What it is and the timeline Weighting, length, planner
The basics
- One written exploration on a mathematical topic of your choice, for Analysis and Approaches (AA) or Applications and Interpretation (AI), at SL or HL. First assessed in 2021 on the current course.
- Worth 20 marks, which is 20% of your final grade at both SL and HL.
- Marked by your teacher against five criteria, then a sample is checked by the IB (moderation). Your teacher's mark can change after moderation.
- The guide describes it as roughly 12 to 20 pages. Treat that as a guide to scale, not a target: a focused 14 pages beats a padded 20.
- It must be your own work. You are expected to use your own words, cite everything you take from elsewhere and keep a record of your sources.
| Criterion | Marks | In one line |
|---|---|---|
| A Presentation | 4 | Is it organised, coherent and concise? |
| B Mathematical communication | 4 | Is the mathematics written and displayed clearly and correctly? |
| C Personal engagement | 3 | Does your own thinking show? |
| D Reflection | 3 | Do you think critically about your results and method? |
| E Use of mathematics | 6 | Is the mathematics of the right level, correct and understood? |
| Total | 20 | E is the biggest single criterion. Mathematics counts for 30% of the IA marks. |
Your planner
You start the IA in Rhetoric (Year 13), in the Lent term. The rough shape is set by five points: getting your idea approved, the mocks, the start, the class-time weeks and the hand-in. If you are reading this early, there is nothing to hand in yet: the first job is just to start thinking about ideas. These are rough guides and your teacher confirms the exact dates. If this page disagrees with your teacher, follow your teacher.
- Idea approved: your topic idea and draft research question are approved by your teacher . See Get your idea approved.
- The mocks: .
- You start: .
- Class time: , when you get time in lessons to work on it.
- Hand-in: .
The window is short, about five to six weeks. Choose a manageable topic and start collecting data in the first week. A focused, finished exploration beats an ambitious one that is not. The half-term holiday is for polishing, not for starting.
- 1. Get your idea approvedBefore Christmas, in the Michaelmas term of Year 13Bring your teacher a topic idea, a draft research question and a backup idea, and have them approved. Use the ideas and the approval checklist. Ask your teacher to show you two marked IAs from the IB first: seeing real work and the marks it got is the quickest way to understand what is wanted. If you are reading this in Year 12, start collecting interests now.
- 2. Tighten the question and planStraight after the mocks, in the first weekTighten your research question until you can say it in one sentence. Outline the sections, say which data you need and where it comes from, find two or three reliable sources, and try the core mathematics once on a small case. If it does not work, switch to your backup now.
- 3. Collect data and start the mathematicsThe weeks before class time, mostly at homeCollect or download all the data. Start building, calculating and graphing. Keep a log of what you tried and why, including failures. This is the raw material for personal engagement and reflection.
- 4. Write it up and get feedbackThe two class-time weeks before half-termWrite the whole exploration, not a half, with your teacher on hand. Check it with the self-marking tool, then give your teacher one draft. The IB allows feedback on one draft only: your teacher can comment on how to improve it but cannot correct, rewrite or edit it.
- 5. Final checksThe February half-term holidayPolish only. Check notation, labels, units and the page count against criteria A to E, and finish the bibliography. Read it aloud once. Do not start new mathematics now.
- 6. Hand inThe first lessons back after half-termSubmit what your school asks for. Keep the work anonymous: no name, candidate number or school name anywhere in it, including the title page, headers and file name.
The teacher's role in general. Your teacher can help you understand the criteria, discuss a topic, suggest what to read and respond to a draft with general advice. They cannot do the thinking or fix the work. Ask them early if you are unsure what counts as acceptable help.
Back to topMarking guide All five criteria with examples
For each criterion: what examiners look for in three bands, what top marks look like, how marks are most often lost, a before and after example and a short self-check. These are our plain-English summaries of the ideas. The official criterion descriptors in the IB Mathematics subject guide are the authority. Read them alongside this page.
APresentation4 marks
What examiners look for
What top marks look like
Introduction with a rationale and a clear aim, logical sections, a conclusion that answers the aim, and no filler. The reader never asks "why am I being shown this?"
Common ways to lose marks
- No stated aim, or an aim that changes halfway.
- Pages of background, biography or history that never feed into the mathematics.
- A conclusion that repeats the introduction instead of answering the question.
- Output pasted in with no explanation of what it shows.
- Going over length by adding extra, not by thinking harder.
