Number worksheet — GCSE Higher

1.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

2.Given that 2⁵ = 32, work out 2⁶.

3.Work out the value of 6² − 4³.

4.Work out (−2)³ + (−3)² − (−4)

5.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.

6.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

7.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.

8.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

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

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

11.Work out −(−3)⁴ + (−3)³

12.Work out the value of √49 + ∛27

13.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

14.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

15.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.