Number worksheet — GCSE Higher

1.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

2.Work out the value of 6² − 4³.

3.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

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

5.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

6.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

7.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.

8.Work out 36 ÷ (2 × 3)

9.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

10.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

11.Write 12 as a product of its prime factors.

12.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

14.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

15.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.