Number worksheet — GCSE Higher

1.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

2.Work out √144 − 2 × 3 + √25

3.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

4.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.

5.Work out −(−3)⁴ + (−3)³

6.Write ∛(x²) as a single power of x.

7.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.

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

9.Work out (−2)² − 3

10.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.

11.Write 0.325 as a fraction in its simplest form.

12.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.

13.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.

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

15.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.