Number worksheet — GCSE Higher

1.Work out ⁴√16

2.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

3.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

4.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

5.Work out 3³ + 2⁴.

6.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

7.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

8.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

9.Write 0.06 as a fraction in its simplest form.

10.Write 0.005 in standard form.

11.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

12.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.

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

14.Work out the value of (1/3)⁻²

15.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.