Number worksheet — GCSE Higher

1.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

2.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.

3.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

4.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

5.Work out the value of 2⁻⁴

6.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

7.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

8.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

9.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

10.Work out 100 − 4 × 5²

11.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

12.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

13.Which one of these statements is true?

14.Work out √3 × √12, giving your answer as an integer.

15.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