IA ideas · Mathematics: applications and interpretation SL
Maths AI SL IA ideas (170)
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.
AI SL explorations are usually built on data: collecting or choosing a dataset, fitting and comparing models with technology, testing a claim with a χ² test, a t-test or a correlation coefficient, or using Voronoi diagrams, financial mathematics and trigonometry in a real place. Technology does the arithmetic (Desmos, GeoGebra, a spreadsheet or your GDC); the marks come from choosing the right method, saying what the technology did and interpreting each result in context.
Next step: shortlist ideas with the free IA topic explorer, which filters starting points by course, interest and how easy the data is to get. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.
Accessible (57)
- Designing an accessible ramp for a real entranceTrig & navigation
- How far does a bouncing ball really travel?Modelling
- Breaking a cipher with letter frequencies and chi-squaredCryptography
- Which function best describes the arch of a famous bridge?Modelling
- Why are camera f-stops 1.4, 2, 2.8, 4, 5.6?Art & music
- Where should you build your first settlement in Catan?Games & puzzles
- How many of each? Planning a charity bake sale with linear programmingOptimisation
- Same ballots, different winners: comparing voting methods in a class voteVoting & game theory
- Which mug keeps tea hot longest? Newton's law of cooling, comparedModelling
- How does the shape of the daylight curve change with latitude?Environment
- Is deforestation in [a country] slowing down?Environment
- Radioactive decay with dice: does chance produce an exponential curve?Probability
- How does bread dough rise? A logistic model in the kitchenDifferential equations
- Why aren't drinks cans the optimal shape?Calculus
- Estimating g from a video of a falling ballKinematics
- Why do guitar frets get closer together? A geometric sequence on the fingerboardArt & music
- How fast does my heart rate recover after exercise?Health & biology
- Is home advantage in football disappearing?Statistics
- How much does a cold month cost my family?Environment
- Do more doctors mean fewer infant deaths?Health & biology
- Does light really follow an inverse-square law?Modelling
- Is crime seasonal? Testing monthly crime countsStatistics
- Infinite perimeter, finite area: designing your own snowflake curveFractals & chaos
- How big is my local lake? Estimating area with the trapezoidal ruleCalculus
- Is a lottery ticket ever worth buying? Expected value and rolloversProbability
- Can height predict lung capacity?Health & biology
- Which method measures a building's height most accurately?Geometry & Voronoi
- A sponge with no volume and infinite surface: the Menger spongeFractals & chaos
- Estimating the area of a leaf with random pointsSimulation
- Is Moore's law still true?Modelling
- Is a longer mortgage ever the better deal?Finance
- Are NBA players getting taller?Statistics
- How long would it take to guess your password? Counting and logarithmsCryptography
- Does a pendulum's period really depend on the square root of its length?Modelling
- Does my phone battery really drain in a straight line?Modelling
- Contract or SIM-only? The real cost of a new phoneFinance
- Has my pocket money kept up with inflation?Finance
- Where should a pool ball hit the cushion? The geometry of bank shotsSport
- What is the best shape for a rain gutter?Calculus
- Are elite footballers more likely to be born early in the selection year?Statistics
- How wide is the river? Measuring a distance you can't crossTrig & navigation
- Can you beat people at rock–paper–scissors?Games & puzzles
- What is the cheapest way to hire coaches for a school trip?Optimisation
- Do we know how long we spend on our phones? Estimates versus screen-time dataSurveys
- Modelling the sun's height from a stick's shadowGeometry & Voronoi
- Do students who sleep less react more slowly?Statistics
- Are popular songs getting faster or shorter? Statistics on music dataArt & music
- How fast does a speaker get quieter? Decibels, logarithms and distanceArt & music
- Why do stopping distances grow so fast? Modelling the Highway Code tableModelling
- Are our summers getting wetter or drier?Statistics
- Measuring the area of an irregular field with trianglesTrig & navigation
- How much does it cost to start saving ten years later?Finance
- What is the chance of hitting every green light on my route?Probability
