Number worksheet — GCSE Higher

1.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

2.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.

3.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

4.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

5.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

6.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

7.Work out (−36) ÷ (−6) × 2

8.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

9.Write down the symbol that makes this statement true: −2/3 ___ −5/6

10.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

11.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

12.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

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

14.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.

15.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56