Number worksheet — GCSE Higher

1.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

2.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.

3.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.

4.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

5.2/3 of an amount of money is £30. Work out the amount.

6.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.

7.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

8.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

9.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

10.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

11.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

12.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

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

14.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

15.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.