The Internal Assessment in IB Mathematics is a piece of individual mathematical work called the mathematical exploration. It is one of the few parts of the course where you choose the topic and the direction, and it contributes a set proportion of your final grade. This guide explains what the exploration is, how to choose a strong topic, how to structure it, and how to avoid the most common mistakes that cost marks.
What Is the IB Maths IA?
The mathematical exploration is a short piece of individual mathematical work in which you investigate a topic of your choice using mathematics at an appropriate level for your course. It is not a research essay about mathematics, and it is not a textbook exercise. The exploration is meant to show that you can do mathematics: frame a question, develop mathematics to address it, interpret your results, and reflect on the process.
Because the exploration is internally marked by your teacher and then externally moderated by the IB, the standard is applied consistently across schools. The assessment criteria reward mathematical communication, mathematical understanding, personal engagement and reflection, not just a correct final answer. A strong exploration reads like a coherent mathematical argument written by a student who genuinely wanted to answer the question.
Choosing a Good IB Maths IA Topic
Topic choice is where most explorations succeed or fail before they even begin. A strong topic has several characteristics:
- Genuine mathematical substance. There must be real mathematics to do, not just a description of an idea. If your topic only requires restating a formula and plugging in numbers, it will not support a high-level exploration.
- Appropriate level of mathematics. The mathematics should be connected to your course (AA or AI, HL or SL) and developed beyond the most routine applications. Using mathematics that is far below the course level limits your mark; using mathematics you cannot explain limits it in a different way.
- Manageable scope. A topic you can investigate meaningfully in a dozen or so pages. Topics like "the mathematics of music" are too broad; a specific question within that field is workable.
- Opportunity for analysis. You should be able to calculate, model, prove or compare, not only describe.
- Room for reflection. A good topic lets you evaluate your method, discuss limitations, and consider what you would do differently.
- Personal engagement where appropriate. A topic connected to something you genuinely care about, a sport, a hobby, a question from another subject, tends to produce more engaged writing and stronger reflection.
Avoid the temptation to pick a topic from a list because it "looks impressive." The best explorations come from questions you actually want to answer. If you are unsure whether a topic has enough mathematics, that is itself a useful signal to refine it before you commit.
AA vs AI: Does the IA Approach Differ?
The exploration is assessed against the same criteria in both Mathematics: Analysis and Approaches (AA) and Mathematics: Applications and Interpretation (AI), but the kind of topic that works well often differs. AA explorations tend to suit topics involving proof, algebraic structure, calculus or abstract reasoning. AI explorations tend to suit modelling, statistics, data analysis and real-world interpretation, reflecting the character of the course.
This is a tendency, not a rule. An AI student can write a strong exploration involving calculus, and an AA student can write a strong exploration involving data, provided the mathematics is appropriate to the course and well developed. What matters is that the mathematics is at a suitable level and that you can explain and interpret it. For more on how the two courses differ, see our IB Maths AA vs AI guide.
A Strong IA Structure
There is no single mandatory structure for the exploration, but a clear one helps the reader follow your mathematics. A typical strong exploration includes most of the following, in an order that suits the topic:
- Introduction and context. State what you are investigating and why. Give the reader enough background to understand the question.
- Rationale. Explain why this topic and why this approach. Personal engagement is partly demonstrated here.
- Mathematical development. Define terms, set up models, derive results. This is the core of the exploration and should be coherent, not a list of disconnected calculations.
- Calculations, modelling or analysis. Carry out the mathematics. Show working, not just outputs.
- Interpretation. Explain what your results mean in the context of your question. Numbers without interpretation earn little.
- Reflection and evaluation. Discuss the strengths and limits of your approach, what you would change, and what your results do and do not show.
- Conclusion. Bring the exploration to a clear close, answering the question you set where possible.
- References where appropriate. Cite any sources, data or ideas that are not your own.