Before and after
Self-check
- A stranger can state my aim after reading page one.
- Each section opens by saying what it will do and closes by saying what it found.
- I deleted at least one section that did not help.
BMathematical communication4 marks
What examiners look for
What top marks look like
Variables are defined once and used consistently. Equations are typeset properly (an equation editor, not typed carets). Graphs have labelled axes with units and a caption. The reader can follow the argument without guessing.
Common ways to lose marks
- Calculator syntax:
2^x,1.5E-3,sqrt(x),B2*C2. - Symbols used before they are defined, or the same letter meaning two things.
- Screenshots with unlabelled axes, tiny text or no explanation.
- A table of 200 raw data points in the main text instead of a summary (put raw data in an appendix if allowed).
- Using equals signs for things that are only approximately equal.
Before and after
Self-check
- Every symbol is defined where it first appears.
- No software syntax anywhere in the main text.
- Every graph and table has labels, units and a caption, and is mentioned in the text.
CPersonal engagement3 marks
What examiners look for
What top marks look like
The topic is plainly yours, and you show it through decisions rather than adjectives. You gathered or generated the data, tried an approach that failed and said why, changed the question or the model, and explored an idea your sources did not hand you.
Common ways to lose marks
- "I have always loved football" with nothing personal in the mathematics.
- Following a published method step by step with your own numbers dropped in.
- Forced enthusiasm: every paragraph says "fascinating" and none shows a choice.
- A topic picked because it sounds impressive, so you have no real view on it.
Genuine or forced?
Self-check
- I can point to three decisions that were mine and say why.
- My data, example or twist is original.
- I mention at least one thing that did not work and what I did next.
DReflection3 marks
What examiners look for
What top marks look like
After each main stage you stop and ask what the result means, how much to trust it and why. You compare with something (another method, real data, a known value) and you explain limits specifically, then link them to a realistic improvement.
Common ways to lose marks
- One reflection paragraph at the very end.
- Generic limits: "more data would be better" with no detail.
- Describing results again instead of judging them.
- Never testing the model against anything.
Prompts that work
- What does this number mean in context, and is it believable?
- Which assumption matters most? What happens if it is wrong by 10%?
- What does a different method give, and why might it differ?
- Where does the model fail, and what causes that?
- What would I do next with another month?
Self-check
- I reflect in at least three places, not only at the end.
- I name a limit and say what causes it.
- I compare my result with an independent check.
EUse of mathematics6 marks
What examiners look for
What top marks look like
There is enough mathematics to be worth marking, it is at least at the level of your course (SL or HL) and it is clear that you understand it. Working is shown, results are checked, assumptions are stated, and the pieces connect rather than sitting side by side.
SL and HL
Both are out of 6, but the top band asks more at HL. At SL your mathematics has to be correct. At HL it also has to be precise and show sophistication and rigour: careful notation, every step justified, and an idea or method that goes beyond routine textbook use. An exploration that would earn 6 at SL can drop a band or two at HL.
Common ways to lose marks
- Everything is done by a calculator command with no working or justification.
- One technique repeated many times (twenty linear regressions) instead of a deeper idea.
- Maths below the course (percentages, mean and mode only).
- Advanced maths copied from a source and not understood, such as a Fourier transform quoted without explanation.
- Errors that are carried through without checking.
Justification
Technology use
Self-check
- I could explain every technique on the page without notes.
- I show or justify the key steps, not only the answers.
- I checked key results a second way.
- The level fits my course and there is more than one main idea.
Self-marking tool Indicative score out of 20
Tick each statement that is honestly true of your current draft. You get an indicative score and your weakest criterion. It is not a prediction of your teacher's mark or the IB's: your teacher marks against the real descriptors and the real thing will differ. Nothing is required and nothing leaves this browser. Ticks are saved on this device only.
Tick the statements that are true to see a score.
Be honest. Ticking things that are not true does not help you. A low score on a first draft is useful: it tells you where to spend the next week.
Back to topTopic and question ideas Filter by course and area
Each idea has a sample research question to adapt, never copy: yours should come from your own interest and your own data. Difficulty is a rough guide for SL against HL. A common idea is one examiners see a lot, so you need a fresh angle. A risky idea tends to go wrong without care.
What to bring
- A draft research question, in one sentence.
- The mathematics you expect to use.
- Where the data or examples will come from.
- The tools you will use (GDC, spreadsheet, Desmos, Python).
- Why you care about it, in a way specific to you.
- A backup idea.
