Number worksheet — GCSE Higher

1.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.

2.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

3.Work out the value of 2⁻⁴

4.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

5.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.

6.Which one of these statements is true?

7.Write 60 as a product of its prime factors, using index notation.

8.Expand and simplify √3(2 + √12).

9.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

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.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

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

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

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

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