Number worksheet — GCSE Higher

1.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

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

3.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

4.Work out ⁴√16

5.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

6.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

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

8.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.

9.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

10.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.

11.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

12.Simplify √8 + √18, giving your answer in the form k√2.

13.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

14.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

15.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.