Number worksheet — GCSE Higher

1.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

2.Simplify x⁷ × x⁴, giving your answer as a single power of x.

3.Work out (−6) + (−4) × 3

4.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.

5.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

6.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

7.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

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

9.Work out the value of (1/3)⁻²

10.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

11.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

12.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

13.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

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.