Number worksheet — GCSE Higher

1.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

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

3.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

4.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

5.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.

6.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

7.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

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

9.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

10.Work out 10% of 30% of £200.

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.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

13.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

14.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

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