Quick self-check
- Is it focused enough to answer in about 14 pages?
- Is the mathematics at or above the level of your course, and can you explain it?
- Can the data be collected in the time? You have about five to six weeks from the mocks.
- Is it your own idea, rather than a copy of an article, video or a friend's topic?
Likely to be approved, and likely to be sent back
- Likely to be approved: "How well does Newton's law of cooling predict the temperature of a hot drink in two different mugs?" It is focused, uses exponentials and logarithms, and the data takes an afternoon.
- Likely to be approved: "Which of the trapezium rule and Simpson's rule gives the better accuracy per step for the area of a lake outline?" There is a clear comparison, an exact answer to check against, and you can do it in the window.
- Likely to be sent back: "The mathematics of space". Too broad: no question to answer.
- Likely to be sent back: "Fit a straight line to the heights and weights of my class". Too thin: the mathematics is below the level of the course and there is little to analyse.
- Likely to be sent back: "Track the happiness of 300 pupils over six months". The data cannot be collected in the time.
You have about five to six weeks. Favour ideas where the data already exists or takes a day or two to collect. Ideas marked long data collection need repeated measurements or careful fitting, so only choose them if you can start in the first week.
Want more? IB Maths Resources has a list of about 300 starting points. Most are one-line prompts, so test any you like against the checklist.
Where to find data
- Official statistics: national statistics offices, the World Bank, WHO and UN data portals, and government open-data sites.
- Sport: league and club websites, the Olympics, and open datasets for cricket, football, athletics and cycling results.
- Science: NASA and ESA data, weather and climate records, public health data.
- Your own data: surveys, timing experiments, measurements, school sports results (with permission), a simulation you write.
- Always record the source, date and licence, and say how reliable it is. Own data scores well on personal engagement but needs a clear method.
Pitfalls to avoid
- Too broad: "The mathematics of space". Narrow to one question you can answer.
- Too thin: a single regression, a single mean, or a calculation that takes one line.
- Too advanced: mathematics you cannot explain. Examiners reward understanding, not name-dropping.
- No data you can get: check the data exists before committing.
- Just a model: fitting a curve and stopping. You need analysis, checking and reflection.
- A copied idea: a topic that follows a well-known article or video closely. Do something of your own with it.
- Topic outside your knowledge: sport or medicine is fine, but you must explain the context in a few lines, not a few pages.
Test your idea. Can you write the research question in one sentence? Can you name the mathematics you will use? Do you know where the data or examples come from, and can you have it all in the first week or two after the mocks? If any answer is no, keep thinking before you commit.
Back to topStructure and writing Outline, formulae, citing
A template outline
Adapt the headings to your topic. The proportions below are a guide for a 14 to 16 page write-up.
- Introduction and rationaleAbout 1 page. Why this topic, in a way specific to you, and the context the reader needs.
- Aim and research questionA few lines. One clear question or aim, and what you will do to answer it.
- Method and planHalf to 1 page. Data, sources, tools, assumptions and how you will check results.
- MathematicsThe core, about 4 to 6 pages. Definitions, derivations, calculations, justification.
- AnalysisAbout 3 to 4 pages. Apply to your data, graphs, tables, interpretation.
- Evaluation and reflectionAbout 1 to 2 pages, plus short reflections placed earlier. Strengths, limits, comparison, extension.
- ConclusionHalf a page. Answer the question, with the evidence in one or two lines.
- BibliographyAll sources, in one consistent style your school accepts.
Presenting formulae, graphs and tables
- Formulae: use an equation editor. Number the key ones, define every symbol, and say where the formula comes from.
- Graphs: labelled axes with units, a caption, a legend if there is more than one series, readable text. Say what the reader should notice.
- Tables: a few rows in the text; long data in an appendix, if your school allows it. Round sensibly and keep the same decimal places in each column.
- Rounding: keep full precision in the calculation, and round only the final answer. Say how many significant figures you use and why.
- Diagrams: draw your own, or give the source. Label them and refer to them.
How long should it be?
The guide talks about pages, not words, and the IB has used a rough range of 12 to 20 pages. In practice a page of text, equations and a graph holds far fewer words than a page of an essay, so a long document is not the aim. A common mistake is padding to reach 20 pages. Quality and focus matter more than length. Ask your teacher about fonts and how appendices count.
Avoiding copying and citing properly
- Write in your own words. If you take an idea, a formula, a figure or data, say where it came from.
- Cite inline (for example a number in brackets) and list full details in the bibliography.
