IB Math AI SL Internal Assessment — the complete guide
The AI SL exploration is where most Applications students pick up their easiest marks of the course — provided the statistics are done properly. Regression, chi-squared tests, financial mathematics and modelling with functions are all "at the level of the course", so a well-designed data investigation can score 6/6 on Criterion E without any HL content.
This page explains what the level actually requires for AI SL, gives six topics you can collect data for yourself, and shows two complete worked explorations.
What Criterion E expects at AI SL
For AI SL, "commensurate with the level of the course" means mathematics from the AI SL syllabus used with understanding: a regression line is SL level only if you interpret the gradient, check the correlation and discuss the residuals; a chi-squared test is SL level only if you check the expected-frequency condition and interpret the p-value correctly. The level comes from the interpretation, which is exactly what the course name promises.
| Clearly at AI SL level | Linear regression with Pearson's r and interpretation; Spearman's rank; chi-squared test for independence or goodness of fit; t-test for two means; binomial and normal distributions with real data; exponential, logistic (with technology) and sinusoidal models; financial mathematics (TVM, amortisation); Voronoi diagrams for a real siting problem; simple differentiation for optimisation. |
|---|---|
| Borderline — add a layer | A single correlation coefficient; a bar chart of survey results; a percentage comparison between two groups. Each becomes SL-level when you run the appropriate test, state hypotheses, check conditions and interpret the result in context. |
| Not enough on its own | Descriptive statistics with no inference, basic probability, mean/median comparisons, drawing a Voronoi diagram with no calculation. |
For the full level descriptors of every criterion, see the IB Math IA criteria and rubric; for the 6-mark criterion in depth, see Criterion E — Use of Mathematics.
Six IA topic ideas at AI SL level
Each one has a research question you could use tomorrow, the mathematics that makes it course-level, and where the data comes from. None of them appears in the general topic list, so they are not the ones every examiner has seen.
Does sleep predict test scores? A survey and regression
Is there a significant correlation between hours of sleep and test scores among 60 students at my school, and how strong is it?
Scatter graphs, Pearson's r, least-squares regression, interpretation of gradient and intercept, residuals, limitations of self-reported data.
Your own survey — primary data is the best Criterion C evidence there is.
Where should a new metro station or clinic go? A Voronoi analysis
Which location for a new facility minimises the largest distance any resident must travel, using a Voronoi diagram of existing sites?
Voronoi diagrams, perpendicular bisectors, distance calculations, the largest empty circle problem, comparison of two candidate sites.
Real coordinates from a map; the comparison of candidates is the analysis that makes it SL-level.
Rent or buy? Financial mathematics for a Dubai apartment
Over a 10-year horizon, is renting or buying a one-bedroom apartment cheaper, and at what interest rate does the answer change?
TVM solver, amortisation, compound interest, geometric series, break-even analysis, sensitivity to interest and rent growth.
Real listings and bank rates; the "at what rate does the answer change" question drives reflection.
Is a dice game or a mobile-game loot box fair? Chi-squared goodness of fit
Do the drop rates in a mobile game match the published probabilities, based on 500 recorded openings?
Chi-squared goodness-of-fit test, expected frequencies, degrees of freedom, p-values, binomial checks on single outcomes.
Record your own outcomes; the condition checks and the honest interpretation are the mathematics.
Modelling the temperature in a classroom through the day
How well does a sinusoidal model describe the temperature cycle in a classroom, and when should the air-conditioning switch on to keep it under 24 °C?
Sinusoidal functions, parameter fitting from data, solving trigonometric equations, comparison with a quadratic model.
A cheap data logger or a phone sensor; two models compared is the SL "layer".
Does the position of a product on a shelf affect sales? A t-test
Do products at eye level sell significantly more than those on the bottom shelf, using two weeks of sales data from a family shop?
Two-sample t-test, hypotheses, assumptions of normality, confidence intervals, effect size and practical significance.
A family business or school canteen gives real data and genuine personal engagement.
Two complete AI SL explorations, summarised
These are two of the 16 worked IA examples on this site, chosen because their core technique sits squarely at AI SL level. Here you get the idea, the mathematics and the reflection; the full page shows every calculation step.
Worked example 9: Does GDP Predict Life Expectancy? A Regression Study
"To what extent does a country's GDP per capita predict average life expectancy, and how reliable is this relationship across 80 countries?"
Mathematical concepts used
- Pearson's r and Spearman's rank correlation (compare both)
- Linear regression and log-transformed regression (y = a·ln(x) + b)
- R² comparison between linear and non-linear models
- Outlier analysis and Cook's distance (leverage)
What the answer means — and how to reflect on it
The exploration's answer: yes, richer countries live longer, but with sharply diminishing returns — the first $5,000 of income is worth more years than the next $50,000. Use the model to make a concrete statement: moving from $2,000 to $4,000 per head predicts about 4 extra years; from $40,000 to $80,000, also 4 years but starting from a much higher base.
