Percentages Explained: Edexcel IGCSE Mathematics Specification A Complete Breakdown

Percentages show up on almost every Edexcel IGCSE Mathematics Specification A paper, and the range of question types is wider than most students expect

The 4MA1 specification treats percentages as one of the core number skills. Simple percentage calculations sit at the Foundation level, while compound interest, repeated percentage change and reverse percentages push into Higher tier territory. The edexcel igcse percentages topic connects to real-world contexts like shopping discounts, salary increases, population growth and depreciation, which is why it appears so reliably in the exam.

Key Facts

What "percentage" actually means

The edexcel igcse mathematics specification a definition is direct: percentage means "number of parts per 100." So 45% means 45 out of every 100. This is the percentages explained starting point that every other calculation builds from. Converting between percentages, fractions and decimals is a routine skill that the exam tests.

• Percentage to decimal: divide by 100. So 35% = 0.35.
• Decimal to percentage: multiply by 100. So 0.72 = 72%.
• Percentage to fraction: write over 100 and simplify. So 60% = 60/100 = 3/5.

Finding a percentage of an amount

Worked example: Find 18% of 450.

• Method 1 (calculator): 450 x 0.18 = 81
• Method 2 (non-calculator): 10% of 450 = 45, 5% = 22.5, 1% = 4.5, so 18% = 45 + 22.5 + 3 x 4.5 = 45 + 22.5 + 13.5 = 81

On the IGCSE 4MA1 exam, calculators are permitted, so Method 1 is faster and less error-prone. But understanding Method 2 helps when the question is embedded in a context where you need to think about what 18% represents before you calculate it.

Expressing one number as a percentage of another

Worked example: 36 students out of 150 chose biology. What percentage chose biology?

• (36 / 150) x 100 = 24%

The what is percentages igcse exam question often wraps this in a real-world scenario. The skill is always the same: divide the part by the whole, then multiply by 100.

Percentage increase and decrease

The multiplier method is the most efficient and least error-prone approach. It reduces a two-step calculation (find the percentage, then add or subtract) to a single multiplication.

Increase: To increase a value by p%, multiply by (1 + p/100).

Decrease: To decrease a value by p%, multiply by (1 - p/100).

Worked example: A coat costs 85 and the price increases by 12%. Find the new price.

• Multiplier = 1 + 12/100 = 1.12
• New price = 85 x 1.12 = 95.20

Worked example: A car worth 18,000 depreciates by 15% per year. Find its value after 1 year.

• Multiplier = 1 - 15/100 = 0.85
• Value after 1 year = 18,000 x 0.85 = 15,300

Reverse percentages

Reverse percentage questions give you the value after a percentage change and ask you to find the original. This is where many candidates go wrong, because they try to "undo" the percentage by applying the same percentage to the new amount.

Worked example: After a 30% reduction, a laptop costs 490. Find the original price.

• 490 represents 70% of the original (because 100% - 30% = 70%)
• Original = 490 / 0.7 = 700

Check: 30% of 700 = 210. 700 - 210 = 490. Correct.

Compound interest and repeated percentage change

Compound interest applies the same percentage increase repeatedly, with each new calculation based on the accumulated total, not the original amount. The edexcel igcse mathematics specification a notes for Higher tier include this formula:

Final amount = P x (1 + r/100)ⁿ

where P is the principal (starting amount), r is the rate per period, and n is the number of periods.

Worked example: 2000 is invested at 5% compound interest per year for 3 years. Find the final amount.

• Final = 2000 x (1.05)³
• = 2000 x 1.157625
• = 2315.25

The interest earned is 2315.25 - 2000 = 315.25. With simple interest, it would have been 2000 x 0.05 x 3 = 300. Compound interest gives more because each year's interest earns interest in subsequent years.

Depreciation works the same way but with a decrease multiplier:

Worked example: A machine worth 50,000 depreciates by 10% per year. Find its value after 4 years.

