Geometry and measures worksheet — GCSE Foundation

1.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

2.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

3.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

4.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

5.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.

6.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

7.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

8.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

9.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?

10.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

11.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?

12.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.

13.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

14.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.

15.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?