Number worksheet — GCSE Higher

1.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

2.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

3.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

4.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

5.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.

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

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

8.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

9.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

10.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

11.Work out the value of (√5)⁴

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

13.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

14.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

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