Number worksheet — GCSE Higher

1.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

2.Work out the value of √49 + ∛27

3.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

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

6.Simplify x⁶ ÷ x²

7.Write 60 as a product of its prime factors, using index notation.

8.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

9.Work out 3³ + 2⁴.

10.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

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

12.After a price increase of 10%, a laptop costs £330. Work out the original price.

13.Given that 2⁵ = 32, work out 2⁶.

14.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

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