Number worksheet — GCSE Higher

1.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.

2.Given that 2⁵ = 32, work out 2⁶.

3.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

4.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

5.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

6.Write 5/6 as a decimal, showing clearly which digit recurs.

7.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

8.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.

9.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.

10.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

11.Work out ∛(−27) + ∛8

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

13.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

14.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

15.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.