Geometry and measures worksheet — GCSE Higher

1.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

2.A flagpole is 12 m tall. Freya stands 9 m from the base of the flagpole on level ground. Work out the angle of elevation of the top of the flagpole from where Freya stands. Give your answer correct to 1 decimal place.

3.A tent frame forms a triangle ABC, where AB = 3.5 m is a sloping pole, BC = 2.8 m is the base and AC = 4.2 m is the guy rope. Work out the size of angle ABC, between the pole and the base. Give your answer to 1 decimal place.

4.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

5.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.

6.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?

7.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

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

9.A ship leaves port P and sails 24 km on a bearing of 040° to a buoy Q. It then sails 31 km on a bearing of 115° to a lighthouse R. Work out the direct distance from P to R. Give your answer to 1 decimal place.

10.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

11.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

12.In triangle ABC, AB = 8 cm, AC = 7 cm and the area of the triangle is 24 cm². Given that angle BAC is acute, work out the size of angle BAC. Give your answer to 1 decimal place.

13.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.

14.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

15.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?