Number worksheet — GCSE Higher

1.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

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

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

4.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

5.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

6.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?

7.Work out (−3) × 4 + 2 × (−5)

8.2/3 of an amount of money is £30. Work out the amount.

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

10.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.

11.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

12.Write 7/12 as a decimal, showing clearly which digit is recurring.

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

14.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.

15.4ˣ = 64. Work out the value of x.