Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

2.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

3.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

4.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.

5.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

6.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

7.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

8.A hiker walks due west. What is the three-figure bearing for this direction?

9.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

10.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

11.A square tile has sides of length 6 cm. Work out the area of the tile.

12.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.

13.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

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

15.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.