to complete: 30 mins Exercise 15.1 1 Water is charged at $0.20 per unit. a Draw a conversion graph on the axes below up to 50 units. [3] b From your graph, estimate the cost of using 23 units of water. Show your method clearly. [2] c From your graph, estimate the number of units used if the cost was $7.50. Show your method clearly. [2] 2 A Science exam is marked out of 180. a Draw a conversion graph to change the marks to percentages. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 53 b Using the graph and showing your method clearly, estimate the percentage score if a student achieved a mark of 130. [2] c Using the graph and showing your method clearly, estimate the actual mark if a student got 35%. [2] Exercise 15.2 1 Find the average speed of an object moving: a 60 m in 12 s [1] b 140 km in 1 h 20 min. [2] 2 How far will an object travel during: a 25 s at 32 m/s [1] b 2 h 18 min at 15 m/s? [2] 3 How long will an object take to travel: a 2.5 km at 20 km/h [1] b 4.8 km at 48 m/s? [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 54 Exercises 15.3–15.4 1 Two people, A and B, set off from points 300 m apart and travel towards each other along a straight road. Their movement is shown on the graph below. a Calculate the speed of person A. [2] b Calculate the speed of person B when she is moving. [2] c Explain how you can deduce which is person is travelling fastest simply by looking at the graph? [2] d Use the graph to estimate how far apart they are 50 seconds after person A has set off. [2] e Explain the motion of person B in the first 20 seconds. [2] f Calculate the average speed of person B during the first 60 seconds. [2] 2 A cyclist sets off at 09 00 one morning and does the following. o Stage 1: Cycles for 30 minutes at a speed of 20 km/h. o Stage 2: Rests for 15 minutes. o Stage 3: Cycles again at a speed of 30 km/h for 30 minutes. o Stage 4: Rests for another 15 minutes. o Stage 5: Realises his front wheel has a puncture so walks with the bicycle for 30 minutes at a speed of 5 km/h to his destination. a At what time does the cyclist reach his destination? [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 55 b How far does he travel during stage 1? [2] c Draw a distance–time graph on the axes below to show the cyclist’s movement. Label all five stages clearly on the graph. [5] d Calculate the cyclist’s average speed for the whole journey. Answer in km/h. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 56 16 Graphs of functions Estimated time to complete: 60 mins Exercise 16.1 Plot the following straight lines on the axes given. a = 1 2 − 1 [2] b = −2 + 4 [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 57 c = − 1 2 − 2 [3] Exercise 16.2 Solve the simultaneous equations: i by graphical means; ii by algebraic means. a – 2 = – 3 4 + 2 = 8 b + – 3 = 0 = – 3 + 1
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 58 Exercise 16.3 For each of the following quadratic functions, complete the table of values and draw the graph on the grid provided. a = 2 + 6 + 8 x −5 −4 −3 −2 −1 y [2] [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 59 b = −2 + 3 + 4 x −2 −1 0 1 2 3 4 5 y [2] [2] Exercise 16.4 Solve each of the following quadratic functions by plotting a graph of the function. a 2 – 4 – 5 = 0 [3] x = ……..……………………………………. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 60 b −2 + 8 − 12 = 0 [3] x = ……..……………………………………. [2] c −2 − 3 + 10 = 0 [3] x = ……..……………………………………. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 61 Exercise 16.5 Using the graphs you drew in the previous exercise, solve these quadratic equations. Show your method clearly. a 2 – 4 – 13 = 0 [2] b −2 + 8 = 0 [2] c −2– 3 + 14 = 0 [2] Exercise 16.6 Complete the table of values and draw on the grid provided the graph of the reciprocal function = 4 . x −4 −3 −2 −1 0 1 2 3 4 y [2] [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 62 Exercise 16.7 Sketch the following linear functions, showing clearly where the lines intersect both axes: a + = 53 [3] b = 2 − 5 [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 63 Exercise 16.8 1 The quadratic equation y = x2 – 3x – 4 has a turning point at � 5 2 , − 21 4 �. Sketch the quadratic on the axes. [2] 2 a Expand y = –(x – 2)(x – 6). [2] b Use your expansion to sketch the graph of y = –(x – 2)(x – 6). Mark the intersections with both axes clearly. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 64 17 Coordinates and straight line graphs Estimated time to complete: 40 mins Exercises 17.1–17.3 1 a On the axes below, plot and join the points in alphabetical order. [2] A(1, 2) B(–2, 3) C(–1, 0) D(4, –3) b Name the quadrilateral produced. [1]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 65 2 a On the axes (right), draw a circle with the centre at (–3, 2) and a radius of 5 units. Draw a second circle with the centre at (4, 3) and also with a radius of 5 units. [2] b Give the coordinates of the two points of intersection of the circles. [2] and Exercises 17.4–17.5 1 What is the position of letters A, B, C and D on the scale below? [4] A = …………………….. B = …………………….. C = ……………………..
