Number worksheet — GCSE Higher

1.Round 592.5 to the nearest 10.

2.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

3.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

4.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.

5.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

6.Work out √144 − 2 × 3 + √25

7.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

8.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

9.Last year a company made a profit of £5,200,000. Write this amount in standard form.

10.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

11.Find the missing number: 17 × ▢ = 391

12.Work out 6² − 4².

13.Work out (5 + 2) × 3²

14.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

15.Simplify (3a²)² × (2a)³