Number worksheet — GCSE Higher

1.Simplify (y³)⁴, giving your answer as a single power of y.

2.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

3.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

4.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

5.Work out 36 ÷ (2 × 3)

6.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

7.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.

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

9.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

10.Find the missing number: 17 × ▢ = 391

11.Work out (−36) ÷ (−6) × 2

12.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

13.Work out 6² − 4².

14.Write 0.005 in standard form.

15.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.