Number worksheet — GCSE Higher

1.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

2.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

3.Work out the value of √49 + ∛27

4.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

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

6.Write 5,000,000 in standard form.

7.Work out −4.5 + 2.8.

8.Work out ⁴√81

9.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

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

11.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

12.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

13.Write 5/6 as a decimal, showing clearly which digit recurs.

14.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

15.Work out 36 ÷ (2 × 3)