Number worksheet — GCSE Higher

1.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

2.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

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

4.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

5.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

6.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.

7.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

8.Write down the symbol that makes this statement true: −2/3 ___ −5/6

9.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

10.Which statement about the number 91 is correct?

11.Work out −(−3)⁴ + (−3)³

12.Write 90 as a product of its prime factors.

13.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

14.Work out the value of 6² − 4³.

15.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.