Number worksheet — GCSE Higher

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

2.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

3.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

4.Work out 3.7 × 24.

5.Work out the value of (√5)⁴

6.Estimate the value of √45, giving your answer to the nearest whole number.

7.Work out (−3) × 4 + 2 × (−5)

8.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

9.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

10.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

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

12.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

13.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.

14.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

15.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.