Geometry and measures worksheet — GCSE Foundation

1.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

2.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

3.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

4.Two similar flags have widths in the ratio 2 : 5. The width of the smaller flag is 8 cm. Work out the width of the larger flag.

5.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

6.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

7.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.

8.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).

9.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

10.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

11.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?

12.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

13.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.

14.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

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