IB Maths AI: Modelling with Functions — What You Actually Need to Know

You need to recognise real-world contexts (population growth, cooling, projectile motion, business costs) and match them to linear, quadratic, exponential, cubic or sinusoidal functions. You must fit a model to data, use it to interpolate and extrapolate, and comment on its limitations — that last part is where most marks get dropped.

AI treats modelling as a core, heavily-weighted skill tested with real data sets and GDC regression; AA touches modelling but leans far more on pure calculus and algebraic proof. If you enjoy fitting curves to messy real data rather than proving results analytically, AI's approach suits you better.

No — you're expected to use your GDC to generate regression equations from data (linear, quadratic, exponential, cubic, sinusoidal), not derive the formulas by hand. What you do need is to interpret the output correctly: the coefficients, the correlation coefficient r, and what they mean in context.

You need to enter bivariate data, run linear, quadratic, cubic, exponential and sine regressions, find intersection points of curves, and locate maximum/minimum/zero values graphically. Practise this on the exact calculator you'll sit the exam with — a TI-84 and a Casio fx-CG50 have different regression menus.

Paper 1 and Paper 2 both test this, plus it's a favourite for the Internal Assessment. Expect a table of data, a request for a suitable model, use of that model to predict a value, and a final comment on the model's reliability or a suggested refinement — often worth 2-3 marks alone.

Forgetting to comment on the model's limitations or its domain of validity. Students often calculate the right numerical answer but skip the sentence explaining why extrapolating far beyond the data range is risky — and that's frequently where the final mark sits.

Look at the shape of the scatter graph and the context. Growth that speeds up suggests exponential; something that rises, peaks, then falls suggests quadratic or cubic; anything repeating in cycles (tides, temperature over a year) suggests sinusoidal. Context clues in the question usually confirm it.

Modelling is one of the most popular IA topics because it lets you collect your own data — sports statistics, spending patterns, physical measurements — and fit a genuine model, then critique it. Criterion B (Mathematical presentation) and Criterion E (Analysis) are where model choice and evaluation earn the most marks.

Practise past-paper questions across every model type until choosing the right function becomes automatic, and always write a sentence evaluating the model — don't just state the equation. In my experience marking mocks, students who lose marks here almost always skip that final evaluative line, not the calculation itself.

Focus practice on Topic 2 (Functions) and Topic 4 (Statistics) crossover questions, since modelling sits exactly between them. On RevisionPrep, the Topical Worksheets for Functions and the Mock Papers under Maths AI give you mixed practice across all five model types with full worked solutions.

It's more conceptually demanding than pure algebra topics because it mixes GDC skill, judgement and written explanation rather than a single correct method. Students who are comfortable with calculator regression but weak at writing evaluative comments tend to find the marks slip away here, not in the maths itself.

IB Maths AI is built around GDC use — regression, curve fitting and finding intersections are all calculator-based skills, not optional extras. A TI-84 Plus or Casio fx-CG50 (roughly USD 90-130) is standard across most IB schools, and your child should be practising on their own model well before mocks.

You don't need to know the maths — ask your child to explain, in plain English, why they chose a particular model for a given data set. If they can justify the choice and describe the model's limitations out loud, they genuinely understand it; if they can only state the equation, they're not there yet.