Percentage questions appear in every IGCSE maths exam, across multiple papers. They range from $1$-mark calculations to $5$-mark compound interest problems. Here is every type, with the exact method examiners expect.
Type 1: Finding a Percentage of an Amount
Method: $\text{Amount} \times \frac{\text{percentage}}{100}$
Example: Find $15\%$ of $240$.
$240 \times \frac{15}{100} = 240 \times 0.15 = 36$
This is the simplest type. The common mistake is forgetting to divide by $100$.
Type 2: Percentage Increase and Decrease
Increase: $\text{New value} = \text{Original} \times (1 + \frac{r}{100})$
Decrease: $\text{New value} = \text{Original} \times (1 - \frac{r}{100})$
Example: A shirt costs $80$. It is reduced by $30\%$. Find the sale price.
$80 \times (1 - \frac{30}{100}) = 80 \times 0.70 = 56$
Multiplier shortcut:
| Change | Multiplier |
|---|---|
| Increase by $5\%$ | $\times 1.05$ |
| Increase by $12\%$ | $\times 1.12$ |
| Decrease by $20\%$ | $\times 0.80$ |
| Decrease by $35\%$ | $\times 0.65$ |
Type 3: Expressing One Quantity as a Percentage of Another
Method: $\frac{\text{Part}}{\text{Whole}} \times 100$
Example: $45$ students out of $180$ chose maths. What percentage is this?
$\frac{45}{180} \times 100 = 25\%$
Common mistake: Dividing the wrong way round. The “whole” is always the total or the reference amount.
Type 4: Percentage Change
Method: $\frac{\text{New} - \text{Original}}{\text{Original}} \times 100$
Example: A house price increased from $250000$ to $285000$. Find the percentage increase.
$\frac{285000 - 250000}{250000} \times 100 = \frac{35000}{250000} \times 100 = 14\%$
Watch: The denominator is always the original value, not the new value.
Type 5: Reverse Percentage (Finding the Original)
This is the type most students struggle with. You’re given the final amount after a percentage change and must find the original.
Method: $\text{Final amount} \div (1 \pm \frac{r}{100})$
Example: After a $20\%$ increase, a TV costs $360$. Find the original price.
$360 \div 1.20 = 300$
Example: After a $15\%$ discount, a bag costs $170$. Find the original price.
$170 \div 0.85 = 200$
The critical mistake: Students calculate $20\%$ of $360$ and subtract it. This gives $288$, which is wrong. The $20\%$ was applied to the original, not to $360$.
Type 6: Compound Interest
Formula: $A = P\left(1 + \frac{r}{100}\right)^n$
Where:
- $A$ = final amount
- $P$ = principal (starting amount)
- $r$ = annual interest rate
- $n$ = number of years
Example: $5000$ is invested at $3\%$ per year compound interest for $4$ years.
$A = 5000 \times (1 + \frac{3}{100})^4$ $= 5000 \times 1.03^4$ $= 5000 \times 1.12550881$ $= 5627.54$ (2 d.p.)
Interest earned: $5627.54 - 5000 = 627.54$
Compound vs Simple Interest
| Feature | Simple | Compound |
|---|---|---|
| Formula | $P + Prn$ | $P(1+\frac{r}{100})^n$ |
| Interest on | Original only | Previous balance |
| Growth | Linear | Exponential |
Exam tip: If the question says “compound interest”, always use the exponential formula. Never multiply by $n$.
Type 7: Depreciation
Same as compound interest but with decrease:
Formula: $V = P\left(1 - \frac{r}{100}\right)^n$
Example: A car worth $20000$ depreciates at $12\%$ per year for $3$ years.
$V = 20000 \times (1 - \frac{12}{100})^3$ $= 20000 \times 0.88^3$ $= 20000 \times 0.681472$ $= 13629.44$
Type 8: Finding the Rate or Time
Given the formula $A = P(1 + \frac{r}{100})^n$, you may need to find $r$ or $n$.
Finding $n$ (number of years): Use trial and improvement or logarithms (if allowed).
Example: $1000$ grows to $1200$ at $5\%$ compound interest. How many years?
$1200 = 1000 \times 1.05^n$ $1.2 = 1.05^n$ $n=3$: $1.05^3 = 1.157625$ (too low) $n=4$: $1.05^4 = 1.21550625$ (above $1.2$)
Answer: $4$ complete years needed.
Practice Percentage Problems
- CIE 0580 Number Practice — percentage and ratio questions
- Edexcel 4MA1 Practice — percentage problems for Edexcel board
- Weekly Targeted Practice — curated exam questions with solutions
Related guides: Edexcel 4MA1: Ratio & Percentage Mistakes · Paper 4: 10 Tips to Gain 20+ Marks · IGCSE Trigonometry Complete Guide