Number worksheet — GCSE Higher

1.Write 200 as a product of its prime factors, using index notation.

2.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

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

4.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

5.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

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

8.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

9.Given that 2⁵ = 32, work out 2⁶.

10.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

11.Work out (−2)³ + (−3)² − (−4)

12.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

13.Work out 4368 ÷ 12.

14.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

15.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.