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Edexcel IGCSE Maths (4MA1) · Unit 1: Number

Edexcel IGCSE 4MA1 Percentages: exam questions and answers, notes and worked examples

Updated October 2026 · By Pete Bromfield

Most percentage questions are one multiplication with the right multiplier: an increase of 15% is ×1.15 and a decrease of 15% is ×0.85. Percentage change is the change divided by the original amount; a reverse percentage divides by the multiplier; and compound interest uses a power, so £2000 at 3% a year for 4 years is worth $2000 \times {1.03}^{4}$ pounds.

Unit 1: Number
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Notes
Formulas
Worked examples
Mistakes
FAQ

Percentages notes

Percentages of amounts and multipliers

35% of 80 is $0.35 \times 80 = 28$ . To increase 80 by 35%, multiply by 1.35: $80 \times 1.35 = 108$ . To decrease 80 by 35%, multiply by 0.65: $80 \times 0.65 = 52$ . One multiplication is quicker, and safer, than finding the percentage and then adding or subtracting it.

Percentage change

Percentage change $= \frac{change}{original} \times 100$ . A price that falls from £250 to £215 has dropped by $\frac{35}{250} \times 100 = 14 %$ . Always divide by the original value, not the new one.

Reverse percentages

When you are given the amount after a change, divide by the multiplier to get back to the original. After a 20% increase a coat costs £84, so the original price was $84 \div 1.2 = 70$ pounds.

Simple and compound interest

Simple interest adds the same amount every year: £500 at 4% a year for 3 years earns $3 \times 20 = 60$ pounds. Compound interest adds interest on the interest: $500 \times {1.04}^{3} = 562.432$ , so the account holds £562.43. The general form is $P {(1 + \frac{r}{100})}^{n}$ .

Depreciation and repeated changes

Depreciation uses a multiplier below 1: a car worth £12 000 that loses 15% of its value each year is worth $12000 \times {0.85}^{2} = 8670$ pounds after 2 years. Changes multiply, they do not add: a 10% rise followed by a 10% fall is $1.1 \times 0.9 = 0.99$ , an overall fall of 1%.

Key formulas

Percentage change Learn it: $\frac{new - original}{original} \times 100 %$
Reverse percentage Learn it: $original = \frac{new}{1 \pm \frac{r}{100}}$
Compound growth / decay Learn it: $A = P {(1 \pm \frac{r}{100})}^{n}$

Learn it = not printed on the 4MA1 Higher formulae sheet, so learn it by heart. The whole 4MA1 formula sheet (free PDF) → · 4MA1 formulas to learn

Percentages worked examples

Worked example 1: Percentage change

A price rises from £64 to £80. Find the percentage increase.

Solution

Increase: $80 - 64 = 16$ .
$\frac{16}{64} \times 100 = 25 %$ .

3 steps

Tip: Divide by the original amount.

Worked example 2: Reverse percentage

After a 15% decrease a price is £68. Find the original price.

Solution

After the decrease the price is 85% of the original: multiplier 0.85.
Original $= 68 \div 0.85 = 80$ .

3 steps

Tip: Do not add 15% of £68 back on.

Worked example 3: Compound interest

£2 500 is invested at 4% per year compound interest. Find its value after 3 years.

Solution

Multiplier: 1.04.
$2500 \times {1.04}^{3} = 2812.16$ .

3 steps

Tip: Compound interest uses a power; simple interest does not.

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Percentages exam-style questions

Try each question before you open the answer (one has its full worked solution open). The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 2 marks

Increase £240 by 15%.

Show the answer and mark scheme

M1 240 × 1.15, or 240 + 36
A1 £276

Answer: £276

Question 2 · medium · 3 marks

The price of a jacket falls from £85 to £71.40. Work out the percentage decrease.

Show the answer and mark scheme

M1 85 − 71.40 = 13.60
M1 13.60 ÷ 85 × 100
A1 16%

Answer: 16%

Question 3 · medium · 2 marks

After a 12% increase, the monthly rent of a flat is £1008. Work out the monthly rent before the increase.

Show the answer and mark scheme

M1 1008 ÷ 1.12
A1 £900

Answer: £900

Question 4 · medium · 2 marks

In a sale, all prices are reduced by 32%. The sale price of a coat is £61.20. Work out the price of the coat before the sale.

