Number worksheet — GCSE Higher

1.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.

2.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

3.Simplify ⁴√(16a⁸b¹²)

4.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

5.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

6.Write 60 as a product of its prime factors, using index notation.

7.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

8.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.

9.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

10.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.

11.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

12.√700 lies between which two consecutive integers?

13.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

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

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