• Value = 50,000 x (0.9)⁴
• = 50,000 x 0.6561
• = 32,805

Exam question patterns

Pattern 1: Simple percentage of an amount. "Calculate 35% of 240." Foundation level. Multiply and go.

Pattern 2: Percentage change in context. "A shop increases all prices by 8%. A shirt was 25. Find the new price." Use the multiplier.

Pattern 3: Reverse percentage. "After a 15% increase, a membership fee is 92. Find the original fee." Divide by 1.15.

Pattern 4: Compound interest or depreciation. Higher tier. Apply the formula with the exponent.

Pattern 5: Percentage profit or loss. "Bought for 40, sold for 52. Calculate the percentage profit." Profit = 12, percentage = (12/40) x 100 = 30%.

Common mistakes

• Adding the percentage to the new value in reverse percentage questions. "After a 20% increase, the value is 360. Original = 360 - 20% of 360 = 288." Wrong. The original is 360 / 1.2 = 300.
• Using simple interest calculations when the question says compound. Read carefully: "compound interest" means the multiplier-to-the-power method.
• Forgetting to subtract the principal when the question asks for interest earned. The formula gives the total amount, not the interest alone.
• Rounding compound interest answers too early. Keep full precision through each year's calculation, then round only the final answer.

Percentage change and its applications

Percentage change is used to compare how much a value has increased or decreased relative to its original amount. The formula is: percentage change = (change / original) x 100.

Worked example: A town's population grows from 12,000 to 13,800. Calculate the percentage increase.

• Change = 13,800 - 12,000 = 1,800
• Percentage increase = (1,800 / 12,000) x 100 = 15%

This formula works in both directions. If the population fell from 12,000 to 10,200:

• Change = 12,000 - 10,200 = 1,800
• Percentage decrease = (1,800 / 12,000) x 100 = 15%

The important point is that the original value is always the denominator. Candidates sometimes divide by the new value instead, which gives the wrong answer.

VAT, tax and real-world percentage problems

The Edexcel IGCSE Mathematics Specification A exam often sets percentage questions in contexts involving VAT, sales tax, profit margins and currency exchange. These questions are testing the same skills described above, but wrapped in language that requires you to identify which value is the "original" and which is the "part" or "change."

Worked example: A shirt is priced at 45 before VAT. VAT is charged at 20%. Find the price including VAT.

• Price including VAT = 45 x 1.20 = 54

Reverse version: A shirt costs 54 including 20% VAT. Find the price before VAT.

• 54 represents 120% of the original
• Original = 54 / 1.20 = 45

In currency exchange questions, the same multiplier approach applies. If 1 GBP = 1.15 EUR, then 200 GBP = 200 x 1.15 = 230 EUR. To convert back, divide: 230 / 1.15 = 200 GBP. The exchange rate is the multiplier.

Connecting percentages to other topics

Percentages appear in probability (expressing probabilities as percentages), statistics (percentage of a data set in a category), and geometry (percentage increase in area when dimensions change). A common Higher tier question asks: "If the radius of a circle increases by 10%, by what percentage does the area increase?" The answer is not 10%. If the new radius is 1.1r, the new area is pi x (1.1r)² = 1.21 x pi x r², which is a 21% increase. Understanding percentage change as multiplication prepares you for these cross-topic applications that test deeper mathematical reasoning on the Edexcel IGCSE exam.

Self-check questions

1. Express 72 as a percentage of 300.
2. A house worth 250,000 increases in value by 6%. Find the new value.
3. After a 25% discount, a television costs 540. Find the original price.
4. 3000 is invested at 4% compound interest for 5 years. Calculate the total amount and the interest earned.
5. A car depreciates by 12% per year. It is currently worth 20,000. Find its value after 3 years.

Practise percentages questions on the Green Bridge CBT platform using Edexcel IGCSE Mathematics Specification A questions filtered by topic and tier, and review the edexcel igcse mathematics specification a explained solutions for full working at every step.