Number worksheet — GCSE Higher

1.Last year a company made a profit of £5,200,000. Write this amount in standard form.

2.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

3.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

4.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

5.Work out the value of √(16 + 9)

6.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

7.Work out 36 ÷ (2 × 3)

8.Write 90 as a product of its prime factors.

9.Work out (−36) ÷ (−6) × 2

10.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.

11.Work out 100 − 4 × 5²

12.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

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

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

15.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.