Geometry and measures worksheet — GCSE Foundation

1.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

2.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.

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

4.How many vertices does a square-based pyramid have?

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

6.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

7.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

8.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

9.Write down how many right angles a rectangle has.

10.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

11.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

12.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

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

14.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

15.Work out the distance between the points (−3, 4) and (5, −2).