510 topic ideas for the Mathematics IA and Extended Essay – page 9.

The investigation explores how “The distribution of asteroids in the Solar System” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The investigation asks which conditions produce the best outcome for “Calculating an optimal group size for effective learning” and how sensitive that optimum is to changed assumptions. Differential calculus and integral calculus support optimisation and total-effect calculations, while statistics and probability show whether the result remains stable with variable or uncertain data.

The investigation explores how “Calculating the risk of base-rate errors in everyday decisions” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The investigation explores how “The mathematics of laminated dough folds” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The focus is on describing “Melting rate of ice shapes: volume, surface area and form” through geometric quantities, proportions and a testable model. Geometry and trigonometry form the core, while differential calculus and integral calculus can investigate curvature, area or volume and statistics and probability can evaluate measurement variation.

The investigation explores how “Fermentation: carbon dioxide loss from yeast-sugar solutions of different concentrations” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The investigation explores how “Photovoltaic power loss under partial shading in series and parallel circuits” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The investigation explores how “Heat capacity of coins made from different alloys” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The investigation examines how “Surface-temperature patterns after different forms of exercise” develops over time or in response to a changing variable and which model best represents the pattern. Differential calculus can determine rates of change and integral calculus can capture total effects, while statistics and probability help assess measurement error, variation and model fit.

The investigation explores how “Household waste separation: mass of different fractions per week” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The focus is on the discrete patterns and rules behind “The Collatz conjecture: convergence behaviour for different starting values”, investigated systematically with original examples, algorithms or simulations. Combinatorics, statistics and probability are often central, while differential calculus and integral calculus become useful only when a continuous comparison model or limiting process is added.

The focus is on the mathematical structures and reasoning behind “Parameter changes in the logistic function”, developed through original examples, derivations or simulations. Depending on the focus, differential calculus or integral calculus can reveal the analytical structure, while statistics and probability are useful when simulations or datasets are also analysed.

The focus is on the mathematical structures and reasoning behind “Bayes' theorem and the reliability of medical tests”, developed through original examples, derivations or simulations. Depending on the focus, differential calculus or integral calculus can reveal the analytical structure, while statistics and probability are useful when simulations or datasets are also analysed.

The investigation explores how “Modelling the spread of wildfires” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The focus is on describing “Calculating sightlines in a theatre or concert hall” through geometric quantities, proportions and a testable model. Geometry and trigonometry form the core, while differential calculus and integral calculus can investigate curvature, area or volume and statistics and probability can evaluate measurement variation.

The investigation explores how “Modelling the effect of inflation on purchasing power” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The focus is on the mathematical structures and reasoning behind “Modelling logic puzzles with propositional logic”, developed through original examples, derivations or simulations. Depending on the focus, differential calculus or integral calculus can reveal the analytical structure, while statistics and probability are useful when simulations or datasets are also analysed.

The investigation explores how “Modelling game strategies with game trees” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The investigation explores how “The mathematics of perfume: evaporation and diffusion” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The focus is on the discrete patterns and rules behind “Modelling negotiation strategies with cooperative game theory”, investigated systematically with original examples, algorithms or simulations. Combinatorics, statistics and probability are often central, while differential calculus and integral calculus become useful only when a continuous comparison model or limiting process is added.

The investigation explores how “Modelling the spread of antibiotic resistance in bacterial populations” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The investigation asks which conditions produce the best outcome for “Optimising solar-panel orientation for maximum energy yield” and how sensitive that optimum is to changed assumptions. Differential calculus and integral calculus support optimisation and total-effect calculations, while statistics and probability show whether the result remains stable with variable or uncertain data.

The investigation explores how “Calculating stability in different yoga poses using centre of mass” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.

The focus is on the discrete patterns and rules behind “Time-series analysis: forecasting share prices with moving averages”, investigated systematically with original examples, algorithms or simulations. Combinatorics, statistics and probability are often central, while differential calculus and integral calculus become useful only when a continuous comparison model or limiting process is added.

The investigation explores how “Analysing the mathematical structure of canons and fugues” can be described and compared quantitatively using original measurements or suitable open data. Statistics and probability can test relationships, variation and uncertainty, while differential calculus and integral calculus can extend trend models through rates of change or cumulative effects.