Number worksheet — GCSE Higher

1.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.

2.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

3.Simplify (x⁻²)³, giving your answer as a fraction.

4.Simplify x⁶ ÷ x²

5.Work out (−3) × 4 + 2 × (−5)

6.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.

7.Work out ∛(−27) + ∛8

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

9.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

10.Work out 5/6 × 2/9, giving your answer in its simplest form.

11.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

12.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

13.Which of these decimals lies between 1/4 and 2/5?

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

15.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.