Geometry and measures worksheet — GCSE Foundation

1.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.

2.Work out the exact value of (cos 45°)² + (sin 45°)².

3.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.

4.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

5.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

6.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

7.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

8.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

9.Write down which one of these statements about quadrilaterals is true.

10.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?

11.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?

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

13.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

14.A tank holds 3.2 m³ of water. Work out this volume in litres.

15.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.