120+ IB Maths IA Topics That Actually Work With Free Ideas, Examples Breakdowns, And Tips

Choosing a strong IB Maths IA topic is one of the most important steps in the internal assessment process. A well chosen topic lets you explore mathematics at your level, stay focused, and create an investigation that feels personal and interesting. A weak topic almost always leads to frustration, shallow analysis, and difficulty meeting the criteria.

This guide gives you more than one hundred IB Maths IA topic ideas across Statistics, Modelling, Calculus, Pure Mathematics, Sports Analytics, Economics, Technology, and Geometry. Every topic has been checked to make sure it contains solid mathematical content suitable for both SL and HL.

You will also find short worked examples, guidance on turning a topic into a research question, and mistakes to avoid when choosing your IA direction.

If you need general IB Maths help, you can read our blogs like How to Score a Level 7 in IB Math or IB Math HL vs SL: Which One Should You Choose.

What Makes a Good IB Maths IA Topic

A strong topic should:

Allow you to apply mathematics that matches your course level
Be narrow enough to investigate in 12 to 20 pages
Have real data or a clear mathematical model
Let you add personal engagement through choices, reasoning, or creativity

A topic that is too broad or too focused on non mathematical theory will make the IA difficult. You should aim for a topic that includes clear mathematics such as regression, optimisation, functions, calculus, probability, or geometry.

100 Plus IB Maths IA Topic Ideas

Below are categories with topic ideas suitable for both SL and HL. All ideas emphasize mathematical modelling, analysis, or statistical methods.

Statistics and Probability IA Topics

Predicting cricket match outcomes using logistic regression
Modelling basketball free throw accuracy using binomial probability
Analysing how weather variables predict air pollution levels using multiple regression
Checking whether exam scores follow a normal distribution
Predicting taxi demand using time series models
Identifying which factors best predict real estate prices in a city
Analysing the effect of sleep hours on reaction time
Checking the fairness of different teachers grading patterns
Modelling badminton rally lengths using geometric distribution
Predicting rainfall using Poisson distribution
Analysing stock volatility with rolling standard deviation
Using chi square tests to study shot selection in basketball
Modelling heart rate recovery using exponential regression
Predicting engagement on social media posts using multiple regression
Analysing supermarket checkout duration using probability distributions
Modelling cryptocurrency price changes using random walk ideas
Studying how class size predicts academic performance
Using ANOVA to compare different study methods
Modelling the growth of YouTube channels using exponential functions
Predicting bike accident frequency using Poisson regression

Modelling With Functions IA Topics

Modelling the cooling of hot drinks using exponential decay
Finding the best launch angle for a projectile using quadratic modelling
Modelling the bounce height of a ball using linear or exponential decay
Modelling population growth of a chosen city using logistic functions
Predicting when a phone battery reaches zero using nonlinear regression
Using sinusoidal functions to model seasonal temperature patterns
Modelling traffic flow using polynomial functions
Fitting different models to car fuel efficiency versus speed
Modelling roller coaster curves using parametric equations
Finding the optimal shape of a soda can using surface area and volume relationships

Calculus Based IA Topics

Modelling caffeine decay in the bloodstream using differential equations
Optimising the volume of a container with minimal material
Modelling pendulum motion using calculus
Finding the angle that maximises solar panel efficiency
Analysing sprint acceleration using derivatives
Modelling water flow from a tank with differential equations
Calculating arc length for complex curves such as logos or tracks
Using integrals to analyse blood glucose area under the curve
Finding the optimal radius for a running track curve
Modelling car braking distance using calculus

Sports Modelling IA Topics

Modelling cricket strike rate using regression
Modelling the path of a football free kick using quadratic or drag models
Analysing speed variation in a 200 meter race using piecewise functions
Modelling the spin rate of a table tennis ball
Using geometry to model the ideal long jump takeoff angle
Predicting tennis serve accuracy using probability
Modelling fatigue in long distance running using decay functions
Using probability to analyse basketball shot selection
Predicting football attendance using time series
Modelling swimming stroke efficiency using sinusoidal functions

Economics and Finance Modelling IA Topics

Predicting gold prices using moving average models
Modelling inflation using exponential growth
Analysing salary growth across industries using regression
Predicting currency exchange rate movement with time series analysis
Modelling interest growth under different compounding structures
Using optimisation to find the best monthly savings strategy
Analysing the relationship between GDP and CO2 emissions using regression
Predicting electricity usage using seasonal patterns
Modelling the relationship between advertising spend and website traffic
Identifying which variables predict home rental prices

