Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

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

3.a is the column vector with top number 3 and bottom number −2. b is the column vector with top number −1 and bottom number 5. Work out 2a + b, giving your answer as a column vector in the form (top, bottom).

4.Write down the exact value of sin 45°.

5.What does the statement AB = CD mean, where A, B, C and D are all points?

6.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

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

8.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?

9.A cube has all of its edges the same length. How many planes of symmetry does it have?

11.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

12.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

13.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?

14.In this question, a curved surface counts as a face. How many faces does a sphere have?

15.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.