Geometry and measures worksheet — GCSE Foundation

1.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

2.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

3.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.

4.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.

5.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

6.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.

7.Work out the exact value of sin 45° × cos 45°.

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

9.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

10.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

11.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

12.A jug holds 750 ml of water. Work out what fraction of a litre this is.

13.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

14.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

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