This module covers how quantities change together: sharing a total in a ratio, scaling a recipe or a map, telling a ratio from a fraction, and recognising direct and inverse proportion. The same idea of “what stays fixed?” sits under speed, density, percentages, similar shapes and graphs.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording of each content point in your exam year. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You need multiplication and division facts, simplifying fractions, and converting between g and kg, ml and litres, cm and km. If those conversions feel slow, work through number sense and exact arithmetic first, because every lesson here depends on them.
An orienting example
A canteen mixes syrup and water in the ratio 1:7. How much syrup is in 2.4 litres of drink?
Step 1, convert: 2.4 litres = 2400 ml.
Step 2, count parts: 1 + 7 = 8 parts.
Step 3, one part: 2400 ÷ 8 = 300 ml. Syrup is 1 part, so it is 300 ml, and water is 7 × 300 = 2100 ml.
Check: 300 + 2100 = 2400 ml.
Now change the question.
If the drink doubles to 4.8 litres, the syrup doubles to 600 ml: that is direct proportion. If the same 2.4 litres is poured into cups, then 12 cups hold 200 ml each and 6 cups hold 400 ml each, because 12 × 200 = 2400 and 6 × 400 = 2400: that is inverse proportion. One situation, three ideas, all in this module.
In which order should you study it?
- Share a quantity in a stated ratio: the parts method that every other lesson reuses.
- Scale a recipe with mixed units: adds unit conversion, where most marks are lost.
- Distinguish a ratio from a fraction of the total: stops the 2:3 versus 2/3 confusion.
- Model direct proportion from a table: tests whether y ÷ x stays constant.
- Recognise inverse proportion from a changing product: tests whether x × y stays constant.
Then work through the mixed practice set. Percentage questions build on the same thinking, so percentages and changing bases is a natural next module.
Which traps catch most students here?
- Dividing the total by each ratio number instead of by the sum of the parts.
- Mixing units, such as writing 600 g : 1.5 kg as 600 : 1.5.
- Reading 2:3 as 2/3 when the fraction of the total is 2/5.
- Calling a table proportional because both columns rise.
- Treating inverse proportion as direct, so fewer workers “take fewer days”.
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 and write the working as you would in an exam. Open the answer only afterwards, and mark which step went wrong, not just whether the final value matched.
The routing notes at the end send each error type back to a lesson. The non-calculator working trainer is useful for checking fraction steps.
If you want teaching beyond self-study, online one-to-one Mathematics tuition means an experienced teacher reads your written working and finds the habit behind the error.