Number worksheet — GCSE Higher

1.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

2.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

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.

5.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

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

8.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

9.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

10.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

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

12.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

13.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

14.Work out 3.7 × 24.

15.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.