IB Math Internal Assessment: Step-by-Step Guide to Writing Your IA

Reviewed by Sandra Steiger, TutorsPlus Education Advisor, July 2026.

The Maths IA is one of the most important parts of your IB assessment. It gives you the freedom to choose your own research topic and methodology, which makes it a truly rewarding piece of work. That said, working autonomously for the first time can feel like a tremendous responsibility, especially when you’re not sure what a high-scoring IA looks like, and when it’s worth a fifth of your final grade.

This guide covers everything you need to know: the requirements, structure, and format of a strong Maths IA, so you can approach it with confidence from the start.

What Is the IB Math Internal Assessment?

The IB Math Internal Assessment, often called the Mathematical Exploration, is a piece of coursework that every IB Mathematics student completes independently. It contributes 20% of your final grade, whether you are studying Mathematics Analysis and Approaches (AA) or Mathematics Applications and Interpretation (AI), at Standard Level or Higher Level.

The aim of the IA is to investigate a mathematical question, problem, or real world situation using mathematics appropriate to your course level. Depending on your chosen topic, this may involve areas such as statistics, calculus, geometry, trigonometry, probability, mathematical modelling, optimisation, graph theory, or data analysis. The strongest explorations usually connect mathematics to a personal interest, helping students demonstrate stronger engagement and more meaningful reflection throughout their work.

Math IA Criteria Explained (How You Are Marked)

The Math IA is assessed out of 20 marks across five criteria. Understanding these criteria before you begin can make a real difference to your final result.

Communication (4 Marks)

Communication is about how clearly and logically you present your exploration. Structure and conciseness matter here. Substance is the priority, not length, so stick to the recommended 12 to 20 pages.

Graphs, tables, and diagrams should be embedded within the text instead of appendices. This creates a smoother reading experience for the examiners and helps them clearly track your train of thought. Don’t forget to acknowledge the work of others by citing sources and including a proper bibliography.

Mathematical Presentation (3 Marks)

This criterion is about how well you communicate mathematical ideas. Define key terms wherever necessary, drawing on textbooks or reputable sources, and reference them appropriately.

Use correct notation, appropriate symbols, and accurate terminology throughout. Avoid overly complex language where simpler phrasing would work just as well. Examiners are more interested in your understanding than in impressive-sounding vocabulary.

Your IA should also include formulas, diagrams, tables, charts, graphs, or models where they genuinely support your analysis. All visuals should be your own work and feature clear labels and titles.

Personal Engagement (4 Marks)

Personal engagement requires you to show your individual connection to the topic through your writing. There are a few clear ways to do this.

First, write in the first person to show ownership of the project and your interest in the subject.

Second, discuss the challenges you encountered along the way. This demonstrates your progress and shows that you’ve genuinely grappled with the investigation rather than followed a script. You can also reflect on unexpected findings and what they meant to you.

Finally, your work should show your growth as a mathematician. Highlight the concepts you’ve developed and explain how the exploration has broadened your understanding and skills.

Reflection (3 Marks)

Reflection is about evaluating your findings critically rather than simply presenting them. If you reached unexpected conclusions, analyse why that happened and consider what you might do differently.

Equally, discuss the strengths of your work alongside its limitations. Did you prove your hypothesis or successfully model a complex concept? Explain what worked well and acknowledge where improvements could be made.

You should also consider exploring alternative approaches and the ways they might have influenced the outcome.

In addition, you may discuss the broader implications of your work such as whether your findings contribute to a wider understanding of the topic or how your research could apply to other areas.

Use of Mathematics (6 Marks)

Scoring well on this criterion doesn’t require complex mathematics. The IBO’s own recommendation is to use mathematics “commensurate with your level,” and that’s worth taking seriously.

Being too ambitious and selecting mathematics well beyond what’s expected at your level can actually work against you. It’s more effective to take a syllabus topic and explore it in greater depth, or to apply familiar methods to a new context — for example, using differentiation to model a real-world scenario.

