Number worksheet — GCSE Higher

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

2.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

3.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.

4.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

5.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

6.Write down the reciprocal of 0.2

7.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

8.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

9.Write 5,000,000 in standard form.

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.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

12.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

13.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

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

15.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.