60+ IB Math IA Topics for 2026 (and How to Pick a Winning One)

The IB Math Internal Assessment is 20% of your final grade in both Math AA and Math AI. It's the single biggest piece of personal work you'll submit, the only major mark you control entirely outside the exam hall, and — for most students — the difference between a 6 and a 7. Yet most students spend their first two weeks picking a topic that sets them up to lose marks in the Mathematical Communication and Personal Engagement criteria before they've written a single equation.

This guide gives you 60+ tested IB Math IA topic ideas (sorted by Math AA HL, Math AA SL, Math AI HL, and Math AI SL), the actual IB criteria a moderator scores you on, and a clear five-step framework for choosing a topic that wins marks instead of bleeding them.

If you'd rather generate a topic in 30 seconds based on your subject and interests, Educifly's free IB IA Topic Generator does exactly that.

What is the IB Math Internal Assessment?

The IB Math Internal Assessment (IA) is a 12–20 page mathematical exploration that every IB Diploma Math student — whether enrolled in Math AA or Math AI, at HL or SL — must complete and submit to the IB. It is internally marked by your teacher and externally moderated by the IB. It is worth 20% of your final IB Math grade.

The IA is graded out of 20 marks, split across five criteria:

The top mark, Criterion E (Use of Mathematics), rewards mathematics that is commensurate with the level of the course. Translation: a Math AA HL IA built around the quadratic formula will be penalised. A Math AI SL IA built around partial differential equations will be penalised for the opposite reason. Topic choice is what determines whether you can score in Criterion E at all.

How to choose an IB Math IA topic — a 5-step framework

Most students pick a topic by Googling "IB Math IA topics", picking the first thing that looks doable, and writing 14 pages around it. The result is usually a 4 or 5. Here is the framework Educifly's IB Math specialists use with students who score 7s.

Step 1: Start with an interest, not a topic

The IB awards 3 marks for Personal Engagement, and moderators can spot a forced personal hook from a mile away. Start with something you genuinely care about — basketball shooting angles, the way Spotify recommends songs, modelling a disease outbreak you read about, predicting cricket scores, optimising your sleep schedule. Then ask: where is the mathematics in this?

Step 2: Find the mathematical content

A topic without mathematics is an essay, not a Math IA. Once you have a genuine interest, identify the mathematical content. Examples:

• "Spotify recommendations" → matrix algebra and cosine similarity

• "Optimising my sleep" → regression analysis of sleep data

• "Basketball free-throw angles" → projectile motion and calculus

• "Predicting cricket scores" → exponential regression and confidence intervals

Step 3: Match the maths to your course level

This is where most students lose Criterion E.

• Math AA HL — calculus (multiple integrals, differential equations), complex numbers, vectors in 3D, advanced statistics. Avoid topics that resolve in basic algebra.

• Math AA SL — single-variable calculus, trigonometry, sequences and series, probability. Avoid topics that only use Year 11 algebra.

• Math AI HL — statistical modelling (multiple regression, chi-squared, Markov chains), graph theory, voting theory, financial mathematics.

• Math AI SL — descriptive and inferential statistics, exponential and trigonometric modelling, basic financial mathematics.

Step 4: Check the question is narrow enough to answer in 14 pages

The single most common Math IA failure mode is a topic that's too broad. "Can mathematics predict the stock market?" is not an IA — it's a PhD. Narrow it down:

• ❌ Too broad: Can mathematics predict the stock market?

• ✅ Just right: Can a logistic regression model predict next-day movement of the NIFTY 50 from the previous 30 days of returns?

Step 5: Pre-check that you can score in every criterion

Before you commit, write a one-paragraph plan and stress-test it:

• Can I show genuine engagement? (e.g., your own data, your own simulation, your own twist)

• Can I use mathematics at the right level?

• Can I reflect critically — discussing limitations, alternative approaches, what you'd do differently?

• Can I structure this with a clear introduction, methodology, analysis, and conclusion?

