Number worksheet — GCSE Higher

1.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.

2.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.

3.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

4.Work out 3³ + 2⁴.

5.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

6.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

7.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

8.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

9.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

10.Work out ∛64.

11.Work out the value of √49 + ∛27

12.Work out 36 ÷ (2 × 3)

13.Simplify (3a²)² × (2a)³

14.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

15.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.