Number worksheet — GCSE Higher

1.Work out (2/3)² + (1/2)². Give your answer as a fraction.

2.Write 0.005 in standard form.

3.Work out 4368 ÷ 12.

4.Work out ∛(−27) + ∛8

5.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

6.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

7.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

8.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

9.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.

10.Which statement about the number 91 is correct?

11.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

12.Work out the value of (√5)⁴

13.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

14.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

15.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.