Number worksheet — GCSE Higher

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

2.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

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

4.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.

5.Write 0.325 as a fraction in its simplest form.

6.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

7.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

8.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

9.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

10.A charity raffle sells 240 tickets at £1.85 each. 40% of the money raised is given to a local hospital. Work out how much money the hospital receives.

11.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

13.Write ∛(x²) as a single power of x.

14.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

15.Simplify 2³ × 2⁴, giving your answer as a single power of 2.