510 topic ideas for the Mathematics IA and Extended Essay – page 6.

The investigation examines how “Absorption rates of toilet paper, kitchen roll and newspaper” 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 “Charging and discharging capacitors of different capacitances” 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 focus is on describing “Evaporation: mass loss versus surface temperature in wind, sun and shade” 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 examines how “Yoghurt fermentation: temperature profile and mass change” 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 “Heat loss from buildings using facade surface-temperature measurements” 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 examines how “Reaction time and naturally observed body-temperature variation” 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 “Electrical conductivity of pencil lines with grades from 2H to 6B” 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 “Fibonacci numbers and the limiting ratio of consecutive terms”, 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 asks which conditions produce the best outcome for “The mathematics of rainbow formation: Snell's law, refraction and optimisation” 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 “Statistical bias in media reporting” 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 “Traffic flow at roundabouts or traffic lights” 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 “Using vectors to model three-dimensional reflections in a kaleidoscope” 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 “An introduction to the Black-Scholes model for option pricing” 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 “Truth tables and their minimisation”, 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 “Heuristics for the travelling salesperson problem” 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 “Analysing the efficiency of water pumps” 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 “Optimal positioning in penalty kicks using mixed strategies” 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 mosquito-population spread” 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 optimal home insulation using heat conduction” 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 launch angles in archery” 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 “Modelling population fluctuations with discrete dynamical systems” 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 “Sound propagation through different materials” 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 “Modelling wave patterns in textile design” 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 “Mathematical patterns in planetary resonances” 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 “Modelling decision fatigue with probability models” 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.