2. Here are some triangles. (a) Write down the letter of the triangle that is. right-angled, ... (ii) isosceles. ... (2)

Transcription

1 Topic 8 Shapes

2 2. Here are some triangles. A B C D F E G (a) Write down the letter of the triangle that is (i) right-angled,... (ii) isosceles.... (2) Two of the triangles are congruent. (b) Write down the letters of these two triangles.... and... (1) (Total 3 marks)

3 3. Here are 8 shapes. A B C D E F G H (a) Write down the letters of two different pairs of congruent shapes.... and and... (2) (b) On the grid, show how the shaded shape will tessellate. You must draw at least 6 shapes. (2) (Total 4 marks)

4 3. 1 cm 1 cm (a) (i) Find the area of the shaded shape.... cm 2 (ii) Find the perimeter of the shaded shape.... cm (2) Here is a solid prism made from centimetre cubes. 1 cm 3 (b) Find the volume of the solid prism.... cm 3 (2) (4 marks) 4. A shaded shape is shown on the grid of centimetre squares. (a) Find the perimeter of the shaded shape....cm (1) (b) Find the area of the shaded shape....cm 2 (1) (2 marks)

5 1. Write down the mathematical name for each of these three different 3-D shapes. (i) (ii) (iii) 2. (i)... (ii)... (iii)... Here is a diagram of a cuboid. Write down the number of (i) faces... (ii) edges... (iii) vertices Write down the mathematical name of each of these 3-D shapes. (i) (ii) (i)... (ii)... (2 marks)

6 8. The diagrams show some solid shapes and their nets. An arrow has been drawn from one solid shape to its net. Draw an arrow from each of the other solid shapes to its net.

7 9. On the grid, show how this shape tessellates. You should draw at least 6 shapes. 10. On the grid, show how this kite will tessellate. You should draw at least 8 kites.

8 1. Here are 5 diagrams and 5 labels. In each diagram the centre of the circle is marked with a cross ( ). Match each diagram to its label. One has been done for you. Diagram Label Circle and tangent Circle and radius Circle and chord Circle and sector Circle and diameter

9 2. Here are some diagrams relating to a circle. Draw an arrow from each of the diagrams to its mathematical name. The arrow showing an arc is drawn for you. Arc Circle and diameter Circle and sector Circle and tangent Circle and segment

10 3. The radius of a circle is 3.60 m. Work out the area of the circle. Give your answer correct to 3 significant figures m Diagram NOT accurately drawn The diameter of a wheel on Harry s bicycle is 0.65 m. Calculate the circumference of the wheel. Give your answer correct to 2 decimal places. Diagram NOT accurately drawn m Diagram NOT accurately drawn The radius of a circle is 4 m. Work out the area of the circle. Give your answer correct to 3 significant figures....

11 9. 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 Diagram NOT drawn accurately Here is a tile in the shape of a semicircle. Diagram NOT accurately drawn 8 cm The diameter of the semicircle is 8 cm. Work out the perimeter of the tile. Give your answer correct to 2 decimal places.... cm cm Diagram NOT accurately drawn The radius of this circle is 8 cm. Work out the circumference of the circle. Give your answer correct to 2 decimal places.... cm

12 12. 6 cm 12 cm 12cm Diagram NOT accurately drawn A circle has a radius of 6 cm. A square has a side of length 12 cm. Work out the difference between the area of the circle and the area of the square. Give your answer correct to one decimal place.... (4 marks) 13. The top of a table is a circle. The radius of the top of the table is 50 cm. (a) Work out the area of the top of the table. cm 2 (2) The base of the table is a circle. The diameter of the base of the table is 40 cm. (b) Work out the circumference of the base of the table. cm (2) (4 marks)

13 14. 4 cm 8 cm 4 cm Diagram NOT accurately drawn The diagram shows two small circles inside a large circle. The large circle has a radius of 8 cm. Each of the two small circles has a diameter of 4 cm. (a) Write down the radius of each of the small circles.... cm (1) (b) Work out the area of the region shown shaded in the diagram. Give your answer correct to one decimal place.... cm 2 (4) (5 marks)

14 3. Here is a trapezium. 6 cm 5 cm 10 cm Diagram NOT accurately drawn Work out the area of the trapezium.... cm 2 (Total 2 marks) 4. The diagram shows a wall with a door in it. 4 m 3 m 1 m Diagram NOT accurately drawn 2 m Work out the shaded area. m 2 (3) (Total 3 marks)

