Geometry and measures worksheet — GCSE Foundation

1.A hiker walks due west. What is the three-figure bearing for this direction?

2.A submarine travels due south. What is the three-figure bearing for this direction?

3.Work out the exact value of tan 30° + tan 30°.

4.Write down the number of lines of symmetry a rhombus has.

5.How many vertices does a cylinder have?

6.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

7.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

8.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

9.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.

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

11.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

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

13.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.

14.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

15.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.