Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

2.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

3.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

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

5.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

6.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

7.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?

8.A zip wire is fixed at an angle of 50° to the horizontal, running from a high platform down to the ground. The zip wire itself, from the platform to the ground, is 12 m long. Work out the horizontal distance covered by the zip wire. Give your answer correct to 1 decimal place.

9.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

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

11.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

12.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

13.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

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

15.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².