Geometry and measures worksheet — GCSE Foundation

1.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

2.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

3.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.

4.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

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

6.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

7.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

8.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.

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

10.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

11.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

12.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

13.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

14.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

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