- Walk, cycle, bus or car? Travel to school and distanceSurveys
- Do TV series really get worse over time?Statistics
- How fast do cars lose value? Modelling depreciation from listingsFinance
- How far off do you end up? Navigating a route by bearingsTrig & navigation
Solid (98)
- How many extra tickets should an airline sell?Probability
- When might the Arctic be nearly ice-free in September?Environment
- Can statistics tell two authors apart?Statistics
- Modelling bacterial growth in the biology labHealth & biology
- What is the best angle to shoot a free throw?Sport
- Why do two nearly-equal notes 'wobble'? Beats and trigonometric identitiesArt & music
- Does Benford's law hold for the populations of the world's towns?Statistics
- Where is the best seat in the cinema?Calculus
- How much does rain reduce bike-share use?Environment
- The birthday problem, extended: what about birthdays within a day?Probability
- Is BMI's “height squared” right? Evidence from OlympiansHealth & biology
- How do doctors estimate your skin area? Comparing body-surface-area formulasHealth & biology
- How fractal is a fern? Box-counting dimension from photographsFractals & chaos
- Estimating π by dropping needles: how fast does the estimate improve?Probability
- Modelling a bus journey between two stops from a phone's sensorsKinematics
- How few staff can a café roster? An integer programming rotaOptimisation
- Does caffeine build up if you drink coffee every few hours?Differential equations
- Are arrivals at the school canteen random? A Poisson model of a queueProbability
- Counting a hidden population: capture–recapture at schoolSurveys
- Why does a random game draw the Sierpiński triangle?Fractals & chaos
- The cheapest healthy weekly shop: a linear programming diet problemOptimisation
- How big is White's advantage in chess, and does it depend on skill?Games & puzzles
- How long is a coastline? Measuring fractal dimensionPure maths
- The Collatz conjecture: what can we say about stopping times?Pure maths
- How many primes are there below n? Testing the prime number theoremPure maths
- Exponential or logistic? Modelling my country's populationModelling
- How fast did COVID-19 spread at the start? Comparing doubling timesHealth & biology
- Are cricket batting scores geometrically distributed?Sport
- How quickly does a swing die down? Exponential or linear decay?Kinematics
- Designing a working sundial for my latitudeGeometry & Voronoi
- How long does a bottle take to drain? Testing Torricelli's lawModelling
- Measuring the Earth with a stick and a partner schoolTrig & navigation
- Why does a piano have twelve notes per octave?Art & music
- What is the fewest number of exam sessions my school needs?Networks & graphs
- How connected is my year group? Analysing a friendship networkNetworks & graphs
- Does money buy a longer life? GDP and life expectancyStatistics
- Measuring inequality: fitting Lorenz curves and computing the Gini coefficientFinance
- How often do big earthquakes happen? The Gutenberg–Richter lawStatistics
- Is a hanging chain a parabola? Catenary versus quadratic modelsModelling
- The hidden angles of a hip roof: 3D trigonometryTrig & navigation
- Is the “hot hand” real? Streaks in my free throwsProbability
- How much is being near a station worth?Statistics
- How big should a school poll be? Sampling from a known populationSurveys
- How far can you see from the top of a hill?Trig & navigation
- Why do a flute and a violin sound different on the same note?Art & music
- Modelling the Keeling curve: trend plus seasonsEnvironment
- Does the best team win? Knockout cups versus leaguesSimulation
- Should I lease or buy my first car?Finance
- Do left-handed tennis players have an advantage?Statistics
- The lifeguard problem: what is the fastest route to a swimmer?Calculus
- Can you average a 1–5 rating? Analysing Likert-scale survey answersSurveys
- What interest rate are you really paying? Solving for the rate by iterationNumerical methods
- Why don't long jumpers take off at 45°?Sport
- How many attempts until the rare item? Drop rates and pity systemsGames & puzzles
- Why is a rolling marble slower than a sliding block?Kinematics
- Can letter transitions tell languages apart? Markov chains for textMatrices & Markov
- A positive test result: how likely is it that you really have the condition?Health & biology
- What is the cheapest way to connect villages with fibre broadband?Networks & graphs