If you answer yes to all four, the topic is worth committing to.

30+ IB Math AA IA topics (HL and SL)

These topics work across Math AA HL and Math AA SL — at HL you go deeper into the calculus, complex numbers, or proof; at SL you stay within the SL syllabus and build genuine depth there.

Calculus and modelling

1. Modelling the trajectory of a free throw in basketball using projectile motion and finding the optimal release angle for a 1.8m vs 2.0m player. Pure calculus, real-world data, personal engagement built in if you play basketball.

2. Using calculus to optimise the dimensions of a cylindrical drink can for minimum surface area at fixed volume — and explaining why real cans don't match the optimal shape.

3. Modelling the spread of a viral video on Instagram using the logistic differential equation and comparing it to actual data from a real post.

4. The mathematics of fluid drainage from a conical funnel (Torricelli's law) — modelled with a differential equation, then tested experimentally.

5. Using related rates of change to model how shadow length changes as the sun moves across the sky in your city.

6. Modelling the volume of a wine bottle as a solid of revolution — and calculating the actual volume to within 5%.

7. Optimising the route between three real locations using Lagrange multipliers (HL only — fits Math AA HL extension into multivariable thinking).

Trigonometry and periodic functions

1. Modelling daylight hours across the year in Singapore vs Geneva using sinusoidal regression — and explaining the difference using axial tilt.

2. Modelling tide heights at a real port using a sum of two sine waves and comparing predicted vs actual.

3. Modelling the swing of a pendulum using simple harmonic motion and explaining where the model breaks down for large angles.

4. The mathematics of a basketball arc — using parametric equations and finding the angle that maximises swish probability.

Statistics and probability

1. Is there a statistically significant difference in spotify song length between top-100 songs of 2010 and 2024? A two-sample t-test using your own scraped data.

2. Modelling exam performance using a chi-squared test of independence — does revision method correlate with grade outcome among your year group?

3. Using binomial distribution to model penalty-kick conversion rates in the Premier League — and testing whether top-six teams beat the model.

4. A Bayesian approach to predicting whether your school's lift will be on your floor when you call it.

5. Modelling COVID-19 case growth in your country during a fixed two-month window using exponential and logistic regression — and discussing which model fits better and why.

Geometry and proof (Math AA HL favourites)

1. A geometric and algebraic proof of Heron's formula, and applying it to find the area of irregular plots of land near your home using Google Maps coordinates.

2. Investigating the relationship between the golden ratio and the proportions of famous paintings — using actual measurement and statistical testing.

3. Proving Euler's formula e^(iπ) + 1 = 0 from the Taylor series, and exploring three of its surprising applications.

4. The mathematics of Voronoi diagrams — and using one to determine the optimal location for a new coffee shop in your neighbourhood.

Number theory and sequences

1. Investigating the Collatz conjecture — testing it computationally on integers up to 10,000 and analysing the distribution of stopping times.

2. Continued fractions and the best rational approximations of π — including a comparison with values used historically.

3. The mathematics behind RSA encryption — explaining and demonstrating the role of modular arithmetic and Fermat's little theorem.

4. Investigating Fibonacci sequences in real biological structures (pinecones, sunflowers, your own pineapple) — with photographs and counts.

Vectors and 3D (Math AA HL)

1. Modelling the optimal angle of a satellite dish in your city using 3D vectors and azimuth/elevation calculations.

2. The mathematics of GPS trilateration — explaining how three satellites locate you and modelling the maximum theoretical error.

3. Using vector calculus to model the path of a hooked penalty kick in football.

Complex numbers (Math AA HL)

1. Mandelbrot and Julia sets — exploring the geometry of complex numbers and generating one yourself using a simple iteration.

2. De Moivre's theorem and how it underpins the fast Fourier transform behind every audio compression algorithm.

3. The mathematics of AC circuits using complex impedance — modelling the resonance frequency of a real circuit.

30+ IB Math AI IA topics (HL and SL)

Math AI rewards modelling real-world phenomena and statistical inference more than pure proof. These ideas play to that strength.

