IB Maths Internal Assessment Topics: Examples & Tips

Choosing a topic for your IB Maths Internal Assessment (IA) can feel overwhelming. You know it's worth 20% of your final grade, but where do you even start? 

The pressure to find the "perfect" topic can leave you feeling stuck, scrolling through endless lists of ideas that all sound either too vague or completely out of your depth. 

In this guide, we'll detail some inspirational IB Maths Internal Assessment topics, and show you what makes a strong IA topic. Whether you're doing AA or AI, SL or HL, you'll find practical, useful advice.

Key Takeaways

• Topic choice matters. A well-chosen topic sets you up for success by making your research clearer and your maths more focused.

• Good topics balance originality with feasibility. You want something interesting and personal, but it also needs to be mathematically rigorous and doable within 12–20 pages.

• Narrowing your idea is crucial. A broad topic like "probability in sports" won't work. You need a specific research question like "How does home advantage affect Premier League match outcomes?"

What Makes a Great IB Maths IA Topic?

A great IA topic (called ‘Exploration’ in IB Maths) ticks several important boxes that align with what the IB examiners are looking for. Here's what matters:

Originality and personal engagement 

Your topic should reflect genuine curiosity. Examiners can tell when you care about what you're investigating. Personal connection doesn't mean it has to relate to your hobbies, but it helps if you're genuinely interested in the question you're exploring.

Clear mathematical aim 

You need a focused research question that can be answered using maths. Vague titles like "Exploring the Golden Ratio" won't cut it. Something like "How does the Golden Ratio appear in the proportions of Renaissance architecture?" gives you a clear direction.

Suitable complexity 

Your topic should challenge you mathematically without being impossible. For Standard Level (SL), this might mean applying functions or basic calculus. For Higher Level (HL), you'll need to dig deeper. Think about using differential equations, complex numbers, or advanced statistics.

Feasibility 

Can you actually complete this investigation in 12–20 pages? Do you have access to the data or measurements you need? A topic that requires a PhD-level understanding of physics or access to NASA data probably isn't practical!

Different considerations for AA vs AI

If you're taking Analysis and Approaches (AA) (opens in a new tab), you'll likely lean towards pure maths topics:

• Calculus, trigonometry, or algebra. 

If you’re taking Applications and Interpretation (AI) (opens in a new tab), you should focus on real-world applications, often involving: 

• Statistics, modelling, or data analysis.

If you’re eager to find out more about IAs, take a look at our 'What Are IB Internal Assessments (IA)?’ overview.

Sample IB Maths IA Topics by Theme

Here are some excellent topic ideas organised by mathematical themes. Each includes a sample title, the maths you'd use, and why it works.

Number and Algebra

Topic: The Fibonacci sequence in nature 

• Sample title: "Investigating the presence of Fibonacci numbers in the spiral patterns of sunflower seed heads" 

• Maths involved: Sequences, ratio, patterns, mathematical proof.

• Why it works: It's visually engaging, uses accessible maths, and allows for both theoretical exploration and practical data collection. According to research published in the Royal Society Open Science (opens in a new tab), Fibonacci patterns appear in 74% of sunflower specimens, giving you reliable data to work with.

Functions

Topic: Predicting house prices 

Sample title: "Using polynomial regression to model the relationship between house size and sale price in London" 

Maths involved: Polynomial functions, regression analysis, curve fitting.

Why it works: Property data is widely available (e.g. from Rightmove or Zoopla), and the investigation allows you to test different function types and justify your choice mathematically.

Geometry and Trigonometry

Topic: Navigation and GPS 

Sample title: "Using spherical trigonometry to calculate the shortest flight path between London and Tokyo" 

Maths involved: Great circle distances, spherical geometry, haversine formula. 

Why it works: It's a sophisticated application of trigonometry that feels modern and relevant. 

Statistics and Probability

Topic: Sports analysis 

Sample title: "Does home advantage exist in the Premier League? A chi-squared test of match outcomes from 2020–2023" 

Maths involved: Chi-squared test, hypothesis testing, probability. 

Why it works: Football data is easy to find (e.g. from Premier League official statistics), and the investigation has a clear yes/no question that can be tested statistically.

Calculus

Topic: Optimisation in engineering 

• Sample title: "Using calculus to design a cylindrical can that minimises material cost while holding 330ml" 

• Maths involved: Differentiation, optimisation, surface area and volume. 

• Why it works: It's a classic optimisation problem that's manageable for both SL and HL, with clear real-world application.

