Number worksheet — GCSE Higher

1.Simplify x⁷ × x⁴, giving your answer as a single power of x.

2.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

3.Work out 3 + 4 × (−2).

4.Work out −4.5 + 2.8.

5.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

6.Work out 100 − 4 × 5²

7.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

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

9.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

10.Write 0.06 as a fraction in its simplest form.

11.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

12.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

13.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

14.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.

15.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.