Number worksheet — GCSE Higher

1.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.

2.Work out ∛64.

3.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

4.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

5.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.

6.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

7.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

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

9.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

10.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

11.Work out 35% of 180.

12.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.

13.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

14.√700 lies between which two consecutive integers?

15.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.