Geometry and measures worksheet — GCSE Higher

1.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.

2.In triangle ABC, BC = 8 cm, AC = 10 cm and angle BAC = 40°. Given that angle ABC is acute, work out its size. Give your answer to 1 decimal place.

3.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.

4.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

5.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

6.Which of these statements about solving a triangle is correct?

7.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

8.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

9.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

10.A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.

11.A drone flies from base station D on a bearing of 065° for 14 km to a checkpoint E. At E it changes course and flies on a bearing of 165° for 20 km to a delivery point F. Work out the direct distance from D to F. Give your answer to 1 decimal place.

12.Two similar company logos are printed at different sizes. The area of the larger logo is 2.25 times the area of the smaller logo. Work out the length scale factor from the smaller logo to the larger logo.

13.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.

14.In triangle ABC, AB = 9 cm, AC = 6 cm, and angle BAC = 65°. Work out the length of BC. Give your answer to 1 decimal place.

15.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.