Geometry and measures worksheet — GCSE Higher

1.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.

2.A surveyor marks two fixed points A and B, with position vectors OA = a and OB = b (in km) from a base station O. A relay mast P is to be placed on the line AB such that AP : PB = 3 : 2. Express the vector OP in terms of a and b.

3.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

4.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.

5.Points P and Q have coordinates P(0, 0, 0) and Q(5, 7, 9) in a three-dimensional coordinate system, with all lengths in centimetres. Work out the distance PQ. Give your answer correct to 1 decimal place.

6.A plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?

7.Two hikers walk from a campsite A to a lookout B, a distance of 14 km on a bearing of 038°. From B they walk to a shelter C, a distance of 20 km on a bearing of 142°. Work out the direct distance from A to C. Give your answer to 1 decimal place.

8.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

9.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

10.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

11.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

12.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

13.In triangle ABC, AB = 9.4 cm, AC = 7.2 cm and angle BAC = 63°, the angle between them. Work out the area of triangle ABC. Give your answer to 1 decimal place.

14.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.

15.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.