IB Maths IA Ideas: 30+ Topics That Actually Work

Choosing the right IB Maths Internal Assessment topic is one of the most important decisions you'll make in the Diploma Programme. The IA is worth 20% of your final grade, and the topic you choose determines how much mathematical depth you can show — which is the single biggest factor in your score.

This guide gives you real, scorable IA ideas organised by syllabus area, with notes on what makes each topic strong and what to avoid.

What Makes a Strong IA Topic?

Before looking at specific ideas, understand the criteria. The IB marks your IA on five criteria:

• A — Presentation: Structure, clarity, use of mathematical notation
• B — Mathematical Communication: Correct and consistent use of notation and language
• C — Personal Engagement: Genuine curiosity; exploring beyond the obvious
• D — Reflection: Considering limitations, unexpected results, and implications
• E — Use of Mathematics: Mathematical sophistication relevant to your level (SL or HL)

Criterion E is where most students either shine or fall short. An SL student using year 10 mathematics cannot score well here. The mathematics must be appropriate to IB Maths level and — crucially — it must be more than just calculations. Exploring why something happens mathematically is valued over just computing results.

IA Ideas for IB Maths AA (Analysis & Approaches)

Calculus and Analysis

• Modelling the spread of a disease using differential equations (SIR model)
• Investigating optimisation in packaging design using calculus
• Exploring the convergence rate of Taylor series approximations for sin x and cos x
• Euler's method vs exact solutions for simple ODEs — where does it break down?
• Modelling the cooling of an object and exploring Newton's law of cooling experimentally (HL)

Statistics and Probability

• Applying the Central Limit Theorem to real datasets — how large does n need to be?
• Modelling scoring patterns in football using the Poisson distribution
• Investigating whether SAT scores follow a normal distribution and what factors affect deviation
• Using Bayes' theorem to model medical testing accuracy

Algebra and Number Theory

• Investigating modular arithmetic and its applications in cryptography (RSA basics)
• Exploring patterns in continued fractions and their convergents
• The mathematics of error-correcting codes (Hamming codes)

Geometry and Trigonometry

• Investigating the area of polygons inscribed in a circle as n → ∞ (approaching π)
• Modelling projectile motion and finding the optimal launch angle for different scenarios
• Exploring properties of conic sections using parametric equations (HL)

IA Ideas for IB Maths AI (Applications & Interpretation)

Statistics and Modelling

• Regression analysis of climate data — modelling temperature change over time
• Investigating correlation between sleep and academic performance using collected data
• Applying linear programming to optimise a real business problem (café, sports schedule, etc.)
• Modelling population growth using logistic functions vs exponential growth
• Chi-squared testing: investigating independence between two categorical variables

Graph Theory and Networks

• Applying Dijkstra's algorithm to real-world route optimisation
• Exploring minimum spanning trees using Prim's or Kruskal's algorithm on a real network
• Modelling social network connectivity using graph theory concepts

Financial Mathematics

• Comparing compound interest strategies for saving goals
• Modelling loan repayment and investigating the effect of interest rate changes

How to Form a Good Research Question

Your research question should be specific, mathematical, and genuinely investigable. Avoid vague questions like "How does mathematics appear in nature?" Instead: "How accurately does a logistic model predict the growth of a bacterial culture under controlled conditions?"

A good research question:

• Has a clear variable to investigate
• Requires mathematics at or above your course level to answer
• Leads naturally to reflection on limitations and extensions
• Is something you're genuinely curious about (this shows in Criterion C)

What Examiners Reward in a High-Scoring IA

After working with many IB Maths students through their IAs, the patterns in high-scoring work are consistent:

• Mathematics that goes beyond what the student learned in class
• Genuine reflection on why results make sense (or don't)
• Acknowledgment and quantification of limitations
• Clear, consistent mathematical notation throughout
• A conclusion that returns to the research question with a substantive answer

If you're looking for personalised IA support — from topic selection through to final write-up — our IB Maths AA HL tutoring and IB Maths AI HL tutoring both include dedicated IA mentorship.