Geometry and measures worksheet — GCSE Foundation

1.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².

2.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

3.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?

4.Work out the exact value of cos 0° − sin 30°.

5.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

6.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

7.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

8.In geometry, which of the following best describes a 'plane'?

9.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.

10.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. Give your answer to the nearest whole number of cubic centimetres.

11.The diagram shows the plan of the base layer of a solid built from identical cubes. A second layer of cubes is added on top, filling the entire base layer to a height of 2 cubes everywhere. Work out how many squares are visible in the plan view of this solid.

12.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.

13.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

14.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

15.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.