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 66 2 a What is the position of the letters P, Q, R and S on the scale below? [2] P = …………………. Q = …………………. R = …………………. S = …………………. b i On the scale above, label the point T that is midway between P and Q. [1] ii Give the position of point T. [1] Exercises 17.6–17.8 1 What is the position of letters A, B, C and D on the scale below? i the gradient of the line ii the equation of the straight line. a i ……………………………………………………….. [1] ii ……………………………………………………….. [1] b i ……………………………………………………….. [1] ii ……………………………………………………….. [1]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 67 c i ……………………………………………………….. [1] ii ……………………………………………………….. [1] d i ……………………………………………………….. [1] ii ……………………………………………………….. [1] e i ……………………………………………………….. [1] ii ……………………………………………………….. [1] 2 In each of the following, identify the coordinates of some of the points on the line and use these to find the equation of the straight line. a ……………………………………………………………………………………………. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 68 b ……………………………………………………………………………………………. [3] c ……………………………………………………………………………………………. [3] d ……………………………………………………………………………………………. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 69 e ……………………………………………………………………………………………. [3] 3 In your own words, explain the significance of ‘m’ and ‘c’ in the equation of a straight line. [3] The general equation of a straight line takes the form y = mx + c. Exercise 17.9 For the following linear equations, calculate both the gradient and y-intercept. a = 4 − 2 [2] b = −(2 + 6) [4] c = − 1 2 + 3 [3] Exercises 17.10–17.11 1 Write down the equation of any two lines that are parallel to the line y = 4x + 7. i ……………………………………………………………………………………………. [1] ii ……………………………………………………………………………………………. [1] 2 Find the equation of the straight line parallel to y = –2x + 6 that passes through the point (2, 5). [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 70 18 Geometrical vocabulary Estimated time to complete: 25 mins Exercises 18.1–18.4 1 Define: a an obtuse angle [1] b a reflex angle. [1] 2 What is the supplementary angle of 125°? [1] 3 a Draw an obtuse-angled triangle PQR. [2] b Name each of the angles in terms of three vertices. [1] …………………. [1] …………………. [1] …………………. [1] 4 Draw and label these lines. a A pair of parallel lines [1] b A pair of perpendicular lines [1] 5 Sketch a regular pentagon. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 71 Exercises 18.5–18.6 1 Examine these triangles. a Explain why the two triangles are similar. [2] b Calculate the scale factor that enlarges the smaller triangle to the larger triangle. [3] c Calculate the value of x. [2] d Calculate the value of y. [2] 2 a Calculate the length a to 4 s.f. [2] b Calculate the length b to 4 s.f. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 72 3 The diagram shows two arcs with the same centre and an angle θ. Write an expression for the length x in terms of r. [2] Exercises 18.7 In the grid below, complete the second shape so that it is congruent to shape A. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 73 19 Geometrical constructions and scale drawings Estimated time to complete: 20 mins Exercises 19.1–19.3 1 On each of the nets below, a face has been marked with an X. If the cubes were assembled, mark, with a Y, the face that would be opposite X. [2] Angle PQR ……………. Angle QRP ……………. Angle RPQ ……………. PQ ……………….……. QR ……………….….…. RP …….………….……. 2 Using only a ruler and a pair of compasses, construct the following triangle XYZ. [3] XY = 5 cm, XZ = 3 cm and YZ = 7 cm. Exercises 19.4 1 The scale of a map is 1 : 20 000. a Two villages are 12 cm apart on the map. How far apart are they in real life? Answer in kilometres. [2] b The distance from a village to the edge of a lake is 8 km in real life. How far apart are they on the map? Answer in centimetres. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 74 2 a A model car is a 1 25 scale model. Express this as a ratio. [1] b If the length of the real car is 4.9 m, what is the length of the model car? [1] Exercise 19.5 1 Three nets A, B and C are shown. Tick which (if any) can be folded to make a cube. [2] 2 On each of the nets below, a face has been marked with an X. If the cubes were assembled, mark, with a Y, the face that would be opposite X. 3 A student is trying to draw the net for a tetrahedron. She does three different drawings, labelled A, B and C, as shown below. Which of the diagrams can be folded to make a tetrahedron? [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 75 4 Using a ruler and a pair of compasses, construct the net of a tetrahedron, of edge length 3cm, in the space below. [3] 5 A right-angled triangular prism is shown below. Draw a possible net of the prism below. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 76 20 Symmetry Estimated time to complete: 25 mins Exercises 20.1–20.2 1 Complete the shapes on the grids below so that the dotted line becomes a line of symmetry. a b [1] [1] 2 Complete the shapes on the grids below so that the dotted line becomes a line of symmetry. a b [1] [1] 3 Sketch each of the shapes below and show their lines of symmetry. a A regular dodecagon [3] b A rhombus [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 77 4 Indicate the order of rotational symmetry for each of the shapes above. a …………………………….. [3] b …………………………….. [3] 5 Complete the diagrams below so that they have rotational symmetry of order 2 about the centre of rotation O. a b [2] [2] 6 Complete the diagram below so that it has rotational symmetry of order 4 about the centre of rotation O. [2] O O O
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 78 7 The diagram shows a grid with some of its squares shaded. Shade four squares in the bottom half of the grid so that the final pattern has rotational symmetry of order 2 about O. [2] 8 The triangular dotted grid below shows a triangle and a point labelled O. Add new triangles to the grid so that the final image has rotational symmetry of order 3 about the point O. [2] O O
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 79 21 Angle properties Estimated time to complete: 30 mins Exercise 21.1 1 In each of the diagrams below, the angles lie on a straight line. Calculate the value of x. a …………………………….. [1] b …………………………….. [3] 2 In the diagram below, the angles lie about a point. Calculate the value of p. p = ………………….. [2] Exercises 21.2–21.7 1 a Calculate the size of each of the labelled angles. [1]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 80 a = ………………………. [1] b = ………………………. [1] c = ………………………. [1] d = ………………………. [1] e = ………………………. [1] b From the above diagram, identify a pair of angles which are i corresponding [1] ii co-interior [1] 2 Calculate the size of the labelled angles in the kite. p = ………………………. [1] q = ………………………. [1] Exercises 21.8 Complete the table below. Enter ‘Yes’ or ‘No’ in each cell. Rhombus Parallelogram Kite Opposite sides equal in length All sides equal in length All angles right angles Both pairs of opposite sides parallel Diagonals equal in length Diagonals intersect at right angles All angles equal
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 81 Exercises 21.9–21.10 1 The size of each interior angle of a regular polygon is 165°. Calculate: a the size of each exterior angle [1] b the number of sides of the regular polygon [2] 2 Find the value of each interior angle of a regular polygon with: a 30 sides [2] b 20 sides [2] 3 Calculate the number of sides of a regular polygon if each interior angle is 4x° and each exterior angle is x°. [3] 4 The pentagon below has angles as shown. a State the sum of the interior angles of a pentagon. [1] b Calculate the value of x. [2] c Calculate the size of each of the angles of the pentagon. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 82 5 The diagram shows an octagon. a Write the angle y in terms of x. [1] b Write an equation for the sum of the interior angles of the octagon in terms of x. [2] c Calculate the value of x. [2] d Calculate the size of the angle labelled y. [1] Exercise 21.11 In the diagram, O marks the centre of the circle. Calculate the value of x. [2] [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 83 Exercise 21.12 In each diagram, O marks the centre of the circle. Calculate the value of the labelled angles in each case. a [2] b [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 84 22 Measures Estimated time to complete: 15 mins Exercises 22.1–22.4 1 Convert these lengths to the units indicated: a 0.072 m to mm [1] b 20 400 m to km [1] 2 Convert these masses to the units indicated: a 420 g to kg [1] b 1.04 tonnes to kg [1] 3 Convert these liquid measures to the units indicated: a 12 ml to litres [1] b 0.24 litres to ml [1] Exercise 22.5 1 Calculate the sum of the following