Keen for more inspiration? Explore our IB Maths Topics guide.

Choosing the Right Topic for Your Level (SL, HL, AA, AI)

IB Maths allows you to choose between two different courses: 

• Analysis and Approaches (AA) and Applications and Interpretation (AI) 

Here's how to match your topic to your level:

Standard Level (SL) topics should use core syllabus content without requiring university-level mathematics. Some ideas include: 

• Quadratic functions

• Basic trigonometry

• Descriptive statistics

Higher Level (HL) topics need to demonstrate greater depth and complexity. You're expected to show more sophisticated mathematical thinking. This could mean using: 

• Differential equations

• Proof by induction

• Complex numbers

Analysis and Approaches (AA) students should lean towards pure or theoretical maths. Your IA might explore:

• Mathematical proof

• Abstract concepts

• The use of calculus and algebra

Applications and Interpretation (AI) students should focus on real-world modelling and data analysis. Your IA should show:

• How maths solves practical problems

• The use of statistics, regression, and probability 

How to Narrow Your Idea Into a Focused Research Question

A common mistake is choosing a topic that's too broad. "Probability in sports" or "The Golden Ratio" aren't research questions - they're subject areas.

Here's how to narrow down:

Start with a general interest. Let's say you're interested in music.

Add a mathematical lens. What aspect of music involves maths? Frequency, rhythm, harmony, sound waves?

Ask a specific question. Instead of "Maths in music," try "How do the frequencies of notes in the major scale follow exponential patterns?"

Make it measurable. Can you collect data or perform calculations to answer this question? If yes, you're on the right track.

Example transformation:

• Broad topic: "Traffic flow"

• Narrowed: "Traffic flow and optimisation"

• Specific question: "How can calculus be used to determine the optimal speed limit that maximises traffic flow on the M25?"

This gives you a clear aim, specific maths (calculus), and a real-world context (the M25 motorway).

Common Pitfalls to Avoid

Even with a great idea, certain mistakes can derail your IA. Here's what to watch out for:

Picking something too simple. Calculating the mean and median of your class heights won't impress examiners. Your IA needs mathematical depth.

Being too descriptive. Your IA isn't a history essay or a Wikipedia article. Don't just explain what exponential functions are. You need to use them to investigate something.

Biting off more than you can chew. If you're SL, don't attempt a topic requiring multivariable calculus. Similarly, don't choose a topic where you can't access the necessary data or resources.

Failing to show personal engagement. If you're not interested in your topic, it will show. Choose something that genuinely excites you.

Ignoring the assessment criteria. Make sure your IA demonstrates mathematical communication, personal engagement, reflection, and use of mathematics. A brilliant idea that doesn't hit these criteria won't score well.

Not leaving enough time. The IA takes longer than you think. Data collection, calculations, writing, and revisions all need time. To avoid any last minute panic, have a read of our Time Management Tips for Students Guide and get organised.

Frequently Asked Questions

Can I use a topic someone else has already done?

Yes, but you need to make it your own. Examiners see lots of IAs, so common topics like "Modelling the spread of disease" need a fresh angle or unique data set.

If your friend investigated coffee cooling, you might look at how adding milk affects the cooling rate, or compare cooling rates of different beverages. The maths might be similar, but your investigation and findings should be original.

Does it have to be a real-world topic?

No. While real-world applications are popular (especially for AI students), you can investigate pure maths topics too. 

Exploring properties of fractals, proving relationships in number theory, or analysing geometric patterns are all valid.

That said, real-world topics often make it easier to show personal engagement and explain why your investigation matters.

Can I use calculus/statistics in SL?

Yes. SL students learn basic calculus (differentiation and integration) and descriptive statistics. You can definitely use these in your IA.

What you shouldn't do is attempt university-level maths that's beyond the SL syllabus. If you're unsure whether a technique is appropriate, check with your teacher or refer to the IB Mathematics syllabus guide (opens in a new tab).

Your Maths AI Awaits

Your IB Maths IA is a chance to explore something you're curious about while showing off your mathematical skills. The best IAs aren't necessarily the most complex. They're the ones that are clear, well-structured, and mathematically rigorous.

Pick a topic that excites you, narrow it down to a specific research question, and make sure the maths is appropriate for your level. Start exploring, stay curious, and enjoy your exploration. 

References

IBO - Analysis and Approaches (opens in a new tab)

IBO - Applications and Interpretation (opens in a new tab)

Royal Society Open Science - Fibonacci Sunflowers (opens in a new tab)

IBO - Maths (opens in a new tab)