IB Math IA Examples

The IB Mathematics Internal Assessment is worth 20% of your final grade — and it is the one component where you control the topic, the approach, and the depth of exploration. That freedom is also what makes it difficult. Most students who score below a 6 do so not because their mathematics is wrong, but because their exploration lacks personal engagement, mathematical sophistication, or a clearly communicated aim. This guide walks through what high-scoring IB Math IA examples actually look like and how to replicate their structure.

What the Examiner Is Looking For

The IB Math IA is marked on five criteria, each worth a maximum of 4 marks (except Criterion E which is 6):

A student who scores 4, 4, 3, 3, 5 = 19/20 has a high chance of a 7 on the IA. A student with correct but shallow mathematics (Criterion E = 3) combined with no reflection (Criterion D = 1) ends up around 14/20 — which is a 5 or low 6.

IB Math IA Examples by Topic Area

Analysis and Approaches (AA) HL/SL — Strong Topic Examples

1. Modelling the spread of a rumour using differential equations

This classic exploration uses a logistic differential equation to model how information spreads through a population. A student who chooses a real data source — for instance, tweet counts from a viral news event — scores highly on the personal-context element of Research design because the context is self-selected and the data is original. The mathematics involves solving the logistic equation, fitting parameters to data, and comparing the model against observed values. At HL, this can be extended to include a delayed-response model (a delay differential equation), pushing Criterion E toward 5 or 6.

Common mistake: Students who simply write out the logistic model without collecting their own data score 2 on Criterion C. The personal engagement comes from the student's specific choice of context and data, not from the mathematics alone.

2. Investigating the golden ratio in architecture or music

A perennially popular topic — but one that frequently scores low because students state that golden ratio connections "prove" aesthetic preference without using any statistical testing. A high-scoring version tests whether the ratio appears in a specific set of buildings or musical compositions using hypothesis testing or regression, then reflects honestly on whether the data supports the claim. The reflection ("the correlation was weaker than expected, which suggests…") is what earns marks on Criterion D.

3. Optimisation of a packaging design

Calculus-based optimisation is reliable AA content. A student who chooses a product they actually use — a protein bar wrapper, a tea tin, a specific shoe box — and measures real dimensions before comparing against the theoretical optimum earns strong marks on Criterion C. The mathematics should include second derivative tests and, for HL, possibly Lagrange multipliers if the constraint is complex.

Applications and Interpretation (AI) HL/SL — Strong Topic Examples

4. Regression analysis of Premier League goal data

An AI exploration built around regression is appropriate if the variables have a plausible relationship and the student goes beyond a single regression line. A strong version compares linear, quadratic, and exponential models, uses residual analysis to evaluate fit, and discusses which model is most appropriate and why. At HL, adding a chi-squared test for independence between two categorical variables (e.g., home/away result versus number of shots on target) strengthens Criterion E.

5. Using Voronoi diagrams to optimise emergency service locations

Voronoi diagrams appear explicitly in the AI HL syllabus. An exploration that applies Voronoi tessellation to a real map — choosing the nearest ambulance station for each postcode in a city, or the nearest recycling point in a neighbourhood — scores well because the application is practical and the mathematics is used rather than described. The student should measure real distances, compute the Voronoi cells, and reflect on what the model ignores (traffic, road layout, capacity constraints).

6. Analysing body mass index data across age groups using statistics

A statistics-heavy AI exploration using publicly available health data. The student collects or downloads data, applies t-tests or ANOVA to compare distributions, and reflects on whether the statistical differences are meaningful in context. The key to Criterion D here is acknowledging that statistical significance does not equal practical significance — a nuance that signals genuine mathematical understanding.

Structure of a High-Scoring IB Math IA

Examiners read hundreds of IAs. A clear structure signals organisation (Criterion A) and makes the mathematics easier to follow (Criterion B). The following structure appears in most top-scoring explorations:

  1. Introduction (150–250 words): Why this topic? What is the aim? State your research question explicitly. Do not start with "Mathematics is everywhere."
  2. Background mathematics (optional, 200–400 words): Explain only the theory a reader needs to follow your exploration. Do not include textbook definitions of concepts your reader already knows.
  3. Exploration (the bulk, 800–1500 words): Your calculations, models, graphs, and reasoning. Show working. Label every figure. Explain what each step means, not just what it is.
  4. Reflection (200–400 words): What did you find? Were you surprised? What are the limitations of your model? What would you do differently?
  5. Conclusion (100–200 words): Restate what you found in relation to your aim. Do not introduce new material here.
  6. Bibliography: Cite every data source, textbook, and website you used.

Total length: 12–20 pages including figures, or roughly 2000–4000 words of prose. Going over 4000 words rarely improves scores and often signals that the student included padding rather than depth.

The Most Common Reasons IB Math IAs Score Below Expectations

Choosing a topic that is too broad

"The mathematics of climate change" cannot be explored in 20 pages. A focused version — "modelling the rate of Arctic ice loss using exponential decay" with a specific dataset — can. Narrow your aim to something you can actually answer with the mathematics you know.

Listing results without explaining them

A student who writes "the derivative is 2x, therefore the minimum is at x=0" without explaining why this matters for the aim is scoring low on Criterion B and D. Every result should be connected back to the research question.

Copying a well-known example

The "SIR model for disease spread" and the "mathematics of music and Fourier series" are among the most submitted IA topics. Examiners recognise them immediately. If you choose a familiar topic, you need an original data source, an unusual angle, or a self-collected dataset to score well on Criterion C.

Weak or absent reflection

Criterion D = 1 is the single most preventable mark loss in the Math IA. Students who write one paragraph at the end saying "in conclusion, my model was reasonably accurate" are describing, not reflecting. Reflection means asking: what did I assume? What could go wrong? How does this connect to real-world constraints? What mathematics could extend this exploration?

How Your IA Draft Compares to the Rubric

Reading high-scoring IB Math IA examples is useful — but the gap between understanding a strong example and writing one yourself is where most marks are lost. When you have a draft, the most efficient use of your time is to get criterion-by-criterion feedback: exactly where is Criterion D weak? Is your Criterion B notation consistent throughout? Are there places where the mathematical reasoning is unclear?

IBLens analyses your IB essay or IA draft against the official IB marking criteria and identifies precisely where marks are being lost — before your teacher submits your final grade.

Upload your Math IA draft to IBLens for rubric-based feedback →