Statistical investigations

1. Is there a relationship between sleep duration and academic performance among IB students in your year? A correlation analysis with chi-squared follow-up.

2. Do English Premier League home teams score significantly more than away teams? A two-sample t-test on a season of data.

3. Modelling the relationship between a country's GDP per capita and life expectancy using your own scraped World Bank data — linear vs logarithmic regression.

4. Are penalty kicks in football biased to one side? Analysing five seasons of data and using a chi-squared goodness-of-fit test.

5. Is there a significant difference between male and female reaction times in your school? Designing the experiment, collecting the data, and running the t-test.

Modelling

1. Modelling cryptocurrency price movement (Bitcoin or Ethereum) using an exponential model vs a logistic model — discussing which fits better and the limitations of both.

2. Modelling the depreciation of three different car models over ten years — exponential vs linear, and predicting future value.

3. Modelling the spread of a rumour through your school using the SIR (Susceptible–Infected–Recovered) compartmental model.

4. Using exponential decay to model caffeine concentration in your bloodstream — and calculating the optimal time to stop drinking coffee before sleep.

5. Modelling the cooling of a cup of coffee using Newton's law of cooling — with your own thermometer data taken every minute for 30 minutes.

Financial mathematics

1. Comparing the long-run return of investing ₹10,000/month in the NIFTY 50 vs a fixed deposit over 20 years — using compound interest and historical return data.

2. The mathematics of credit card debt — modelling how minimum payments turn a ₹50,000 balance into a multi-year liability.

3. The mathematics of a mortgage — modelling the actual interest paid on a $400,000, 30-year fixed-rate mortgage at 6%.

4. Is a Tesla cheaper than a Toyota over 10 years? A full cost-of-ownership model including depreciation, fuel, electricity, and maintenance.

Voting theory and graph theory (Math AI HL)

1. Comparing first-past-the-post and ranked-choice voting using real election data — and showing how the winner can change.

2. Using graph theory to model the London Underground — finding the shortest route between two stations using Dijkstra's algorithm.

3. The mathematics of Google PageRank — building a mini PageRank model on a 10-node graph of websites.

4. The travelling salesman problem applied to a real itinerary — finding an approximate solution using the nearest-neighbour heuristic.

Probability and games

1. The mathematics of Monopoly — using a Markov chain to find the long-run probability of landing on each square, and identifying the most valuable properties.

2. Is the casino game roulette beatable? Using expected value and standard deviation to disprove three popular betting strategies (Martingale, D'Alembert, Fibonacci).

3. The mathematics of Wordle — modelling optimal first-guess strategy using letter frequencies and information theory.

4. The mathematics of dating apps — modelling the optimal stopping problem (the "37% rule") and discussing where it actually applies.

Geometry and trigonometry in real contexts

1. Calculating the actual height of a building in your city using trigonometry, a phone-mounted angle sensor, and three measurement points — and comparing to the published height.

2. Modelling the optimum cover-image dimensions for Instagram engagement using regression on a dataset of posts.

3. The geometry of M.C. Escher's tessellations — analysing the underlying symmetry groups in three of his works.

What separates a 7-grade IA from a 5-grade IA?

Educifly's Math specialists have read and coached hundreds of IB Math IAs. The pattern at the top is consistent. A 7-grade IA does five things at once.

It has a clearly stated, narrow research question — usually a single sentence with a specific number, period, or population in it. Not "Can we use mathematics to model exam performance?" but "Is there a statistically significant correlation between weekly self-reported study hours and final IB Predicted Grade among 60 students in my school's IBDP2 cohort?"

It uses mathematics at the level of the course, not above and not below. A Math AA HL student investigating a real-world question with single-variable calculus is doing it right. A Math AA HL student using only descriptive statistics is undermarking Criterion E. A Math AI SL student trying to do measure theory is overreaching and will lose marks in Communication and Reflection.

