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.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.

3.2/3 of an amount of money is £30. Work out the amount.

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

5.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

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

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

8.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

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.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

11.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.

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

13.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

14.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

15.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.