IGCSE Mathematics (0580)

Percentages

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

To find the sale price after a percentage discount, subtract the discount percentage from 100% and multiply the original price by the remaining percentage as a decimal.
Common mistake: Students often mistakenly subtract the discount amount from the percentage or multiply by the discount percentage instead.
Percentage profit is calculated by dividing the profit by the original cost price, not the selling price.
Common mistake: Students often mistakenly use the selling price as the denominator, leading to an incorrect lower percentage.
To find what percentage one number is of another, divide by the total or reference amount (the 'of' value), not the part.
Common mistake: Students often mistakenly divide the larger by the smaller or reverse the order.
Compound interest requires multiplying the principal by the annual multiplier raised to the number of years (using powers), not just multiplying the interest rate by the years as in simple interest.
To find a percentage of a number, convert the percentage to a decimal (by dividing by 100) before multiplying.
Common mistake: A common mistake is multiplying by the percentage as a whole number, making the answer 100 times too large.
Simple interest is calculated only on the original principal, not on accumulated interest, so multiply the yearly interest by the number of years instead of compounding it each year.

Calculate the amount Leah pays.

Try it first, then show the working

Calculate the percentage of the marked price Leah pays after the discount.

100\% - 6.5\% = 93.5\%
Calculate the amount Leah pays as $32 538.00.

\[34\ 800 \times 0.935 = 32\ 538.00\]

Answer: $32 538.00

19 exam-style questions on Percentages, each marked to the scheme.