IB Maths IA hub · AA & AI · SL & HL
Everything you need to write a strong Maths IA
The Maths IA (exploration) is 12–20 pages of your own maths, marked out of 20 on five criteria (A–E) and worth 20% of your grade in AA and AI, SL and HL. Here: 239 ideas, criterion guides, annotated exemplars and a free planner, from Pete Bromfield, a former Head of Maths with IB examining experience (independent of the IB).
Start here: the IA in six steps
New · IA modelling, step by step
Modelling your data? Paste it, see every step, send it back
Every common model — straight line, quadratic, sinusoidal, exponential, logarithmic, power, logistic and more — worked step by step, with a criterion tip at each step. Model my data does the same with your numbers.
- Paste your data from Desmos, GeoGebra, Google Sheets or Excel.
- Get the play-by-play: parameters, working, residuals, SSR and R², and what earns marks at each step.
- Send it back: the regression, the fitted equation or the data, to Desmos or GeoGebra — or save it to your account.
Model my data The modelling workflow
Top models: straight line · quadratic · sinusoidal · exponential · choosing and comparing models. Straight-line and quadratic pages are free to read in full; the rest open with a free account.
How the Maths IA is marked
| Criterion | Marks | In one line |
|---|---|---|
| A · Presentation | 4 | The organisation, coherence and conciseness of the exploration as a whole |
| B · Mathematical communication | 4 | Whether the mathematical language |
| C · Personal engagement | 3 | The extent to which you engage with the exploration and make it your own |
| D · Reflection | 3 | How you review, analyse and evaluate the exploration |
| E · Use of mathematics | 6 | Whether the mathematics you use is relevant to the exploration and at an appropriate level for your course, whether you show understanding of it (not just results), and whether it is correct. At HL the top bands also expect sophistication and rigour. |
| Total | 20 | 20% of your final IB Maths grade (SL and HL) |
Grade yourself against the descriptors on the criteria self-grade sheet, or answer the guided questions in the free IA self-check for a rough band per criterion. Our summaries follow the current criteria (exams up to 2028). New criteria apply to students who start the DP in August 2027 — see the FAQ.
Criterion guides
IA ideas library
239 ideas across 24 topics, each with a research question, the maths it needs for AA/AI and SL/HL, real data sources, an outline and the pitfalls.
- Modelling with functions13 ideas
- Calculus & optimisation10 ideas
- Differential equations & dynamics10 ideas
- Statistics & hypothesis testing13 ideas
- Probability & chance13 ideas
- Geometry, trigonometry & Voronoi diagrams12 ideas
- Finance & economics11 ideas
- Sport10 ideas
- Environment & climate11 ideas
- Health, biology & medicine9 ideas
- Networks, graphs & algorithms9 ideas
- Pure maths, number & proof12 ideas
- Art, music & design14 ideas
- Games & puzzles11 ideas
More types of IA: Optimisation · Simulation · Cryptography · Numerical methods · Fractals & chaos · Matrices & Markov · Trig & navigation · Kinematics · Voting & game theory · Surveys
By course: AA SL · AA HL · AI SL · AI HL · By interest: Computer science · Physics and engineering · Psychology and social sciences · Geography and travel · Chemistry · Biology · Economics · Business management · Sports, exercise and health science · Environmental systems and societies · Music · Visual arts · Design technology
A few to start with
- Where should my town put its next defibrillator? A Voronoi analysisAI SLAI HLSolid
- Is a hanging chain a parabola? Catenary versus quadratic modelsAA SLAA HLAI SLAI HLSolid
- Is home advantage in football disappearing?AI SLAI HLAA SLAA HLAccessible
- How long does a game of Snakes and Ladders last?AI HLAA HLAmbitious
- How long does a skydiver take to reach terminal velocity?AA HLAI HLAmbitious
- Should I lease or buy my first car?AI SLAI HLSolid
Annotated exemplars
13 original explorations written for teaching — AA SL, AA HL, AI SL, AI HL: calculus, differential equations, trigonometric modelling, complex numbers, statistics, Voronoi and graph theory — each marked criterion by criterion, including six written to a top-band (full-marks) standard, plus four deliberately mid-band drafts that show how to improve.
- Is a hanging chain a parabola? Comparing catenary and quadratic modelsAA SL · 19/20
- How long does a skydiver take to reach terminal velocity?AA HL · top-band standard · 20/20
- Should I lease or buy my first car?AI SL · 17/20
- How long does a game of Snakes and Ladders last on my grandmother's board?AI HL · 18/20
- Do students who sleep less react more slowly?AI SL · 18/20
- Sleep and reaction time: a mid-band draft, annotated to show how to improveAI SL · 10/20
- Where should our town put its next defibrillator? A Voronoi analysisAI SL · 18/20
- How far can a stack of books lean over the edge of a table?AA HL · top-band standard · 20/20
- Is my 07:40 bus late because of the rain?AI SL · top-band standard · 20/20
- What is the quickest way to deliver a leaflet to every house on my estate?AI HL · top-band standard · 20/20
- When can we launch? Modelling the tide at our sailing club's slipwayAA SL · top-band standard · 20/20
- Drinks-can optimisation: a mid-band AA SL draft, annotated to show how to improveAA SL · 12/20
- Predicting Spirograph patterns with complex numbersAA HL · 16/20
- Is it cheaper to leave the heating on low overnight? A two-temperature model of my bedroomAI HL · top-band standard · 20/20
- Are arrivals at the school canteen random? A mid-band AI HL draft, annotated to show how to improveAI HL · 12/20
- When is the sea warm enough for our swimming club? A sinusoidal model of sea temperatureAI SL · top-band standard · 20/20
- Where should the 125 ml line go on a wine glass? A mid-band AA HL draft, annotated to show how to improveAA HL · 13/20
IA modelling, step by step
Have your data? The modelling guide shows the whole workflow — plot, choose, fit, check, compare, test, reflect — with a fully worked example for every common model, GDC keys and Desmos syntax, a criterion tip at every step, and a helper that runs the same steps on your own data (paste it from Desmos, GeoGebra or a spreadsheet).
