- What Makes a Strong Maths AI IA Idea?
- Maths AI IA Requirements at a Glance
- Maths AI Tools You Can Use at SL and HL
- Statistics and Hypothesis Testing IA Ideas
- Regression and Modelling IA Ideas
- Financial Maths IA Ideas
- Networks, Voronoi Diagrams and Markov Chain IA Ideas
- Probability and Distribution IA Ideas
- Calculus, Geometry and Differential Equation IA Ideas
- Example: Turning an Idea Into an Exploration
- Where to Find Reliable Data for a Maths AI IA
- Using Technology Well in Maths AI
- Maths AI Key Concepts and Your IA
- New Maths AI Guide: What Changes for Exams From 2029
- Common Maths AI IA Mistakes
Quick Answer
The best Maths AI IA ideas start with a real question you can answer with data or a model: a chi-squared test on sports results, regression on World Bank data, a loan comparison, a Voronoi diagram for a new shop or, at HL, Markov chains and differential equations. The exploration is worth 20% at SL and HL, runs to 12-20 double-spaced pages and is marked out of 20.
What You'll Learn
- The Maths AI exploration is worth 20% at SL and HL, is about 12-20 double-spaced pages and is marked out of 20 on criteria A to E
- AI ideas work best with real data or a genuine modelling problem, with technology supporting your reasoning rather than replacing it
- Collect enough data for your test or model to mean something, and judge the model in context, not just by its fit statistic
- HL explorations can use HL-only tools such as non-linear regression, Markov chains, graph algorithms and differential equations
- New maths guides apply from first exams in 2029; if you sit exams in 2026, 2027 or 2028, the current criteria apply
What Makes a Strong Maths AI IA Idea?
A strong Maths AI idea starts with a practical question that mathematics can actually answer, such as 'do teams win more at home?' or 'where should a new bike dock go?'. It needs data you can trust or a model you can build and test, mathematics at the level of the AI course, and room to judge the result. The strongest explorations make a decision, test a claim or compare models, then explain how far the conclusion can be trusted.
Pro Tip
Before committing, sketch the graph or table you expect to produce and the test or model you will apply to it. If you cannot picture either, the idea is not ready.
Maths AI IA Requirements at a Glance
The Maths AI internal assessment is the mathematical exploration, a written report on a topic you choose, marked by your teacher and moderated by the IB. It has the same requirements and criteria as the Maths AA exploration. These come from the current guide (first assessment 2021), which applies if you sit your exams in 2026, 2027 or 2028.
- Weighting: 20% of your final grade at both SL and HL
- Length: approximately 12-20 pages with double line spacing, including diagrams and graphs but excluding the bibliography
- Class time: the guide recommends about 10-15 hours of teaching time for the exploration
- Criterion A, Presentation: 4 marks
- Criterion B, Mathematical communication: 4 marks
- Criterion C, Personal engagement: 3 marks
- Criterion D, Reflection: 3 marks
- Criterion E, Use of mathematics: 6 marks, with different descriptors at SL and HL, for a total of 20 marks
Watch Out
If you collect data from other students, for example through a survey or reaction-time test, get informed consent, keep responses anonymous and follow your school's ethics guidance. The guide expects ethical practice throughout.
Maths AI Tools You Can Use at SL and HL
Matching your idea to tools in your course keeps criterion E on track. Everything listed for SL is available to HL students too. Each idea below is marked SL and HL or HL only according to the tools it needs.
- SL statistics: chi-squared tests for independence and goodness of fit, the t-test, Pearson's and Spearman's correlation, and linear regression
- SL modelling: linear, piecewise linear, quadratic, exponential, cubic and sinusoidal models
- SL finance: compound interest, depreciation, amortisation and annuities using a financial solver
- SL geometry and calculus: Voronoi diagrams, optimisation, and the trapezoidal rule for areas
- HL statistics: non-linear regression, confidence intervals, the Poisson distribution, hypothesis tests for means and proportions, and Type I and II errors
- HL modelling: logistic and natural logarithm models, matrices with eigenvalues and eigenvectors, and Markov chains
- HL networks and dynamics: graph theory (minimum spanning trees, the Chinese postman and travelling salesman problems), slope fields, Euler's method and coupled differential equations
Statistics and Hypothesis Testing IA Ideas
Hypothesis tests are the most popular route for Maths AI, so the question and the data are what make yours stand out. State hypotheses before collecting data, check the conditions of the test, and interpret the p-value in plain words.
