Shape, space and measures

Transcription

1 Shape, space and measures Non-Calculator Exam Questions 1. Here is the plan and side elevation of a prism. The side elevation shows the cross section of the prism. On the grid below, draw the front elevation of the prism. Haringey Sixth Form Mathematics Department 1

2 2. Here are the plan and front elevation of a prism. The front elevation shows the cross section of the prism. Plan Front elevation (a) On the grid below, draw a side elevation of the prism. (3) (b) In the space below, draw a 3-D sketch of the prism. (Total 5 marks) Haringey Sixth Form Mathematics Department 2

3 3. The diagram shows a solid object made from centimetre cubes. (a) In the space below, sketch the front elevation of the solid object from the direction marked with an arrow. (b) In the space below, sketch a plan of the solid object. Area and Volume (Total 4 marks) 4. A semicircle has a diameter of 20 cm. 20 cm Work out the perimeter of the semicircle. Take the value of to be cm Haringey Sixth Form Mathematics Department 3

4 5. 20 cm 9 cm 4 cm 8 cm The diagram shows a shape. Work out the area of the shape. cm 2 (Total 4 marks) 6. The diagram shows a wall with a door in it. 4 m 3 m 1 m 2 m (a) Work out the shaded area. m 2 (3) Haringey Sixth Form Mathematics Department 4

5 Meg can cover the shaded area with 680 tiles. She buys extra tiles in case she breaks some. To work out the total number of tiles to buy, Meg increases 680 by 10%. (b) (i) Increase 680 by 10%. The tiles Meg is going to use are sold in boxes of (ii) Work out the number of boxes of tiles Meg should buy... (5) (Total 8 marks) 7. The diagram shows a 6-sided shape made from a rectangle and a right-angled triangle. 2 cm 7 cm 12 cm 6 cm Work out the total area of the 6-sided shape....cm 2 Haringey Sixth Form Mathematics Department 5

6 8. The diagram shows a wedge in the shape of a triangular prism. 15 cm 2 10 cm The cross section of the prism is shown as a shaded triangle. The area of the triangle is 15 cm 2. The length of the prism is 10 cm. Work out the volume of the prism The diagram shows a prism. 9.3 cm 2 10 cm The cross section of the prism is a triangle of area 9.3 cm 2. The length of the prism is 10 cm. Work out the volume of the prism. State the units of your answer.... Haringey Sixth Form Mathematics Department 6

7 Angles 10. N N Hospital Cinema 72 Art gallery The diagram shows the position of each of three buildings in a town. The bearing of the Hospital from the Art gallery is 072. The Cinema is due East of the Hospital. The distance from the Hospital to the Art gallery is equal to the distance from the Hospital to the Cinema. Work out the bearing of the Cinema from the Art gallery. Haringey Sixth Form Mathematics Department 7

8 11. D 62 y E F 64 G DE is parallel to FG. Find the size of the angle marked y.... (Total 1 mark) 12. D 72º 130º yº C E xº B A AC and BD are straight lines which cross at E. AD is parallel to BC. (a) (i) Find the size of the angle marked x. (ii) Give a reason for your answer. Haringey Sixth Form Mathematics Department 8

9 (b) (i) Find the size of the angle marked y. (ii) Give a reason for your answer. (Total 4 marks) 13. P A Q 108º B C x R D AB is parallel to CD. Explain why angle x is 72º. S (Total 2 marks) 14. (a) S xº 50º P Q R Haringey Sixth Form Mathematics Department 9

10 PQR is a straight line. SQ = SR. (i) Work out the size of the angle marked x... (ii) Give reasons for your answer (b) D 62º yº E F 64º G DE is parallel to FG. (i) Find the size of the angle marked y.... (ii) Give a reason for your answer.... (Total 2 marks) 15. Calculate the size of the exterior angle of a regular hexagon.... (Total 2 marks) Haringey Sixth Form Mathematics Department 10

11 Transformations 16. y A O x (a) On the grid, rotate triangle A 180 about O. Label your new triangle B. y B A O x Haringey Sixth Form Mathematics Department 11

12 Describe fully the single transformation which takes shape A onto shape B y 4 3 B 2 1 A C O x Shape A is rotated 90 anticlockwise, centre (0, 1), to shape B Shape B is rotated 90 anticlockwise, centre (0, 1), to shape C Shape C is rotated 90 anticlockwise, centre (0, 1), to shape D (a) Mark the position of Shape D (b) Describe the single transformation that takes shape C to shape A.... (Total 4 marks) Haringey Sixth Form Mathematics Department 12

13 19. y O x Enlarge the shaded triangle by a scale factor 2, centre 0. y P O x Haringey Sixth Form Mathematics Department 13