four volumes and convert your answer to litres: [2] 440 ml 870 ml 1650 ml 540 ml 2 a A container has a volume of 3.6 m3 . Convert the volume into cm3 . [2] b A box has a volume of 3250 cm3 . Convert the volume into: [1] i mm3 [1]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 85 ii m3 [1]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 86 23 Perimeter, area and volume Estimated time to complete: 120 mins It is recommended that you do not attempt the exercises for this chapter all in one go. Exercises 23.1–23.6 1 Find the area and perimeter of the following shapes: a A rectangle 4.5 cm by 3.5 cm. Area …………………………….. [1] Perimeter …………………………….. [1] b A right-angled triangle of base 1.5 cm, height 2 cm and hypotenuse 2.5 cm. Area …………………………….. [1] Perimeter …………………………….. [1] 2 Calculate the shaded area of the compound shape. Area …………………………….. [3] 3 The rectangle and trapezium have the same area. Calculate the value of x. [4] Exercises 23.7–23.8 1 Calculate the circumference and area of the circle. Circumference ……………. [1] Area ………….. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 87 2 A circle has an area of 12.25π cm2. Calculate: a its diameter [2] b its circumference [2] 3 Calculate the circumference and area of the circle. If the semicircle has a radius of 7 cm, calculate the shaded area remaining. [3] 4 A trapezium and parallelogram are joined as shown: If the total area is 53.2 cm2, calculate the value of x. [3] 5 Five thin semi-circular chocolate pieces are placed in a rectangular box as shown: Calculate: a the length of the box [2] b the area occupied by one piece of chocolate [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 88 c the area of the box not covered by chocolate pieces. [2] 6 A circular hole is cut out of a circular shape as shown: The area remaining is the same as the area of the hole removed. The circumference of the original piece is 15π cm. Calculate the radius of the circular hole. [4] Exercises 23.9–23.12 1 A cuboid has a length of 7 cm, a width of 2.5 cm and a total surface area of 114.8 cm2 . Calculate its height. [2] 2 A cylinder has a total surface area of 100 cm2. If the radius of its circular cross-section is 3.6 cm, calculate its height. [2] 3 A cylinder and a cuboid have dimensions as shown: a Write an expression for the total surface area of the cuboid. [2] b Write an expression for the total surface area of the cylinder. [2] c If the total surface area of the cylinder is twice that of the cuboid, find the value of h. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 89
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 90 4 A metal hand weight is made from two cubes and a cylinder joined as shown: Calculate the volume of the shape. [3] 5 A cylinder and a cylindrical pipe have the same volume and diameter. a Calculate the volume of the solid cylinder. Give your answer in terms of π. [2] b Write an expression for the volume of the cylindrical pipe. [3] c Calculate the value of x. [3] Exercises 23.13–23.14 1 A sector has a radius of 6 cm and an arc length of 2 3 π cm. Calculate the angle of the sector θ. [2] 2 A sector has an angle of 120° and an arc length of 14 cm. Calculate the length of the sector’s radius, giving your answer in terms of π. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 91 Exercises 23.15–23.16 1 Two sectors, A and B, are shown below: a Calculate the area of sector A. Give your answer in terms of π. [1] b What is the ratio of the areas of sectors A : B? Give your answer in the form 1 : n. [2] 2 A prism with a cross-section in the shape of a sector is shown below: Calculate: a the angle θ [1] b in terms of π, the area of the cross-section [2] c the total surface area of the prism, to the nearest whole number [3] d in terms of π, the volume of the prism. [1]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 92 Exercises 23.17–23.18 1 A sphere has a volume of 0.5 m3 . Calculate the sphere’s radius, giving your answer in cm to 1 d.p. [2] 2 The diagram below shows a sphere of radius 3 cm and an open-topped container in the shape of a cube of side length 10 cm. The container is filled with water to a depth of 6 cm. a Calculate the volume of the sphere, giving your answer in terms of π. [2] b The sphere is submerged in the water. Determine whether the water spills over the rim of the container. You must show your working to justify your answer. [2] c The sphere