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Six original Paper 3 investigations to support problem solving skills to prepare for the Paper 3 Higher Level paper. These investigations also are excellent for coursework explorations. Full markschemes also included.
Description
Six original Paper 3 investigations to support problem solving skills to prepare for the Paper 3 Higher Level paper. These investigations also are excellent for coursework explorations. Full markschemes also included.
1. Investigating Body Mass Index.
The students carry out a statistical investigation to inform a decision on how to decrease BMI. The mathematics includes: regression lines, z tests, paired t-tests, 2 sample t-tests and Chi squared test for independence.
2. Life’s a Beach.
The students carry out an investigation using Markov chains to investigate time spent on the beach. The mathematics includes: transition matrices, matrix operations, eigenvalues and eigenvectors and steady state calculations.
3. Avoiding a Magical barrier.
The students explore a scenario where they must minimise their journey. The mathematics includes: forming equations, finding averages, differentiation using the chain rule, optimization, and graphing.
4. Who killed Mr. Potato?
Students explore a scenario where they must decide the time that a potato was first removed from an oven using Newton’s Law of Cooling. The mathematics includes: solving differential equations by separating variables, curve fitting, log regression, differentiation of exponentials, graphing to solve equations.
5. Hare vs. Lynx
Students explore a predator prey system to see what happens when population parameters are changed. The mathematics includes: understanding equilibrium and saddle points, finding eigenvalues, Euler’s method to approximate differential equations, sketching phase portraits, curve fitting a trigonometric model and graphical skills.
6. Rolling dice
Students conduct a dice rolling investigation which mimics radioactive decay. The mathematics includes: equations of linear regression, exponential regression, Chi squared goodness of fit, Euler’s method to approximate differential equations, solving differential equations by separating variables, percentage error.