Show the answer and mark scheme

M1 100 − 32 = 68, so 61.20 ÷ 0.68
A1 £90

Answer: £90

Question 5 · medium · 3 marks

Mia invests £4500 for 4 years at 3.2% per year compound interest. Work out the value of her investment at the end of the 4 years. Give your answer to the nearest penny.

Full worked solution Free, no sign-in

M1 4500 × 1.032ⁿ with n ≥ 2
M1 4500 × 1.032⁴
A1 £5104.24

Answer: £5104.24

Every question here has a full worked solution. See them all →

Question 6 · hard · 3 marks

A shop increases the price of a lamp by 30%. Later it reduces the new price by 25%. Work out the overall percentage change in the price of the lamp, saying whether it is an increase or a decrease.

Show the answer and mark scheme

M1 1.3 × 0.75
A1 0.975
A1 2.5% decrease

Answer: 2.5% decrease

Question 7 · hard · 3 marks

The population of a town went up by 8% in one year and then by 5% in the next year. At the end of the two years the population was 22 680. Work out the population at the start of the two years.

Show the answer and mark scheme

M1 1.08 × 1.05 (= 1.134)
M1 22 680 ÷ 1.134
A1 20 000

Answer: 20 000

Question 8 · very hard · 5 marks

A car cost £24 000 when new. Its value fell by 18% in the first year and by 11% in each year after that. (a) Work out the value of the car after 3 years. Give your answer to the nearest penny. (b) After how many whole years is the car first worth less than £10 000?

Show the answer and mark scheme

M1 24 000 × 0.82
M1 × 0.89²
A1 £15 588.53
M1 continues × 0.89 each year: 13 873.79, 12 347.67, 10 989.43, …
A1 7 years (value £9780.59)

Answer: (a) £15 588.53 (b) 7 years

Common percentages mistakes

Dividing by the new amount. Percentage change always divides by the original value. From £250 to £215, divide 35 by 250, not by 215.
Taking the percentage off the new price. To undo a 20% increase, divide by 1.2. Taking 20% off £84 gives $84 \times 0.8 = 67.2$ , which is wrong: the original price was £70.
Simple interest when the question says compound. Compound interest needs the power. Multiplying one year's interest by the number of years only works for simple interest.
Adding the percentages over several years. Three years at 5% compound is ${1.05}^{3} \approx 1.158$ , an increase of about 15.8%, not 15%.

Where students lose marks across 4MA1, from the examiner reports →

Percentages FAQ

Is the compound interest formula on the 4MA1 formula sheet?

No. Compound interest and percentage change are not printed on the 4MA1 Higher formulae sheet, so learn them. With a multiplier you rarely need the full formula: multiply by 1 + r/100 once for each year.

How do I know a question needs a reverse percentage?

If you are given the amount after an increase or decrease and asked for the amount before it, it is a reverse percentage. Divide by the multiplier; never take the percentage of the amount you were given.

Can I use a calculator for percentages in 4MA1?

Yes. A calculator may be used in all four 4MA1 papers, so both Higher papers (1H and 2H) allow one. Most marks are for the method you write down, so show your working.

How long are the 4MA1 Higher papers?

Papers 1H and 2H are 2 hours each and 100 marks each, worth 50% each. Each tier has its own formulae sheet in the exam.

Next steps

Percentages revision notes · 4MA1 formula sheet · Taking Cambridge 0580 instead? Cambridge 0580 percentages questions

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and every result was re-solved independently before publishing.

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Edexcel IGCSE 4MA1 Percentages: exam questions and answers, notes and worked examples

Try it first

Percentages notes

Percentages of amounts and multipliers

Percentage change

Reverse percentages

Simple and compound interest

Depreciation and repeated changes

Key formulas

Percentages worked examples

Worked example 1: Percentage change

Solution

Worked example 2: Reverse percentage

Solution

Worked example 3: Compound interest

Solution

Percentages exam-style questions

Question 1 · easy · 2 marks

Question 2 · medium · 3 marks

Question 3 · medium · 2 marks

Question 4 · medium · 2 marks

Question 5 · medium · 3 marks

Full worked solution Free, no sign-in

Question 6 · hard · 3 marks

Question 7 · hard · 3 marks

Question 8 · very hard · 5 marks

Common percentages mistakes

Percentages FAQ

Next steps

Practise percentages with your progress saved

More Unit 1 topics: Number