It shows your fingerprints all over the work. Your own data collection. Your own choice of model. Your own admission of where the model breaks down. The IB's Personal Engagement criterion is impossible to fake — moderators have read 200 IAs about Newton's law of cooling, and they know exactly which ones were written by a student who actually held a thermometer.

It reflects critically — repeatedly. Not just a "limitations" paragraph at the end. Reflection threaded throughout: I initially modelled this exponentially, but the residuals showed a clear pattern, so I switched to a logistic model. The logistic model still has limitations because…

It is presented well. Equations rendered properly (LaTeX or Word's equation editor — not photographed handwriting). Graphs labelled axes-and-units. Tables with captions. A logical structure: introduction → research question → methodology → analysis → conclusion → reflection.

Three common Math IA mistakes that cost marks

1. Choosing a topic that's been done to death without adding anything new. A modelling exploration of Newton's law of cooling that ends with "the temperature decreases exponentially" is a Personal Engagement 0. Same model, but you collected your own data on three different cup materials and compared cooling constants → suddenly engaging.

2. Submitting a topic without doing the maths first. Many students commit to a topic before checking that the actual mathematics is doable. By the time they realise it isn't, it's too late to switch. Spend two hours doing a miniature version of the maths before committing.

3. Treating the IA like a research paper instead of a mathematical exploration. Long-winded introductions about the history of statistics waste pages. The moderator wants the mathematics, your reasoning, your data, your reflection. Cut everything else.

How Educifly helps with the Math IA

Educifly's IB Math tutors provide structured IA coaching as part of every 1-on-1 programme. We help with:

• Topic selection — narrowing your interest to a question that scores in every criterion

• Methodology design — making sure the maths is at the right level and the data is collectable

• Mark scheme alignment — going line-by-line through the IB criteria to identify where marks are won and lost

• Drafting and revision — multiple structured rounds of feedback

• Final review — a pre-submission audit against the IB rubric

Most of our students see at least a full grade-band lift on their IA after structured coaching. Book a free 30-minute trial class with an IB Math specialist and we'll diagnose where you are and map out exactly what your IA needs.

FAQ — IB Math IA Topics

How many pages should an IB Math IA be?

The IB recommends 12 to 20 pages. Most 7-grade IAs land between 14 and 18 pages. There is no penalty for being shorter — there is a soft penalty for being longer, because moderators stop reading carefully past 20 pages.

Can I change my IA topic after starting?

Yes, until your school's internal deadline. After your supervisor signs off on the topic and you've drafted significant work, changing becomes very expensive in time. Most schools allow one structured topic switch in the first three weeks.

What's a good IA topic for Math AA HL?

A topic that requires mathematics from the HL syllabus — typically calculus (differential equations, integration techniques), complex numbers, vectors in 3D, or non-trivial proof. Examples from this list: 1, 7, 17, 19, 25, 28.

What's a good IA topic for Math AI SL?

A topic that uses statistical inference (hypothesis testing, regression) or real-world modelling at the SL level. Examples from this list: 31, 34, 38, 40, 41.

Can I use AI tools like ChatGPT for my Math IA?

You can use AI for brainstorming and clarifying concepts, but submitting AI-generated text or analysis as your own work is academic misconduct under the IB's policy and will result in your IA being invalidated. The Personal Engagement criterion is also designed to make this difficult — moderators are increasingly trained to spot AI-generated reasoning.

Does the IB Math IA need primary data?

No, but primary data (data you collected yourself) usually scores higher in Personal Engagement than data downloaded from Kaggle. If you use secondary data, make sure you've cleaned it, transformed it, or combined it in a way that's clearly your own work.

What is the IA worth in my final IB Math grade?

20% — the same as one full exam paper. It's also the only component you control entirely outside the exam hall, which makes it the highest-leverage piece of work in the course.

Ready to lock in your Math IA topic with a specialist? Book a free trial class with an Educifly IB Math tutor — 30 minutes, no card, no commitment.