Geometry and measures worksheet — GCSE Foundation

1.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

2.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

3.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

4.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

5.Work out the distance between the points (−3, 4) and (5, −2).

6.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?

7.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

8.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

9.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

10.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

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

12.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

13.In triangle ABC, point D lies on side AB and point E lies on side AC, so that DE is parallel to BC. AD = 3 cm, DB = 6 cm and DE = 4 cm. Work out the length of BC.

14.How many edges does a triangular prism have?

15.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?