510 topic ideas for the Mathematics IA and Extended Essay – page 2.

The investigation explores how “Compound interest versus simple interest over different periods” 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 “Mathematical induction for sums and divisibility identities”, 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 “Graph-colouring problems” 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 recipes: ratios and scaling” 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 “Modelling medication concentration and dosage over time with pharmacokinetics” 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 asks which conditions produce the best outcome for “Optimising waste separation with probability models” 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 “Mathematical analysis of rotation in figure skating using angular momentum” 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 “A basic Fourier-based classification of music genres”, 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 double pendulum and its unpredictability” 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 “Overtone series in different musical instruments”, 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 “Calculating perspective in painting using one-point perspective” 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 “Modelling tidal forces and their mathematical periodicity” 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 focus is on describing “Modelling the Ebbinghaus forgetting curve with exponential decay” 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 smoking risk with life-expectancy data” 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 “Modelling coffee brewing through extraction rates and temperature” 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 examines how “Insulating performance of cup materials: time taken to approach room temperature” 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 focus is on describing “Determining the density of different woods from mass and volume” 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 “Solar-cell power at different light angles and distances” 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 “Electrolysis of water: electrode mass change versus applied voltage” 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 “Which teapot material retains heat longest: cast iron, glass or porcelain?” 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 examines how “Rainwater: precipitation amount, temperature and electrical conductivity” 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 examines how “Skin-surface temperature recovery after a safe cold-water exposure” 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 “Heat distribution around skateboard or longboard axles after riding” 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 population growth: logistic versus exponential models”, 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 “Newton's law of cooling: modelling with differential equations”, 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.