Maths IA criteria · 6 marks
Criterion E: Use of mathematics
Criterion E is the largest criterion — 6 of the 20 marks — and the only one that differs between SL and HL. It rewards mathematics that is relevant to your aim, demonstrated with understanding, and correct. It does not reward complicated mathematics for its own sake.
What Criterion E assesses
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.
This is our summary, not the IB's wording. The descriptors themselves, with a checklist and a self-grade sheet, are on the IA criteria page.
What the mark bands look like in practice
| Band | What the examiner typically sees |
|---|---|
| Low (1–2) | Some relevant mathematics, but mostly results without reasoning — a correct answer alone, or technology output with no explanation, caps the mark here. |
| Middle (3–4) | Relevant mathematics at the level of the course, partially or mostly correct, with some understanding demonstrated through explanation. |
| Top (5–6) | Relevant, correct mathematics throughout, with thorough understanding demonstrated at every step. At HL: sophisticated and rigorous — precise reasoning, justified steps, correct use of conditions and assumptions. |
Checklist for Criterion E
- Every technique is relevant to your aim — it helps answer the question.
- Mathematics at the level of your course (or similar), not only prior-knowledge mathematics.
- Reasoning shown: why each method is appropriate and what each step does.
- Technology used with understanding: say what the software computed and interpret it.
- One full worked example of each repeated calculation, then a table.
- Conditions checked before a test (sample size, expected frequencies, independence).
- Correlation computed and interpreted before any line of best fit is drawn.
- Models tested — against data you did not use, or by checking residuals.
- Correct results (minor slips are tolerated; errors that change conclusions are not).
- HL: rigour — justified steps, precise statements, proofs or derivations where appropriate.
Examiner tips
If you cannot explain it, do not use it.
Advanced mathematics you do not understand costs more than it earns. The examiner is looking for understanding, and a copied technique usually shows.
Substitution is not understanding.
Putting numbers into a formula is not enough. Derive or explain the formula, justify why it applies, and interpret the result.
Build up the mathematics.
Start with what you know, then extend: a simple model, then a better one; a special case, then the general result. That progression demonstrates understanding naturally.
Technology is allowed — explain it.
Using Desmos, GeoGebra, a GDC or a spreadsheet is fine and often sensible. Show that you know what the technology is doing (e.g., least squares) and what the numbers it gives mean.
Weak vs strong: an example
Loses marks
“Using my calculator, the equation of the line is y = 2.31x + 4.02.”
Earns marks
“The scatter graph (Figure 3) suggests a linear relationship, and r ≈ 0.94 confirms a strong positive linear correlation, so a least-squares regression line is appropriate. Technology gives y ≈ 2.31x + 4.02; the gradient means each extra hour of revision is associated with about 2.3 more marks.”
Common Criterion E mistakes
- Drawing a line of best fit on a scatter graph without first calculating r and justifying a linear model — the single most common error Pete sees.
- Stating a result from a calculator with no working or explanation (caps E at 2).
- Mathematics below the level of the course throughout (e.g., only percentages and means).
- Using a test without checking its conditions.
- Over-complicated mathematics copied from a paper and never explained.
Frequently asked questions
How hard does the maths need to be for a 6 in Criterion E?
At the level of your course, and used well. Only 6 of the 20 marks are for the mathematics itself, and relevance, understanding and correctness matter more than difficulty.
What is different about Criterion E for HL?
The HL descriptors expect mathematics commensurate with the HL course and, for the top marks, sophistication and rigour. The other four criteria are the same for SL and HL.
Can I use maths that is not on the syllabus?
Yes, if it is relevant and you explain it clearly in your own words. Say that it is new to you. Unexplained advanced mathematics does not earn marks.