Optional modules within your course can also be a useful source of inspiration. As a Standard Level student, you might explore Higher Level optional modules, such as graph theory using Dijkstra’s and Kruskal’s algorithms. Examiners are more interested in how clearly you demonstrate your understanding than in the complexity of the mathematics itself.

All calculations must be relevant to your research question and accurate throughout.

How to Choose a Math IA Topic

Choosing the right topic is one of the most important decisions you’ll make during the IA process. A strong topic creates opportunities for meaningful mathematical exploration while helping you demonstrate personal engagement.

What Makes a Good Math IA Topic

A good Math IA topic needs to meet several criteria. It should be personally interesting, mathematically focused, manageable within 12 to 20 pages, suitable for your course level, and rich enough to allow analysis and reflection.

Topics connected to sports, music, gaming, architecture, finance, social media, science, or your own hobbies often work well because you already have a natural interest in them. Before committing to a topic, run through these questions.

• Can I collect data or build a model?
• Is there enough mathematics involved?
• Can I analyse the results meaningfully?
• Will I still find this topic interesting several weeks from now?

If the answer to all of those is yes, you’ve probably found a strong IA topic.

Math IA Topic Ideas (HL & SL Examples)

The following examples are intended as inspiration to get you started. There are many directions you could take them.

• Statistics and Data Analysis: These topics involve working with real data to identify patterns and relationships. Examples include sleep and academic performance, social media usage, football statistics, and weather data analysis.
• Calculus and Optimisation: These explorations focus on finding the most efficient solution to a problem. Popular topics include container optimisation, basketball projectile motion, packaging design, and population growth models.
• Geometry and Trigonometry: These areas can be applied to architecture, art, engineering, and sports. Examples include the golden ratio, bridge construction, and stadium design.
• Probability: Probability investigations explore uncertainty and decision making through topics such as lotteries, card games, sports predictions, and insurance risk.
• Mathematical Modelling: These topics use mathematics to represent real-world situations, such as social media trends, traffic flow, disease transmission, or investment growth.

Topics to Avoid

Some topics create real difficulties because they limit your opportunities for mathematical analysis. It’s best to steer clear of the following.

• Topics with very little mathematics content.
• Investigations that are more descriptive than analytical.
• Research questions that are too broad to answer properly.
• Mathematics far beyond your current understanding.
• Topics where sufficient data simply isn’t available.
• Subjects copied or closely adapted from online exemplars.

The best Maths IA topics strike a balance between challenge and accessibility. A topic that’s too simple will limit your marks, and a topic that’s excessively complex can make it difficult to demonstrate understanding.

How to Write a High-Scoring Math IA (Step-by-Step)

A successful Math IA is built through careful planning, clear communication, and thoughtful reflection. Following a structured process makes the whole task much more manageable.

Choose a Strong Topic

Everything starts with selecting the right topic. The strongest explorations combine personal interest with mathematical depth. A topic connected to a hobby, sport, academic interest, or real-life situation tends to offer more opportunities for engagement and reflection. 

Before settling on a topic, make sure you can gather data or create a mathematical model, apply mathematics at an appropriate level, analyse results meaningfully, and draw conclusions from your findings. A focused topic almost always performs better than a broad one.

Plan Your Exploration

Once you have your topic and research question, create a clear plan for your exploration. This will help keep your investigation organised and focused from the beginning. Start by defining your research question, identifying the mathematical techniques you will use, collecting or generating data, and deciding how you will present and analyse your results.

It is also worth considering any limitations that could affect your investigation, such as assumptions, data quality, or the scope of your study. Careful planning at this stage will make it much easier to maintain a logical structure and produce a clear, coherent IA.

Apply Mathematics Clearly

Mathematics should remain at the centre of the exploration throughout. Focus on explaining your mathematical reasoning rather than simply presenting calculations. When presenting mathematics, keep the following in mind.

• Define your variables clearly at the outset.
• Show the important calculations and working.
• Explain why you chose the methods you used.
• Label graphs and tables properly.
• Use correct notation consistently throughout.

