510 topic ideas for the Mathematics IA and Extended Essay – page 19.

The investigation examines how “Dashboard and seat colour as determinants of surface temperature in an empty car” 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 “Effectiveness of different sunshades against heating in an empty vehicle” 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 “Window gap and air exchange: effects on heating in an empty parked car” 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 “Prediction model and warning threshold for dangerous in-car temperatures” 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 “Football-club player wages and league points achieved” 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 “Transfer spending and final league position” 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 “Squad market value and probability of progressing in a tournament” 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 “Attendance and a club's sporting performance during a season” 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 “Ticket price, stadium occupancy and home-match revenue” 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 “Possession and win probability across different leagues” 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 “Expected goals and actual goals: model performance over a season” 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 “Manager changes and variation in average points per match” 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 “Travel distance and the strength of home advantage” 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 “Youth-academy investment and later first-team market value” 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 “Employee count and revenue across an industry” 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 “Employee count and company profit” 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 “Revenue per employee as a function of company size” 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 “Workforce growth and subsequent revenue development” 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 “Employee turnover and operating profit margin” 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 “Number of patent applications and company profit” 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 “Citation-weighted patents and company market value” 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 “Research-and-development spending, patent count and revenue growth” 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 lag between patent applications and measurable changes in profit” 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 “Technological diversity of a patent portfolio and profitability” 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 “Daily company-news volume and stock return” 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.