Number worksheet — GCSE Higher

1.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

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

3.Work out (5 + 2) × 3²

4.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

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

6.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

7.Work out 6² − 4².

8.Write 0.35 as a fraction in its lowest terms.

9.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

10.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

11.Work out √144 − 2 × 3 + √25

12.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.

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

14.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

15.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.