IB Maths Extended Essay Ideas: Topics & Tips

Are you looking to complete your IB extended Essay in Maths? Choosing a topic can feel overwhelming. You know it needs to be interesting, mathematically rigorous, and meet the IB criteria – but where do you even start?

This guide is here to help. We've broken down plenty of IB Maths Extended Essay ideas into clear categories, complete with real-world applications and tips on how to turn them into strong research questions. Whether you're studying AA or AI, HL or SL, you'll find practical inspiration that actually works.

At Save My Exams, we've helped IB students, just like you, navigate their Extended Essays with confidence. Our expert team knows exactly what examiners are looking for – and we're here to share that knowledge with you.

Key Takeaways

• Start with your interests. The best topics combine mathematical depth with something you genuinely care about – whether that's sports, music, or gaming.

• Make sure there's enough maths. Your EE must demonstrate sophisticated mathematical techniques and analysis.

• Narrow your focus early. Broad topics like "the golden ratio in nature" won't work. You need a specific, focused research question you can actually answer in 4,000 words.

• Check your data sources. Before committing to a topic, make sure you can access the data or mathematical tools you'll need to complete your investigation.

What Makes a Great IB Maths EE Topic?

A strong IB Maths Extended Essay topic hits several key criteria that examiners specifically look for.

Mathematical depth is essential

Your topic must allow you to use and explain sophisticated mathematical concepts appropriate to your level. 

According to the International Baccalaureate Organisation (IBO) Extended Essay guidelines (opens in a new tab), successful essays demonstrate "knowledge and understanding of relevant research methods." This means using mathematical processes, analyses, and modelling effectively.

Real-world relevance strengthens your work

The best topics connect abstract maths to tangible applications. This doesn't mean every EE needs to solve a global problem, but showing how mathematical concepts apply to real situations makes your work more engaging and demonstrates deeper understanding.

Originality matters, but don't overthink it

You're not expected to discover new mathematics. Originality in an IB EE means: 

• Taking a fresh approach to a known topic

• Applying mathematical methods to an unusual dataset

• Investigating a question that interests you personally

Feasibility is crucial

Can you actually complete this investigation with your current mathematical knowledge? Do you have access to the data or tools you need? The best topic in the world won't work if you can't execute it properly within the time and word limits.

Clear scope makes marking easier

Examiners appreciate essays with well-defined boundaries. A focused investigation of one specific question will always score better than a rambling exploration of multiple loosely related ideas.

Tips for Choosing Your Maths EE Topic

Selecting the right topic is half the battle. Here's how to approach it strategically.

• Start with what genuinely interests you. You're going to spend months working on this essay, so pick something that excites you. 

  • Love football? Explore probability models in penalty shootouts. 

  • Passionate about music? Investigate the mathematics of sound waves or rhythm patterns.

• Match the topic to your mathematical level. Be honest about your abilities. 

  • HL students should choose topics that showcase advanced techniques like complex calculus or matrix algebra. 

  • SL students can still write excellent EEs using statistics or geometric investigations.

• Test your topic with a simple question. Can you explain what you want to investigate in one clear sentence? If not, your idea is probably too vague. 

  • Try writing down your research question before you commit.

• Consider data availability early. If your topic requires specific data, check you can actually access it. 

  • Public databases, sports statistics websites, and scientific repositories - like the UK Solar System Data Centre or Harvard Dataverse - are great sources. 

• Talk to your supervisor. Your supervisor has seen dozens of EEs and knows what works. 

  • Run your ideas past them early, even if they're half-formed. 

• Start broad, then narrow down. Begin with a general area (like "calculus" or "probability"). Then:

  • Brainstorm specific applications.

  • Refine to a precise question.

Explore our IB Maths Topics Guide for more inspirational ideas.

IB Maths Extended Essay Topic Ideas by Category

Here are plenty of topic ideas organised by IB Maths subject area. Each suggestion includes potential approaches and real-world connections to help you develop your investigation.

Calculus-Based Topic Example

Calculus is perfect for modelling change and optimisation problems. 

Topic: Optimisation in Sports

Investigation: Investigate the optimal launch angle for a javelin throw or a football kick that maximises horizontal distance. Use principles of differential calculus to model projectile motion, incorporating variables such as: 

• Initial velocity

• Air resistance

• Release height

Real performance data from athletics competitions can be used to validate the model.

Why it Works: This topic allows the application of calculus and physics to a real-world scenario that is measurable and data-driven. 

Statistics and Probability Example

Statistical investigations work brilliantly because real data is widely available. 

Topic: Climate Change Trends

Investigation: Analyse long-term global temperature or sea-level data using regression analysis to identify and model trends over time. Use datasets from reliable sources such as NASA or the UK Met Office, and apply statistical methods to work out whether the observed changes are statistically significant.

