How to write the IB Maths AI Exploration

The Maths AI Exploration is the one piece of coursework your Mathematics: Applications & Interpretation grade is marked on internally — worth about 20% of your final grade at both SL and HL. Most students lose marks not because they cannot do the mathematics, but because they pick a topic with no real-world data behind it, or never learn what each marking criterion actually rewards. This guide walks you through the whole thing: what the Exploration is, how it is marked, exactly how to write each part, and what separates a top-band investigation from an average one. The Exploration is sometimes called the maths IA, but its proper name is the Exploration, and for the AI course that word leans towards the real world: you are modelling a real situation, not reciting abstract theory.

That orientation towards the real world is the single most important thing to internalise, because it shapes every later decision. Applications & Interpretation exists for students who want to use mathematics to make sense of the world — to model, to predict, to test claims with data — and the Exploration is where that purpose is assessed directly. The strongest pieces start from something the student genuinely wanted to understand: how quickly a coffee cools, whether a streaming service's ratings predict viewing figures, how a town's bus timetable could be optimised. The mathematics then earns its place by answering a real question about a real situation. The weakest pieces invert this: they start from a technique the student happens to know, invent some tidy numbers to feed it, and produce an answer about nothing in particular. An examiner can tell the difference within a page, and the marks follow.

One more framing point before the detail. The five criteria are not weighted equally, and that should shape where you spend your effort. Use of mathematics alone carries six of the twenty marks — almost a third — and Presentation, communication, engagement and reflection share the rest. For AI specifically, those six marks reward mathematics that is correct, relevant and genuinely tied to your real-world question; a model fitted to real data and interpreted in context will always outscore a flashy technique applied to nothing. A common error is to spend hours on the presentation of a model that was never connected to a real situation in the first place. Balance is the goal: a sound model on real data, clearly communicated, genuinely owned, and honestly reflected upon.

The IB Maths AI Exploration at a glance

The Maths AI Exploration is a written investigation of a mathematical topic of genuine personal interest. There is no strict word count; instead it is expected to run to roughly 12–20 pages, with the length governed by how much mathematics the question genuinely needs rather than by padding. It is marked out of 20 across five criteria, and it is worth about 20% of the final grade for both Standard and Higher Level. Because Applications & Interpretation is the more applied of the two Mathematics courses, the strongest Explorations lean on real-world modelling, statistics, probability, finance and optimisation — ideally on real data you collect or source yourself, interpreted in its context rather than left as abstract numbers.

The page guidance is a guide, not a target, and it is easy to misread. Twelve to twenty pages does not mean you should stretch a thin idea until it fills twelve, nor compress a rich one to fit twenty. It means a focused investigation usually needs about that much room to be developed properly: enough space to introduce your data, build and justify your model, present the graphs and tables that matter, and reflect on validity as you go, but not so much that the argument drowns. If your Exploration is running short, the honest fix is almost never to add words — it is to deepen the analysis or gather better data. If it is running long, the fix is to cut the passages that do not move the investigation forward. Length is a symptom, not a goal.

It is also worth knowing what counts as an AI-appropriate topic. Applications & Interpretation rewards the applied strand of the syllabus, so real-world modelling (fitting curves to data, optimisation of a practical quantity), statistics (regression, correlation, hypothesis tests, sampling), probability, financial mathematics and the interpretation of results all sit comfortably at the centre of a strong Exploration. Abstract, self-contained theory with no real situation behind it belongs more naturally in the Analysis & Approaches course; if your idea is essentially "explore the properties of a function for its own sake", it may be in the wrong subject. For AI, aim for an idea where the interesting part is what the mathematics tells you about the world — a prediction you can test, a model you can validate, a claim you can support or refute with data you actually have.

How the Maths AI Exploration is marked: the five criteria

Every mark comes from one of these five criteria. Write your Exploration with the criteria beside you and check what each one rewards:

How to write a Maths AI Exploration, step by step

1. Choose a real-world context of genuine interest. Start from a real situation you actually care about — a sport, a business, a local issue, something you can measure — so your personal engagement is real, and fix a clear aim.
2. Frame a research question. Sharpen the context into one focused, answerable question that real-world mathematics can address, such as a "How accurately…?" or "To what extent…?" question.
3. Gather or source real data. Collect your own data or source a reliable real data set, so the model has something genuine to fit rather than invented numbers.
4. Build an appropriate AI-level model or statistical analysis. Develop a model, regression, statistical test, probability or financial calculation suited to the data and to the course.
5. Communicate with correct notation. Define your variables and present results in proper mathematical notation with clear, labelled graphs and tables.
6. Reflect critically on the model's limitations. Evaluate how well the model fits, the assumptions it rests on, its validity and where it breaks down — as the work unfolds, not as an afterthought.
7. Self-check against the five criteria. Read the draft against Presentation, Mathematical communication, Personal engagement, Reflection and Use of mathematics, and rewrite the weakest one.

