510 topic ideas for the Mathematics IA and Extended Essay – page 7.

The investigation explores how “The probability of natural disasters at a particular location” 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 fermentation in bread and yoghurt with exponential growth” 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 “Cooling curves of aluminium, copper and iron from the same starting 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 “Osmosis: mass change of potato slices in salt solutions from 0% to 20%” 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 “Electrical conductivity of water, juice, cola and salt water” 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 “Freezing-point depression: dissolved salt or sugar mass versus minimum 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 explores how “Water and mass loss from cheese or cured food during refrigerated storage” 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 “Algal growth: biomass and aquarium-water temperature over time” 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 “Number systems and modular arithmetic in computer science”, 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 “Modelling roller-coaster curves with cubic and quintic functions” 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 “Correlation between study time and predicted IB grades” 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 music: frequency ratios and overtones” 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 “Non-Euclidean geometry: angle sums on a sphere and a hyperbolic surface” 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 “Returns across different types of investment” 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 “Different proofs that there are infinitely many primes”, 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 “Hash functions and collisions” 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 photography: exposure and aperture” 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 mathematics behind bidding strategies in The Price Is Right”, 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 “BMI and its statistical validity across different 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 explores how “Correlation between air quality and asthma incidence” 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 analysis of the Magnus effect in a football free kick” 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 Netflix-style recommendations with simple distance measures”, 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 vibrato frequency and its perception” 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 “Analysing proportions in fashion: clothing sizes and golden-ratio claims” 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 optimal launch windows with Hohmann transfers” 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.