Number worksheet — GCSE Higher

1.Write 12 as a product of its prime factors.

2.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

3.Find the missing number: ▢ ÷ 15 = 24

4.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

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

6.Work out (5 + 2) × 3²

7.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

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

9.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

10.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

11.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

12.Write 0.325 as a fraction in its simplest form.

13.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.

14.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

15.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.