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Drop it straight into the free Maths AI Exploration frame. Planning your topic and question is free; unlock the full step-by-step Exploration — modelling, statistics, graphs with correct notation, reflection and evaluation — to take it to the top band.
Start this Exploration in the Maths AI frame →MODELLING REAL-WORLD DATA — CURVES & REGRESSION
Fitting a function to data you collected yourself is the AI exploration's home turf — rich data, a clear model, and plenty to evaluate.
1 · How accurately does Newton's Law of Cooling model how a cup of coffee cools?
A classic for a reason: easy data to collect with a thermometer and a timer, a clean exponential model to fit, and a built-in evaluation — where and why does the model drift from reality?
2 · Modelling the spread of a viral video or trend with a logistic growth curve.
Real public data, a model richer than a straight line, and a natural reflection on the carrying capacity and where the S-curve assumption breaks down.
3 · How well does a sinusoidal model predict daylight hours (or tides) across the year?
Periodic real data with a model whose parameters all carry meaning; comparing the fitted period to the known 365-day cycle gives an honest accuracy check.
4 · Is the relationship between a car's age and its price linear, or better modelled by a curve?
Lets you compare two models on the same data and justify the better fit with R² — a real piece of analysis rather than a single forced line.
STATISTICS & HYPOTHESIS TESTING
A well-chosen test turns an everyday hunch into a quantified result — exactly the kind of real-world reasoning the AI course rewards.
5 · Is there an association between sleep hours and exam performance?
Your own survey data drives personal engagement, the test gives a clear yes/no result, and the reflection on sample size, bias and self-reporting practically writes itself.
6 · Do two coffee shops really fill their cups to the same volume?
A cheap, repeatable measurement, a textbook-perfect use of a t-test, and a satisfying real-world verdict on whether a difference is real or just noise.
7 · Does reaction time depend on the time of day? Correlation and significance.
Self-collected data, a clear correlation coefficient to interpret, and a careful distinction between correlation and cause for the reflection.
8 · Are penalty-shootout outcomes consistent with a fair 50/50 model?
Public sports data, a clear null model to test against, and a strong evaluation about confounding factors the simple model ignores.
Ready to investigate it properly?
The Maths AI Exploration frame walks you through every criterion — and the unlock builds your modelling, statistics, graphs and critical reflection into one export-ready document.
Open the Maths AI Exploration frame →PROBABILITY & RISK
Probability lets you reason about uncertainty in games, insurance and everyday risk — and expected value gives a clean, decision-ready answer.
9 · What is the expected value of a loyalty-card scratch promotion, and is it worth playing?
A genuine consumer question answered with E(X); comparing the expected return to the cost gives a crisp, real-world conclusion and a neat sensitivity check.
10 · How well does a Poisson model predict goals (or buses, or call-centre arrivals) per interval?
Real count data, a named distribution to test against reality, and an honest evaluation of whether the "constant average rate" assumption actually holds.
11 · Simulating a casino or board-game strategy with a Monte Carlo method.
Technology does real work here; comparing simulated probabilities to a theoretical calculation shows strong command and a clear convergence story to reflect on.
12 · Should you switch? A probability analysis of the Monty Hall problem with simulation.
A vivid hook with a result most people get wrong; pairing the theoretical 2/3 with a simulation turns it into your own investigation rather than a retold puzzle.
FINANCE, OPTIMISATION & DECISION-MAKING
Applied maths at its most useful — money, planning and the best choice under constraints, all squarely in the AI course's real-world remit.
13 · How much will a regular monthly investment grow? Modelling compound interest and annuities.
Genuinely useful financial maths with a clear model; vary the rate and contribution to explore scenarios, then reflect on inflation and the assumption of a fixed rate.
14 · Using linear programming to plan the cheapest balanced weekly meal.
Real data, a constrained optimisation with a clear objective, and a graphical feasible region — a strong, self-contained piece of applied analysis.
15 · What are the optimal dimensions for a drinks can (or package) to minimise material?
Compare your optimal design to the real packaging and explain the gap — branding, grip, manufacturing — which makes for a genuinely interesting reflection.
16 · Is a phone contract or a loyalty subscription actually worth it? A break-even analysis.