- Is home advantage real? (SL and HL): use a chi-squared goodness of fit test on home wins, draws and away wins in a football league, then a t-test on goal differences. Needs published league results for one or more seasons.
- Do the leading digits follow Benford's law? (SL and HL): test whether town populations, river lengths or election counts fit Benford's distribution with a chi-squared goodness of fit test. Needs a large published data set.
- Subject choice and gender (SL and HL): test for association between gender and choice of science subjects in your year group with a chi-squared test for independence. Needs anonymised school data and permission to use it.
- Do critics and audiences agree? (SL and HL): compare critic and audience scores for 30 or more films with Spearman's rank correlation, then look at where they disagree most. Needs published review scores.
- Are summers getting warmer? (SL and HL): compare mean summer temperatures for two 30-year periods at one weather station with a t-test. Needs national weather service station data.
- Sleep and reaction time (SL and HL): measure reaction times with an online test and collect sleep hours, then test the correlation. Needs consent from participants and a consistent testing routine.
- Left-handers and right-handers (SL and HL): compare reaction time or grip strength between groups with a two-sample t-test, discussing sample size and bias. Needs your own measurements.
- Does a manufacturer's claim hold? (HL): weigh 40 or more packets of a product, build a confidence interval for the mean and test the stated mass. Needs a kitchen scale and HL hypothesis tests for means.
- Is the dice fair? (HL): test a die or a random number generator with a chi-squared test, then calculate the probabilities of Type I and Type II errors for your sample size. Overdone at SL; the error analysis makes it HL-worthy.
- Height and points in basketball (SL and HL): test whether taller players score more points per game using Pearson's correlation and regression on published player statistics, then discuss what else explains the scatter.
Regression and Modelling IA Ideas
Modelling explorations score well when you compare several models, explain what each parameter means in context, and test predictions on data you did not use to build the model.
- How fast does a car lose value? (SL and HL): collect 30 or more listings for one model at different ages, compare linear and exponential depreciation models, and compare two brands. HL can use non-linear regression and compare fits.
- Will the Olympic 100 m record stop falling? (SL and HL): model winning times since 1900 with linear and exponential models and test their predictions. HL can fit a logistic model with a limiting time.
- Wealth and life expectancy (SL and HL): plot GDP per capita against life expectancy for 100 or more countries from the World Bank, then linearise with logarithms. HL can fit a natural logarithm model directly.
- Kepler's third law from real data (SL and HL): use NASA planetary or exoplanet data, linearise with logarithms and find the power law. Needs logarithms and regression.
- Daylight hours or temperature through the year (SL and HL): fit a sinusoidal model to published monthly data for your city and compare with a city at another latitude. HL uses radians and can compare models more formally.
- Smartphone battery discharge (SL and HL): log your battery percentage under controlled use and fit linear, piecewise and exponential models. Needs repeated runs under the same conditions.
- Cooling coffee (SL and HL): record temperature every 30 seconds and fit an exponential model with an offset for room temperature. HL can set up and solve the differential equation.
- How fast did an outbreak spread? (HL): fit a logistic model to published case data for a past outbreak, interpret the carrying capacity and growth rate, and test where the model fails.
- House prices and distance from the city centre (SL and HL): use published sale prices for one type of home and test linear and exponential models, discussing outliers and confounding variables.
- Learning curves (SL and HL): time yourself solving the same type of puzzle 30 or more times and compare power and exponential models of improvement. Needs careful, consistent timing and a clear definition of an attempt.
Financial Maths IA Ideas
Finance ideas are easy to personalise because the decisions are real. Use current, sourced figures and test how sensitive your answer is to interest rates or inflation.
- Rent or buy? (SL and HL): compare the total cost of renting and buying a home over 25 years using amortisation, then test how the answer changes with interest rates and house price growth. Needs local rents, mortgage rates and a financial solver.
