50+ IB Maths IA Ideas for AA & AI That Actually Work

Last revised June 2026 by Sandra Steiger, TutorsPlus Education Advisor

Most students start their IB Maths IA with plenty of ideas but no clear direction. A topic might sound interesting, but is it mathematical enough? Is it too broad? Will it generate meaningful analysis? These questions often make the early stages of the IA more difficult than expected.

Successful IAs come in many forms. Some students use statistics and real world data, while others focus on modelling, optimisation, geometry, finance, or game theory. 

Whether you’re studying IB Maths AA or AI, this guide includes over 50 IA topic ideas, along with advice on developing a strong research question, understanding what examiners look for, and avoiding common mistakes.

Why Choosing a Unique Topic Actually Matters

Your topic can have a major impact on your Maths IA. It influences how engaged you stay throughout the process, how clearly you communicate your ideas, and how much mathematical understanding you can demonstrate. The person evaluating it wants to see independent thinking and meaningful personal engagement with the investigation.

Popular topics such as the Golden Ratio, Fibonacci sequences, and population growth models can still work well, but your investigation should have a clear personal angle. Using a unique dataset, a specific real world application, or a topic connected to your interests can help make your IA more original and meaningful.

The best maths IA ideas tend to share a few qualities. They combine the following elements:

• Personal interest in the topic
• Clear and relevant mathematical content
• Access to reliable data
• A focused and answerable research question
• Room for reflection and honest evaluation

Getting this right at the start saves a lot of time and stress later on.

IA Ideas for AA and AI Students

Both courses use the same assessment criteria, but the mathematical focus is quite different, and that should guide your topic choice.

If you’re completing a Maths AA IA, you’ll generally be expected to engage with more theoretical mathematics. Calculus, functions, modelling, graph theory, differential equations, and optimisation all fit well within this course. Some popular starting points for AA students include the following topics:

• Modelling projectile motion in sport
• Optimising packaging dimensions
• Population growth modelling
• Graph theory and transportation networks
• Differential equations in epidemiology

For Maths AI students, the focus shifts towards mathematics in real world contexts. Statistics, probability, data analysis, finance, and technology-based applications tend to work particularly well. AI students often find strong material in these areas:

• Social media usage patterns
• Sports performance analysis
• Financial forecasting
• Consumer behaviour studies
• Weather prediction models

Both pathways can absolutely achieve top marks. The important thing is choosing mathematics that fits your course level and gives you enough to work with analytically. If you’re still weighing up the two courses, our guide to IB Maths AA vs AI can help you think that through.

How to Turn a Broad Idea into a Research Question

Most students start with a general area they’re interested in, not a polished research question. That’s completely fine. The skill is in narrowing things down until your question is specific, measurable, and mathematically driven.

Let’s take a look at how that progression works in practice.

Example 1 

Broad idea: Basketball

Weak question: How does maths apply to basketball? 

Strong question: To what extent can projectile motion equations predict free throw success rates in professional basketball?

Example 2 

Broad idea: Traffic 

Weak question: How does traffic work? 

Strong question: How accurately can graph theory model traffic flow between key intersections in central London?

Example 3 

Broad idea: Finance 

Weak question: How does investing work? 

Strong question: How effective is the Markowitz Portfolio Model when applied to a selected group of technology stocks?

A strong research question is focused, manageable, and clearly mathematical. It should include defined variables, a specific area of mathematics to explore, and access to data or information that you can realistically collect and analyse.

Spending time on this stage before you start writing is one of the most valuable things you can do for your IA.

What Makes a High-Scoring Topic

The strongest Maths IAs tend to share a handful of characteristics worth keeping in mind.

Personal interest. Students consistently produce better work when the topic means something to them. Sports, music, travel, gaming, architecture, finance, and science can all lead to excellent investigations. If you’re curious about something, that curiosity and excitement tends to come through in the writing.

Strong mathematical content. The maths needs to sit at the heart of the investigation. The marker is rewarding mathematical understanding, not descriptive writing. If you could remove most of the maths and still have a coherent piece of writing, the topic probably needs rethinking.

