Number worksheet — GCSE Higher

1.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

2.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

3.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

4.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

5.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

6.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

7.Work out 3.7 × 24.

8.Work out (−2)² − 3

9.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

10.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

11.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

12.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

13.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

14.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

15.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.