Number worksheet — GCSE Higher

1.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

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

3.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

4.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

5.Given that 2⁵ = 32, work out 2⁶.

6.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

7.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

8.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

9.Work out the exact value of √(2² + 3²)

10.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

11.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

12.Write down the symbol that makes this statement true: −2/3 ___ −5/6

13.Simplify ⁴√(16a⁸b¹²)

14.Write 0.36 as a fraction in its simplest form.

15.Simplify x⁶ ÷ x²