This module covers percentages beyond the first step: finding a percentage of an amount, reversing a change, separating percentage from percentage-point change, stacking changes, and explaining why the base matters. The same ideas run through discounts, interest, profit and population questions.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording in your exam year. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You need fractions and decimals, division by 10 and 100, and a comfortable feel for multiplying decimals. The number sense module and the ratio module are useful companions, because a percentage is a ratio out of 100.
An orienting example
A shop raises the price of a bag by 20%. The new price is RM150. Find the original price, and then the price after a further 20% discount on the new price.
Step 1, reverse the rise: 150 ÷ 1.2 = 125. The original price was RM125.
Step 2, apply the discount to RM150: 150 × 0.8 = 120.
Check: 125 × 1.2 = 150, and 150 × 0.8 = 120. Both are consistent.
The discount did not return the price to RM125. The 20% was taken from RM150, so it removed RM30, while the rise had added only RM25. That is the central idea of the module: a percentage always belongs to a base, and the base changes.
In which order should you study it?
- Find a percentage of an amount without a calculator: builds every percentage from easy blocks.
- Reverse a percentage increase: works back from the new amount to the original.
- Compare percentage change with percentage-point change: stops a common wording error with rates.
- Apply successive increases and decreases: uses multipliers to stack changes.
- Explain why equal percentage rise and fall do not cancel: turns the multiplier idea into a clear reason.
Then work through the mixed practice set. One lesson a day and the practice set on the weekend is a steady pace.
Which traps catch most students here?
- Using the wrong base, such as taking a percentage of the new amount when the original is needed.
- Subtracting instead of dividing when reversing a change.
- Adding percentages from separate stages.
- Confusing percentage points with a percentage change.
- Assuming an equal rise and fall cancel.
Each lesson shows one of these slips in full and then corrects it.
How should you use the practice set?
Attempt each question on paper before opening the answer, and write your working as in an exam. Label the base at every step. The percentage-base explorer lets you check a chain of changes, and the non-calculator working trainer helps with the arithmetic.
When you get something wrong, read the routing notes at the end of the practice set and return to the lesson it names. A mistake log and retest queue helps you come back to the same error type a few days later.
If you keep picking the wrong base in percentage questions, a teacher in online one-to-one Mathematics tuition can go through your written working and fix that habit with you.