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IB Math IA Topic Ideas
The Internal Assessment is worth 20% of your final grade, and the topic you choose shapes everything. Here are 30+ curated ideas for AA and AI, plus exactly what examiners are looking for.
OVERVIEW
What Is the IB Math Internal Assessment?
The IB Math Internal Assessment (IA), officially called the Mathematical Exploration, is a 12–20 page written piece in which you investigate a mathematical topic of your own choosing. It is internally marked by your teacher and externally moderated by the IB.
It is worth 20% of your final grade. That is a huge proportion. A student who scores 7/7 on every exam but gets 12/20 on their IA can still miss the grade boundary. The IA is not an afterthought, it deserves serious preparation.
| Criterion | Marks | What it Means |
|---|---|---|
| A, Presentation | 4 | Clear structure, well-written, appropriate use of notation and graphs |
| B, Mathematical Communication | 4 | Correct and consistent use of mathematical language, variables, and notation |
| C, Personal Engagement | 3 | Evidence of genuine curiosity; the exploration feels like yours, not a template |
| D, Reflection | 3 | Discussion of limitations, extensions, surprises, and what the results mean |
| E, Use of Mathematics | 6 | Appropriate, accurate, and meaningful mathematics used throughout |
Criterion E, Use of Mathematics, carries the most weight at 6 marks. This is where level matters most. AA HL students are expected to use HL-level mathematics. Using only SL content in an HL exploration will cap your score on this criterion.
TOPIC IDEAS
AA Topics: Analysis and Approaches
AA IA topics reward depth in calculus, proof, and algebraic reasoning. If you are in AA HL, your topic should involve HL content, calculus, sequences, differential equations, or number theory.
Higher Level Topics
- The Mathematics of Epidemics: SIR Model Use differential equations to model the spread of disease. Explore how parameters like transmission rate affect the outcome. Solve numerically and analytically.
- Euler's Identity and Complex Numbers Explore e^(iπ) + 1 = 0 through a proof and investigation. Connect complex numbers, Maclaurin series, and polar form. Extend to applications in physics or signal processing.
- Optimisation in Architecture: Minimal Surface Area Apply calculus (Lagrange multipliers or single-variable optimisation) to find shapes minimising material usage. Connect to real design problems.
- Chaos Theory and the Logistic Map Explore iteration and bifurcation in the logistic function. Investigate when stable cycles become chaotic. Use sequences and recursive functions.
- Fourier Series: Approximating Periodic Functions Use infinite series to approximate non-smooth functions (square wave, sawtooth). Connect to music, signals, and heat flow. Rigorous HL calculus throughout.
- The Basel Problem and π²/6 Prove the sum of 1/n² converges to π²/6. Explore Euler's original approach and modern alternatives using integration or Fourier analysis.
Standard Level Topics (Also Strong at HL)
- The Golden Ratio in Nature and Art Investigate Fibonacci sequences, the golden ratio φ, and its appearance in spirals, architecture, and biology. Use sequences, limits, and proof.
- Modelling Projectile Motion with Drag Compare ideal projectile trajectories with realistic models including air resistance. Use calculus or numerical methods to find range and maximum height.
- Cryptography and Modular Arithmetic Explore the RSA algorithm or Caesar cipher using modular arithmetic, prime numbers, and number theory. Investigate how key length affects security.
- How Do Rollercoasters Work? Clothoid Curves Investigate the Euler spiral used in loop design to prevent sudden curvature changes. Use parametric equations and arc length to model the geometry.
- Population Growth Models: Logistic vs Exponential Compare exponential and logistic growth using real population data. Fit parameters and evaluate which model predicts better over time.
- The Mathematics of Music: Frequency Ratios Explore why certain musical intervals sound harmonious using frequency ratios, logarithms, and arithmetic/geometric sequences. Connect to equal temperament tuning.
TOPIC IDEAS
AI Topics: Applications and Interpretation
AI IA topics reward data collection, statistical analysis, and real-world modelling. The best AI IAs use genuine data, ideally collected by the student, and go beyond basic descriptive statistics into inferential or predictive analysis.
Higher Level Topics
- Network Analysis of Social Connections Use graph theory to model friendships, transport networks, or internet links. Calculate degree sequences, shortest paths, and clustering coefficients. Apply Kruskal's or Prim's algorithm.
- Markov Chains and Brand Switching Model consumer behaviour across competing products using transition matrices. Find steady-state vectors and investigate how advertising changes equilibrium probabilities.
