IB Maths AI · Topic 2 · Functions · last updated 21 October 2026

Functions practice questions (IB Maths AI)

Topic 2 covers linear, quadratic, exponential, direct and inverse variation and sinusoidal models, the modelling cycle, and solving equations graphically with technology. There are no free sample questions on it yet, so this page gives 7 key terms with the formulas typeset, and a door to make an IB Maths AI-style paper on this topic from your own notes. The free exams are typeset PDFs with an answer key; the exam downloads without a signup.

Make a practice exam from your notes →Upload your notesIB Maths AI style preselected; tick "Topic 2 · Functions" on the next screen. Free to try, no card.

Sample questions

No free sample questions on functions yet. The key terms below cover what IB Maths AI expects you to know for this topic; to practise it, make a paper from your notes or from the IB outline with the unit ticked.

Make a practice exam from your notes →Upload your notes

Key terms

The definitions and formulas IB Maths AI expects for functions, typeset as they appear on the paper.

Linear model: A straight-line relationship with constant rate of change $m$ and initial value $c$ . Parallel lines share $m$ ; perpendicular lines have gradients whose product is $-1$ .
$f(x) = mx + c, \qquad m = \frac{y_2 - y_1}{x_2 - x_1}$
Quadratic model: A parabola with vertex on the axis of symmetry $x = -\frac{b}{2a}$ ; its zeros, vertex and intercepts are read from the GDC. Used for projectile heights and revenue curves.
$f(x) = ax^2 + bx + c$
Exponential model: Growth or decay by a constant factor each unit of time, with $c$ a horizontal asymptote. Half-life and doubling time questions solve $a^x = \frac{1}{2}$ or $2$ with logarithms or the GDC.
$f(x) = k a^x + c$
Direct and inverse variation: Models where $y$ is proportional to a power of $x$ . Negative $n$ gives inverse variation, with both axes as asymptotes.
$y = k x^n$
Sinusoidal model: A sine or cosine curve with amplitude $|a|$ , period $\frac{2\pi}{b}$ (or $\frac{360}{b}$ in degrees), horizontal shift $c$ and principal axis $y = d$ . Used for tides, temperatures and Ferris wheels.
$f(x) = a\sin\big(b(x - c)\big) + d, \qquad \text{period} = \frac{2\pi}{b}$
The modelling cycle: Pose the problem, choose a model, fit it to the data (often by regression on the GDC), test it against new values, and refine or reject it. Examiners ask for a comment on the model's limitations and its appropriate domain.
Logistic model (HL): Growth that starts exponential and levels off at a carrying capacity $L$ , used for populations and the spread of a product.
$f(x) = \frac{L}{1 + Ce^{-kx}}$

Frequently asked questions

Are there free functions practice questions for IB Maths AI?

Not as a ready-made sample yet. The key terms on this page cover what IB Maths AI expects for functions. To practise it, open the generator with the IB Maths AI style, tick "Topic 2 · Functions" and the questions are written from the IB outline for that topic; or upload your own notes on it.

How do I make an IB Maths AI practice paper on functions from my notes?

Open the create page with the IB Maths AI style preselected, tick "Topic 2 · Functions" under the units to cover (or upload your notes and slides on it), choose the question mix and time limit, and generate. You get a typeset PDF in the IB format with a separate answer key, in about a minute. It is free to try, no card needed.

What does IB Maths AI expect you to know about functions?

Topic 2 covers linear, quadratic, exponential, direct and inverse variation and sinusoidal models, the modelling cycle, and solving equations graphically with technology. The terms to have cold: Linear model, Quadratic model, Exponential model, Direct and inverse variation, Sinusoidal model. Each is defined below with its formula typeset where one applies.

What is the IB Maths AI exam format?

The IB Maths AI guide explains the papers, their timing and mark allocation, with a sample question and mark scheme and the common mistakes, and links to the generator with the IB Maths AI style preselected.

Make an IB Maths AI paper on functions from your notes

Open "Pick your exam" with the IB Maths AI style preselected and tick "Topic 2 · Functions", or upload your notes on it. You get a typeset paper in the IB format with a separate answer key.