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Mathematics Extended Essay structure: sections, criteria and word count

The Mathematics Extended Essay takes a theoretical, practical or data-driven approach, or a mix, in up to 4,000 words, marked out of 30 on 5 criteria. This structure has 13 sections, including a literature review, mathematical development in subsections and a discussion of relevance, plus the 500-word RPF statement and a reflection log.

At a glance

TaskThe independent research essay
GuideExtended essay guide, first assessment 2027, Mathematics section
SessionsMay 2027 onward
LevelsCore
AssessmentExternal, assessed by IB examiners and graded A to E
WeightingWith TOK, 0 to 3 diploma points
HoursAbout 40 hours of student work, plus 3 to 5 hours of supervision
Limit4,000 words, plus a 500-word RPF statement. Examiners stop reading at the limit. RPF statement: up to 500 words, counted apart from the rest.
CriteriaA Framework for the essay (6), B Knowledge and understanding (6), C Analysis and line of argument (6), D Discussion and evaluation (8), E Reflection (4): 30 marks. Criteria A to D are marked on the whole essay by best fit. Criterion E is marked only on the RPF statement, which is uploaded separately.
What is changingFirst assessed in May 2027: the 5 criteria and the 2 pathways apply, and the guide gives Mathematics its own section.

The structure, section by section

1. Title page

Required by the IB · Criterion: A (structure) · Outside the word count

Your personal code, the research question, the subject and the word count, plus a statement when explanatory footnotes are counted.

  1. Enter your IB personal code.
  2. Leave out your name, your supervisor's name, your session number and your school.
  3. Paste the research question exactly as it stands in the introduction.
  4. Name your subject: Mathematics.
  5. Insert the word count from the counter.
  6. Add the footnote statement if you used explanatory notes.

2. Acknowledgements or dedication

Common practice (Optional, uncounted and unassessed) · Outside the word count · Only when it applies

Thanks or a dedication with no identifying names.

  1. Decide whether you need it.
  2. Remove any name that identifies you, your supervisor or your school.
  3. Keep it to a few lines.

3. Contents page

Required by the IB · Criterion: A (structure) · Outside the word count

Headings with page numbers.

  1. Generate it from your headings.
  2. Start page numbers on the page after it.
  3. Regenerate it after your last edit.

4. Introduction

Required by the IB · Criterion: A

The research question, the approach, and a starting point in familiar course mathematics.

  1. State the research question.
  2. Say which approach you take: theoretical, practical, data-driven or a mix.
  3. Start from mathematics a classmate in your course would know.
  4. Outline the route through the essay.

5. Literature review

Required by the IB (Secondary research is mandatory in mathematics) · Criterion: A (methods), B

What the main sources contribute to your question.

  1. Find the main sources on your topic.
  2. Explain in your own words what each one contributes.
  3. Cite every borrowed result and proof.
  4. Note what the sources leave open.

6. Mathematical development, in subsections

Required by the IB (Required as the body; subheadings are Convention) · Criterion: B, C

The theory built step by step, with worked examples.

  1. Plan subsections that follow your argument.
  2. Put each algebra step on its own line.
  3. Typeset every equation in an equation editor, with no calculator notation such as * or ^.
  4. Illustrate each key result with a worked example.
  5. If you quote a theorem without proof, explain its role and show it in an example.
  6. Compare 2 methods only if you can show full understanding of both.

7. Data presentation and analysis

Rewarded by a criterion (For practical and data-driven essays) · Criterion: C · Only when it applies

Raw data, graphed first, then analysed.

  1. Collect or source raw data.
  2. Graph it before you choose a technique.
  3. Choose the technique the data supports, and keep it out of the research question.
  4. Move large data sets to an appendix.

8. Discussion and evaluation

Rewarded by a criterion · Criterion: D

The relevance, strengths and limitations of the mathematics and the data, throughout the essay and in a closing evaluation.

  1. Discuss relevance at each stage.
  2. Note strengths and limitations as they arise.
  3. Close with an evaluation of the whole approach.