Examiners are looking for understanding, not pages filled with equations.

Show Personal Engagement

Personal engagement is often one of the key factors that separates an average IA from a high-scoring one. You can demonstrate this by explaining why you chose the topic, discussing the challenges you faced, describing the decisions and adjustments you made throughout the exploration, and reflecting on what you learned during the process. Using first-person language where appropriate can further highlight your personal connection to the investigation and show that the work is truly your own.

Reflect and Evaluate Your Results

Reflection should appear throughout your exploration rather than only in the conclusion. This involves evaluating your assumptions, discussing limitations, considering alternative approaches, analysing unexpected results, and suggesting possible improvements or future extensions. Being honest about what did not go as planned can actually strengthen your IA, as it demonstrates critical thinking and a deeper understanding of the mathematical process.

Edit and Proofread

Before submitting your IA, take time to review it carefully, as many students lose marks through avoidable mistakes. Check that your mathematics is accurate, grammar and spelling are correct, notation is used consistently, references are properly formatted, graphs include clear labels and units, and each section flows logically into the next.

A clean, well-presented IA is easier for the examiner to follow and tends to score more highly on the Communication criterion.

Math IA Structure and Format

Your work must have concise and well-defined sections. A clear structure benefits both you and the examiner. By presenting your work in an easy-to-follow manner, you’ll help the marker understand your reasoning and potentially award higher marks.

There are no particular requirements when it comes to the structure of your IA. IBO encourages creativity and flexibility in your Maths IA. Having said that, the following format can help you structure your work more efficiently:

Cover Page

Your cover page should clearly identify the exploration. Include the following information.

• Mathematics course and level.
• Title of the exploration.
• Your candidate number.
• School name.
• Examination session.
• Submission date.
• Total page count.

Some schools may have additional requirements, so always check with your teacher before finalising your cover page.

Introduction

The introduction provides context for your investigation. This section should explain the background of the topic, why it interests you, the mathematical area being explored, and the overall purpose of the investigation. Keep it concise and focused. A long, meandering introduction can make a poor first impression.

Rationale

In this section, you need to justify your investigation. But don’t just restate your introduction. Instead, explain the specific mathematical concepts you’ll explore and how they address the chosen problem. You can also showcase examples, evidence, or preliminary calculations to justify your approach. If possible, you may briefly mention how your exploration relates to broader mathematical concepts or theories.

Aim

Here you should specify the goal of your exploration. However, instead of a vague “understanding of the topic,” you need to set clear, measurable objectives. For instance, “modelling the relationship between X and Y with an error margin of less than 10%.”

Exploration (Main Body)

This is the part where you show your calculations. But as we have already pointed out, Maths AI doesn’t just test your ability to use formulas and maths concepts. It also contributes to the development of fundamental skills, such as critical thinking. To demonstrate them, you can present different perspectives on solving the problem. It is beneficial to discuss and analyse alternative approaches even if they weren’t successful.

It is also critical to illustrate your calculations and reasoning with graphs, diagrams, and tables. Make them visually appealing and informative.

Conclusion

Don’t just summarise your findings, but explain their significance and how they align with your initial aims. Did you come across limitations, unexpected results, or difficulties? Then make sure to explain them as well as your approach to overcoming the issues.

The conclusive part of your IA may suggest future research questions, applications of your findings, and potential improvements for your work.

References

Proper referencing is one of the requirements of the ‘Mathematical Presentation’ criterion. Whenever you mention any sources, you worked with to support your background, theory, calculations, etc., you need to reference them. These could be textbooks, publications in scientific magazines, online databases, etc.

Please note that the proper referencing style depends on your school. Most commonly, it is either in-text citations (the so-called Harvard style) or a bibliography list. You must consult your teacher to find out which one to use.

Common Mistakes in IB Math IA and How to Avoid Them

Many students lose marks because of common issues that can easily be prevented. Here’s what to watch out for.

Choosing a Topic That Is Too Simple or Too Complex

A topic with very little mathematics limits your opportunities for analysis. A topic that’s excessively advanced can make it difficult to demonstrate understanding. Choose something that challenges you while remaining manageable within the scope of the course.

