Number worksheet — GCSE Higher

2.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.

3.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.

4.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

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

6.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

7.Work out 10% of 30% of £200.

8.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

9.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

10.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

11.Round 0.006482 to 2 significant figures.

12.A charity raffle sells 240 tickets at £1.85 each. 40% of the money raised is given to a local hospital. Work out how much money the hospital receives.

13.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

14.Work out 35% of 180.

15.Which of these is written correctly in standard form?