Number worksheet — GCSE Higher

1.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.

2.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

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

4.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

5.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

6.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

7.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

8.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

9.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.

10.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

11.A café orders 340 bread rolls at 24p each and 85 cakes at £1.35 each. Work out the total cost of the order.

12.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.

13.After a price increase of 10%, a laptop costs £330. Work out the original price.

14.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.

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