In Applications and Interpretation SL, the IB suggests 31 of the 150 teaching hours for functions – second only to statistics. But AI functions are not about abstract algebra. They are about modelling: choosing a function that describes a real situation, fitting it to data, and judging whether it makes sense. That last step is where most marks are won or lost.
The six models AI SL students must know
| Model | Typical form | Typical context |
|---|---|---|
| Linear | f(x) = mx + c | Constant rate: taxi fares, phone plans |
| Quadratic | f(x) = ax² + bx + c | Projectiles, area problems, profit |
| Exponential | f(x) = kaˣ + c or ke^(rx) + c | Growth and decay: populations, cooling |
| Direct and inverse variation | f(x) = axⁿ | Scaling laws, inverse-square effects |
| Cubic | f(x) = ax³ + bx² + cx + d | Volumes, smooth curves through data |
| Sinusoidal | f(x) = a sin(b(x − c)) + d | Tides, temperatures, daylight hours |
For each, students should know the shape, what each parameter means in context, and how to find parameters from information or data.
Choosing a model
Ask three questions:
- What does the graph or data look like? Straight, curving up, levelling off, repeating?
- What does the context say? "Increases by 5% each year" → exponential; "repeats every 12 hours" → sinusoidal.
- What happens at the extremes? An exponential decay model levels off; a quadratic eventually turns round. Does that match reality?
Fitting a model
- From information: substitute known points and solve for parameters (often with the GDC's equation solver).
- From data: use the GDC's regression features – linear, quadratic, cubic, exponential, power, sine – and record the equation and, where relevant, the coefficient of determination.
- Sinusoidal models: find the amplitude from (max − min)/2, the principal axis from (max + min)/2, and b from the period (b = 2π/period, or 360°/period in degrees).
"Interpret" and "comment": the marks that matter
AI questions often end with "interpret the value of…" or "comment on the validity of the model". Strong answers:
- Give meaning with units: "c = 12 represents the fixed monthly charge of $12."
- Refer to the context, not just the maths.
- Name a specific limitation: "The model predicts negative temperatures after 40 minutes, which is not possible in a warm room."
- Avoid vague statements such as "the model is not accurate".
Common mistakes
- Using degrees when the model is in radians (or the reverse).
- Confusing horizontal and vertical shifts in sinusoidal models.
- Rounding parameters too early and losing accuracy later.
- Extrapolating far outside the data without comment.
- Giving a number for "interpret" without words.
A practice plan
- Week 1: linear and quadratic models with real contexts.
- Week 2: exponential and variation models; GDC regression.
- Week 3: sinusoidal models from tables and graphs.
- Week 4: mixed past-paper modelling questions, focusing on interpretation.
Modelling is also a natural area for the internal assessment – see the IA criteria explained.
How Maths Bodhi helps AI SL students
- A diagnostic to see whether marks go in choosing, fitting or interpreting.
- Context reading drills that turn a paragraph into a model.
- GDC regression practice on the student's own calculator.
- Written feedback on interpretation answers – the part examiners reward most.
Ajay Vatsyayan (M.Tech, 14+ years teaching maths) teaches IB DP maths at Maths Bodhi and has taught students from schools across Gurgaon, including Scottish High International School, Shiv Nadar School, Amity Global School and Lancers International School. Maths Bodhi is independent and not affiliated with any school. Read Ajay's profile, or see our AI SL tutor and IB functions tutor pages.
Home sessions across Gurgaon – including Golf Course Road and Sector 54 – or online. Book a free demo class.
Related: AI SL statistics, GDC skills and the IB DP maths guide for Gurgaon families.
Topic hours verified against the current IB AI guide by the Maths Bodhi team (October 2026). Teaching plan reviewed by Ajay Vatsyayan.
Frequently asked questions
- Which function models are in IB maths AI SL?
- Linear, quadratic, exponential, direct and inverse variation, cubic and sinusoidal models.
- How do I find a sinusoidal model in IB maths?
- Amplitude = (max − min)/2, principal axis d = (max + min)/2, b = 2π divided by the period (in radians), and the horizontal shift from where the maximum or principal axis crossing occurs.
- How do I answer "comment on the validity of the model"?
- Refer to the context and give a specific limitation – for example, an impossible prediction outside the data range – rather than saying the model is "not accurate".