The Extended Essay is the 4,000-word research essay every IB Diploma student writes, and together with TOK it can add up to 3 points to the diploma. This guide explains what makes a good mathematics EE according to the IB's own guide, eight kinds of topic that tend to go wrong and how to fix them, the new criteria from May 2027, and the rules on word count and outside help.
Updated regularlyLast updated 21 October 2026
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The IB describes two kinds of maths EE: exploring mathematics outside the syllabus, or using mathematics to investigate an issue or data that interests you. Many essays mix the two, and a review of the literature is mandatory either way.
The IB calls knowledge and understanding “arguably the most important criterion” in a maths EE. Choose mathematics you can explain step by step in your own words, not the most impressive-sounding topic.
Five criteria worth 30 marks, including 4 for a 500-word reflective statement written after three reflection sessions with the supervisor. The last session is a short interview, the viva voce.
Help with the research, writing or proofreading beyond what the supervisor may give is not permitted, and IA work cannot be reused. AI tools may be used only if what they produce is credited.
Most disappointing EEs go wrong at the start, with the topic. Here is what the IB's guide says a maths EE should be, three conditions to test a topic against, and eight common kinds of topic that need reworking.
Explore a problem or an area of mathematics outside the syllabus that caught your interest, and explain it clearly with your own examples and proofs.
Use mathematics to investigate something you care about: an issue from a hobby, CAS, a future career or another subject, or data you can collect. Mathematics beyond the syllabus is not essential here; applying mathematics you know well to a new situation is enough.
Many essays mix the two. In either kind, a review of the literature (secondary research) is mandatory.
The six examples in the Mathematics section of the IB's Extended essay guide (first assessment 2027). The research questions are quoted; the approaches are summarised.
| Topic | Kind | Research question | Approach |
|---|---|---|---|
| Cryptography | Theoretical | What is RSA (Rivest–Shamir–Adleman) encryption and how does it help make the internet secure? | Explain how RSA works, showing full understanding of any mathematics beyond the syllabus, then how it secures online transactions. |
| To infinity and beyond | Theoretical | How many infinities are there? | Explore countably infinite sets with clear explanations and proofs, then move on to the uncountable continuum. |
| Fractal dimension | Theoretical | What are fractals and what is fractal dimension? | Explain how fractals develop and limit problems such as a finite area with an infinite perimeter, then a coastline's length or fractal dimension. |
| The last rhinoceros | Practical | How long do the rhinos have left? | Model the population size and the habitat area, and find which reaches zero first. |
| Getting to school by public transport | Practical | What is the quickest and/or cheapest route from your home to school? | Estimate travel and walking times and use an algorithm such as Dijkstra's to choose a route. |
| Winning the English football Premier League | Practical | What is “home advantage”, and are Premier League football champions equally successful away from home? | Use raw match results to compare goals at home and away, and test whether the champions overcome home advantage. |
You can answer it fully in 4,000 words. The IB asks for a topic that is narrow and sufficiently focused, and warns against taking on too much.
A mathematics teacher, not a physics or economics teacher, is the right person to mark it. If the question really belongs to another subject, the interdisciplinary pathway may suit it better.
Something new to you that you can explain (theoretical), or mathematics you know well applied to a new situation (practical), with every essential step in your own words.
Each starts from a topic students often bring, says what goes wrong, and shows one way to turn it into a workable question. The improved questions are our own examples, not the only answers.
Example questions of a size that fits an EE (our examples). The notes are a rough guide; what matters is that you can explain the mathematics.
| Area | Example question | Notes |
|---|---|---|
| Number theory | “Which whole numbers can be written as the sum of two squares?” | Proofs and your own examples; reachable from SL. |
| Combinatorics and graphs | “How many spanning trees does a complete graph have?” (Cayley's formula) | Counting arguments; Prüfer sequences make the proof accessible. |
| Probability | “What is the expected number of turns to finish Snakes and Ladders, and how does one extra ladder change it?” | Markov chains and matrices; suits HL. |
| Geometry | “How does the area of a triangle on a sphere depend on its angles, and what does that mean for flight routes?” | Spherical geometry; clear diagrams matter. |
| Numerical methods | “How fast does Newton's method converge to a square root, and when does it fail?” | Error analysis and your own computations; suits HL. |
| Differential equations | “How does vaccination change the peak of an SIR epidemic model?” | Keep the mathematics of the model at the centre, not the biology. |
| Statistics | “Do MRT trains arrive at random, or to a pattern?” | Collect raw data; choose the tests after looking at it. |
| Game theory and voting | “Is there a voting method that always elects the candidate who beats every other one head to head?” | Definitions and proofs; Arrow's theorem can be quoted without proof. |
Both are pieces of mathematical writing on a topic you choose, so students often confuse them. They are marked differently, count differently and must not overlap.