Lack of Personal Engagement

Some explorations read like textbook reports. Examiners want to see evidence that you’ve made decisions, solved problems, and engaged with the investigation on a personal level. Connect the exploration to your own interests wherever possible, and let your voice come through in the writing.

Describing Instead of Analysing Mathematics

Many students explain what they did but fail to explain why. Strong IAs focus on interpretation and analysis rather than description alone. After each result, take a moment to discuss its significance and what it means in the context of your investigation.

Weak or Missing Reflection

Reflection is often left until the final stages, which is a missed opportunity. Throughout the IA, keep asking yourself what worked well, what assumptions were made, what limitations exist, and what could be improved. Regular reflection strengthens several assessment criteria at the same time.

Poor Structure and Organisation

A disorganised IA makes it difficult for examiners to follow your reasoning. Use clear headings, a logical progression, consistent formatting, and smooth transitions between sections. A good organisation makes a direct contribution to your Communication marks.

Incorrect or Unclear Mathematical Notation

Notation errors can make otherwise strong mathematics hard to follow. Always define your variables, label axes clearly, include units, and use consistent symbols throughout. A simple notation mistake can create unnecessary confusion and cost you marks.

Overuse or Misuse of Technology

Tools such as Excel, GeoGebra, Desmos, and graphing calculators can strengthen an exploration. However, technology should support your analysis rather than replace it. Always explain what the software was used for, how the results were generated, and why the technology was appropriate. Mathematics should remain the focus at all times.

Ignoring the IB Marking Criteria

One of the biggest mistakes is writing the IA without regularly checking the rubric. Throughout the process, compare your work against all five criteria: Communication, Mathematical Presentation, Personal Engagement, Reflection, and Use of Mathematics. This helps ensure no criterion is overlooked as you go.

Final Thoughts

The IB Math Internal Assessment gives you the opportunity to explore a mathematical question that interests you while demonstrating your analytical, problem solving, and critical thinking skills. It is one of the few parts of the IB where you have the freedom to choose your own direction and investigate a topic in greater depth.

A successful IA starts with a focused research question, applies mathematics clearly, and includes thoughtful reflection throughout the exploration. Examiners want to see that you understand the mathematics you are using and can evaluate your findings critically. Start early, stay organised, seek help from experienced IB Maths IA tutor, and refer to the marking criteria regularly as you write. Small improvements in communication, reflection, and structure can make a significant difference to your final score. 

If you would like additional guidance, TutorsPlus can help you refine your ideas, strengthen your mathematical analysis, and approach your IA with greater confidence.

Frequently Asked Questions

How do I choose a topic for my Math IA?

Choose a topic that interests you and allows for meaningful mathematical exploration. The best topics provide opportunities for analysis, reflection, and personal engagement while remaining manageable within the scope of the IA.

How long should my Math IA be?

Most successful Math IAs are between 12 and 20 pages long, including graphs, tables, and diagrams. Focus on clarity and quality rather than length. A concise, well-structured IA will nearly always outperform a padded, repetitive one.

What makes a Math IA score highly?

High-scoring IAs typically include clear communication, strong mathematical understanding, meaningful personal engagement, consistent reflection, appropriate use of mathematics, and a logical structure. Depth of understanding is often more important than mathematical complexity.

Can I use Excel or GeoGebra in my Math IA?

Yes. Technology is encouraged when used appropriately. Software such as Excel, GeoGebra, Desmos, and graphing calculators can help with modelling, graphing, and analysis. You should clearly explain how the technology was used and interpret the mathematical results yourself rather than letting the software do all the thinking.

Do IB examiners assess HL and SL Math IAs differently?

No. Examiners assess all IAs using the same five criteria. Higher Level students are expected to use mathematics appropriate to HL, while Standard Level students are assessed according to SL expectations. The focus remains on understanding, communication, reflection, and mathematical exploration, rather than difficulty alone.

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.

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