IB Math AI SL · Topic 2
Functions
The spine of Applications and Interpretation. Six model families, one repeating cycle examined everywhere: choose a model, justify it, find its parameters, state a reasonable domain, and interpret predictions back into context.
What the syllabus covers
Six assessed sections, SL 2.1 to 2.6 — less algebra than AA, far more interpretation.
How it is examined
Modelling chains are Paper 2's signature — one real-world scenario unfolding over five or six connected parts.
Real papers open with extended sinusoidal models — a Ferris wheel's height over time, tides in a harbour — where you must find the parameters before you may use them.
Marks are reserved for interpretation sentences: what the asymptote means, whether the domain is reasonable, why this model fits this data.
Parameter-hunting questions expect the working that produced them, not just the values.
The formula booklet gives exactly two things for this topic: the three forms of a straight line with the gradient formula, and the axis of symmetry x = −b/2a. Everything else — quadratics solved, exponentials fitted, sinusoids constructed — is examined as GDC fluency plus interpretation.
Command terms distinguish three kinds of graph question: 'sketch' wants shape and key features freehand, 'draw' wants an accurate curve on labelled axes, 'plot' wants points marked precisely — and examiners mark the difference.
Transferring a graph from the GDC screen to paper is an explicitly listed skill: shape, labelled axes and intercepts, not a copy of pixels.
A marked question, mark by mark
A sinusoidal model built from a context, marked the way the scheme would mark it.
Drill the full modelling cycle, marked
Generated exercises across all six SL 2.x model families, marked line by line — including the interpretation sentences that static question banks can't teach because their answers are already printed.
Start free trialNew to the codes? M1, A1, R1 explained →
Sinusoidal models · SL 2.5 / 2.6
Seed 5C13
Water depth in a harbour is modelled by D(t) = a sin(bt) + c metres, with t in hours. The depth oscillates between 3 m and 9 m with a period of 12 h.
- (a)Find the values of a, b and c.
- (b)Interpret the meaning of c in this context.
Your work
a = (9 − 3)/2 = 3
c = (9 + 3)/2 = 6
b = 2π/12 = π/6
Marks awarded
- M1Mark awarded. Amplitude taken as half the range and axis as the midpoint — correct use of the model's structure.
- A1Mark awarded. a = 3, b = π/6, c = 6 all correct.
- R1Mark not awarded. c reported as a number only — never linked to the mean water depth about which the tide oscillates.
Where marks are actually lost
The interpretation layer is where this topic is decided.
Choosing a model family from the scatter alone, without justifying it from the context or the data's behaviour.
CostAppropriateness is a marked judgement, not a formality.
Predicting far outside the observed data with no comment on the domain.
CostExtrapolation without a reasonable-domain statement loses the communication mark attached to it.
Reporting regression or model parameters without saying what each represents in context.
CostA parameter named correctly is a mark; a bare number is not.
Sketching from memory instead of transferring key features from the GDC screen.
CostShape, intercepts and labels are individually assessed — a generic curve earns none of them.
Other Math AI SL topics