Geometry and measures worksheet — GCSE Foundation

1.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

2.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?

3.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

4.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.

5.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.

6.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.

7.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

8.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.

9.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

10.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

11.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?

12.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

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

14.An angle is measured with a protractor as 47°. What type of angle is this?

15.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?