22 questions on percentage change, reverse percentages, simple and compound interest, and depreciation.
💷 Percentages and compound interest
Percentages appear on all three papers and in more contexts than any other single topic — prices, wages, interest, VAT, population, depreciation. This sheet covers the whole of it in order. It begins with percentage of an amount and percentage change, including finding the percentage rather than applying it; moves to multipliers, which make everything after this easier; then to reverse percentages, where you are given the value after the change and asked for the original, and where subtracting instead of dividing is the commonest error in the topic; then to simple interest, compound interest and depreciation, where the multiplier is raised to a power rather than multiplied by the number of years. The last few questions mix the types without labelling them, because on the paper they are not labelled either.
- 1.A pack contains 20 stickers. Noah gives 1/5 of the pack to his sister. Work out how many stickers he gives away.
- 2.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.
- 3.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.
- 4.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
- 5.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.
- 6.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.
- 7.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.
- 8.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.
- 9.A company's profit this year is 130% of last year's profit. Last year's profit was £40,000. Work out this year's profit.
- 10.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
- 11.A laptop costs £720. A carrying case for it costs 1/9 of the price of the laptop. Work out the cost of the carrying case.
- 12.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
- 13.Work out 1/2 of 1/4 of 80.
- 14.2/3 of an amount of money is £30. Work out the amount.
- 15.A population of penguins on an island is 2400. The population is predicted to grow by 7% each year. Work out the predicted population after 2 years, to the nearest whole number.
- 16.Work out 50% of 60.
- 17.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.
- 18.Work out 35% of 180.
- 19.Write 3/4 as a percentage.
- 20.A company had 8000 employees. The number of employees decreased by 5% in the first year, and then increased by 5% in the second year. Work out the number of employees at the end of the second year, to the nearest whole number.
- 21.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
- 22.The value of a motorbike falls by 12% each year. The motorbike is worth £3200 now. Write down the calculation that gives its value after 3 years.
What is on this worksheet?
The sheet holds 22 questions drawn from the MathsUK bank — the content areas covered: Ratio, proportion and rates of change, Number (statements R9, R16, N12). It is pitched at GCSE Foundation and takes about 40 minutes to work through in full. It is built for independent practice, with full answers at the end for self-marking.
How to use the sheet well
- Print it or open it on screen — both work. Printing is A4; the screen view fits phones and tablets.
- Do all 22 questions before checking — about 40 minutes is the guide, but there is no time pressure.
- Check the answers — press “Show answers” or print the answer page separately.
- Redo the questions you got wrong — twice as effective as doing 22 fresh ones.
- “New questions” — builds a fresh sheet on the same statements, so you can practise again without repeats.
Why this sheet helps
MathsUK worksheets use questions graded by difficulty and a fair spread of correct-answer positions (the answer is not always (a)) — so the student really has to think about each question rather than guess a pattern. Every question is tagged to a DfE content statement and checked before it enters the bank. The answers come with a step-by-step explanation, not just a value — so a wrong answer becomes a lesson.
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