Treat this as a framework, not a rigid template. The best structure is the one that lets your mathematics flow logically.
What Makes the Mathematics Strong?
Strong mathematics in an exploration is not the same as difficult mathematics. The criteria reward:
- Appropriate techniques. Methods connected to your course and developed to a suitable depth.
- Coherent progression. Each step follows from the last; the reader can follow your reasoning.
- Correct calculations. Accuracy matters, and errors that change your conclusions are costly.
- Justified choices. Explain why you used a particular method or model, not just that you used it.
- Interpretation. Results are explained in context, not left as bare numbers.
- Mathematical communication. Correct notation, clear definitions, well-labelled diagrams and readable working.
- Appropriate sophistication. Mathematics that is genuinely at your course level, developed beyond routine repetition.
If you include a technique, you should be able to explain it. Mathematics pasted in without understanding tends to score poorly, because the reflection and communication criteria depend on your ability to discuss what you did.
Common IB Maths IA Mistakes
The same mistakes appear in weak explorations year after year:
- Topic too broad. "The mathematics of football" cannot be explored in a short piece; a specific question about it can.
- Mathematics too simple for the course. An HL exploration using only routine arithmetic or basic graphs will not reach the higher marks.
- Mathematics included without explanation. Software output, formulas or methods that appear without justification read as decoration.
- Excessive description. Long sections of background that contain no mathematics waste space and marks.
- Weak reflection. A short paragraph saying "I enjoyed this" is not reflection. Reflection means evaluating your method and results.
- Unexplained technology output. Screenshots from a calculator or software with no accompanying working or interpretation.
- Mistakes in notation. Inconsistent or incorrect notation makes mathematics harder to follow and marks down communication.
- Lack of connection between mathematics and the question. Mathematics that does not actually address the stated aim.
How to Improve an Existing IA
If you have a draft, review it against a simple framework:
- Does the mathematics answer the question? If not, either narrow the question or change the mathematics.
- Can you explain every line? If there is working you cannot explain, remove it or learn it.
- Is the progression logical? Reorder sections so each follows from the last.
- Is there genuine reflection? Add evaluation of method, limitations and possible improvements.
- Is the communication clean? Fix notation, labelling and layout.
- Is the level appropriate? If the mathematics is too simple, develop it; if it is too advanced to explain, simplify it.
IB Maths IA Support From HK Study Hub
Legitimate tutoring support for the exploration focuses on helping you produce better work, not on producing it for you. A tutor can help with topic refinement, mathematical reasoning, structure, feedback on clarity, and understanding what the assessment criteria expect. The student remains responsible for producing and submitting their own assessed work. If you would like support, see our IB Maths tutoring in Hong Kong.
IB Maths IA FAQs
How long should the IA be? The IB does not set a fixed word count. Most successful explorations are around 12 to 20 pages, but quality matters more than length. Your school will have its own guidance.
Can I change my topic? Yes, and it is better to change a weak topic early than to force a poor exploration. The earlier you commit, the more time you have to develop the mathematics.
Can I use AI, calculators or software? Tools are allowed, but any output you include must be explained and interpreted by you. The rules around the use of AI tools in assessed work are set by your school and the IB; check current official IB guidance rather than assuming, and follow your school's policy.
Does the IA differ for AA and AI? The criteria are the same, but the topics that suit each course differ. See our AA vs AI guide.
How much mathematics should I include? Enough to answer your question at a level appropriate to your course. More mathematics is not automatically better; well-developed, well-explained mathematics is.
Can a tutor review my IA? A tutor can give feedback on clarity, structure and mathematical reasoning. They cannot write or rewrite assessed work for you.
Can a tutor write any part of it? No. The exploration must be your own work. Tutoring that crosses into writing the exploration for you is academic misconduct and risks your result.
For more IB Maths resources, browse the IB Maths resource hub, or see our guide to IB grade boundaries. You can also explore all IB resources or IB tutoring in Hong Kong.