Geometry and measures worksheet — GCSE Foundation

1.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

2.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?

3.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

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

5.A regular nonagon has 9 sides. Work out the sum of its interior angles.

6.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

7.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

8.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.

9.An angle measures 108°. Write down the name given to an angle of this size.

10.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

11.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.

12.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

13.Each of these has an exact value. Write down the one whose value is the greatest.

14.The perimeter of a square is 20 cm. Work out the area of the square.

15.Work out the exact value of (cos 45°)² + (sin 45°)².