510 topic ideas for the Mathematics IA and Extended Essay – page 18.

The investigation examines how “A bridge expansion-joint model for seasonal temperature changes” 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 “Buffon's needle experiment: effects of needle length and line spacing on estimating π” 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 “Monte Carlo approximation of π using random points in a square” 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 “Circumference and diameter of real objects: experimental evidence for π with error analysis” 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 “Estimating π from pendulum periods with known length and gravitational acceleration” 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 “Wheel rotations and travel distance as an experimental approximation of π” 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 mathematical structures and reasoning behind “Compound interest with increasingly short intervals as an approximation to e”, 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 “Numerical investigation of the sequence (1 + 1/n)^n as evidence for e”, 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 “Estimating e by fitting exponential growth and cooling models”, 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 “Products of uniform random numbers and the expected count before crossing a threshold”, 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 “Capacitor discharge and the time constant as an experimental route to e”, 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 “Leaf arrangements in a plant and their proximity to the golden angle” 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 “Proportions of everyday products compared with the golden ratio” 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 “Composition and the golden ratio in original photographs” 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 “Hand and finger proportions compared with the golden ratio” 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 “Convergence of consecutive Fibonacci ratios to the golden ratio” 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 “Reaction time to different colours using a Raspberry Pi and touchscreen” 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 “Auditory or visual stimuli: comparing reaction time with a Raspberry Pi” 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 “Learning curve across repeated touchscreen tasks” 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 “Display duration and recalled character count in a digital short-term-memory test” 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 “Fitts's law: target size, distance and tapping time on a touchscreen” 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 “Virtual-key size and the relationship between typing speed and error rate” 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 “Adaptive quiz: response time, difficulty and accuracy on a Raspberry Pi” 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 “Time of day, experiment duration and changes in reaction speed” 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 “Interior temperature of an empty parked car as a function of outdoor temperature and 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.