14 (a) On the grid, rotate the shaded shape P one quarter turn anticlockwise about O. Label the new shape Q. (3) (b) On the grid, translate the shaded shape P by 2 units to the right and 3 units up. Label the new shape R. (1) (Total 4 marks) 21. Triangle A and triangle B have been drawn on the grid. (a) Reflect triangle A in the line x = 3. Label this image C. (b) Describe fully the single transformation which will map triangle A onto triangle B... (Total 4 marks) Haringey Sixth Form Mathematics Department 14

15 Shape, space and measures (calculator section) 2D and 3D shapes 22. The diagram shows a solid object. (a) In the space below, sketch the front elevation from the direction marked with an arrow. (b) In the space below, sketch the plan of the solid object. (Total 4 marks) Haringey Sixth Form Mathematics Department 15

16 Area and Volume 23. Here is the net of a 3-D shape. P The net is folded to make the 3-D shape. Two other vertices meet at P. Mark each of these vertices with the letter P. (Total 2 marks) cm The diagram shows a semi-circle. The diameter of the semi-circle is 15 cm. Calculate the area of the semi-circle. Give your answer correct to 3 significant figures.... Haringey Sixth Form Mathematics Department 16

17 25. A can of drink is in the shape of a cylinder. The can has a radius of 4 cm and a height of 15 cm. 15 cm 4 cm Calculate the volume of the cylinder. Give your answer correct to 3 significant figures. 26. The diameter of a circle is 12 centimetres. (a) Work out the circumference of the circle. Give your answer, in centimetres, correct to 1 decimal place. 12 cm drawn accurately... cm Haringey Sixth Form Mathematics Department 17

18 The length of each diagonal of a square is 20 cm. (b) Work out the area of the square. 27. The diagram shows a trapezium of height 3 m. 2 m... cm 2 (Total 4 marks) 3 m 6 m Find the area of this trapezium State the units with our answer.... Haringey Sixth Form Mathematics Department 18

19 28. The diagram shows a cylinder with a height of 10 cm and a radius of 4 cm. (a) Calculate the volume of the cylinder. Give your answer correct to 3 significant figures.... (3) The cylinder is solid. (b) Calculate the total surface area of the cylinder. Give your answer correct to 3 significant figures.... (3) (Total 6 marks) Haringey Sixth Form Mathematics Department 19

20 Angles 29. A x 62 B C D Triangle ABC is isosceles, with AC = BC. Angle ACD = 62. BCD is a straight line. (a) Work out the size of angle x. x = x The diagram shows part of a regular octagon. (b) Work out the size of angle x. x = (3) (Total 5 marks) Haringey Sixth Form Mathematics Department 20

21 30. A 48 B 30 C D E x y F G BEG and CFG are straight lines. ABC is parallel to DEF. Angle ABE = 48. Angle BCF = 30. (a) (i) Write down the size of the angle marked x. x =... (ii) Give a reason for your answer.... (b) (i) Write down the size of the angle marked y. y =... (ii) Give a reason for your answer.... (Total 4 marks) 31. (a) Work out the size of each interior angle of a regular octagon. Haringey Sixth Form Mathematics Department 21

22 (3) The size of each exterior angle of a regular polygon is 30. (b) Work out the number of sides of the polygon. (Total 5 marks) 32. The size of each exterior angle of a regular polygon is 40. Work out the number of sides of the polygon. (Total 2 marks) Haringey Sixth Form Mathematics Department 22

23 33. B xº A 43º C Triangle ABC is isosceles. AB = BC Angle C = 43 (i) Work out the value of x. x =... (ii) Give reasons for your answer A B C 38º xº yº D E F G Haringey Sixth Form Mathematics Department 23

24 ABC is parallel to DEFG. BE = EF. Angle ABE = 38. (a) (i) Find the value of x. x =... (ii) Give a reason for your answer.... (b) Work out the value of y. y =... (Total 4 marks) Pythagoras Theorem 35. X 3.2 cm Y 1.7 cm Z XYZ is a right-angled triangle. XY = 3.2 cm. XZ = 1.7 cm. Calculate the length of YZ. Give your answer correct to 3 significant figures.. cm Haringey Sixth Form Mathematics Department 24

25 36. P 6 cm Q 4 cm R PQR is a right-angled triangle. PR = 6 cm. QR = 4 cm. Work out the length of PQ. Give your answer correct to 3 significant figures....cm 37. A 8 cm ABC is a right-angled triangle. AB = 8 cm, BC = 11 cm. B 11 cm C Calculate the length of AC. Give your answer correct to 3 significant figures. cm Haringey Sixth Form Mathematics Department 25