Number worksheet — GCSE Higher

1.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.

2.Work out √144 − 2 × 3 + √25

3.Find the missing number: ▢ ÷ 15 = 24

4.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

5.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

6.Round 592.5 to the nearest 10.

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

8.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

9.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

10.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

11.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

12.Given that 2⁵ = 32, work out 2⁶.

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

14.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

15.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.