Geometry and measures worksheet — GCSE Foundation

1.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

2.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

3.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

4.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

5.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

6.A garden water trough is a prism whose cross-section is a right-angled triangle with base 40 cm and height 30 cm. The trough is 120 cm long. Work out the volume of water needed to fill the trough completely.

7.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?

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

9.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?

10.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.

11.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.

12.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).

13.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

14.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

15.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.