- Bayesian Updating in Medical Testing Use Bayes' theorem to calculate how a test result updates the probability of disease. Investigate false positives and how prior probability changes outcomes dramatically.
- Optimal Delivery Routes: Travelling Salesman Problem Apply graph theory to find efficient routes for a real city (e.g., delivery locations or tourist sites). Compare nearest-neighbour heuristics with brute-force and discuss optimality.
Standard Level Topics (Also Strong at HL)
- Does Screen Time Affect Sleep Quality? Collect data via survey. Use Pearson's or Spearman's correlation, chi-squared test, and linear regression. Discuss confounding variables and limitations of self-reported data.
- Modelling COVID-19 Spread in Your Country Use publicly available data to fit logistic or SIR-inspired models. Investigate how R₀ changed over time and evaluate model accuracy at predicting peaks.
- Is There a Home Advantage in Football? Analyse goal data from a league season. Use chi-squared tests, t-tests, or regression to test whether home teams win significantly more often.
- Predicting House Prices with Multiple Regression Use real estate data (publicly available in many countries) to build a multiple regression model. Investigate which variables predict price best and evaluate the model's fit.
- The Birthday Problem and Probability Simulations Investigate the birthday paradox theoretically and through simulation. Extend to related problems (coincident last digits, shared initials) and compare theoretical vs observed probability.
- Financial Planning: Loans, Mortgages, and Amortisation Model a real mortgage or loan scenario using geometric series and TVM calculations. Investigate how interest rate changes affect total cost and monthly payments.
- Carbon Footprint Modelling Gather data on transport, diet, or energy use and model personal or community carbon output. Use regression and modelling to project future emissions under different scenarios.
AVOID THESE
6 Common IA Mistakes
Topic Too Broad
"The Mathematics of Climate Change" covers decades of research. Narrow it: "Modelling CO₂ concentration using a logistic function and comparing it to IPCC projections."
No Personal Angle
Examiners deduct marks for Personal Engagement when the IA reads like a textbook chapter. Explain specifically why you chose this topic and what questions genuinely puzzled you.
Mathematics Too Simple for Level
An AA HL student who only uses SL-level statistics will struggle to score well on Criterion E. HL explorations must include HL content, this is non-negotiable.
Weak Reflection
Criterion D rewards critical thinking: what surprised you? What limitations exist? How could this be extended? One paragraph of "the results matched my hypothesis" is not sufficient reflection.
Copied or Formulaic Approach
Examiners see hundreds of IAs on the golden ratio, Fibonacci, and basic projectile motion. These topics can still score well, but only if you bring a fresh angle and genuinely explore rather than recite.
Leaving It Too Late
The IA requires time: for data collection, drafting, revisions, and teacher feedback. Students who start 3 weeks before the deadline consistently produce weaker work. Start early in Year 2.
BEFORE YOU SUBMIT
IA Topic Selection Checklist
Use this before committing to a topic. Every "no" is a warning sign worth fixing early.
- I can explain in one sentence why this topic interests me personally
- My exploration has a clear, specific mathematical question to answer
- The mathematics required is appropriate for my level (HL topics use HL content)
- I have access to the data or resources I need (before I start writing)
- My topic is not too broad, I can meaningfully explore it in 12–20 pages
- My topic is not too narrow, there is enough to write about with real depth
- I can identify at least 2 limitations or extensions to discuss in my reflection
- My teacher has approved or given feedback on the topic direction
- I have not copied a topic structure from a sample IA I found online
- I understand all the mathematics I plan to use, not just the steps, but the concepts
COMMON QUESTIONS
IB Math IA, FAQs
How long should the IA be?
The IB guidance is 12–20 pages. Most strong IAs are 14–18 pages. Going over 20 pages does not earn extra marks, examiners often stop reading carefully after that point. Focus on quality: clear structure, precise mathematics, and thoughtful reflection.
Can I use a topic my teacher suggested?
Yes, your teacher may suggest areas or broad topics. But the exploration must feel genuinely yours. Examiners assess personal engagement. If the IA reads like a template someone handed you, Criterion C will be low. Find an angle that genuinely interests you within the suggested area.
Can I use a GDC or computer software in the IA?
Yes, software, GDC, Desmos, Excel, and other tools are all permitted. For AI students, using technology is expected. For AA students, using software is fine, but the mathematical reasoning should still be shown, not delegated entirely to the tool.
Do I need to collect my own data?
Not necessarily. Secondary data (from published sources) is accepted and very common in AI explorations. If you use secondary data, cite your sources properly and ensure you understand the context of the data. For Personal Engagement marks, self-collected or personally motivated data tends to help.
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