Applications Paper 3s 1-6

I’ve just finished making six Paper 3 practice papers for HL students sitting the Applications examination.   The Paper 3 pack is 41 pages and includes over 180 marks of questions and full typed up markscheme.  I’ve paid close attention to the IB’s provided examples for the course to make sure these look and feel very similar to how I would expect the papers to be in the summer.

The six questions are:

Investigating Body Mass Index [30 marks]

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.

Life’s a Beach [32 marks]

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.

Avoiding a Magical barrier [33 marks]

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.

Who killed Mr. Potato? [32 marks]

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.

Hare vs. Lynx [32 marks]

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.

Rolling dice [32 marks]

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.

You can download the questions and markschemes here:

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