IA ideas · Mathematics: applications and interpretation SL
Maths AI SL IA ideas (121)
Applications and interpretation SL explorations are at their best with real data: modelling it with technology, testing a hypothesis about it, or making a decision with it. Criterion E rewards choosing the right model or test for the question, using it correctly and interpreting the result in context.
Every idea below fits AI SL. Most use data you can collect yourself or download from a source we have checked, and the maths is squarely in the SL course — regression, statistical tests, Voronoi diagrams, financial mathematics and simple calculus.
Accessible (39)
- How far does a bouncing ball really travel?AA SLAI SLAA HLAI HLAccessible
- Which function best describes the arch of a famous bridge?AA SLAI SLAccessible
- Why are camera f-stops 1.4, 2, 2.8, 4, 5.6?AA SLAI SLAA HLAI HLAccessible
- Where should you build your first settlement in Catan?AA SLAI SLAA HLAI HLAccessible
- Which mug keeps tea hot longest? Newton's law of cooling, comparedAA SLAA HLAI SLAI HLAccessible
- How does the shape of the daylight curve change with latitude?AA SLAI SLAA HLAI HLAccessible
- Is deforestation in [a country] slowing down?AI SLAI HLAA SLAccessible
- Radioactive decay with dice: does chance produce an exponential curve?AA SLAI SLAA HLAI HLAccessible
- How does bread dough rise? A logistic model in the kitchenAA SLAA HLAI SLAI HLAccessible
- Why aren't drinks cans the optimal shape?AA SLAI SLAA HLAI HLAccessible
- How fast does my heart rate recover after exercise?AA SLAI SLAA HLAI HLAccessible
- Is home advantage in football disappearing?AI SLAI HLAA SLAA HLAccessible
- How much does a cold month cost my family?AI SLAI HLAA SLAccessible
- Do more doctors mean fewer infant deaths?AI SLAI HLAA SLAccessible
- Does light really follow an inverse-square law?AA SLAI SLAccessible
- Is crime seasonal? Testing monthly crime countsAI SLAI HLAccessible
- How big is my local lake? Estimating area with the trapezoidal ruleAI SLAI HLAA SLAA HLAccessible
- Is a lottery ticket ever worth buying? Expected value and rolloversAA SLAA HLAI SLAI HLAccessible
- Can height predict lung capacity?AI SLAI HLAA SLAccessible
- Which method measures a building's height most accurately?AA SLAI SLAccessible
- Is Moore's law still true?AA SLAI SLAA HLAI HLAccessible
- Is a longer mortgage ever the better deal?AI SLAI HLAA SLAA HLAccessible
- Are NBA players getting taller?AI SLAI HLAA SLAA HLAccessible
- Does a pendulum's period really depend on the square root of its length?AA SLAI SLAA HLAI HLAccessible
- Does my phone battery really drain in a straight line?AI SLAI HLAA SLAccessible
- Contract or SIM-only? The real cost of a new phoneAI SLAA SLAccessible
- Has my pocket money kept up with inflation?AI SLAA SLAI HLAccessible
- Where should a pool ball hit the cushion? The geometry of bank shotsAA SLAI SLAccessible
- What is the best shape for a rain gutter?AA SLAI SLAA HLAI HLAccessible
- Are elite footballers more likely to be born early in the selection year?AI SLAI HLAA SLAA HLAccessible
- Can you beat people at rock–paper–scissors?AI SLAI HLAA SLAA HLAccessible
- Modelling the sun's height from a stick's shadowAA SLAI SLAA HLAI HLAccessible
- Do students who sleep less react more slowly?AI SLAI HLAA SLAA HLAccessible
- Why do stopping distances grow so fast? Modelling the Highway Code tableAA SLAI SLAccessible
- Are our summers getting wetter or drier?AI SLAI HLAA SLAccessible
- How much does it cost to start saving ten years later?AI SLAI HLAA SLAA HLAccessible
- What is the chance of hitting every green light on my route?AI SLAI HLAA SLAA HLAccessible
- Do TV series really get worse over time?AI SLAI HLAccessible
- How fast do cars lose value? Modelling depreciation from listingsAI SLAI HLAA SLAccessible
Solid (69)
- How many extra tickets should an airline sell?AA SLAA HLAI SLAI HLSolid
- When might the Arctic be nearly ice-free in September?AA SLAA HLAI SLAI HLSolid
- Can statistics tell two authors apart?AI SLAI HLAA SLSolid
