Number worksheet — GCSE Higher

1.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

2.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

3.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

4.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

5.Work out 4368 ÷ 12.

6.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

7.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

8.Simplify x⁷ × x⁴, giving your answer as a single power of x.

9.Write down the symbol that makes this statement true: −2/3 ___ −5/6

10.2/3 of an amount of money is £30. Work out the amount.

11.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

12.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

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

14.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

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