- Straight line y = mx + c
- Quadratic: three points, completing the square, regression
- Sinusoidal y = a sin(b(x − c)) + d
- Logarithmic y = a ln x + b
- Reciprocal y = a/x + b and a/(x − h) + k
- Exponential y = a e^(kx) + c and y = a·bˣ
- Power y = a·xⁿ (log–log)
- Logistic y = L/(1 + C e^(−kx))
- Cubic and polynomials (and overfitting)
- Piecewise models
- Choosing and comparing models
IA statistics, step by step
Testing a question with data? The statistics guide covers the whole workflow — sampling, cleaning, describing, choosing the right test, checking its conditions and interpreting — with a worked example for each technique, every number shown, and Analyse my data to run the same steps on your own data.
- Choosing the right test
- Sampling and collecting data
- Cleaning data and outliers
- Descriptive statistics and box plots
- Pearson's correlation and regression
- Spearman's rank correlation
- Chi-squared test for independence
- Chi-squared goodness of fit
- t-test: two-sample and paired
- Is my data normal?
- Confidence intervals for a mean
- Binomial and Poisson models
The IA package
Everything above is free. The package adds 13 full annotated exemplars (6 at a top-band standard) and four mid-band drafts, plus 5 AI feedback credits for your own drafts — €39 once, no subscription, 14-day money-back guarantee. See what's included. Want a person to read your draft? IA Review with Pete (€100).
Guides
- How to write a Maths IA, step by step
- Structure and format: a section-by-section template
- Word count and page limit: how long it should be
- AA vs AI, SL vs HL: how the IA differs
- Using Desmos, GeoGebra and Excel
- IA modelling, step by step: every model worked, plus a data helper
- IA statistics, step by step: every test worked, plus Analyse my data
- IA data bank: open datasets to model, cited and licensed
- Free data sets for maths IAs: where to find more real data, ranked, with licences
- Weekly modelling challenge: practise on real data
- IA modelling planner: paragraph feedback as you draft
- How IA marks count: weighting, boundaries, moderation
- Mistakes that cost marks
- Timeline from your deadline, and a printable planning template
- IA in 8 Weeks: a free week-by-week plan to your deadline, with a Monday email
- AI tools and academic integrity
- My IA marking checklist (PDF)
- IB Maths IA tools compared: ideas, data and feedback
- Criteria descriptors, checklist and self-grade sheet
- Free IA self-check: a rough band for each criterion
- Interactive IA topic explorer
- For teachers: IA launch pack and class tracker
- For teachers: IA standardisation practice
- For schools: free IA resources to link to
- Writing a maths Extended Essay? Ideas, research questions and an EE planner
- TOK and maths: knowledge questions, exhibition objects and essay help
- CAS ideas for students who love maths: clubs, tutoring, data for charities, maths art
Frequently asked questions
What is the IB Maths IA?
The internal assessment (the “exploration”) is a 12–20 page piece of mathematics on a topic you choose. It is marked by your teacher and moderated by the IB against five criteria, and counts for 20% of your final grade in both AA and AI, at SL and HL.
What are the Maths IA criteria?
A: Presentation (4 marks), B: Mathematical communication (4), C: Personal engagement (3), D: Reflection (3) and E: Use of mathematics (6) — 20 marks in total. Only Criterion E differs between SL and HL.
How do I choose a Maths IA topic?
Start with something you care about, turn it into a precise question with an answer, check it needs mathematics at the level of your course, and check you can get the data. Our ideas library has 239 worked-up starting points.
Are the IA criteria changing?
Yes, for students who start the Diploma Programme in August 2027 (first exams in May 2029). The exploration stays, but criteria A–E are replaced by four inquiry criteria (problem specification, abstraction, computation and interpretation), the same at SL and HL and still out of 20. Everything on this hub follows the current criteria, which apply to exams up to and including 2028.
Is using this site for my IA allowed?
Yes, as coaching: ideas, guides, exemplars and feedback help you write your own exploration. Everything in your IA must be your own work, and you should acknowledge any tools you used, following your school's policy.
Start your IA plan, free
Answer the planning questions: your question, the maths, the data and milestones back from your deadline. Then take it to your first teacher meeting.
Your plan is kept in this browser. A free account keeps it with your drafts on any device: Join free · Sign in
- Free IA self-check: guided questions give a rough band for each criterion. No upload.
- The A–E checklist as a PDF, free by email.
- Have a draft? AI feedback against A–E (Criterion A free), or a one-to-one review with Pete (€100).