Number worksheet — GCSE Higher

1.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

2.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.

3.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

4.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

5.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

6.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

7.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

8.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

9.Work out √225 ÷ 3.

10.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

11.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

12.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

13.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?

14.Work out the value of 6² − 4³.

15.Work out 3.7 × 24.