The Maths IA intimidates students more than almost any other IB assessment…and it's easy to see why. But here's the thing, the students who score 7s aren't necessarily the best mathematicians in the room. Instead, they're the ones who picked a focused topic that can be engaged with and followed the criteria. This guide shows you exactly how to do that.
Note: The Maths IA accounts for 20% of your final IB Maths grade at both SL and HL.
Table of Content
- What Is the IB Maths Internal Assessment?
- What are examiners looking for in the IB Maths Internal Assessment?
- How to Choose Your Topic for IB Maths Internal Assessment
- Common Mistakes to Avoid in Your IB Maths Internal Assessment
What Is the IB Maths Internal Assessment?
The IB Maths Internal Assessment is a written exploration of any mathematical topic, typically between 12 and 20 pages long. Unlike an exam, the IA isn't testing your ability to execute techniques under pressure. It's testing genuine mathematical curiosity and communication.
What Are Examiners Looking For?
Examiners aren't looking for the most complex mathematics. No matter if you’re in SL or HL, they're looking for mathematics that is appropriate to your level, applied thoughtfully to a question you've genuinely engaged with. A focused exploration of a simple topic, done exceptionally well, will outscore an ambitious exploration of an advanced topic that the student clearly doesn't understand.
The Criteria
The IA is marked out of 20 marks across five criteria.
Hot tip: Criterion E carries the most marks, but Criterion C (Personal Engagement) is what often separates a 6 from a 7. Remember, examiners read hundreds of IAs, the ones that feel genuinely curious and individual stand out immediately!
Criterion A: Communication (4 marks)
Your exploration needs to read like a coherent piece of mathematical writing instead of a collection of calculations dropped onto a page. There should be a clear introduction and a logical progression through your ideas that leads to your conclusion that ties everything together. A reader who didn't watch you work should be able to follow your thinking from start to finish.
🔥 Hot tip: Every graph, table, and equation should be labelled and explained.
Criterion B: Mathematical Presentation (3 marks)
This criterion is about mathematical literacy, that is, the correct notation throughout. Variables should be defined before they're used and functions written properly. If you introduce a formula, explain what each term represents. Sloppy notation is one of the fastest ways to lose marks that should be easy to keep!
Criterion C: Personal Engagement (3 marks)
This is the criterion that makes the Maths IA different from a typical textbook chapter. Examiners want to see that you drove this exploration and that you asked your own questions. However, this doesn't mean the IA should read like a personal essay. Instead, it means the mathematics itself should feel directed by a curiosity, not copied from a source.
Criterion D: Reflection (3 marks)
Reflection means stepping back from your results and thinking critically about them. Did your findings surprise you? Do your results have real-world limitations? Is the model you used a simplification? What does that mean for the conclusions you drew? Are there extensions or alternative approaches you could have taken?
🔥 Hot tip: A strong reflection runs throughout the exploration, not just in a final paragraph.
Criterion E: Use of Mathematics (6 marks)
This is the big one. Your mathematics must be correct to your exploration and sufficiently sophisticated for your level. For SL students, this means going beyond routine techniques. For example, applying concepts in new contexts or combining them. For HL students, the bar is higher and the mathematics should reflect the depth and breadth of the HL course. It's worth noting that there is no written IB rule requiring your IA topic to remain strictly within the bounds of the course, nor, on the opposite end, any requirement that HL students must extend beyond it. What matters is that whatever mathematics you use, you can demonstrate genuine understanding of it. Using a sophisticated technique that you can't explain is not ideal. Using course-level mathematics with real depth and insight will always outscore borrowed complexity.
🔥 Hot tip: The "sufficiently sophisticated" bar differs by level. HL students are expected to use mathematics of genuine complexity and depth. If you're HL and your exploration could have been written by an SL student, that's a problem.
How to Choose Your Topic for IB Maths Internal Assessment
This is where most students go wrong. Either they pick something so broad it becomes nearly impossible to handle within 20 pages, or they pick something so obscure and advanced that they can't demonstrate genuine understanding of it.
Hot tip: Think about what you're interested in outside of maths. There is almost always a mathematical angle into anything you care about. Starting from personal interest is the most reliable route to genuine personal engagement marks.
Topic Examples
The below topics can produce strong explorations because they are naturally more focused areas with appropriate levels of mathematics and personal angles. However, they should only act as inspiration and not a template.