15 6. 4 cm 2 cm 10 cm 4 cm 2 cm Diagram NOT accurately drawn 4 cm 2 cm 8 cm The diagram shows 3 small rectangles inside a large rectangle. The large rectangle is 10 cm by 8 cm. Each of the 3 small rectangles is 4 cm by 2 cm. Work out the area of the region shown shaded in the diagram. cm 2 (Total 3 marks)

16 7. 9cm 7cm 5cm 12cm Diagram NOT accurately drawn Work out the area of the shape.... cm 2 (Total 4 marks)

17 3. Here are the plan and front elevation of a prism. The front elevation shows the cross section of the prism. Plan Front elevation On the grid below, draw a side elevation of the prism. (3) (Total 3 marks)

18 4. The diagram shows a sketch of a solid object. The solid object is made from five centimetre cubes. Diagram NOT accurately drawn (a) On the grid of centimetre squares, draw the elevation of the solid object in the direction marked with an arrow. Elevation (2) (b) On the grid of centimetre squares, draw the plan of the solid object. Plan (2) (Total 4 marks)

19 1. (a) On the shape, draw all the lines of symmetry. (2) The shape below has rotational symmetry. (b) Write down the order of rotational symmetry.... (1) (Total 3 marks) 2. Here is a rectangle. (a) Draw all the lines of symmetry of this rectangle. (2) Here is a regular pentagon. (a) Write down the order of rotational symmetry of this regular pentagon.... (1)

20 4. Here are five shapes. Two of these shapes have only one line of symmetry. (a) Write down the letter of each of these two shapes.... and... (2) Two of these shapes have rotational symmetry of order 2 (b) Write down the letter of each of these two shapes.... and... (2) (Total 4 marks) 5. (a) This shape has rotational symmetry. Mark with a cross ( ) the centre of rotation. (1)

21 (b) Complete this shape so that it has rotational symmetry of order 4 (Total 2 marks) (1) 6. (a) Shade two more triangles to make a pattern with 1 line of symmetry. (b) Shade two more triangles to make a pattern with rotational symmetry of order 3 (1) (1) (Total 2 marks)

22 3. A Diagram NOT accurately drawn 8 cm B 11 cm C ABC is a right-angled triangle. AB = 8 cm, BC = 11 cm. Calculate the length of AC. Give your answer correct to 3 significant figures. cm 4. L Diagram NOT accurately drawn 3.7 m M 6.3 m N Angle MLN = 90. LM = 3.7 m. MN = 6.3 m. Work out the length of LN. Give your answer correct to 3 significant figures. LN =... m

23 7. A rectangular television screen has a width of 45 cm and a height of 34 cm. Diagram NOT accurately drawn Work out the length of the diagonal of the screen. Give your answer correct to the nearest centimetre.... cm (4 marks) 8. A 7 cm 7 cm B M 8 cm Diagram NOT accurately drawn C Work out the length, in centimetres, of AM. Give your answer correct to 2 decimal places. cm

24 9. A 2.1 m D 1.9 m 3.2 m B C ABCD is a trapezium. AD is parallel to BC. Angle A = angle B = 90. AD = 2.1 m, AB = 1.9 m, CD = 3.2 m. Diagram NOT accurately drawn Work out the length of BC. Give your answer correct to 3 significant figures. m (4 marks) 10. B 9 cm A 6 cm C Diagram NOT accurately drawn ABC is a right-angled triangle. AC = 6 cm. BC = 9 cm. Work out the length of AB. Give your answer correct to 3 significant figures.... cm

25 11. B 10cm A 20cm C Diagram NOT accurately drawn In triangle ABC, AB = 10 cm AC = 20 cm angle BAC = 90 Work out the length of BC. Give your answer correct to 3 significant figures. You must state the units in your answer (4 marks) 12. X 5.6 cm Y 10.5 cm Z Diagram NOT accurately drawn In the triangle XYZ XY = 5.6 cm YZ = 10.5 cm angle XYZ = 90 Work out the length of XZ.... cm

26 13. ABCD is a trapezium. AD = 10 cm AB = 9 cm DC = 3 cm Angle ABC = angle BCD = 90 Calculate the length of AC. Give your answer correct to 3 significant figures. 14. A ladder is 6 m long. The ladder is placed on horizontal ground, resting against a vertical wall.... cm ( 5 marks) The instructions for using the ladder say that the bottom of the ladder must not be closer than 1.5 m from the bottom of the wall. How far up the wall can the ladder reach? Give your answer correct to 1 decimal place.... m (4 marks)

27 3. Here is a cuboid. 5 cm 6 cm 10 cm What is the total surface area of the cuboid? State the units with your answer. Diagram NOT accurately drawn. (Total 4 marks) 4. Work out the surface area of the triangular prism. State the units with your answer.. (Total 4 marks)

