Number worksheet — GCSE Higher

1.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

2.Write ∛(x²) as a single power of x.

3.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

4.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

5.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.

6.Simplify x⁷ × x⁴, giving your answer as a single power of x.

7.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

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

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

10.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

11.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

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

13.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

14.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

15.Work out the value of 6² − 4³.