1. Calculus & Optimisation: Optimising the shape of a can
Use calculus to find the dimensions of a cylinder that minimises surface area for a given volume. Extend by comparing to real product dimensions and reflecting on why manufacturers may deviate from the mathematical optimum.
2. Statistics & Probability: Modelling sports performance
Apply regression analysis or probability distributions to real sporting data. For example, shot accuracy or race times. Investigate whether performance follows a distribution and what that means for prediction.
3. Geometry & Trigonometry: The mathematics of a spiral staircase
Model a helical staircase using parametric equations. Calculate arc length, pitch angle, and compare the mathematical model to actual architectural designs.
4. Sequences & Series: The Golden Ratio in nature and art
Derive the Golden Ratio from the Fibonacci sequence, investigate its appearance in natural growth patterns, and critically evaluate claims about its prevalence in art and architecture using measurement data.
5. Differential Equations (HL): Modelling population growth
Compare exponential and logistic growth models using differential equations. Fit parameters to real population data and reflect on the assumptions and limitations of each model.
6. Probability & Distributions: The mathematics of blackjack
Calculate probabilities of outcomes using combinatorics and conditional probability to investigate how the mathematics of the game plays out across different scenarios.
7. Functions & Modelling: Modelling the spread of a trend
Use logistic functions to model how a social media trend, disease, or technology adoption spreads through a population. Fit the model to real data and critically assess its accuracy.
🔥 Hot tip: Try to steer clear of extremely overused topics as these explorations are seen by examiners hundreds of times per year. They're not entirely off-limits, but you'd need to bring a very original angle to stand out.
Common Mistakes to Avoid in Your IB Maths Internal Assessment
- Choosing a topic that's too broad
- Using mathematics you don't understand
- Neglecting to explain your mathematics
- Saving all reflection for the last paragraph
- Only mentioning personal engagement in the introduction
- Using incorrect or inconsistent notation
- Exceeding 20 pages of main body content
- Producing a report, not an exploration
Formatting
- All mathematical notations must be correct and consistent throughout
- Every variable, function, and symbol must be defined before it is used
- All graphs and diagrams must be clearly labelled with titles and axis labels
- All tables must be clearly headed with appropriate units
- Your IB candidate code appears on the document
- The title appears on the front page
- Page count is within the expected range
- Reflection appears throughout, not only in the conclusion
- The level of mathematics is appropriate and goes beyond routine application
That's it. That's the formula. It's not about impressing examiners with complexity; instead, it's about convincing them that a curious mathematician asked a question and followed it wherever it led.
Check out more of our IB Maths study guides to learn how to score top marks.
Manoj Arachige
Manoj Arachige
Manoj Arachige
Manoj Arachige
FAQs
Does my topic for my IB Maths Internal Assessment have to be from the IB syllabus?
No. Some of the strongest IAs venture into mathematical territory that goes slightly beyond the syllabus. What matters is that the mathematics is appropriate to your level and that you demonstrate genuine understanding of it. If you use advanced techniques you haven't been taught, you need to be able to explain them to demonstrate that you understand them.
Can I use technology such as GDCs, software, spreadsheets for my IB Maths Assessment?
Yes, and you should. Using tools like Desmos, GeoGebra, Excel, or Python is entirely appropriate and often expected. What matters is that you understand and explain what the technology is doing and don't just copy and paste without interpretation.
My exploration for IB Maths didn't lead where I expected. Is that a problem?
Absolutely not! In fact, it can be an advantage. Unexpected results give you something genuine to reflect on, which is exactly what Criterion D is looking for. Explain why you think the results diverged from your expectation and what that tells you. This shows your critical thinking skills and your genuine curiosity for the mathematics you’re presenting.
Can I include an appendix for longer calculations in my IB Maths Internal Assessment report?
Yes. Lengthy or repetitive calculations that interrupt the flow of the exploration can be moved to an appendix. However, make sure you reference them clearly in the main body and include a brief summary of the key result in the main body. Examiners may not read appendices in detail, so the important mathematics should always appear in the main body.
Want more personalised study guidance to help drastically improve your marks? A private tutor from KIS Academics can make the biggest difference!
What Our Students & Parents Say
600+ Five-Star reviews across all our tutoring programs — hear why below !👇
Written by KIS Academics Tutor for IB Maths AA HL/SL, Biology HL/SL, Economics HL/SL, Chemistry SL, Alice Xu. Alice is currently pursuing a Bachelor of Biomedicine at the University of Melbourne and has received stellar reviews from her past KIS Academics students. You can view Alice’s profile here and request her as a tutor.
