IB Maths IA Topics: Ideas by Course and Level
The best IB Maths IA topic is one you are curious about, that fits the maths of your course and level, and that is narrow enough to explore in depth. Below you will find topic ideas for AA and AI, a section on matrices, sample research questions, and a short checklist for testing any idea before you commit.
TL;DR
- Pick a topic you can ask a specific question about, not a broad theme such as “probability” or “sport”.
- Match the mathematics to your course. AA topics lean towards algebra, calculus and proof. AI topics lean towards modelling and statistics.
- Matrices work well for Markov chains, transformations and systems of equations, but check they sit at your level.
- Start with a question you can test with data or a derivation, then choose the method.
- Use your teacher as a sounding board early, before you have written pages on the wrong idea.
Table of Contents
- What makes a good IA topic
- Matching the topic to your course and level
- IB Maths IA topic ideas for AA
- IB Maths IA topic ideas for AI
- IB Maths matrices IA ideas
- Turning an idea into a research question
- Mistakes to avoid
- Our perspective
- Build the maths behind your IA with Tiber Tutor
- FAQ
- Sources
What makes a good IA topic
A strong topic has three qualities. It is focused: you can state it as one question. It is personal: you have a reason to care about the answer. It is mathematical: the work is driven by maths you can explain, not by description.
A quick test helps. Can you write the research question in one sentence? Can you name the main mathematical tools you will use? Could a classmate follow your method after reading it once? If the answer to any is no, narrow the idea.
Topics that sound impressive often fail the third test. A student who writes about “the mathematics of music” without a precise question tends to describe rather than investigate. A student who asks how the ratio of string lengths relates to frequency, and models it, has something to analyse.
Matching the topic to your course and level
Your course decides which mathematics feels natural. The AA guide from the IB organises the course into number and algebra, functions, geometry and trigonometry, probability and statistics, and calculus. Each topic contains SL content followed by additional HL content, so your IA should use mathematics appropriate to the level you are enrolled in.
The two courses have different personalities. One school’s programme information describes AA as emphasising algebraic, analytic and proof-oriented thinking, with AA HL extending into complex numbers, induction, vectors, differential equations and Maclaurin series. The same document describes AI as focused on using mathematics to describe the real world, with modelling and statistics prominent, and places matrices, graph theory, Markov chains and eigenvectors in AI HL.
In practice:
| Course and level | Natural territory | Example direction |
|---|---|---|
| AA SL | Functions, calculus, trigonometry | Optimising a shape or modelling a curve |
| AA HL | Complex numbers, vectors, series, differential equations | Maclaurin approximations, de Moivre patterns |
| AI SL | Statistics, modelling, finance | Regression on real data, hypothesis testing |
| AI HL | Graph theory, Markov chains, matrices | Network routing, long-run behaviour of a system |
Use this as a guide, then confirm with your teacher what counts as appropriate for your syllabus.
IB Maths IA topic ideas for AA
AA suits students who enjoy derivations and structure. Each idea below is a starting point to narrow, not a finished question.
- Optimisation in design. Find the dimensions of a container, a can or a running track that minimise material or maximise volume. Research question: how does the optimal shape change when a constraint, such as a fixed surface area, is altered?
- Approximating functions. Compare Maclaurin polynomials with the true function for sine or an exponential. How many terms do you need for a given accuracy, and where does the approximation break down? (HL)
- Projectile motion. Model a ball’s flight with and without a drag term. Which differential equation describes it, and how well does the solution match data you film yourself?
- Number patterns. Explore Fibonacci-type sequences and their link to the golden ratio, proving a closed form by induction. (HL for induction)
- Geometry and trigonometry. Investigate how the area of a polygon inscribed in a circle approaches the circle’s area, and use it to estimate pi.
- Calculus in context. Use integration to find the volume of a solid of revolution that models a vase or a bottle, then compare your answer with a measured volume.
If you want to sharpen the underlying skills while you choose, our IB Maths AA notes and AA questions cover the syllabus topics these ideas draw on.
IB Maths IA topic ideas for AI
AI rewards a real data set and a clear modelling question.
- Sports statistics. Does home advantage change with the sport or the season? Use a chi-squared test on results from a league you follow.
- Regression and prediction. Model how a city’s bike-share usage depends on temperature, then test how well the model predicts a new month.
- Finance. Compare loan repayment schedules, or model compound growth in a savings plan, and ask how a small change in interest rate shifts the total cost.
