Number worksheet — GCSE Higher

1.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

2.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

3.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

4.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

5.Write down the reciprocal of 0.2

6.Write 12 as a product of its prime factors.

7.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

8.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

9.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

10.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

11.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

12.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

13.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

14.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.

15.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.