28 9. Diagram NOT accurately drawn Work out the total surface area of the L-shaped prism. State the units with your answer.... (Total 4 marks)

29 1. Here is a cuboid. Work out the volume of the cuboid.... *2. The diagram shows two fish tanks, each in the shape of a cuboid. Diagram NOT accurately drawn 35 cm A B 30 cm 95 cm 65 cm 35 cm 45 cm Finley fills both fish tanks with water. Which fish tank holds the most water? You must show all your calculations. (4 marks)

30 3. The diagram shows a prism. Work out the volume of the prism....cm 3 (4 marks)

31 8. The diagram shows a triangular prism. The cross-section of the prism is a trapezium. The lengths of the parallel sides of the trapezium are 8 cm and 6 cm. The distance between the parallel sides of the trapezium is 5 cm. The length of the prism is 20 cm. Work out the volume of the prism.... (4 marks)

32 1. 4 cm 24 cm Diagram NOT accurately drawn A cylinder has a height of 24 cm and a radius of 4 cm. Work out the volume of the cylinder. Give your answer correct to 3 significant figures. cm 3 (Total 2 marks)

33 cm 1.2 cm Diagram NOT accurately drawn The diagram shows a piece of wood. The piece of wood is a prism of length 350 cm. The cross-section of the prism is a semi-circle with diameter 1.2 cm. Calculate the volume of the piece of wood. Give your answer correct to 3 significant figures. cm 3 (Total 4 marks)

34 6. 18 cm 12 cm Diagram NOT accurately drawn The diagram shows a solid cylinder. The cylinder has a diameter of 12 cm and a height of 18 cm. Calculate the total surface area of the cylinder. Give your answer correct to 3 significant figures. cm 2 (Total 4 marks)

35 1. Shapes ABCD and EFGH are mathematically similar. C F cm G B 7.5 cm 120 E 6 cm H A 9 cm D Diagrams NOT accurately drawn (a) Calculate the length of BC.... cm (2) (b) Calculate the length of EF.... cm (2) (Total 4 marks)

36 3. Triangles ABC and DEF are similar. AB = 4 cm. AC = 9 cm. DE = 6 cm. EF = 10.5 cm. (a) Work out the length of DF. (2)... cm (b) Work out the length of BC. (2)... cm (Total 4 marks)

37 5. Triangle ABC is similar to triangle ADE. AC = 15 cm. CE = 6 cm. BC = 12.5 cm. Work out the length of DE.... cm (Total 3 marks)

38 *6. Pictures NOT accurately drawn A 20 Euro note is a rectangle 133 mm long and 72 mm wide. A 500 Euro Note is a rectangle 165 mm long and 82 mm wide. Show that the two rectangles are not mathematically similar. (Total 3 marks)

39 2. 7 cm C Diagram NOT accurately drawn A 43 8 cm B ABC is a triangle. AB = 8 cm. AC = 1 cm. Angle A = 43. In the space below, make an accurate drawing of triangle ABC.

40 4. In the space below, use ruler and compasses to construct an equilateral triangle with sides of length 6 centimetres. You must show all your construction lines.

41 5. Use the ruler and compasses to construct the perpendicular to the line segment AB that passes through the point P. You must show all construction lines. B P A 6. Use ruler and compasses to construct the bisector of angle PQR. You must show all your construction lines.

42 1. Diagram NOT accurately drawn ABC is a right-angled triangle. Angle B = 90. Angle A = 36. AB = 8.7 cm. Work out the length of BC. Give your answer correct to 3 significant figures.... cm 2. Calculate the value of x. Give your answer correct to 3 significant figures....

43 5. LMN is a right-angled triangle. MN = 9.6 cm. LM = 6.4 cm. Calculate the size of the angle marked x. Give your answer correct to 1 decimal place Diagram NOT accurately drawn Work out the value of x. Give your answer correct to 1 decimal place. x =...

44 10. The diagram shows a quadrilateral ABCD. AB = 16 cm. AD = 12 cm. Angle BCD = 40. Angle ADB = angle CBD = 90. Calculate the length of CD. Give your answer correct to 3 significant figures.... cm (5 marks)

45 11. B 7 cm 12 cm A 65º D C Diagram NOT accurately drawn ABC is a triangle. ADC is a straight line with BD perpendicular to AC. AB = 7 cm. BC = 12 cm. Angle BAD = 65. Calculate the length of AC. Give your answer correct to 3 significant figures.... cm (6 marks)