Number worksheet — GCSE Higher

1.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

2.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?

3.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

4.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.

5.Write 5,000,000 in standard form.

6.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

7.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

8.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

9.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

10.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

11.Simplify x⁶ ÷ x²

12.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

13.Work out 6² − 4².

14.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

15.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.