"Pick a topic you're interested in" is technically good advice, but it rarely helps in the moment — most students freeze not because they lack interests, but because they don't know how to turn "I like football" into a mathematical exploration. Below are starting points organised by interest area, each pointing at a specific technique rather than a vague theme.
None of these are ready-made titles — they're directions. A strong IA takes something like "modelling population growth" and narrows it to a specific species, dataset, or context you found or collected yourself. Prefer our interactive version? Try the IA Topic Generator to filter by course and level automatically.
Sports
- Modelling a basketball free-throw trajectory — quadratic functions, optimal launch angle (AA SL)
- Sprint fatigue and velocity decay — differentiation applied to race data (AA HL)
- Shooting accuracy vs field position — collected data, statistical testing (AI SL)
- Predicting Olympic record times — regression on historical results (AI HL)
Music
- Decay of piano note volume over time — exponential functions (AA SL)
- String vibration and harmonics — trigonometric functions, calculus (AA HL)
- Tempo trends across genres or decades — statistical comparison (AI SL)
- Chord progressions as matrices — matrix representations of music theory (AI HL)
Finance & Economics
- Compound vs simple interest growth — exponential modelling (AA SL)
- Optimising a loan repayment strategy — calculus-based optimisation (AA HL)
- Volatility of a small stock portfolio — standard deviation, variance (AI SL)
- Modelling currency exchange rate trends — regression analysis (AI HL)
Nature & Environment
- Logistic growth of an endangered species — carrying-capacity models (AA SL)
- Predator-prey population cycles — simplified differential equations (AA HL)
- CO2 levels vs global temperature — correlation analysis on real data (AI SL)
- Animal territory boundaries — Voronoi diagrams from GPS or observed data (AI HL)
Gaming
- Probability of loot box outcomes — expected value, probability distributions (AA SL)
- Game theory in a simple strategy game — Nash equilibria (AA HL)
- Win rate vs character or class choice — hypothesis testing (AI SL)
- Player progression as a Markov chain — transition matrices (AI HL)
Art & Design
- The golden ratio in classical art — measurement and comparison (AA SL)
- Symmetry in Islamic geometric patterns — matrix transformations (AA HL)
- Colour trends across art movements — statistical analysis of a painting sample (AI SL)
- Fractal dimension in natural or generative art — fractal geometry (AI HL)
Medicine & Health
- Drug concentration decay in the bloodstream — exponential decay (AA SL)
- Modelling a disease outbreak — simplified SIR-style differential equations (AA HL)
- Sleep vs academic performance — survey data and correlation (AI SL)
- BMI vs health outcomes — regression on a public dataset (AI HL)
Technology
- Smartphone battery degradation over charge cycles — exponential or power models (AA SL)
- Basic cryptography (RSA) — modular arithmetic (AA HL)
- App download trends — statistical modelling of growth data (AI SL)
- Social network structure — graph theory (AI HL)
Architecture
- Parabolic vs catenary curves in bridges — comparing real structures to equations (AA SL)
- Optimising structural load distribution — calculus-based optimisation (AA HL)
- Building height trends in a city — statistical analysis over time (AI SL)
- Proportions in famous buildings — trigonometry and geometry (AI HL)
Travel & Food
- Great circle flight distances — spherical trigonometry (AA SL)
- Newton's law of cooling for food or drink — exponential decay (AA SL)
- Flight delay patterns by airline or airport — statistical comparison (AI SL)
- Optimising a multi-city travel route — simplified route optimisation (AI HL)
Want a personalised shortlist?
Use our interactive generator to filter ideas by your course, level and interests.
✦ Try the IA Topic GeneratorFrequently asked questions
How narrow does my topic need to be?
Narrower than most students expect. "Modelling population growth" is a theme, not a topic — a strong IA specifies the species, location, dataset, and exact technique before the exploration even starts.
Can two students in my class do the same general idea?
The general theme can overlap, but the specific data, context, and personal angle should be your own — copying another student's approach closely risks academic integrity issues.