Number worksheet — GCSE Higher

1.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

2.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

3.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

4.Simplify (3a²)² × (2a)³

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

6.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

7.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

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.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

11.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

12.Work out the value of (√5)⁴

13.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

14.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

15.Write 7/12 as a decimal, showing clearly which digit is recurring.