510 topic ideas for the Mathematics IA and Extended Essay – page 13.

The investigation asks which conditions produce the best outcome for “Modelling the amount of coffee needed to maximise caffeine extraction” 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 “Filtration efficiency measured by suspended-solid mass in different water samples” 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 focus is on the mathematical structures and reasoning behind “Voltage distribution in series and parallel circuits with identical lamps”, 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 examines how “Battery discharge across different temperatures using safe manufacturer-approved conditions” 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 the discrete patterns and rules behind “The mathematics of ISBN and IBAN check digits”, 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 describing “Areas between curves and their meaning in economics” 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 “Comparing probabilities in different games of chance” 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 climate change with simple climate 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.

The focus is on describing “Calculating areas with Pick's theorem” 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 asks which conditions produce the best outcome for “Calculating economic order quantity with the EOQ model” 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 focus is on the mathematical structures and reasoning behind “A proof of the fundamental theorem of arithmetic”, 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 describing “The mathematics of soap bubbles and minimal surfaces” 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 “Temperature changes in chemical hot and cold packs” 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 “Surface resistance of wood, metal, plastic and water” 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 “Drying curves of wet clay or paper: mass loss and surface temperature” 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 the discrete patterns and rules behind “Number sequences and their explicit formulae”, 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 “Modelling oscillations with damped harmonic oscillators”, 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 “Correlation between weather and mood” 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 propagation of light through different media” 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 “Voronoi diagrams in natural structures” 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 “Depreciation methods in accounting” 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 “Axiom systems through the example of geometry” 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 “Analysing the distribution of stars in the night sky” 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 “Thermal radiation from matte black and shiny metal surfaces at the same temperature” 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 “Comparing fat content in crisps by supervised solvent extraction” 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.