Number worksheet — GCSE Higher

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

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

3.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

4.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

5.Work out 5/6 × 2/9, giving your answer in its simplest form.

6.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

7.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.

8.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

9.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

10.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

11.Simplify (x⁻²)³, giving your answer as a fraction.

12.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

13.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

14.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

15.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.