Number worksheet — GCSE Higher

1.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

2.Work out √3 × √12, giving your answer as an integer.

3.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

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

5.Work out 36 ÷ (2 × 3)

6.Write 0.325 as a fraction in its simplest form.

7.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.

8.Work out the value of √49 + ∛27

9.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

10.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

11.Simplify (3a²)² × (2a)³

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

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

14.Work out √(4 × 9)

15.Work out 3³ + 2⁴.