Maths EE criteria · 6 marks

Criterion B: Knowledge and understanding in a maths EE

Provisional The criteria, marks and reflection details on this page are from the new IB Extended essay guide (first assessment May 2027) as we understand it, and are being checked against the published guide. Treat them as provisional until this note goes.

This criterion looks at how well you know the mathematics behind your question: correct definitions, results stated and used accurately, sources chosen with care, and explanations that show you understand the ideas rather than repeat them.

What examiners look for in a maths EE

  • Definitions and results stated correctly, with conditions ("for a continuous function on a closed interval…").
  • Mathematics beyond the syllabus explained in your own words, with worked examples that show you understand it.
  • Sources that are reliable for mathematics: textbooks, university lecture notes, journal articles, original works.
  • The context of the question placed in the wider mathematics, briefly and accurately.

Common pitfalls

  • Quoting a theorem you cannot explain or apply.
  • Copying a proof's steps without saying why each step holds.
  • Relying on a single website for all the mathematics.
  • Errors in definitions (a missing condition, a wrong domain) that undermine later work.

How to reach the top band

  1. For every result you use, ask: could I explain this to a classmate, and could I check it on an example?
  2. Work at least one example of each new idea by hand before using it in general.
  3. Use two or more independent sources for the key results, and cite them where you use them.
  4. Explain why a method is valid, not only how to apply it.

Check your own draft

  • Every definition and theorem I use is stated correctly, with its conditions.
  • I explain new mathematics in my own words and illustrate it with my own worked examples.
  • My sources for the mathematics are reliable and cited where I use them.
  • I could explain every step of every proof or derivation in the essay if my supervisor asked.

Answer these for every criterion in the free EE self-check.

What is expected of a maths essay

  • The essay should be about mathematics: the mathematics is the subject of the essay, not a tool used in passing for another subject.
  • The mathematics may go beyond the DP syllabus, but you must show you understand everything you use; quoting results you cannot explain does not earn credit.
  • Arguments are expected to be precise: terms defined, notation consistent, and results proved or justified (or properly referenced) where a mathematician would expect it.
  • Applications and modelling are allowed, but the focus stays on the mathematics: why the method works and how good the model is, not only the context.
  • A history-of-mathematics essay has to engage with the mathematics itself (for example by working through the original method), not only with biography.
  • Technology (graphing software, spreadsheets, code) is welcome; say what it did and make sure the mathematics behind it is explained.

Our summary of the subject guidance for mathematics (being checked against the guide).

Frequently asked questions

Can a maths EE use mathematics beyond the IB syllabus?

Yes, and most do, as far as we know from the subject guidance. What matters is that you show you understand the mathematics you use: explain it, apply it correctly and illustrate it with your own examples.

What sources are best for a maths EE?

University-level textbooks, lecture notes from university courses, journal articles (including expository ones written for students and teachers) and original historical works. Websites can help you find these but should rarely be your only source for a result.

IB Math Revision is independent and not affiliated with or endorsed by the IB. Criterion descriptions are our own summaries; for the official wording see the IB's Extended essay guide (your EE coordinator has it).