The trajectory of a basketball shot
Investigate how release angle, velocity and release height affect the trajectory. Personal video or measurement data can be compared with a mathematical model.
IB Mathematics · Topic ideas
Turn personal interests into focused mathematical questions.
Mixed suggestions provide starting points for the IA and EE—clearly explained, filterable and deliberately not written as ready-made research questions.
Mixed idea feed
Not organised by chapter—designed for discovery.
Calculus, statistics, geometry, number theory, modelling and application areas are deliberately mixed. Each card initially contains only a heading and a concise explanation.
Not ready-made research questionsThe suggestions are starting points. A strong question emerges only after the topic has been focused, matched to the course and level, and shaped by independent decisions.
Ideas: 12 of 12
Catenaries in bridges and cable structures
Explore why freely hanging cables are described by hyperbolic functions and how the model can be applied to real structures.
Waiting times in public transport
Analyse real departure and waiting-time data. Distributions, averages and simulations can show how reliable a timetable is from a passenger's perspective.
Prime numbers and the mathematics behind RSA
Investigate selected number-theory foundations of encryption, such as modular arithmetic, primality testing or the role of difficult factorisation problems.
Material use in packaging shapes
Compare shapes with equal volume and investigate how surface area, dimensions and real constraints affect material use.
Mathematical structures of musical consonance
Investigate frequency ratios, tuning systems or spectra and examine how mathematical models describe musical intervals.
Probability and strategy in penalty kicks
Evaluate shot directions and scoring rates. Conditional probabilities or simple game models can reveal strategic decisions.
The fractal dimension of natural boundaries
Compare measurements of a coastline or another irregular shape at different scales and investigate the connection with fractal dimension.
Growth models for the spread of disease
Compare exponential, logistic or simple compartment models and investigate which assumptions limit the meaning of the results.
Shortest paths in transport or data networks
Model a real network as a graph and compare methods for finding short or robust routes under different conditions.
Comparing mathematical voting systems
Investigate how different counting methods produce different outcomes from the same preferences and which fairness criteria they satisfy.
Solar-panel orientation throughout the year
Model the effect of solar position, tilt and location. Trigonometry and optimisation can be combined with real weather or energy-yield data.
No topic idea currently matches this selection.
From idea to question
Three checks before starting.
An interesting topic becomes suitable only when the mathematics, data and scope fit together.
Mathematical core
Which relationship, structure, optimisation or uncertainty is actually being investigated?
Feasibility
Are the data, methods, software and required prior knowledge available?
Independent direction
Which decisions, comparisons or extensions make the investigation individual?
Next development stage
Every idea will later have its own detail page.
Possible mathematics, data sources, tools, risks, extensions and relevant example work will be presented separately. The structured topic source is already bilingual and can be extended to further languages.
Found a possible topic?
The next step is to decide whether it fits the IA or Extended Essay and which curriculum version applies.