Number worksheet — GCSE Higher

1.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

2.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

3.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

4.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

5.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

6.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

7.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

8.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

9.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

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

11.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

12.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.

13.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

14.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

15.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.