is removed. Another sphere of radius r cm is submerged in the container. Show that the increase in height (h cm) of the level of water in the container is given by ℎ = π3 75 . [2] Exercises 23.19 1 A hemisphere has a radius of 5 cm. a Calculate, in terms of π, the area of its flat base. [1] b Calculate, in terms of π, its total surface area. [3]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 93 2 A solid shape is made from two hemispheres joined together. The base of each hemisphere shares the same centre. a Calculate the surface area of the smaller hemisphere. [2] b Calculate the total surface area of the shape. [4] Exercises 23.20–23.21 1 A rectangular-based pyramid is shown: a Calculate the volume of the pyramid. [2] b Calculate the total surface area of the pyramid, using Pythagoras’ theorem. [4]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 94 2 Two square-based pyramids are joined at their bases. The bases have an edge length of 6 cm. a Calculate the volume of the pyramid on the left. [2] b If the volume of the pyramid on the left is twice that of the pyramid on the right, calculate the value of x. [2] c By using Pythagoras as part of the calculation, calculate the total surface area of the shape. [4] Exercises 23.22–23.24 1 A cone has a base diameter of 8 cm and a sloping face length of 5 cm. a Calculate its perpendicular height. [2] b Calculate the volume of the cone. [2] c Calculate the total surface area of the cone. [4]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 95 2 The curved surface area (A) of a cone is given by the formula A = rl, where r is the base radius and l is the slant length. The volume (V ) of a cone is given by the formula = 2 ℎ 3 , where r is the base radius and h is the vertical height. A solid cone has a slant length of 10 cm, a base radius of 6 cm and a vertical height of 8 cm. It is bisected and one half is kept, as shown. a Calculate the area of the triangular face of the bisected shape. [2] b Calculate the volume of the bisected shape. Give your answer correct to 3 s.f. [3] c Calculate the total surface area of the bisected shape. Give your answer correct to 3 s.f. [4]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 96 24 Bearings Estimated time to complete: 20 mins Exercises 24.1–24.2 1 Maya draws a bearing diagram as shown below. She states that the bearing of B from A is 120°. a What mistake has she made? [1] b Assuming the size of the angle shown is correct, what is the correct bearing of B from A? [1] 2 Estimate the bearing of Y from X in each of the following diagrams. a Estimate ………………………. [1] b Estimate …………………….. [1] a Estimate ………………………. [1] b Estimate …………………….. [1]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 97 3 Two lifeboat stations P and Q are on the same coastline. A boat B is in trouble and sends out a distress signal. If B is on a bearing of 070° from station P and a bearing of 320° from station Q, mark its position on the diagram below. [3] 4 A boat sets off from a point A on a bearing of 130° for 4 km to a point B. At B it changes direction and sails on a bearing of 240° to a point C, 7 km away. At point C it changes direction again and heads back to point A. a Using a scale of 1 cm : 1 km, draw a scale diagram of the boat’s journey. [4] b From your diagram work out: i the distance AC [1] ii the bearing of A from C. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 98 c Without measuring, deduce the bearing of A from B. Explain clearly how you calculate your answer. [2] 5 A hiker sets off on a bearing of 050° from point A until he reaches point B. At B he changes course and heads back to A. a What bearing does the hiker travel on to get from B to A? [1] b Justify your answer to (a) above. [2]
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 99 25 Right-angled triangles Estimated time to complete: 40 mins Exercises 25.1–25.3 1 Calculate the value of x in each triangle. Give your answers to 1 d.p. a …………………………………….. [2] b …………………………………….. [2] c …………………………………….. [2] d …………………………………….. [2] e …………………………………….. [2] f
Cambridge IGCSE™ Mathematics Core Worksheets Cambridge IGCSE™ Mathematics Core 5th edition © Hodder & Stoughton Limited 2023 100 …………………………………….. [2] g …………………………………….. [2] h …………………………………….. [2] Exercises 25.4–25.5 1 In each diagram, calculate the length of the marked side. Answer to 1 d.p. a …………………………………….. [2] b …………………………………….. [2]