Geometry and measures worksheet — GCSE Foundation

1.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

2.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

3.Write down the exact value of cos 60°.

4.A cuboid-shaped shipping crate has a length of 12 m, a width of 5 m, and a volume of 360 m³. Work out the height of the crate, in metres.

5.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.

6.Write down the exact value of tan 45°.

7.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

8.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).

9.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

10.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

11.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

12.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.

13.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

14.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?

15.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.