Why it Works: This investigation integrates mathematics with environmental science, allowing the use of real-world data and statistical modelling. It demonstrates understanding of regression, correlation, and hypothesis testing.

Number Theory Example

Number theory offers pure mathematics investigations. 

Topic: Fibonacci Sequences in Nature

Investigation: Explore the mathematical properties of the Fibonacci sequence and its connection to the golden ratio through formal proofs and algebraic analysis. Investigate seed arrangements or shell spirals.

Why it Works: This topic blends pure and applied mathematics, encouraging critical thinking about mathematical claims in nature.

Geometry Example

Geometric investigations offer visual appeal and clear mathematical structure.

Topic: Tessellations and Tiling

Investigation: Investigate which regular and irregular polygons can tessellate the plane, and explain why using geometric and algebraic reasoning. Extend the exploration to more complex examples such as Penrose tilings, Islamic geometric designs, or M.C. Escher’s mathematical art.

Why it Works: This topic connects geometry, symmetry, and pattern recognition in mathematical theory and art. The blend of aesthetics and mathematics is unique and will hold your interest for the EE.

Modelling Example

Mathematical modelling lets you tackle real-world problems with quantitative tools.

Topic: Traffic Flow Optimisation

Investigation: Model vehicle movement and congestion using mathematical tools such as:

• Queuing theory

• Graph theory

• Differential equations 

Investigate optimal traffic light timings or the mathematics behind traffic jams.

Why it Works: This topic applies advanced mathematical modelling to a real and relatable problem. It allows the use of calculus, statistics, and systems modelling while connecting theory to urban design and human behaviour. 

Abstract Topics

For students who love mathematical theory, abstract topics can be deeply satisfying.

Topic: Set Theory Paradoxes

Investigation: Explore famous logical puzzles like Russell’s Paradox and the Barber Paradox, which question how sets and logic work. Investigate why these paradoxes appear and how mathematicians changed set theory to avoid contradictions. 

Why it Works: This topic helps you understand the foundations of mathematics: how logic and reasoning make maths consistent. It encourages deep thinking, creativity, and clear explanation of abstract ideas in an understandable way. 

How to Turn a Topic Into a Research Question

Having a general topic is just the starting point. You need to transform it into a focused, investigable research question. Here’s an example of how you could do this:

Common Mistakes to Avoid in Your Maths EE

Learning from others' mistakes can save you months of frustration. Here are the pitfalls to watch out for.

1. Insufficient mathematical content. The biggest mistake is choosing a topic that doesn't contain enough actual mathematics. You need analysis.

2. Lack of personal engagement. Examiners want to see your thinking, your choice of method, and your interpretation of results.

3. Poor structure and presentation. Mathematical work must be clearly explained. Every mathematical step should be justified, variables defined, and notation consistent. Need more guidance? Take a look at our How to Structure Your EE overview. 

4. Choosing an overly ambitious topic. Pick something challenging but achievable. It's better to thoroughly investigate a modest question than to skim a grand problem.

5. Inadequate citations. You must reference all sources, including datasets, online tools, and mathematical concepts you didn't develop yourself. 

6. Leaving it too late. Mathematical investigations take time. Starting early gives you time to pivot if your initial approach doesn't work.

Frequently Asked Questions

How much Maths do I need to include in my EE?

Your Extended Essay should be mathematical throughout. There's no specific percentage, but a good rule is this: if someone could understand your entire argument without any mathematical knowledge, you haven't included enough maths. 

Do I need to use original data or just analyse existing data?

Both approaches are completely valid. What matters is the quality of your mathematical analysis, not whether you collected the data yourself.

The key is demonstrating sophisticated mathematical treatment of your data, whether it's yours or from external sources. Examiners care about your analysis, not your data collection skills.

Can I write a successful EE with just SL-level maths?

Absolutely. You don't need advanced HL mathematics to write an excellent Extended Essay.

The difference is in complexity, not quality. An HL student might use multivariable calculus, while an SL student uses single-variable optimisation. Both can produce equally strong essays if the mathematics is well-chosen and thoroughly explained.

Ready For Your Maths EE?

If you’re keen to complete your IB Extended Essay in Maths, you have the chance to explore some exciting real world problems.

The key is finding that sweet spot where genuine personal interest meets mathematical rigour. Use our ideas for inspiration and let your curiosity drive the process. The best EEs don’t just solve equations, they reveal how mathematics shapes the world around us.

Excel in IB Maths With Save My Exams

At Save My Exams, you’ll find everything you need to excel in IB Maths, including expertly written revision notes and past papers tailored to both AA and AI courses. Our resources are designed to help you master challenging concepts, boost your confidence, and achieve your full potential.

References

IBO - EE Guidelines (opens in a new tab)