Number worksheet — GCSE Higher

1.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

2.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

3.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.

4.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

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

6.Work out the reciprocal of (2 + 3)

7.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

8.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

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

10.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

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

12.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

13.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

14.Simplify (x⁻²)³, giving your answer as a fraction.

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