Number worksheet — GCSE Higher

1.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

2.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

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

4.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

5.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

6.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

7.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

8.Expand and simplify √3(2 + √12).

9.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

10.Simplify √8 + √18, giving your answer in the form k√2.

11.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

12.Simplify (x⁻²)³, giving your answer as a fraction.

13.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

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

15.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.