Then look at the outliers, because they carry the insight. The USA has the highest income in the sample but a life expectancy several years below the log model's prediction; Qatar is similar. Costa Rica and Japan are well above their predictions. Discuss what the model leaves out — healthcare systems, inequality, diet — and emphasise that correlation is not causation: both income and longevity may be driven by stable government and education. Suggest a multiple-regression extension with healthcare spending as a second predictor. That is critical reflection with a specific, testable next step.
See every calculation step for this exploration, explained line by line →Worked example 10: Does Home Advantage Exist in the Premier League?
"Is there a statistically significant home advantage in Premier League football, based on 380 matches from the 2022–23 season?"
Mathematical concepts used
- Chi-squared test for independence: χ² = Σ(O−E)²/E
- Degrees of freedom: df = (rows−1)(cols−1)
- Critical value vs calculated value; p-value interpretation
- Expected frequency calculation under H₀
What the answer means — and how to reflect on it
Quantify the advantage, not just its existence. Home teams won 47% of matches, away teams 34%, so a home team is about 1.4 times as likely to win as an away team. Compute a 95% confidence interval for the home-win proportion (0.47 ± 1.96√(0.47 × 0.53/380) ≈ 0.42 to 0.52) and show that a third lies well outside it.
Then ask the question that turns this into a genuine investigation: why? The 2020–21 season was played without crowds. Repeat the test on that season — the home-win rate fell to about 38% — and run a chi-squared test of independence comparing the two seasons. If the advantage shrank significantly when fans were absent, you have evidence that crowds (not travel or familiarity) drive it. Designing that comparison yourself is the clearest possible demonstration of personal engagement and critical reflection in a statistics IA.
See every calculation step for this exploration, explained line by line →How the AI SL IA is marked — the five criteria
20 marks in total, identical for every course except the level descriptors of Criterion E. Your teacher marks it; the IB moderates a sample.
| Criterion | Marks | What full marks look like |
|---|---|---|
| A — Presentation | 4 | Coherent, well organised and concise. Clear sections, numbered figures, 12–20 pages. |
| B — Mathematical communication | 4 | Correct notation, variables defined with units, graphs and tables labelled, consistent throughout. |
| C — Personal engagement | 3 | Your own question, your own data or decisions, independent thinking that is visible in every section. |
| D — Reflection | 3 | Critical reflection on results, assumptions, limitations and extensions — throughout, not just at the end. |
| E — Use of mathematics | 6 | Relevant mathematics at SL level, correct, precise, with thorough understanding shown. |
| Total | 20 | 20% of the final grade |
How to start your AI SL IA this week
AI SL IA — word count, format and other questions
Does an AI SL IA need a hypothesis test?
Not necessarily — modelling with functions, financial mathematics or a Voronoi analysis are equally valid. But if your exploration is a data investigation, a correctly performed test (chi-squared, t-test or a test on r) is the clearest way to show mathematics at course level rather than descriptive statistics.
How much data do I need for an AI SL IA?
Enough for the method to be valid: at least 30 paired observations for regression, expected frequencies of at least 5 in every cell for chi-squared, and ideally 20+ in each group for a t-test. More data does not earn more marks — a clean, well-justified sample of 50 beats a messy download of 5,000.
Is there a word count for the IB Math IA?
No — the IB sets a page limit, not a word count. The exploration should be 12–20 pages including graphs and tables but excluding the bibliography and appendices. Most strong IAs land at 14–18 pages and roughly 2,500–4,000 words of prose; if you are over 20 pages you lose the "concise" descriptor in Criterion A, so the maximum there drops to 3/4.
What format should the IA be in?
A typed document (Word, Google Docs or LaTeX) exported to PDF, with page numbers, a title that states the research question, headed sections, numbered figures and tables, and an equation editor for every piece of mathematics. Double spacing is not required; 11–12 pt text is normal. Raw data and repetitive calculations go in an appendix.
How much of my grade is the IA worth?
The exploration is worth 20% of the final grade for every IB Mathematics course (AA SL, AA HL, AI SL and AI HL). The remaining 80% comes from the written papers. It is marked by your teacher out of 20 and then moderated by the IB.
Can I use technology — a GDC, Excel, Desmos, Python?
Yes, and for most explorations you should. Technology is expected for data fitting, graphs and repetitive calculation, but Criterion E rewards the mathematics you show: formula → substitution → result, with technology used to check or to extend. "My calculator gave r = 0.81" with no formula earns little; showing the formula, one worked calculation and then the technology output earns full credit.
How many drafts can my teacher look at?
The IB allows the teacher to give written feedback on one draft. They may discuss ideas and answer questions throughout, but only one full draft receives written comments, so make that draft as complete as possible — including the bibliography and appendix.
Want a second pair of eyes on your AI SL IA?
Mr Ahmad has guided IB Mathematics: Applications and Interpretation SL students in Dubai and online from topic choice to final draft — including the honest "is this at course level?" conversation that saves marks in Criterion E.
IA tutoring — how it works →