Number worksheet — GCSE Higher

1.Simplify (3a²)² × (2a)³

2.Work out 3.7 × 24.

3.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

4.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

5.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.

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

7.Work out the value of (1/3)⁻²

8.Work out the value of 6² − 4³.

9.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

10.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

11.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

12.Work out (−2)³ + (−3)² − (−4)

13.The rainfall in a town during April is recorded as 62.4 mm, correct to 1 decimal place. Write down the error interval for the actual rainfall, r mm.

14.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

15.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.