- What will a student loan really cost? (SL and HL): model repayments under published loan rules for different salary paths and find who repays the most in total. Needs official loan terms.
- Lease, finance or buy a car? (SL and HL): compare monthly costs and total cost, including depreciation, across the three options. Needs real quotes and depreciation data.
- Saving against inflation (SL and HL): find the real value of regular savings under different interest and inflation rates and when a target is reached. Needs published inflation data.
Networks, Voronoi Diagrams and Markov Chain IA Ideas
These ideas turn a map or a system into mathematics. They suit students who like puzzles and planning, and several are HL only.
- Where should a new shop, defibrillator or bike dock go? (SL and HL): build a Voronoi diagram of existing locations and find the point furthest from all of them, the largest empty circle. Needs a scaled map and coordinates.
- The shortest delivery or bus route (HL): model a local area as a weighted graph and solve the Chinese postman problem, or find upper and lower bounds for the travelling salesman problem. Needs real distances from a map.
- Designing a cable or path network (HL): use Kruskal's or Prim's algorithm to find a minimum spanning tree linking buildings on your campus, then compare its length with the existing paths.
- Which station matters most? (HL): represent a metro or bus network with an adjacency matrix, count walks between stations and rank stations by connectivity.
- Predicting tomorrow's weather (HL): record daily weather states for several weeks, build a transition matrix and find the long-term steady state using eigenvectors. Needs your own records or published daily data.
- Snakes and ladders as a Markov chain (HL): build the transition matrix for a small board and find the expected number of turns to finish, then check with a simulation.
Probability and Distribution IA Ideas
Probability ideas work when you compare a theoretical model with data you collect or find, and explain any gap between them.
- Is the lottery worth playing? (SL and HL): calculate the expected value of a ticket from the published prize structure, then explore how a rollover changes it. Needs discrete random variables.
- Are crisp packets or biscuits normally distributed? (SL and HL): weigh 50 or more items, fit a normal model and find the probability of an item falling below the labelled mass. HL can add a confidence interval.
- Customers arriving at a cafe (HL): count arrivals per minute over several sessions, test whether a Poisson model fits and use it to plan staffing. Needs your own counts and permission from the cafe.
- Penalty or free-throw success (SL and HL): model your own or a player's attempts with a binomial distribution and test whether success depends on pressure or fatigue.
- Queue lengths at lunch (SL and HL): record arrival and service times, model the queue with probability and simulation, and test a change such as a second till.
- Shared birthdays in football squads (SL and HL): calculate the probability that a squad of 23 contains a shared birthday, then compare with real squad lists from a recent tournament.
Calculus, Geometry and Differential Equation IA Ideas
Calculus and geometry ideas suit students who prefer modelling a physical situation to analysing a data set. At HL, differential equations open up dynamic systems.
- Cheapest packaging for a fixed volume (SL and HL): minimise the material for a box or can using optimisation, then compare with real products and explain the difference.
- The area of a lake or park (SL and HL): estimate it from a scaled map using the trapezoidal rule with different numbers of strips and compare with the official figure.
- The best shooting angle in basketball (SL and HL): use video analysis to fit quadratic models to shots and find the launch angle with the widest margin for error.
- The most fuel-efficient speed (SL and HL): fit a quadratic model to fuel consumption at different speeds and find the optimum speed for cost per kilometre.
- Foxes and rabbits (HL): model a predator-prey system with coupled differential equations, solve it with Euler's method and compare with a published historical data set, such as fur-trading records of lynx and hare.
- How diseases spread through a school (HL): build an SIR model with coupled differential equations, solve it numerically and test how vaccination rates change the peak. Needs Euler's method and reasonable published parameters.
- Falling with air resistance (HL): drop paper cones, film them, and compare a second-order differential equation model with your measured speeds. Needs video analysis and Euler's method.
- Draining a water bottle (HL): time how the water level falls through a hole, set up a differential equation and compare its solution with your data.
- The volume of a rugby ball or an egg (HL): fit a function to its profile from a photograph, find the volume of revolution and compare with the volume of water it displaces.
