01
Are eye colour and handedness independent in a sampled population?
Approach · Survey a sample, build a contingency table, and apply a chi-squared test of independence with expected-frequency checks.
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Math: Applications & Interpretation · IA research questions
12 IB Mathematics Applications and Interpretation IA ideas
Written and cross-checked by IB Diploma graduates: Alexander (41), Alejandro (40), Martina (40), Victoria (38), Martin (35), Maria (34)
· Checked against official IB guidance · Editorial policy
A strong Maths AI exploration is built on real data and a real-world decision. Statistics (regression, chi-squared, confidence intervals), modelling (exponential, trigonometric, numerical integration) and applied topics like graph theory and Voronoi diagrams all fit well — the point is to interpret the answer, not just compute it.
Scope: Gather your own data (survey, measurement, or a clean published dataset) with enough points for the technique to be valid. State assumptions and evaluate the model's fit. 12–20 pages.
02
How does house price vary with distance from the city centre in your area?
Approach · Collect listing data, fit linear and non-linear regression models, report R², and give a confidence interval for the slope.
03
Does a cup of coffee cool according to an exponential (Newton's law) model?
Approach · Log temperature over time, fit T = T_room + Ae^(−kt), and assess the fit with residual analysis.
04
Where should a new defibrillator (or bus stop) go to minimise the distance people must travel?
Approach · Plot existing sites, construct a Voronoi diagram, and identify the largest under-served cell.
05
Can a shortest-path or travelling-salesman heuristic improve a real delivery or school-run route?
Approach · Model the road network as a weighted graph, apply Dijkstra / a nearest-neighbour TSP heuristic, and compare to the current route.
06
How accurately can a trigonometric model predict daylight hours across the year for your city?
Approach · Fit h(t) = a sin(b(t − c)) + d to monthly data and test its predictions for the equinoxes and solstices.
07
Do exam scores in a large cohort follow a normal distribution?
Approach · Collect or use published score data, standardise, and run a goodness-of-fit test against the normal model.
08
What is the volume of a local lake or reservoir, estimated from depth-contour data?
Approach · Use the trapezium rule (or Simpson's rule) on cross-sectional areas from a contour map and give an uncertainty.
09
Is there a relationship between screen time and sleep, and how strong is it?
Approach · Survey a sample, compute the correlation coefficient, fit a regression line, and give a confidence interval for the gradient.
10
How well does a logistic model forecast the adoption of a technology (EVs, a streaming service) from published data?
Approach · Fit a logistic curve to historical adoption figures and evaluate its short-term forecast against held-back data.
11
Which sampling method — simple random or stratified — estimates a school mean more precisely?
Approach · Simulate both repeatedly from a known population, compare the spread of the estimates, and relate it to standard error formulas.
12
Which loan repayment term costs the least in total interest, and how sensitive is that to the rate?
Approach · Model the loan as an annuity, compute total interest for several terms and rates, and present the trade-off.
Sources & verification
Primary-source references used to verify key assessment facts on this page. Last source check: September 22, 2026.
These Math: Applications & Interpretation ideas are original iBacalao starting points, not official IB research questions. Check the current Math: Applications & Interpretation subject guide, your assessment session and your school's safety/ethics rules before committing to a question.
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