Geometry and measures worksheet — GCSE Higher

1.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

2.A trapezium has vertices (0, 2), (4, 2), (3, 5) and (1, 5). It is rotated 180° about the point (2, 2), and the image is then translated by the vector (1, −5). Work out the coordinates of the image of (0, 2).

3.A scale drawing uses a scale of 1 : 60. A path on the drawing is measured as 9.8 cm long. What is the real length of the path, in metres, to 1 decimal place?

4.Points A, B, C and D lie on a circle with centre O, in that order around the circle, and AC is a diameter. Which of the following circle facts does NOT apply to this diagram?

5.In triangle ABC, AB = 9 cm, AC = 6 cm and angle BAC = 110°. Work out the length of BC. Give your answer to 1 decimal place.

6.A triangular field ABC is to be fenced all the way round. AB = 45 m, AC = 38 m and angle BAC = 110°. Fencing costs £6.50 per metre. Work out the total cost of the fencing. Give your answer to the nearest penny.

7.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

8.Two cylindrical storage tins are geometrically similar. The smaller tin has height 4 cm and the larger tin has height 6 cm. Work out the ratio of the surface area of the smaller tin to the surface area of the larger tin, giving your answer in the form a : b in its simplest form.

9.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.

10.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

11.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.

12.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.

13.A stage designer is building a triangular platform ABC for a school play. AB = 11.5 m, AC = 8.2 m and angle BAC = 72°, the angle between them. The flooring for the platform costs £15.80 per square metre. Work out the total cost of the flooring, to the nearest pound.

14.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

15.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.