9. Conclusion

Required by the IB · Criterion: C, D

The answer to the research question.

  1. Answer the research question directly.
  2. Summarise the key results.
  3. Add no new mathematics.

10. References or bibliography

Required by the IB (Also an academic integrity rule: every source must be acknowledged) · Criterion: A (structure) · Outside the word count

Every source used, in 1 standard style chosen by the school.

  1. Use 1 style throughout.
  2. List every source you cited, including images, data and AI output.
  3. Add URLs and access dates for online sources.
  4. Check that each in-text citation has an entry.

11. Appendices

Common practice (Optional, and examiners need not read appendices; the signed external mentor form is the one required item) · Outside the word count · Only when it applies

Data too long for the body, other supporting material, and the mentor form.

  1. Move only bulky data here.
  2. Refer to it from the text.
  3. Insert the signed mentor form if you had a mentor.

12. Reflection sessions log

Required by the IB (The 3 sessions are mandatory and are recorded on the RPF, which is uploaded separately from the essay) · Outside the word count · Submitted separately

The 3 formal reflection sessions, each with its month, your DP year (1 or 2) and your supervisor's initials.

  1. After the first reflection session, log its month and your DP year.
  2. Log the interim session the same way.
  3. Log the viva voce as the third session; it runs 20 to 30 minutes, after your supervisor has read the final version.
  4. Ask your supervisor to initial each row; the form carries initials only.
  5. If you are retaking, record the current year as DP year 2.
  6. Leave informal check-ins off the log.
  7. Check that all 3 rows are complete before your supervisor initials and dates the form.

13. RPF reflective statement

Required by the IB (A mandated form, uploaded separately from the essay and marked under criterion E) · Criterion: E · Outside the word count · Submitted separately

Up to 500 words, written after the viva voce, evaluating how the EE shaped you as a learner and which skills you will carry forward.

  1. Keep dated notes after each session, ideally in a researcher's reflection space.
  2. Reread them after the viva.
  3. Evaluate specific decisions and turning points, and keep any account of the process brief.
  4. Show how you grew and where you will use the skills.
  5. Write every word yourself; an AI-written reflection counts as fabrication.
  6. Write in the essay's language and stop at 500 words.

What counts toward the limit

Counted: the introduction, body and conclusion, including quotations and explanatory footnotes or endnotes. Left out: the title page, acknowledgements, contents, page headers, maps, charts, diagrams, annotated illustrations, tables, equations, calculations, citations, reference notes, the bibliography, appendices, the RPF statement and a footnote that gives a quotation's original-language text. The guide does not mention section headings, captions or table titles, so the counter leaves them out as well.

The limit: 4,000 words, plus a 500-word RPF statement. Examiners stop reading at the limit. RPF statement: up to 500 words, counted apart from the rest.

Graphs and visuals

The frequencies are our estimates, from what the IB guide expects and what teachers advise. We did not count them in marked work.

Citations

No subject-specific style is given. Explain borrowed mathematics in your own words, and follow the general EE referencing rules. Some study guides suggest APA for mathematics essays.

The workspace keeps your sources and writes the bibliography in APA 7th to start with. You can switch to MLA 9th, Chicago author-date, Chicago notes (footnotes) or Harvard at any point.

Pitfalls

Write it in the workspace

These sections in order with their steps, a word counter that counts the way this page says, your sources and a bibliography, and graphs from your own data. Export to Word or PDF.

Open this structure in your workspace

The workspace is free with an account, and it never writes or rewrites your text. What we will and will not do with your coursework →

Sources

The IB documents behind this page, checked 29 October 2026. The linked ones are on ibo.org; the others are IB documents we read in copies hosted elsewhere, so we name them without a link. Everything above is in our own words: the official wording is in your subject guide, which your coordinator can give you. LimeAdmissions is independent of the International Baccalaureate Organization, which has not endorsed this page. Every coursework structure →