A word on each of these steps in practice. The third — gathering or sourcing real data — is the one students most often skimp on, and it is the one that quietly decides whether the whole Exploration feels real. Data you collect yourself (measurements, surveys, timed observations) carries the strongest personal engagement, but a reliable external data set is perfectly acceptable provided you cite where it came from and understand its limitations. The fourth step is where you match the tool to the data: do not reach for the most advanced technique you know, reach for the one that actually answers the question, and be ready to justify why it suits the data you have. Steps six and seven are where most marks are quietly won or lost — reflection on a model's validity that runs throughout reads as genuine, whereas a single paragraph of "limitations" bolted on at the end reads as exactly that.

Maths AI Exploration structure: what goes in each section

There is no single mandated layout, but the clearest structure that maps onto the criteria is:

• Introduction & rationale — the real-world context, why it interests you, and the aim of the exploration.
• Research question — one focused, answerable question stated explicitly.
• Data & background — the data you collected or sourced, and the techniques you will need.
• Model or analysis — the modelling, regression, statistics or finance, carried out step by step in correct notation.
• Results — outcomes presented in clearly labelled graphs and tables, interpreted in context.
• Reflection — critical evaluation of the model's fit, assumptions and limitations, woven through rather than bolted on.
• Conclusion — a direct answer to the research question, with what you found and what it means.
• Sources — a consistent citation style throughout, including where the data came from.

Notice that this structure is a skeleton, not a script. The sections need not appear as rigid headings, and the best Explorations let one flow into the next so that the data section introduces exactly the model the analysis then builds, and the reflection picks up the questions the results leave open. What matters is that an examiner can always tell where they are: what the question is, where the data came from, what model you fitted, why you chose it, and what you concluded. If a reader cannot tell whether a number came from real data or an assumption, the communication is working against you. Keep the research question visible, label every figure and table, and make sure every section is doing a job that the criteria reward.

What a strong vs weak Maths AI Exploration looks like

The fastest way to lift your marks is to see the difference. The three pairs below isolate the moves that most often separate a middling Exploration from a top-band one: whether the question is genuinely real-world, whether the data is real or invented, and how honestly the model is reflected upon. In each pair the underlying topic is identical — what changes is the execution, and it is the execution that the criteria reward.

The research question

Using real data

Reflection on the model

Common mistakes that cost marks

• No real-world data. A purely theoretical topic with no data or model caps Use of mathematics for the AI course — ground it in something real.
• Invented numbers. Making up tidy values instead of collecting or sourcing real data weakens both the model and your personal engagement.
• No personal angle. A generic textbook topic caps Personal engagement; show why you chose this context and made it your own.
• Calculator notation. Writing x^2 or 3*x throughout caps Mathematical communication — use proper mathematical notation.
• Trivial mathematics. A single plotted line with no analysis cannot reach the top band of Use of mathematics.
• Description instead of reflection. Narrating the steps is not reflection; evaluate the model's fit, assumptions and limitations.
• Padding to fill pages. Length should come from the mathematics, not from filler — a concise exploration scores better than a bloated one.

If you take one thing from this list, let it be the central role of real data tied to a real question. Almost every mistake above traces back to a topic that was abstract, invented or thin. A focused real-world question with genuine data behind it makes the rest of the Exploration easier to write: it tells you which model to build, it gives your reflection something concrete to evaluate when the fit is imperfect, and it keeps your presentation focused because every section is visibly serving the same real-world end. Spend disproportionate effort choosing that question and sourcing that data, get a teacher to challenge both before you commit, and the remaining marks become far easier to earn.

Maths AI Exploration — frequently asked questions

Guidance written by experienced IB examiners and aligned to the current Mathematics: Applications & Interpretation guide. Not affiliated with or endorsed by the International Baccalaureate Organization.