Number worksheet — GCSE Higher

1.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

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.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

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

5.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

6.Work out ∛64.

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

8.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

9.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

10.Simplify x⁷ × x⁴, giving your answer as a single power of x.

11.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.

12.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

13.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

14.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

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