Physics Based Mathematical Modelling IA Topics

Modelling the trajectory of a projectile with air resistance using differential equations
Using Hooke’s law and regression to analyse spring motion
Modelling pendulum period changes with small angle approximations
Predicting LED brightness decay with exponential functions
Modelling rebound height on different surfaces with polynomial functions
Modelling sound wave interference using sinusoidal functions
Modelling torque efficiency with functions
Using regression to model friction effects on motion
Modelling capacitor charge and discharge with exponential functions
Analysing water flow from a leaking container using calculus

Computer Science and Technology IA Topics

Modelling typing speed distribution using normal curves
Analysing how image compression reduces file size using ratio mathematics
Modelling Wi Fi signal loss using inverse square relationships
Predicting website load time using regression
Analysing packet loss in online gaming using probability
Using clustering to group student study patterns
Modelling smartphone storage growth with exponential functions
Predicting app usage using Markov chains
Analysing latency versus frame rate using functions
Modelling the spread of a hashtag using exponential growth

Pure Mathematics IA Topics

Investigating patterns in Pascal’s triangle
Modelling convergence of infinite series
Exploring patterns in modular arithmetic
Studying fractal dimensions of geometric shapes
Analysing different approximations of pi
Investigating friendly and perfect numbers
Exploring the mathematics of continued fractions
Modelling random walks on grid structures
Analysing prime gaps using statistical tools
Exploring L systems and fractal growth

Geometry and Optimisation IA Topics

Finding the optimal packing arrangement of spheres in a box
Modelling the shape of an arch for maximum strength
Optimising seating layouts using geometric tools
Using Voronoi diagrams to model city regions
Exploring the optimal shape of parachute canopies
Modelling the area of irregular shapes using numerical methods
Optimising road intersection angles to reduce congestion
Modelling the geometry of curved staircases
Finding the best shape for soap bubble clusters
Using trigonometry to model shadow lengths throughout the year

Mini IA Examples With Clear Mathematical Focus

1. Predicting cricket match outcomes using logistic regression

Possible research question
How accurately can logistic regression predict match outcomes in professional cricket competitions

Math involved
Logistic regression, probability, evaluation metrics, residual analysis

Data
Match statistics from international or domestic competitions

What to explore
Test different predictor sets such as toss outcome, run rate, recent form, and team rankings. Compare model performance and discuss limitations such as data quality or season structure.

2. Modelling cooling of a hot drink

Possible research question
How well does an exponential decay function model the cooling rate of a hot drink in different cup materials

Math involved
Curve fitting, exponential functions, parameters and residuals

Data
Temperature readings over time for different cups such as paper, ceramic, or metal

What to explore
Compare models across materials, measure error, and reflect on assumptions like constant room temperature.

3. Finding the optimal solar panel angle

Possible research question
Which fixed angle maximises predicted solar energy output in a chosen city

Math involved
Trigonometry, optimisation, periodic functions

Data
Sun elevation data for the city over the year

What to explore
Compare seasonal variation, create a yearly model, and test whether a single angle is optimal for the full year.

Mistakes To Avoid When Choosing a Maths IA Topic

Choosing a topic with very little mathematics
Selecting a topic that is too broad
Gathering data that is unreliable or difficult to obtain
Using mathematics far above your level
Writing a descriptive essay instead of an analytical investigation
Ignoring the assessment criteria
Picking a topic that depends on long theoretical explanations

How To Turn a Topic Into a Focused Research Question

A topic becomes strong when you add specificity, measurable variables, and a mathematical method.

Examples:

Topic: Football performance
Research question: How accurately can a regression model predict football match outcomes using possession and shots on target

Topic: Car braking
Research question: How well does a quadratic model describe the relationship between speed and braking distance for a specific car

You can follow the same pattern: choose a variable, choose a mathematical tool, and define a measurable outcome.

Final Tips for Choosing Your Topic

• Choose something you find interesting
• Select mathematics you are comfortable learning
• Keep the scope narrow and realistic
• Start collecting data early
• Check your work against the criteria often

A good topic sets the foundation for a successful IA. Use the ideas above or the generator to find a direction that fits your style and strengths.

If you need help choosing your IA topic, refining your research question, or improving your draft, you can sign up on Baccalytics to work with experienced IB tutors who guide students through the entire process.