Number worksheet — GCSE Higher

1.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

2.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

3.Simplify (y³)⁴, giving your answer as a single power of y.

4.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.

5.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

6.Work out √225 ÷ 3.

7.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

8.2/3 of an amount of money is £30. Work out the amount.

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

10.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.

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

12.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

13.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

14.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

15.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.