Number worksheet — GCSE Higher

1.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

2.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

3.Write 60 as a product of its prime factors, using index notation.

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

5.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

6.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

7.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

8.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

9.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.

10.Work out the value of √49 + ∛27

11.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

12.Write 200 as a product of its prime factors, using index notation.

13.Work out the value of (1/3)⁻²

14.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

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