Geometry and measures worksheet — GCSE Foundation

1.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

2.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

3.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?

4.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?

5.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

6.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

7.A children's slide is built as a right-angled triangle: the vertical ladder side is 2.4 m, the horizontal base along the ground is 3.2 m, and the sloping slide is the third side. Work out the exact length of the sloping slide.

8.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

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

10.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

11.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?

12.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?

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

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.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.