Number worksheet — GCSE Higher

1.£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.

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

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

4.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.

5.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

6.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

7.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

8.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

9.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

10.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.

11.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

12.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

13.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

14.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

15.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.