Number worksheet — GCSE Higher

1.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

2.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.

3.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.

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

5.Work out 35% of 180.

6.2/3 of an amount of money is £30. Work out the amount.

7.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

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

9.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.

10.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

11.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.

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

13.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.

14.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

15.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?