Number worksheet — GCSE Higher

1.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

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

3.Estimate the value of √45, giving your answer to the nearest whole number.

4.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

5.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.

6.Simplify (3a²)² × (2a)³

7.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

8.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

9.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

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

11.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

12.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

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

14.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

15.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.