Modelling is one of the central habits of IB Mathematics AI. The task is not simply to fit a curve. Students must decide what variables matter, select a mathematical form, justify assumptions, use technology appropriately, interpret results and evaluate limitations.
A modelling loop
- Define the real question.
- Choose variables and units.
- State assumptions.
- Select a plausible functional form.
- Estimate parameters or fit the model.
- Interpret outputs in context.
- Check residuals, sensitivity or limitations where appropriate.
- Refine the model.
Function families
AI modelling can use linear, polynomial, exponential, logarithmic, sinusoidal and logistic-type relationships depending on the course generation and problem context. The important skill is matching the mathematical behaviour to the phenomenon.
Technology should expose structure
Regression and graphing tools are useful when they help compare models, inspect residuals or visualise behaviour. They become dangerous when students accept an equation simply because the calculator produced it.
Continue through the Functions and Graphs Knowledge Object.
World Mathematics route: return to the World Mathematics Atlas for the wider map across examinations, curricula, competitions, mathematical objects and university routes.
IB Mathematics AI modelling and functions: make assumptions visible
A model is a deliberate simplification
Identify variables, assumptions, domain and purpose. A useful model can be imperfect if its limitations are understood.
Choose function families from behaviour
Linear, exponential, polynomial, logarithmic, logistic or periodic forms encode different patterns. Plot data and inspect context before fitting.
Parameters need meaning
Slope, intercept, growth factor, carrying level or period should be interpreted in the units of the problem. A regression equation without parameter interpretation is incomplete modelling.
Fit is not validity
A high numerical fit over observed data does not guarantee sensible extrapolation. Check residual behaviour, domain and whether the model respects the mechanism.
Piecewise models can be more realistic
Different regimes may need different functions. State boundaries clearly and check continuity if the context requires it.
Technology expands the modelling toolkit
GDC and software can fit models and solve equations, but students still choose variables, transformations and meaningful windows.
Sensitivity matters
Ask how predictions change if parameters or inputs vary. A model whose output changes dramatically under small uncertainty should be interpreted cautiously.
Validate against data or constraints
Compare predictions with unused observations or known boundary behaviour. Validation is a separate step from fitting.
Communicate limitations
State what the model ignores and where it should not be used. This is mathematical maturity, not an admission that the model failed.
Transfer
Use unfamiliar real contexts and require students to defend why a function type is appropriate rather than simply select from a calculator menu.