- Spread of an idea. Fit a logistic model to the adoption of a new app or product and interpret the parameters.
- Sampling and bias. Compare different sampling methods on a school-wide survey and explain why the estimates differ.
- Voronoi diagrams. Use them to decide where a new facility should go in your town. (Check your teacher’s view on level.)
To build confidence with the statistics behind these, try the AI topic tests and the AI definitions, which help you use the right terms in your write-up.
IB Maths matrices IA ideas
Matrices are popular because they connect algebra to real systems. They also tend to arrive at higher levels, so first confirm your course includes the content you plan to use.
Here are five directions:
- Markov chains for a weather or customer-loyalty model. Build a transition matrix, find the steady state, and ask how sensitive the long-run result is to a change in one probability.
- Geometric transformations. Represent rotations, reflections and shears as matrices, then investigate what happens when you combine them. Does the order matter?
- Eigenvalues and population growth. Use a Leslie matrix to project an animal population and examine which survival rate affects growth most.
- Solving systems. Compare matrix methods for systems of equations with other approaches, using a traffic-flow or budget scenario.
- Cryptography. Encode and decode a message with a matrix key, then explore why some keys fail.
Each one gives you a question to ask, a calculation to justify and a result to reflect on. That last part matters: an IA is stronger when you can say what the answer means and where the model is limited.
Turning an idea into a research question
A topic is a subject. A research question is something you can answer. Compare these:
| Too broad | Focused |
|---|---|
| Probability in games | How does the probability of winning a best-of-seven series change with the chance of winning a single game? |
| Calculus in architecture | Which parabolic arch height maximises the enclosed area for a fixed span and material length? |
| Statistics and health | Is there a relationship between daily steps and resting heart rate in a sample of 40 classmates? |
Notice that each focused question contains a variable you can change, a measure you can compute and a method you could justify.
Mistakes to avoid
- Choosing something too advanced. Copying university-level maths you cannot explain will cost you in communication and use of mathematics.
- Choosing something too thin. A topic that needs only one formula leaves nothing to explore.
- Letting technology do the thinking. Software is useful, but you should show why each step is valid.
- Ignoring personal engagement. Pick something from your own interests, such as a sport, an instrument or a game, and say why it matters to you.
- Leaving it late. Students who wait often rush the reflection. Settle on a question early and refine it with your teacher.
- Overused ideas. Common topics can still work, but you need a distinctive angle, your own data or a new constraint.
Our perspective
We have seen the same pattern in strong IA work: the student understood the syllabus mathematics deeply before they tried to extend it. Our resources are written by IB examiners, so we build everything around how the course is actually assessed.
That is why we link our notes, questions, definitions and topic tests to one another. When you meet a tool in an IA, such as a transition matrix or a hypothesis test, you can move straight to the matching notes and then practise exam-style questions on it. Our progress tracking shows which syllabus areas are secure, so you know where your mathematics is solid enough to build an exploration on.
We believe Tiber Tutor offers the best value for money among IB STEM platforms, because examiner-written content, integrated analytics and syllabus monitoring sit together in one place. We are not aware of another site that offers all of this.
Oliver
Build the maths behind your IA with Tiber Tutor
A good IA stands on solid core mathematics. Tiber Tutor gives you examiner-written notes, exam-style questions, flashcards, topic tests and mock exams for IB Maths, with performance analytics that show your strengths and gaps. The All-Access Plan is $19 per month and the Per-Subject Plan is $9 per month, both after a free 7-day trial.
See the options on our pricing page, or explore what we offer for IB students. Parents can start with our page for IB parents.
FAQ
How do I choose an IB Maths IA topic?
Start with something you already enjoy, then ask what you could measure, model or prove about it. Turn it into one focused question. Check that the mathematics fits your course and level, then talk it through with your teacher.
Can I use the same topic for AA and AI?
Sometimes, but the approach will differ. A topic such as population growth could be explored through differential equations in AA or through data and regression in AI. Choose the method that fits your course content.
Are matrices allowed in an SL IA?
The IA should use mathematics appropriate to your enrolled course and level. Matrix topics such as Markov chains and eigenvectors are placed in AI HL by the programme information, so confirm the details with your teacher before you commit.
Can I choose a topic from another subject?
Yes. Many strong explorations come from sport, music, finance or science. What matters is that the maths is central, and that you explain it clearly rather than describing the context.