A relatable decision modelled with competing cost functions; finding and interpreting the break-even point gives a clear, defensible recommendation.
NETWORKS, GEOMETRY & SPATIAL MATHS
Mapping, routing and shape in the real world — where geometry and graph theory turn a place or a plan into a problem you can solve.
17 · Which supermarket is nearest? Mapping a town with a Voronoi diagram.
A directly AI-syllabus tool applied to your own town; the diagram answers a real question and the evaluation about straight-line vs road distance is rich.
18 · What is the shortest route that visits every place on my list? A graph-theory tour.
A travelling-salesman-flavoured problem on real distances; comparing a heuristic route to the best you can find shows genuine algorithmic reasoning.
19 · How much paint (or material) does an irregular real object need? Estimating area and volume.
Your own measurements feed a numerical method, and the gap between estimate and reality drives an honest evaluation of measurement error.
20 · How efficient is a transport or social network? Centrality and connectivity in a graph.
Matrices do real work — counting routes and finding key nodes — on a network you care about, with a clear interpretation of what "important" means.
MORE REAL-WORLD MODELLING & DATA
21 · How well does a model predict a sprinter's (or your own) improving race times?
Real performance data with a tempting but dangerous extrapolation — naming where the model must fail is exactly the critical reflection the top band wants.
22 · Does a song's tempo or energy predict its popularity? Multivariate exploration of a music dataset.
A genuinely personal hook with a large open dataset; exploring which features matter most makes for a modern, data-driven exploration with plenty to reflect on.
23 · How accurately can a model predict your city's daily temperature from past data?
Real time-series data, a forecast you can test against held-back values, and a clear-eyed evaluation of how far ahead the model can usefully predict.
24 · How fair is a voting or ranking system? Comparing outcomes mathematically.
Your own data, a comparison of methods that can disagree, and a thoughtful reflection on what "fair" should even mean — distinctive and genuinely engaging.
From a topic to a top-band Exploration
An idea is the easy part — the marks are in how you build it. The Maths AI Exploration is scored out of 20 across five criteria: A Presentation, B Mathematical communication, C Personal engagement, D Reflection and E Use of mathematics. Whichever topic you pick, the same moves win: a focused real-world research question ("How accurately…?" / "To what extent…?"), real data you collect or properly source, mathematics that is correct and appropriate to AI level used with correct notation and clearly labelled graphs, genuine personal engagement, and a critical reflection on the model's or test's validity, assumptions and limitations.
Build your chosen idea into a full Exploration
The examiner-written Maths AI Exploration frame takes you through every section with the rubric, worked examples and the traps that cost marks. Planning your topic and question is free — unlock the full Exploration to develop the modelling, statistics, reflection and evaluation and export it to Word or PDF.
Open the Maths AI Exploration frame →Maths AI Exploration ideas — FAQ
What makes a good IB Maths AI Exploration topic?
A focused real-world question that AI-level mathematics can genuinely answer — modelling, statistics, probability, finance, optimisation or spatial maths. It should let you use real data where possible, apply a correct and appropriately challenging technique (regression, a χ²/t-test, expected value, linear programming), communicate with correct notation, and reflect critically on how valid the model or test really is. Phrase it as "How accurately…?" or "To what extent…?".
Where can I get real data for a Maths AI IA?
Collect your own where you can — measurements, timings and surveys boost personal-engagement marks. Otherwise use open data: government statistics portals, sports databases, weather and climate records, financial price histories, or large public survey/streaming datasets. Whatever the source, cite it, describe how it was collected, and be honest about sample size and bias in your evaluation.
What level of mathematics should I use?
Mathematics that is correct, relevant and appropriately challenging for the Applications & Interpretation course — regression and correlation, modelling with functions, statistics and hypothesis tests, probability and expected value, financial maths, optimisation or geometry in context. Going beyond the syllabus is fine if you understand it, but examiners reward maths that genuinely answers your question and is used correctly far more than difficulty for its own sake.
How do I turn the idea into a top-band Exploration?
Build it section by section in the free Maths AI Exploration frame — a focused research question, real data, an appropriate modelling or statistics technique used correctly, clear notation and labelled graphs, and a critical reflection on assumptions, validity and limitations with meaningful extensions.
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