Ratio, Proportion & Percentages
MYP1 Mathematics — Number strand: Ratio, Proportion & Percentages
This whole topic is really one skill wearing different costumes: is the rate/ratio staying the same, or is a percentage being taken of a fixed amount? Every question you'll see — rice by the kilo, pay by the hour, discounted jackets, shared allowances — is testing whether you can spot which one is happening and then set up the correct multiplication or division. Get that identification right and the arithmetic is easy; get it wrong and you'll do a perfectly neat calculation that answers a different question entirely.
Overview
Why this topic keeps showing up
Ratio, proportion and percentages are the maths of everyday fairness and scaling — splitting a bill, resizing a recipe, working out if a 'sale' is actually a good deal. Examiners love this topic because it tests reasoning, not just arithmetic: the calculate parts are usually easy, but the describe/justify parts (which appear in almost every question in the bank) catch students who can compute but can't explain why the method works.
- Direct and inverse proportion describe how two quantities change together — same direction (direct) or opposite direction (inverse).
- Percentages are just ratios out of 100 — every percentage question is secretly a proportion question in disguise.
- Ratios and proportion share one engine: find the value of 'one part' (or one unit), then scale up or down.
The shape of the chapter
Command terms this topic actually uses
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State / Identify | Give the answer directly from given data — no explanation or working expected. | AO1 | 1 mark for the correct value alone; writing a paragraph here wastes time and gains nothing extra. |
| Calculate | Produce a numerical answer, showing the method used to get there. | AO2 | Marks split as method + accuracy — a correct final answer with zero working can lose the method mark if the final answer is wrong or ambiguous. |
| Describe | Give a specific account of a pattern, behaviour, or reason — not just repeat the question. | AO2/AO3 | Needs a concrete reason tied to the numbers (e.g. 'the ratio cost÷mass stays at 3 for every row') — vague statements like 'it goes up' score 0. |
| Justify / State whether... and describe how | Make a claim (correct/incorrect, yes/no) AND back it with evidence from the working. | AO3 | The claim alone is worth nothing without the supporting calculation — this is where Q5(c)-style questions lose marks. |
Key point
Overview