Geometry and measures worksheet — GCSE Foundation

1.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

2.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

3.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

4.Write down the term for the distance all the way around the edge of a circle.

5.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

6.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

7.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?

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

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

10.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

11.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.

12.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

13.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

14.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

15.Which of the following is NOT one of the four basic conditions used to prove two triangles are congruent?