1037 topic ideas – page 39 of 42.

Investigate how “Expansion during heating and contraction during cooling: investigating hysteresis” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.

Investigate how “Curvature of a bimetallic strip as a function of temperature” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.

Investigate how “Model of a bridge expansion joint for seasonal temperature changes” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.

The focus is on describing “Buffon's needle experiment: effect of needle length and line spacing on the approximation of π” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability 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; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

The focus is on describing “Circumference and diameter of real objects: experimental verification of π with error analysis” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

The focus is on describing “Determining π from pendulum periods with known pendulum length and gravitational acceleration” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

The focus is on describing “Wheel rotations and distance travelled as an experimental approximation of π” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

The investigation centres on the mathematical structures and reasoning behind “Compound interest with ever shorter compounding intervals as an approximation to e”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.

The investigation centres on the mathematical structures and reasoning behind “Numerical investigation of the sequence (1 + 1/n)^n as evidence for e”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.

The investigation centres on the mathematical structures and reasoning behind “Estimating e by fitting exponential growth and cooling models”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.

The investigation centres on the mathematical structures and reasoning behind “Products of uniformly distributed random numbers and the expected number of factors before falling below a threshold”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.

The investigation centres on the mathematical structures and reasoning behind “Capacitor discharge and the time constant as an experimental route to e”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.

The focus is on describing “Leaf arrangements in a plant and their closeness to the golden angle” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability 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; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

The focus is on describing “Image composition and the golden ratio in self-taken photographs” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

The focus is on describing “Proportions of the hand and finger segments compared with the golden ratio” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

The focus is on describing “Convergence of successive Fibonacci ratios to the golden ratio” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.

Investigate how “Reaction time to different colours using a Raspberry Pi and touchscreen” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.

Investigate how “Auditory or visual stimuli: comparing reaction time with a Raspberry Pi” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.

Investigate how “Learning curve in repeated touchscreen tasks” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.

Investigate how “Display time and number of recalled characters in a digital short-term memory test” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.

Investigate how “Fitts's law: target size, distance, and tapping time on a touchscreen” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.

Investigate how “Virtual keyboard size and the relationship between typing speed and error rate” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.

Investigate how “Adaptive quiz: response time, difficulty, and accuracy on a Raspberry Pi” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.