Available data. Even a brilliant topic will fall apart if you can’t access enough reliable information. Public datasets, surveys, experiments, and historical records are all good sources. Check this before you commit.

A clear scope. Broad topics lead to shallow analysis. The more focused your question, the more depth you can bring to mathematics.

Opportunities for reflection. Top-scoring students don’t just present results. They evaluate limitations, discuss their assumptions, and suggest how the investigation could be improved. A good topic gives you something meaningful to reflect on.

When you’re choosing between a few different ideas, go with the one that gives you the best balance across all five of these areas.

Over 50 Maths IA Ideas to Inspire You

These categories cover a wide range of mathematical areas. Use them as a starting point and personalise from there.

Modelling and Simulation

Mathematical modelling is a popular area because it connects abstract concepts to real world behaviour. These topics work especially well for AA students. Here are some ideas to consider:

• Modelling the spread of infectious diseases
• Optimising disaster relief resource allocation
• Modelling population growth and sustainability
• Simulating traffic flow using agent-based modelling
• Modelling football trajectories using calculus
• Predator-prey dynamics with differential equations
• Planetary motion using trigonometric functions
• Population interactions through differential equations

Topics in this category tend to reward students who enjoy building and testing mathematical systems.

Statistics and Data Analysis

Statistics-based investigations are among the most popular choices for AI students, and for good reason. Here are some well-suited topics:

• Analysing voting systems and fairness
• Sports statistics and performance prediction
• Mathematical fairness in elections
• Social media algorithms and recommendation systems
• Sports analytics using probability
• Evaluating medical treatment effectiveness
• Regression analysis of NBA player performance
• Risk analysis using Markov chains
• Quality control and statistical methods

These topics give you plenty of opportunity to collect, process, and interpret real data, which is exactly what examiners want to see.

Applied Mathematics

Applied mathematics links theory to practical decision-making. These investigations often draw on several mathematical concepts at once. Some strong directions include:

• Fair division problems
• Supply chain optimisation using linear programming
• Optimising travel routes with calculus
• Investment strategy optimisation
• Manufacturing schedule optimisation
• Shortest path problems using graph theory
• London bus route optimisation
• Portfolio optimisation using the Markowitz Model
• Vector applications in engineering
• Renewable energy optimisation

The variety here means there’s likely something that connects with your interests.

Practical Mathematics

These topics explore how maths shows up in everyday situations, and they’re more accessible than they might look. Consider exploring:

• Financial modelling and investment analysis
• The Monty Hall Problem
• Optimal packing strategies
• Probability in weather forecasting
• Matrices in image processing
• Mathematics behind machine learning algorithms

Don’t underestimate these areas. They’re accessible on the surface but can support real depth when approached well.

Geometry and Visualisation

Geometry can produce some of the most visually engaging and creative IAs. If you enjoy visual thinking, these might appeal to you:

• Fractal geometry in nature
• Topology and graph theory
• Romanesco broccoli fractals
• Alhambra tiling patterns
• Linear algebra in electrical circuits
• Computer graphics mathematics
• The Golden Ratio in art and nature
• Complex numbers and fractals
• Mathematics of music and harmony

These topics let you combine creativity with rigorous mathematical analysis.

Number Theory and Cryptography

If you’re interested in computer science or security, these topics are worth considering:

• Breaking simple ciphers
• Public key cryptography
• Number theory applications in encryption

Cryptography in particular can be a rewarding area for students who enjoy logical reasoning and want to connect maths to technology.

Game Theory

Game theory looks at strategic decision-making and has strong links to economics and social science. Some directions to explore include:

• Mathematics of games and puzzles
• Game theory in economics and politics
• Voting systems and strategic voting

These topics work well for students who want to apply mathematical thinking to human behaviour and real world decisions.

Chaos Theory

Chaos theory examines systems that appear unpredictable but follow underlying mathematical rules. Two strong starting points are:

• Applications of chaos theory
• Chaos theory and weather prediction

These investigations can lead to rich discussions about the limits of modelling, which gives you a lot to reflect on in your evaluation.