- Modelling bacterial growth in the biology labAA SLAA HLAI SLAI HLSolid
- What is the best angle to shoot a free throw?AA SLAA HLAI SLAI HLSolid
- Does Benford's law hold for the populations of the world's towns?AI SLAI HLAA HLSolid
- Where is the best seat in the cinema?AA SLAA HLAI SLAI HLSolid
- How much does rain reduce bike-share use?AI SLAI HLSolid
- The birthday problem, extended: what about birthdays within a day?AA SLAA HLAI SLAI HLSolid
- Is BMI's “height squared” right? Evidence from OlympiansAI SLAI HLAA SLAA HLSolid
- How do doctors estimate your skin area? Comparing body-surface-area formulasAA SLAA HLAI SLAI HLSolid
- Estimating π by dropping needles: how fast does the estimate improve?AA HLAA SLAI SLAI HLSolid
- Does caffeine build up if you drink coffee every few hours?AA SLAA HLAI SLAI HLSolid
- Are arrivals at the school canteen random? A Poisson model of a queueAI HLAI SLSolid
- How big is White's advantage in chess, and does it depend on skill?AI SLAI HLAA HLSolid
- How long is a coastline? Measuring fractal dimensionAA SLAA HLAI SLAI HLSolid
- The Collatz conjecture: what can we say about stopping times?AA SLAA HLAI SLAI HLSolid
- How many primes are there below n? Testing the prime number theoremAA SLAA HLAI SLSolid
- Exponential or logistic? Modelling my country's populationAA SLAA HLAI SLAI HLSolid
- How fast did COVID-19 spread at the start? Comparing doubling timesAA SLAA HLAI SLAI HLSolid
- Are cricket batting scores geometrically distributed?AI SLAI HLAA HLAA SLSolid
- Designing a working sundial for my latitudeAA SLAA HLAI SLAI HLSolid
- How long does a bottle take to drain? Testing Torricelli's lawAA SLAA HLAI SLAI HLSolid
- Why does a piano have twelve notes per octave?AA SLAA HLAI SLAI HLSolid
- What is the fewest number of exam sessions my school needs?AI HLAA HLAI SLSolid
- How connected is my year group? Analysing a friendship networkAI HLAI SLSolid
- Does money buy a longer life? GDP and life expectancyAI SLAI HLAA SLAA HLSolid
- Measuring inequality: fitting Lorenz curves and computing the Gini coefficientAA SLAA HLAI SLAI HLSolid
- How often do big earthquakes happen? The Gutenberg–Richter lawAI SLAI HLAA SLAA HLSolid
- Is a hanging chain a parabola? Catenary versus quadratic modelsAA SLAA HLAI SLAI HLSolid
- Is the “hot hand” real? Streaks in my free throwsAI SLAI HLAA SLAA HLSolid
- How much is being near a station worth?AI SLAI HLAA SLSolid
- Why do a flute and a violin sound different on the same note?AA SLAA HLAI SLAI HLSolid
- Modelling the Keeling curve: trend plus seasonsAA SLAA HLAI SLAI HLSolid
- Should I lease or buy my first car?AI SLAI HLSolid
- Do left-handed tennis players have an advantage?AI SLAI HLAA HLSolid
- The lifeguard problem: what is the fastest route to a swimmer?AA SLAA HLAI SLAI HLSolid
- Why don't long jumpers take off at 45°?AA SLAA HLAI SLAI HLSolid
- How many attempts until the rare item? Drop rates and pity systemsAA SLAA HLAI SLAI HLSolid
- A positive test result: how likely is it that you really have the condition?AA HLAA SLAI SLAI HLSolid
- What is the cheapest way to connect villages with fibre broadband?AI HLAI SLSolid
- The Monty Hall problem when the host is forgetfulAA SLAA HLAI SLAI HLSolid
- Is a penalty shoot-out fair to the team that shoots second?AA SLAA HLAI SLAI HLSolid
- How accurate is the perspective in a Renaissance painting?AA SLAI SLAA HLAI HLSolid
- Is solar power growing logistically?AA SLAA HLAI SLAI HLSolid
- What are the odds in a Risk battle?AA SLAA HLAI SLAI HLSolid
- How fast does news spread through a year group?AI SLAI HLAA SLAA HLSolid
- What price maximises profit at our school bake sale?AA SLAI SLAA HLAI HLSolid
- Will the sofa fit round the corner? The longest object through a corridorAA SLAA HLAI SLAI HLSolid
- What is the best tilt for a solar panel at my home?AA SLAI SLAA HLAI HLSolid
- How fast is a sprinter at each moment? Differentiating 100 m splitsAA SLAA HLAI SLAI HLSolid
- How many packs does it take to finish a sticker album?AA SLAA HLAI SLAI HLSolid
- Will I ever repay my student loan?AI SLAI HLAA SLSolid
