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.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

3.Simplify (x⁻²)³, giving your answer as a fraction.

4.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.

5.Work out ⁴√81

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

7.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

8.Work out √25 + 4² − 12 ÷ 3

9.Round 0.006482 to 2 significant figures.

11.Work out the exact value of √(2² + 3²)

12.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.

13.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

14.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

15.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.