- The Monty Hall problem when the host is forgetfulProbability
- What speed minimises the total cost of a long drive?Optimisation
- One snake queue or a queue at every till? Simulating supermarket checkoutsSimulation
- Square or hexagonal? Packing tins into a boxOptimisation
- Left, right or centre? Game theory for penalty kicksVoting & game theory
- Is a penalty shoot-out fair to the team that shoots second?Probability
- How accurate is the perspective in a Renaissance painting?Art & music
- Cutting shelves from planks with the least wasteOptimisation
- Does the wording change the answer? A split-sample survey experimentSurveys
- Is solar power growing logistically?Environment
- What are the odds in a Risk battle?Games & puzzles
- How fast does news spread through a year group?Differential equations
- What price maximises profit at our school bake sale?Finance
- Turning votes into seats: D'Hondt, Sainte-Laguë and largest remainderVoting & game theory
- Who should pay what for a shared taxi? The Shapley valueVoting & game theory
- How fast does a sledge go? Acceleration, friction and slopeKinematics
- Will the sofa fit round the corner? The longest object through a corridorCalculus
- What is the best tilt for a solar panel at my home?Environment
- How fast is a sprinter at each moment? Differentiating 100 m splitsCalculus
- How many packs does it take to finish a sticker album?Probability
- Will I ever repay my student loan?Finance
- Why do sunflower seeds form spirals? The golden angleArt & music
- How much does a small edge on each point matter in tennis?Probability
- Is the golden ratio really everywhere? Testing a popular claimArt & music
- How many different games of noughts and crosses are there?Games & puzzles
- Can a sum of sine waves predict the tides?Environment
- Balancing traffic flow through a road network with linear equationsMatrices & Markov
- Trapezoidal rule or Simpson's rule? Areas under the normal curveNumerical methods
- Can you predict a tree's height from its trunk?Modelling
- Which Underground station is the most central?Networks & graphs
- How much vaccination is enough to stop measles?Health & biology
- Would a Voronoi diagram have pointed John Snow to the Broad Street pump?Geometry & Voronoi
- Where should my town put its next defibrillator? A Voronoi analysisGeometry & Voronoi
- Do school catchment areas match the Voronoi diagram of the schools?Geometry & Voronoi
- Who lives furthest from a supermarket? Food access with Voronoi diagramsGeometry & Voronoi
- Who answers online surveys? Measuring non-response biasSurveys
- Where should a winger shoot from? Maximising the angle to goalSport
- Will women's Olympic times ever match men's?Sport
- Is there a limit to how fast humans can run 100 m?Sport
- What are the chances of rolling a Yahtzee in one turn?Games & puzzles
Ambitious (15)
- Are Atlantic hurricanes becoming more frequent?Environment
- Where should I aim on a dartboard?Sport
- Can a simple rating system predict football results?Sport
- Is the euro–dollar exchange rate a random walk?Finance
- When should a Formula 1 driver pit? Modelling tyre degradationSport
- How many flights does it take to get anywhere?Networks & graphs
- Why do flight paths curve on the map?Geometry & Voronoi
- How many shuffles does it take to mix a deck of cards?Games & puzzles
- Will the pension pot last? Monte Carlo savings with random returnsSimulation
- Designing a smooth roller-coaster drop with piecewise functionsCalculus
- How strongly is global temperature linked to ln(CO₂)?Environment
- Which airport is really closest? Voronoi diagrams on a curved EarthGeometry & Voronoi
- Voronoi diagrams in a grid city: Euclidean or taxicab distance?Geometry & Voronoi
- Should bigger hospitals get bigger regions? Weighted Voronoi diagramsGeometry & Voronoi
- Why do buses come in bunches? A simulation of a bus routeSimulation
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 modelling questions · Bivariate data questions · Statistical testing questions · Voronoi diagrams questions · Financial mathematics questions. How AI SL differs from the other courses: AA vs AI, SL vs HL.
Less common types of IA that suit AI SL: Survey-based investigations · Simulation & Monte Carlo methods · Optimisation & linear programming · Trigonometry, navigation & surveying · Voting, fairness & game theory · Kinematics & physics-style modelling.
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.
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