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.
Next step: check your plan or draft free with the IA self-check — guided questions give a rough band for each criterion, no upload. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
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. For a rough band for your own draft, answer the guided questions in the free IA self-check.
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. |
Our summary in plain English, not IB wording — see the official IB guide via your teacher.
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.
What the IB subject reports say about Criterion E
- Understanding is shown by explaining why a method suits your aim. Software or GDC output pasted in without explanation, or formulas substituted into without understanding, stays in the lower levels.
- Modelling: plot the data first, then choose a function from the trend and the context, not from R² alone (a higher-degree polynomial always fits better but usually predicts badly), and think about the domain.
- Statistics: check a test's conditions (distribution, expected frequencies greater than 5, independence). A χ² test works only on frequencies and cannot test how well a curve fits. Correlation is not causation, and outliers need a reason before you remove them.
- Mathematics far beyond the course that you cannot explain often leads to errors. At HL, work that stays at SL level cannot reach the top bands, but a deep treatment of a simpler idea scores better than a shallow use of a complex one.
- Long calculations by hand that technology could do add length, not credit.
Our own summary of the moderators' comments in the IB's Mathematics subject reports (AA and AI, SL and HL, May 2024 to November 2025), which the IB releases to schools. Not the IB's wording, and not an IB publication.
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.
Modelling data? Worked examples for Criterion E
If your exploration fits a model to data, the IA modelling guide takes you through every step — plot, choose, fit, check, compare, test and reflect — with a fully worked example for each model: straight line, quadratic, sinusoidal, logarithmic, reciprocal, exponential, power, logistic, cubic and polynomials, piecewise. Each ends with an “is this good enough for Criterion E?” checklist and marks every step with a criterion tip; how modelling earns marks sums up what Criterion E expects at SL and HL, and the model-my-data helper shows the same steps with your own numbers.
Statistics: worked examples for Criterion E
Choosing the right technique and carrying it out correctly is Criterion E. Choosing the right test matches your question to a technique and your course; each guide (χ² test for independence, t-test, Spearman's rank …) works one example with every number shown, and Analyse my data runs the same steps on your own data.
Related: all five criteria with a self-grade sheet · annotated exemplars marked on every criterion · have Pete review your draft one-to-one · IA structure and format · how Criterion E differs at SL and HL
Types of IA where the mathematics goes beyond a curve fit: optimisation & linear programming · numerical methods & error analysis · matrices, transformations & Markov chains · cryptography & number theory.
Free: the Criterion E checks, and the other four, in one PDF
The checklist Pete uses with his own students: every check for Criteria A–E (including the Criterion E list above) in a 4-page PDF, the mistakes that cost the most marks, and a self-assessment grid. We'll email it to you, and for three weeks your weekly email carries one IA tip, timed to your deadline if you give it. Free — no account, no payment.
While you wait for the email: see Criterion E at the top band in a free annotated excerpt →