Graphs and Relations
MYP Mathematics Framework — Graphs and Relations (Year 5 Extended)
This chapter is really three skills wearing one name: building a graph from an equation, reading a graph that's already drawn, and shifting a graph you already understand to describe a new situation. Examiners love the shift-and-read combination — give you , translate it, and ask what a specific point means in context (a drone's height, a sound level, a garden bed's depth). Get the sign conventions right and this whole topic becomes mechanical.
Overview — How This Topic Fits Together
What 'Graphs and Relations' actually tests
A relation links an input () to an output (). A function is a relation where every input gives exactly one output — that's the whole reason notation is safe to use. This chapter tests whether you can move between three representations of the same relationship: the equation, the table of values, and the graph — and translate between them without losing information (Q1 is built entirely around this trap).
- Transformations describe how changing an equation moves, flips or stretches a graph — without needing to re-plot every point.
- Real-life graphs need you to read gradient and area as physical quantities (rate of change, total distance), not just as lines on paper.
- Linear, quadratic, cubic and exponential graphs each have a signature shape — recognising the shape from the equation (and vice versa) is non-negotiable at this level.
- Parallel and perpendicular lines are just gradient rules dressed up in geometry language.
The shape of the chapter
Command terms this topic loves
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| State / Write down | Give the answer directly, no working required | AO1 | 1 mark for the correct value alone — no method needed, but no credit if it's wrong even with correct-looking working nearby |
| Calculate | Obtain a numerical answer showing the working steps | AO2 | Method mark for correct substitution, answer mark for final value |
| Deduce | Reach a conclusion using given information or a previous result — not from scratch | AO2/AO3 | Must explicitly link to the given data or earlier part; a bare correct answer with no link loses the reasoning mark |
| Sketch | Draw a graph showing general shape and key features (intercepts, vertex, asymptote) — not a precise plot | AO2 | Marks for correct shape, correct intercept/vertex labels; axes must still be labelled |
| Interpret / Explain | Connect a mathematical feature to its real-world meaning in words | AO3 | No marks for the number alone — the sentence explaining what it means in context is what's assessed |
| Analyse | Break down a relationship and describe how the parts connect (e.g. how relates to ) | AO3 | Needs both the numerical pattern (add/subtract constant) and the graphical description (shift direction) for full marks |
Key point
Overview