Common Mistakes to Avoid

Many students lose time and marks because of avoidable mistakes in the early stages. Here are the ones that come up most often.

Choosing a topic that’s too broad. A question like “The Mathematics of Football” covers too much ground and leads to shallow analysis. Narrow it down to something like predicting goal outcomes using expected goals data, or modelling free kick trajectories using calculus. A tighter scope almost always leads to stronger mathematics.

Not putting maths at the centre. The IA is a mathematics investigation, not a research essay. Some students write a lot about their topic and very little mathematics. Before you commit, check that the maths is the main event, not the background.

Choosing maths that’s too complicated. Complex mathematics doesn’t automatically earn higher marks. A well-executed investigation using accessible concepts often outperforms a technically ambitious project that’s hard to follow. Choose mathematics you can explain confidently.

Copying common examples too closely. Topics like the Golden Ratio and Fibonacci sequences appear in thousands of submissions every year. If you go down this route, make sure your data, context, and approach are clearly your own. It’s easy to tell when a project lacks personal engagement.

Not checking your data sources early enough. Plenty of strong ideas fall flat because the data simply isn’t available. Before you settle on a topic, confirm that you can access enough reliable information to support meaningful analysis. Useful sources include public datasets, sports databases, government statistics, surveys, and personal experiments. A bit of early planning goes a long way.

Avoiding these common mistakes from the start will make your IA easier to manage and give you a stronger foundation for success. 

Frequently Asked Questions

What is a good IB Maths IA topic? 

A good topic combines personal interest with strong mathematical content. It should let you apply mathematical concepts, analyse results, and reflect honestly on limitations. Statistics, modelling, optimisation, finance, and sports analytics are all areas where strong IAs regularly emerge.

How do I choose a high-scoring topic? 

Start with something you enjoy, then look for ways to apply mathematics in a meaningful way. You’ll want a clear focus, accessible data, and mathematics that suits your course level. The strongest projects tend to balance personal engagement with analytical depth.

What’s the difference between AA and AI topics? 

AA students typically work with calculus, functions, proofs, modelling, and theoretical mathematics. AI students tend to focus on statistics, probability, financial mathematics, and real world data analysis. Both pathways can score well when the mathematics is appropriate and clearly communicated.

Can I use the same topic as another student? 

Yes, but your investigation must be your own. Similar themes come up across many IAs, and that’s fine. What matters is that your research question, data, calculations, analysis, and conclusions are yours. Copying another student’s work directly is a serious breach of academic integrity.

How difficult should the topic be? 

It should be challenging without becoming unmanageable. Examiners reward understanding and clear communication, not complexity for its own sake. A well-executed project using accessible mathematics will often score higher than an ambitious one that’s poorly explained.

What does a top-scoring IA look like? 

The highest-scoring IAs tend to demonstrate several things consistently. They include clear and precise communication, strong mathematical understanding, personal engagement with the topic, effective use of appropriate mathematics, thoughtful reflection throughout, and critical evaluation of results and limitations. Students who explain their reasoning clearly and assess their work honestly tend to do best.

What mistakes should I avoid? 

Avoid topics that are too broad, lack mathematical depth, or rely on data you can’t actually access. Steer clear of mathematics you don’t fully understand, and don’t leave topic selection until the last minute. Starting early gives you time to refine your question and build a stronger investigation.

Final Thoughts

A strong IB Maths IA starts with a focused research question, meaningful mathematics, and a topic that interests you. Whether you’re exploring statistics, modelling, finance, geometry, or game theory, the key is applying mathematics in a clear and purposeful way.

These maths IA ideas are starting points, not finished projects. If you’d like extra support, TutorsPlus’ experienced IB Maths teachers can help you refine your ideas, strengthen your analysis, and structure your investigation for success.

By Sara Lloyd

Sara has been an education consultant for TutorsPlus for 15 years, and is an expert on international IB education.  She is also a parent of two lively children.

Find a Tutor