Number worksheet — GCSE Higher

1.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

2.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

3.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

4.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

5.Work out 100 − 4 × 5²

6.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

7.Work out 35% of 180.

8.Work out √25 + 4² − 12 ÷ 3

9.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

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

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

12.Work out √3 × √12, giving your answer as an integer.

13.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

14.Find the missing number: ▢ ÷ 15 = 24

15.Write 0.06 as a fraction in its simplest form.