Number worksheet — GCSE Foundation

1.Which of these decimals lies between 1/4 and 2/5?

2.4ˣ = 64. Work out the value of x.

3.Simplify (y³)⁴, giving your answer as a single power of y.

4.A café offers 3 types of soup and 4 types of bread roll. Work out how many different combinations of one soup and one bread roll are possible.

5.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

6.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.

7.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

8.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

9.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

10.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.

11.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

12.Work out 3 + 4 × 2²

13.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

14.The length of a nail is 12 cm, correct to the nearest centimetre. Using L for the length of the nail in centimetres, write down the error interval for L.

15.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.