| Extended Essay | Maths IA (exploration) | |
|---|---|---|
| Who marks it | IB examiners (external) | Your teacher; the IB moderates a sample |
| What it counts for | With TOK, up to 3 diploma points; an E means no diploma | 20% of the IB Maths grade |
| Length | Up to 4,000 words (equations, tables and graphs not counted), plus a 500-word reflective statement | 12–20 pages, double-spaced |
| Criteria | Five criteria, 30 marks (from May 2027) | Five criteria, 20 marks |
| Level of mathematics | Theoretical essays go beyond the syllabus; in practical essays that is not essential | In line with your course (SL or HL) |
| Help | The supervisor comments on one draft; three reflection sessions, the last a viva voce | The teacher comments on one draft |
The EE and the IA must not share content. If they touch the same area, the IB guide asks for a substantially different angle and focus.
The IB's new Extended Essay is first assessed in the May 2027 exams; sessions up to November 2026 are marked on the previous criteria. Every subject uses the same five criteria, and the guide adds advice on applying them in each subject.
| From May 2027 | Marks | Up to November 2026 | Marks | |
|---|---|---|---|---|
| A | Framework for the essay | 6 | Focus and method | 6 |
| B | Knowledge and understanding | 6 | Knowledge and understanding | 6 |
| C | Analysis and line of argument | 6 | Critical thinking | 12 |
| D | Discussion and evaluation | 8 | Presentation | 4 |
| E | Reflection | 4 | Engagement | 6 |
| Total | 30 | 34 |
Maths essays are often well under 4,000 words, because equations do not count. What does count, and four rules from the IB's guide:
Share of extended essays at each grade in the May sessions, from the IB's final statistical bulletins. The bulletins report the EE by subject group, so “Mathematics” covers every maths essay.
| Session | Maths EEs | A | B | C | D | E |
|---|---|---|---|---|---|---|
| May 2025 | 3,542 | 11.3% | 35.5% | 39.9% | 12.4% | 0.3% |
| May 2024 | 3,226 | 8.7% | 29.1% | 46.0% | 15.3% | 0.2% |
| May 2023 | 2,947 | 8.9% | 27.1% | 44.2% | 18.8% | 0.3% |
| May 2022 | 2,881 | 15.5% | 33.7% | 37.3% | 12.4% | 0.2% |
| Subject group | EEs | A | A or B | D or E |
|---|---|---|---|---|
| Mathematics | 3,542 | 11.3% | 46.8% | 12.7% |
| Sciences | 17,558 | 8.9% | 41.0% | 13.1% |
| Individuals and societies | 44,528 | 9.9% | 37.9% | 20.7% |
| Studies in language and literature | 20,783 | 14.3% | 42.2% | 17.1% |
| Language acquisition | 6,230 | 13.2% | 36.8% | 19.3% |
| The arts | 6,288 | 14.5% | 36.2% | 25.2% |
| Interdisciplinary | 1,978 | 10.6% | 37.1% | 20.6% |
| All extended essays | 100,907 | 11.2% | 39.5% | 18.6% |
In every May session from 2022 to 2025, maths EEs had a higher share of A or B grades than all EEs (46.8% against 39.5% in 2025) and a lower share of D or E. Their share of A grades alone was below the average in 2023 and 2024.
Percentages are of all registered essays, including those with no grade (N, about 1%), so each row adds up to slightly less than 100%. All of these essays were marked on the previous criteria.
Source: IB Diploma Programme and Career-related Programme final statistical bulletins, May 2022–2025.
The EE grade is combined with the Theory of Knowledge grade. An E in either is a failing condition: no diploma, whatever the total.
| TOK ↓ · EE → | A | B | C | D | E |
|---|---|---|---|---|---|
| A | 3 | 3 | 2 | 2 | Fail |
| B | 3 | 2 | 2 | 1 | Fail |
| C | 2 | 2 | 1 | 0 | Fail |
| D | 2 | 1 | 0 | 0 | Fail |
| E | Fail | Fail | Fail | Fail | Fail |
The diploma also needs at least 24 points in total, among other conditions. The 2027 EE guide keeps the rule of up to three points.
Source: IB, DP passing criteria.
Parents help most by keeping track of the school's EE deadlines and asking how the research is going. Writing or editing any part of the essay is not allowed.
Checked on IB documents in October 2026.
In the IB Pathway Diagnostic (90 minutes, S$500), we look at current results and plans and choose the IB maths course, level and university route.
This is an independent summary by Math with Alex of documents published by the International Baccalaureate. It is not affiliated with or endorsed by the IB. It is general information only: a student's Extended Essay is guided by their school supervisor under the IB's rules.
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