Number worksheet — GCSE Higher

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

2.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

3.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

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

5.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

6.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

7.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

8.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

9.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.

10.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

11.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

12.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

13.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

14.Round 0.006482 to 2 significant figures.

15.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³