- Use one consistent referencing style that your school accepts. Include author, title, publisher or website, date and the date you accessed web pages.
- Quoting a definition is fine if it is short and credited. Pasting paragraphs is not.
- Do not use a source you do not understand. If you cannot explain it, you cannot use it in E.
- AI tools: the IB allows them, but any text or image you take from one, even reworded, must be credited where you use it, not just in the bibliography. Put quoted text in quotation marks with the tool's name and the year, and in the bibliography give the prompt you typed and the date. The thinking and the mathematics must be yours, and you must be able to explain every line. Using AI without crediting it is treated the same as copying someone else's work. Ask your teacher if you are not sure.
Academic honesty
The IA must be your own work. Copying, collusion, making up data and having someone else do your thinking are serious breaches and are treated under the IB's academic integrity rules. Your school will explain them. Keep your drafts, notes and data as evidence of your own work.
Back to topTechnology GDC, spreadsheet, Desmos, Python
Technology is welcome and often expected, but it should serve the mathematics. Examiners reward technology that does something you could not sensibly do by hand, and a clear explanation of what it did and why.
What examiners reward
- You say what the tool is doing, and why it is the right tool.
- You check an output another way (a hand calculation, a sketch, a second tool).
- You interpret the output in context and comment on its accuracy.
- You show enough method that someone else could repeat it.
What loses marks
- Screenshots with no explanation.
- Calculator syntax in the written working (see criterion B).
- Using a command you cannot explain.
- Technology doing something trivial, like a single sum.
The tools
| Tool | Good for | In the write-up |
|---|---|---|
| GDC (TI-Nspire) | Regression, solving equations, numerical integration, statistical tests, distributions, finance solver, checking by hand. | Describe the command in words, then show the result in proper notation. A screenshot can support but never replace working. |
| Spreadsheet (Excel, Sheets) | Data tables, iterations and recurrence, simulation, numerical methods such as Euler or trapezium, charts. | Show a small extract of the table and explain the formula in words (for example "each row adds the previous value times 1.05"). Keep the whole sheet out of the main text. |
| Desmos, GeoGebra | Exploring functions, sliders for parameters, geometry, visual checks of a model. | Export a clean graph, label it, and say what changing the slider shows. |
| Python | Simulation, large datasets, numerical methods, optimisation, plotting. | Put the code in an appendix if your school allows it, explain the idea in the text, and do not include code you did not write or cannot explain. |
When to use which
- Fitting a curve or testing a hypothesis on modest data: the GDC or a spreadsheet.
- Something that changes with a parameter: Desmos or GeoGebra with sliders.
- Many repeated trials or large data: a spreadsheet or Python.
- Always use the tool you know. A simple tool used well beats an advanced tool used badly.
TI-Nspire help
Step-by-step guides with screenshots for the CX II-T. These four come up most in IAs:
- Regression
- Numerical integration
- A statistical test (chi-squared, t-tests and more)
- Finance solver
FAQ Short answers
Can I use someone else's data?
Usually yes, if it is public, reliable and you cite it. Say where it came from, why you trust it and what you did with it. Your own thinking is what earns the marks, so doing something original with the data matters.
How many sources do I need?
There is no magic number. A handful of reliable, relevant sources is typical. Quality and honest citation matter more than quantity.
Can the IA be on a topic outside the syllabus?
It can use mathematics beyond the syllabus, but that is not required and carries risk if you cannot show full understanding. Mathematics at the level of your course, done well and understood, is safer.
How much help may my teacher give?
General advice, discussion of the criteria and feedback on a draft. They cannot write, correct or edit it for you. Feedback is on one draft only.
What if my model fails?
That can be good material. Say what you expected, what happened, why you think it failed, and what you changed. Reflection and personal engagement reward honest evaluation, and a model that fails with good analysis often scores better than one that works because it was too simple. Start early so you have time to change course.
Do I need to use technology?
It is encouraged where it helps, not required for its own sake. See the technology section.
Is AA or AI better for the IA?
Neither. Both use the same criteria. Pick a topic that fits the mathematics you know and can explain. Applied and data-based topics suit AI, while proof, geometry and calculus-based topics suit AA, but these are tendencies, not rules.
Where are the official documents?
The IB Mathematics: Analysis and Approaches and Applications and Interpretation subject guides (the Internal assessment section) and the IB's own materials for teachers. Your teacher or IB coordinator can give you the current version and the school's deadlines.