Number worksheet — GCSE Higher

1.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

2.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.

3.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

4.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

5.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

6.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.

7.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

8.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

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

10.Work out ⁴√16

11.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

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

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

14.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.

15.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.