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 sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
- 2.A laptop is bought for £600. Its value decreases by 20% after 1 year. Work out the value of the laptop after 1 year.
- 3.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.
- 4.A box holds 140 pens. 25% of the pens are red. Work out how many of the pens are red.
- 5.Write 0.25 as a percentage.
- 6.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.
- 7.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
- 8.Maya buys a vintage car for £15000. Its value is expected to increase by 4% each year for 2 years. She then plans to sell the car and use £2000 of the money from the sale to buy a trailer. Work out how much money she will have left after selling the car and buying the trailer.
- 9.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.
- 10.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.
- 11.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.
- 12.£3000 is invested in a savings account that pays 4% compound interest each year. Work out the value of the investment after 2 years.
- 13.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
- 14.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.
- 15.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.
- 16.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.
- 17.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
- 18.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.
- 19.Work out 2/5 of 45.
- 20.Work out 1/2 of 1/4 of 80.
- 21.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.
- 22.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.
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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