Number worksheet — GCSE Higher

1.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

2.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

3.√700 lies between which two consecutive integers?

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

6.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

7.Work out 5/6 × 2/9, giving your answer in its simplest form.

8.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

9.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.

10.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

11.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

12.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

13.Write 0.06 as a fraction in its simplest form.

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

15.Work out 36 ÷ (2 × 3)