Geometry and measures worksheet — GCSE Higher

1.A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.

2.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.

3.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

4.Point P has coordinates (4, 2). P is rotated 90° clockwise about the point (1, 1), and the image is then reflected in the line x = 1. Work out the coordinates of the final image of P.

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

6.Triangle A has vertices (2, 1), (5, 1) and (2, 4). It is translated by the vector (−3, 2) and the image is then reflected in the x-axis. Work out the coordinates of the image of (5, 1).

7.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.

8.A circular table mat has diameter 20 cm. Yasmin has a 70 cm length of ribbon and sews it around the edge of the mat with no overlap. Using π = 3.14, work out how much ribbon is left over after going around the mat once.

9.In triangle ABC, AB = 5 cm, BC = 3 cm and AC = 7 cm. Work out the size of angle ABC.

10.A model of a bridge is built to a scale where every length on the model is 1/240 of the matching length on the real bridge. A support beam on the model measures 3.6 cm. Work out the length of the real support beam, giving your answer in metres.

11.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

12.Two bronze statues are geometrically similar and made from the same solid bronze. Their heights are 30 cm and 45 cm. The smaller statue has a mass of 12 kg. Work out the mass of the larger statue, in kg.

13.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

14.Two similar model cars have a length scale factor of 2 from the small model to the large model. Priya works out that the area scale factor is 2² = 4, and then says the volume scale factor must also be 4, since that is the number she just calculated. Is Priya correct?

15.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.