Number worksheet — GCSE Higher

1.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

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.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

4.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.

5.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

6.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

7.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.

8.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.

9.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

10.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

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

12.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

13.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.

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

15.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.