Example: Turning an Idea Into an Exploration
Here is an illustrative example. A student whose family is buying a used car starts with 'cars and depreciation'. A workable aim is: which model best describes how the price of one car model falls with age, and how confident can a buyer be in its prediction for a five-year-old car?
- 1Aim: explain the question and why it matters to you in two or three sentences (criterion C)
- 2Data: record price, age and mileage for 40 or more listings of one model, and explain how you sampled them
- 3Models: fit linear and exponential models, then a model that also uses mileage, and justify each choice
- 4Mathematics: show how the parameters are found, interpret them in context and compare fits with residuals as well as R squared (criterion E)
- 5Test: check each model's predictions against listings you held back
- 6Reflect: discuss sampling bias, outliers and the limits of extrapolating beyond your data (criterion D)
- 7Present: label every graph, define every variable and keep the full data set in an appendix (criteria A and B)
Where to Find Reliable Data for a Maths AI IA
Secondary data is allowed and often better than a small survey, but you must say where it came from and why you trust it. Primary data shows strong personal engagement when you design the collection carefully.
- Official statistics: national statistics offices, such as the UK's Office for National Statistics, and the World Bank's open data
- Science data: NASA planetary and exoplanet data, and national weather services' historical station records
- Sport: official league and competition results, which are usually complete and consistent
- Finance: published loan rules, central bank interest rates and inflation figures
- Your own measurements: timed experiments, video analysis, sensor readings or counts, recorded with a clear method
- Large community data sets: useful, but check how they were collected and clean them before analysis
Using Technology Well in Maths AI
Technology is expected in Maths AI, but it should never replace explanation. The guide says merely substituting values into a formula does not necessarily show understanding, and understanding must be shown to score above the lowest level of criterion E.
- 1Choose software or a graphing calculator that genuinely helps your analysis, and say what you used
- 2Explain why each model or test is appropriate before you run it
- 3Show one calculation by hand or in full, then use technology for the rest
- 4Interpret every output, such as a p-value, a parameter or an R squared value, in the context of your question
- 5Write results in proper mathematical notation, not calculator syntax
Watch Out
A polished exploration full of software output but light on interpretation usually scores lower than students expect, especially on criteria B, D and E.
Maths AI Key Concepts and Your IA
The current Maths AI guide lists the same twelve key concepts as Maths AA: approximation, change, equivalence, generalisation, modelling, patterns, quantity, relationships, representation, space, systems and validity. They are not an IA criterion, but they are a useful lens. Most AI explorations are about modelling, relationships and validity, so asking 'how valid is my model, and where does it stop working?' is a good starting point for criterion D.
New Maths AI Guide: What Changes for Exams From 2029
So far the IB has published only the subject brief for the new Maths AI course. The full guide launches in February 2027, for first teaching in August 2027 and first assessment in May 2029. It affects students whose final exams are in 2029 or later, most of whom start the course in 2027. If you sit your exams in 2026, 2027 or 2028, the requirements above apply. According to the subject brief, the exploration stays at 20% at SL and HL, the recommended time rises to 30 teaching hours, and the criteria follow four stages of mathematical inquiry, the same at SL and HL (check the exact wording in the full guide once it is out):
- A, Problem specification: 4 marks (problem in context, desired outcomes)
- B, Abstraction: 6 marks (assumptions, selected techniques and tools, mathematical form)
- C, Computation: 4 marks (calculations, mathematical communication)
- D, Interpretation: 6 marks (interpretation of results, evaluation of desired outcomes, refinement)
Common Maths AI IA Mistakes
These are the weaknesses that most often hold Maths AI explorations back. An IB Maths AI tutor can help you test whether a data-driven topic is workable and explain which statistical or modelling tools suit which kinds of question.
- Lots of real-world context but very little mathematics
- Data sets that are too small, unreliable or not relevant to the question
- Running a test without checking its conditions or stating hypotheses first
- Treating a high R squared value as proof that a model is right
- Relying on software output without explaining it
- Trying several unrelated models or tests instead of one focused line of inquiry
- Extrapolating far beyond the data without discussing the risk