Number worksheet — GCSE Higher

1.Given that 2⁵ = 32, work out 2⁶.

2.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

3.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

4.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

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.Write 60 as a product of its prime factors, using index notation.

7.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.

8.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

9.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

10.Work out √(4 × 9)

11.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

12.Work out 10% of 30% of £200.

13.Work out ⁴√81

14.Work out −4.5 + 2.8.

15.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.