Number worksheet — GCSE Higher

1.Simplify (3a²)² × (2a)³

2.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

3.Work out √(4 × 9)

4.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

5.√700 lies between which two consecutive integers?

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

7.Work out ∛64.

8.Work out √3 × √12, giving your answer as an integer.

9.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

10.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

11.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

12.Work out (−36) ÷ (−6) × 2

13.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

15.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.