- Why do sunflower seeds form spirals? The golden angleAA SLAA HLAI SLAI HLSolid
- How much does a small edge on each point matter in tennis?AA SLAA HLAI SLAI HLSolid
- Is the golden ratio really everywhere? Testing a popular claimAI SLAI HLAA SLAA HLSolid
- How many different games of noughts and crosses are there?AA SLAA HLAI SLAI HLSolid
- Can a sum of sine waves predict the tides?AA SLAA HLAI SLAI HLSolid
- Can you predict a tree's height from its trunk?AI SLAI HLAA SLSolid
- Which Underground station is the most central?AI HLAI SLSolid
- How much vaccination is enough to stop measles?AI SLAI HLAA SLSolid
- Would a Voronoi diagram have pointed John Snow to the Broad Street pump?AI SLAI HLSolid
- Where should my town put its next defibrillator? A Voronoi analysisAI SLAI HLSolid
- Do school catchment areas match the Voronoi diagram of the schools?AI SLAI HLSolid
- Who lives furthest from a supermarket? Food access with Voronoi diagramsAI SLAI HLSolid
- Where should a winger shoot from? Maximising the angle to goalAA SLAA HLAI SLAI HLSolid
- Will women's Olympic times ever match men's?AI SLAI HLAA SLAA HLSolid
- Is there a limit to how fast humans can run 100 m?AA SLAA HLAI SLAI HLSolid
- What are the chances of rolling a Yahtzee in one turn?AA SLAA HLAI SLAI HLSolid
Ambitious (13)
- Are Atlantic hurricanes becoming more frequent?AI SLAI HLAmbitious
- Where should I aim on a dartboard?AI SLAI HLAA HLAmbitious
- Can a simple rating system predict football results?AI SLAI HLAA HLAmbitious
- Is the euro–dollar exchange rate a random walk?AI SLAI HLAA HLAmbitious
- When should a Formula 1 driver pit? Modelling tyre degradationAA SLAI SLAA HLAI HLAmbitious
- How many flights does it take to get anywhere?AI HLAI SLAmbitious
- Why do flight paths curve on the map?AA SLAA HLAI SLAI HLAmbitious
- How many shuffles does it take to mix a deck of cards?AI HLAA HLAI SLAmbitious
- Designing a smooth roller-coaster drop with piecewise functionsAA SLAA HLAI SLAI HLAmbitious
- How strongly is global temperature linked to ln(CO₂)?AI SLAI HLAA SLAA HLAmbitious
- Which airport is really closest? Voronoi diagrams on a curved EarthAI SLAI HLAmbitious
- Voronoi diagrams in a grid city: Euclidean or taxicab distance?AI SLAI HLAA HLAmbitious
- Should bigger hospitals get bigger regions? Weighted Voronoi diagramsAI HLAI SLAmbitious
AI SL mathematics that works well in an IA
- Linear, exponential, power and sinusoidal models fitted with technology
- Pearson's and Spearman's correlation; regression
- Chi-squared and t-tests, with conditions checked
- Voronoi diagrams: perpendicular bisectors and the largest empty circle
- Financial mathematics: compound interest, loans and annuities
Revise the techniques: Exponential models · Correlation regression · Chi squared · Voronoi · Financial maths. How AI SL differs from the other courses: AA vs AI, SL vs HL.
Frequently asked questions
What is a good Maths AI SL IA topic?
A real question answered with real data: modelling a trend, testing whether two things are related, or using a Voronoi diagram or financial calculation to make a decision. Choose something where you can get enough good data.
Are Voronoi diagram IAs good for AI SL?
Yes, when there is a real decision to make (where to put a new facility, who is poorly served) and you calculate some of the diagram by hand before using technology.
Is a statistics IA enough for AI SL Criterion E?
It can reach the top if the test is appropriate, its conditions are checked, one calculation is shown and the result is interpreted in context. A chi-squared test with no discussion of expected frequencies or sampling rarely does.
Free: the IA checklist an examiner uses
Every check for Criteria A–E in a 4-page PDF, the mistakes that cost the most marks and a self-assessment grid. We'll email it with a short IA tip every few days, timed to your deadline if you give it.
By course: AA SL · AA HL · AI SL · AI HL · By interest: Computer science · Physics and engineering · Psychology and social sciences · Geography and travel · Chemistry · All 153 ideas