The IB Maths Internal Assessment (IA) is worth 20% of your final grade — and for many students, it's the most stressful part of the entire course. Unlike exams, you have weeks to work on it, which sounds like a gift. In practice, that open-ended freedom is exactly what makes it so hard.

This guide walks you through every stage of the IA, from choosing a topic to submitting a polished 12-page exploration. Whether you're on Analysis & Approaches (AA) or Applications & Interpretation (AI), the principles are the same.

What Is the IB Maths IA?

The IA is a mathematical exploration — a written piece of roughly 12–20 pages in which you investigate a mathematical topic of your choice. It is marked by your teacher and then moderated by the IB.

It is assessed on five criteria:

A – Presentation (4 marks): Is it well-structured, coherent, and easy to follow?
B – Mathematical Communication (4 marks): Are notation, terminology, and diagrams used correctly?
C – Personal Engagement (3 marks): Does it feel genuinely yours, not copied from a textbook?
D – Reflection (3 marks): Do you critically evaluate your methods and results?
E – Use of Mathematics (6 marks): Is the maths correct, relevant, and sufficiently sophisticated?

Total: 20 marks. The biggest single criterion is Use of Mathematics — so the quality and depth of your maths matters most.

Step 1: Choose a Topic You Actually Care About

This is the single most important decision. A topic you find genuinely interesting will produce a better exploration than a "safe" topic you chose because you found a template online.

Good starting points:

A real-world phenomenon you want to model (sports statistics, music, architecture, finance)
A puzzle or paradox that surprised you in class
A connection between maths and another subject you study (Biology, Economics, Physics)

Avoid topics that are too broad ("The Golden Ratio") or too narrow ("Calculating the area of my bedroom"). Aim for something with a clear question and enough mathematical depth to sustain 12–20 pages.

Example of a strong topic: "How accurately can a logistic growth model predict the spread of a viral trend on social media?"

Step 2: Frame a Clear Aim

Your IA needs a focused aim — one or two sentences that tell the reader exactly what you are exploring and why. Think of it like a research question.

Weak aim: "I will explore calculus."
Strong aim: "I will investigate how the derivative of a position function models the velocity of a falling object, and compare the theoretical model with real experimental data."

A clear aim keeps your exploration on track and makes it much easier to score well on Presentation and Reflection.

Step 3: Build the Mathematical Core

This is where most marks are won or lost. The IB expects mathematics that goes beyond routine procedures. For AA HL students, that means genuine complexity — proofs, multi-step derivations, or non-trivial applications. For AI SL students, it means using tools like regression, statistics, or financial modelling in a thoughtful, non-mechanical way.

A few principles:

Show your working. Every step should be visible. Don't skip algebra "for brevity."
Use correct notation. Write $$\frac{dy}{dx}$$ not "dy/dx" in running text. Use proper summation notation $$\sum_{i=1}^{n} x_i$$ rather than "x1 + x2 + … + xn".
Interpret your results. After every calculation, explain what the number means in context.
Acknowledge limitations. If your model assumes constant acceleration, say so — and reflect on what that means for accuracy.

For example, if you are modelling population growth with the logistic equation:

$$P(t) = \frac{K}{1 + \left(\frac{K - P_0}{P_0}\right)e^{-rt}}$$

Don't just plug in numbers. Derive the carrying capacity $K$ from your data, explain what $r$ represents biologically, and discuss what happens as $t \to \infty$.

Step 4: Demonstrate Personal Engagement

Criterion C is often misunderstood. Personal engagement does not mean writing "I found this topic fascinating." It means the exploration shows your thinking — your own examples, your own data, your own extensions.

Practical ways to show personal engagement:

Collect your own data (measure, survey, record) rather than using a pre-packaged dataset
Pose your own "what if" questions mid-exploration and actually investigate them
Make a conjecture and test it — even if it turns out to be wrong
Connect the maths to something from your own life or another subject you study

Step 5: Reflect Throughout — Not Just at the End

Many students write a single paragraph of reflection at the end: "In conclusion, my model was quite accurate." That earns minimal marks.

Strong reflection is woven through the entire exploration:

After choosing a method: "I chose linear regression over polynomial regression because my data showed no clear curvature, though I acknowledge this may oversimplify the relationship."
After a surprising result: "The residuals were larger than expected for values above $x = 50$, which suggests the linear model breaks down at higher inputs."
At the end: A genuine critical evaluation — what worked, what didn't, and what you would do differently.

Common Mistakes to Avoid

Copying a topic from the internet. Moderators have seen every "Golden Ratio in nature" IA. It signals low personal engagement immediately.
Too much introduction, not enough maths. Background context should be brief. The maths is the point.
Undefined variables. Every symbol you use must be defined the first time it appears.
No conclusion. Always return to your aim and answer it directly.
Leaving it too late. The IA rewards iteration. Start early, get feedback from your teacher, revise.

A Note on Length

The IB recommends 12–20 pages, but quality beats quantity every time. A tight, well-argued 13-page exploration will outscore a padded 20-page one. Cut anything that doesn't directly serve your aim.

Final Checklist Before Submission

✅ Aim is clearly stated in the introduction
✅ All mathematical notation is correct and consistent
✅ Every variable is defined
✅ Working is shown for all non-trivial steps
✅ Results are interpreted in context after each calculation
✅ Reflection appears throughout, not just at the end
✅ Limitations are acknowledged
✅ Conclusion directly answers the aim
✅ Bibliography is included (if sources were used)

The IB Maths IA is genuinely one of the most rewarding pieces of work you'll do in the Diploma Programme — when approached with curiosity rather than dread. Pick something that interests you, let the maths lead, and reflect honestly on what you find.

Ready to achieve your academic peak? Book a free trial lesson with A Star Academy — email us at [email protected]