IA ideas library

Maths IA modelling ideas: fit a function to something real

Modelling is the most common kind of Maths IA, and for good reason: you collect or find data, propose a function that might describe it, fit the function, and then test how well it works. Done well, it hits every criterion — a clear aim, precise notation, real decisions you made, honest reflection on where the model breaks, and mathematics that is used rather than just shown.

The ideas below are chosen so that the modelling is genuinely interesting: there is more than one sensible model, the data is either easy to collect yourself or available from a trustworthy source, and there is a natural way to test the model on data you did not use to build it.

Next step: shortlist ideas with the free IA topic explorer, which filters starting points by course, interest and how easy the data is to get. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

How modelling explorations reach the top bands

Personal engagement (C)

Make the modelling decisions visibly yours: why this family of functions, why these data points, why you rejected the first model. A prediction before each fit, checked afterwards, is engagement an examiner can see.

Reflection (D)

Reflect on each model as soon as you have it: what the parameters mean in context, where the residuals show a pattern, and which assumption is failing. Then let that reflection choose your next model.

Use of mathematics (E)

SL: Two or more justified models, fitted correctly, compared with residuals or the sum of squared residuals, and tested on data you did not use to build them.

HL: An HL modelling IA derives at least one model from assumptions (often a differential equation) rather than only fitting curves, and treats the fitting rigorously: linearisation with logarithms, or minimising the error analytically.

An HL version

Derive the model from a differential equation built on stated assumptions, solve it (analytically for AA HL, or with Euler's method and a slope field for AI HL) and compare it with your fitted curves.

Modelling with functions ideas (13)

Also relevant (51)

Frequently asked questions

What makes a modelling IA score well?

Comparing at least two plausible models, justifying each choice from the context, measuring how well each fits (residuals, R² or sum of squared errors), and testing the chosen model on data you held back. A single regression line with an R² value rarely gets beyond the middle mark bands for Use of mathematics.

Can I use technology to fit the model?

Yes. Desmos, GeoGebra or your GDC can do the fitting, but you must explain what the technology is doing — for example, that least-squares regression minimises the sum of the squared vertical distances — and interpret the parameters it returns.

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