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Percentage Change - Edexcel GCSE Higher Maths

Typically 2-4 marks per paper, more when it is buried inside a longer problem · Spec 1MA1

Percentage change covers three related jobs on Edexcel's 1MA1 specification: increasing or decreasing an amount by a given percentage, writing one amount as a percentage of another, and working out the percentage by which a value has changed. All of it sits under spec reference R9, which is common to both tiers, so on Higher you rarely meet it as a bare two-mark question. It arrives wrapped in profit and loss, VAT, a price rise followed by a sale, or a comparison between two sets of figures.

It can turn up on any of the three papers. Papers 2 and 3 allow a calculator, and the habit that costs marks there is building a percentage up in chunks, 10 percent then 5 percent then 1 percent, instead of multiplying by a decimal multiplier. Chunking takes longer, the part-answers usually go unlabelled, and when the arithmetic slips there is nothing on the page for an examiner to give method marks to. Paper 1 is non-calculator, where the numbers are chosen so the change is a tidy fraction of the original and the percentage falls out of the fraction.

Most of the credit is process credit for a correct method, so write the division down before you evaluate it. The move that costs the most marks is dividing by the wrong number: percentage change is a fraction of the original value and percentage profit is a fraction of the cost price, never of the new value or the selling price. Practise the two-stage versions as well, where a rise is followed by a fall, since combining the multipliers is the only reliable way to get the overall figure, and adding the two percentages together gives the wrong answer every time.

Worked example

A market trader buys 60 mugs at a cost of £4.50 each. She sells 45 of the mugs for £8 each and the remaining 15 mugs for £5 each. Work out her percentage profit. Give your answer correct to 1 decimal place.
[4 marks]
  1. Total cost: 60×4.50=27060 \times 4.50 = 270, so the mugs cost £270.
    P1: a complete method for the cost price, which is the number the final division must use
  2. Total income: 45×8=36045 \times 8 = 360 and 15×5=7515 \times 5 = 75, giving £435 altogether.
    P1: both selling prices used, not just the £8 batch
  3. Profit: 435−270=165435 - 270 = 165, so she makes £165.
    P1: subtracting cost from income; a loss would show here as a negative
  4. Percentage profit: 165270×100=61.11…\frac{165}{270} \times 100 = 61.11\ldots, which is 61.1 to 1 decimal place.
    A1: divided by the cost price of £270; dividing by the £435 income gives 37.9 and scores nothing here

Practice questions

These are original questions written in Edexcel 1MA1 Higher style, covering increases and decreases with multipliers, percentage change between two values, profit and loss, and repeated changes. Try the ones with tidy numbers without a calculator, the way Paper 1 would set them, and use a calculator for anything asking for a decimal place. Where a question says correct to 1 decimal place, type the rounded value.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

  1. Question 1 Exam pace [3 marks]
    A car is bought for £8400 and sold three years later for £5670. Work out the percentage loss.
  2. Question 2 Exam pace [3 marks]
    The price of a season ticket increases by 10 percent, and the following year it increases by 10 percent again. Work out the overall percentage increase.
  3. Question 3 Exam pace [3 marks]
    In a sale, all prices are reduced by 20 percent. On the last day of the sale, the sale prices are reduced by a further 15 percent. Work out the single percentage reduction that has the same effect as these two reductions together.
  4. Question 4 Exam pace [3 marks]
    A school has 900 students. 60 percent of the students are girls. 35 percent of the girls walk to school. Work out how many girls walk to school.
  5. Question 5 Exam pace [4 marks]
    In one shop the price of a game rises from £45 to £51. In a second shop the price of the same game rises from £60 to £67. Work out the larger of the two percentage increases, correct to 1 decimal place.
  6. Question 6 Exam pace [3 marks]
    The number of visitors to a museum in a week rose from 250 to 800. Work out the percentage increase.

Common mistakes examiners see

  • Dividing the change by the new value instead of the original. In the worked example above that turns £165 out of £270 into £165 out of £435, so 61.1 percent becomes 37.9 percent.

    Write the fraction with the original value, or the cost price, on the bottom before you touch the calculator. Label it: cost 270, profit 165, so 165 divided by 270.

  • Adding two successive percentages together. A 20 percent reduction followed by a further 15 percent off the reduced price is read as 35 percent off, giving 0.65 of the original instead of 0.68.

    Multiply the multipliers: 0.8×0.85=0.680.8 \times 0.85 = 0.68, so the single reduction is 32 percent. The second percentage is taken from a smaller amount, which is why the total is never the sum.

  • Answering with the size of the change when the question wanted the new amount. A coat at £480 reduced by 15 percent gets the answer £72, which is the discount, not the £408 sale price.

    Underline the last six words of the question. If it says work out the sale price, multiply by 0.85; if it says work out the reduction, find 15 percent and stop.

  • Building the percentage up in chunks on a calculator paper, then rounding each chunk. Ten percent, five percent and one percent added together often lands a penny or two out, and the accuracy mark goes.

    Use one multiplier and one keystroke sequence: for a 6.5 percent decrease multiply by 0.935. Keep the full display value on screen and only round on the answer line.

  • Treating the two directions of the same pair of numbers as the same percentage. Going from 48 to 60 and going from 60 to 48 both involve a change of 12, but they are 25 percent and 20 percent.

    Decide which number the question calls the starting value, then divide by that one. Reading it back as a sentence helps: 12 out of the 48 we started with is a 25 percent increase.

Frequently asked questions

Is percentage change on the Foundation paper too?
Yes. Spec reference R9 is common content, so it is examined at both tiers. What changes on Higher is the setting: the percentage step is usually one part of a longer problem about profit, a two-stage price change, or a comparison, rather than a question on its own.
Is the percentage change formula on the Edexcel formulae sheet?
No. The Exam Aid sheet issued with 1MA1 papers for the 2025 to 2027 windows carries the trapezium, circle, Pythagoras, trigonometry and quadratic formulae, and the compound interest formula, but not percentage change. You need to know it is the change divided by the original value, multiplied by 100.
How many marks is a percentage change question worth?
A straight increase or decrease is usually 2 marks and a percentage change between two values 2 or 3. Once it is folded into a multi-step problem, for example working out a percentage profit from several purchases and sales, it runs to 4 or 5 marks, with most of those awarded for the method rather than the final figure.
Can percentage change come up on the non-calculator paper?
Yes, Paper 1 is non-calculator and percentages appear there regularly. The numbers are picked so the fraction cancels, for example a fall from 3500 to 3150 giving 350 out of 3500, which is one tenth, so 10 percent. If the fraction is not cancelling neatly, check you have used the right starting value.

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