Geometry and measures worksheet — GCSE Foundation

1.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

2.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

3.Write down the name given to a triangle whose three sides are all the same length.

4.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

5.Write down the exact value of sin 60°.

6.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

7.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

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

9.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

10.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

11.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?

12.Write down the exact value of sin 0°.

13.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

14.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?

15.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.