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**New Paper 3s for Applications!**

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 purchase this Paper 3 exam pack below (you do not need a PayPal account, just click on the relevant credit card picture).

Paper 3 exam pack (Applications HL)

Six paper 3 investigations to help prepare for the summer exams. Please note this is not an automatic download but will be sent the same day.

$8.00

**Paper 3 investigations**

**Introduction**

Below are a selection of the Paper 3 investigations I’ve made over the years. Many of these bridge between Paper 3 practice (exposure to novel or new mathematical ideas) and the Exploration coursework. All of these could be easily adapted to make some very interesting coursework submissions.

If you are a teacher and find these useful, then please also visit my new site: intermathematics.com for over 3000+ pages of content for teaching IB mathematics including worksheets, mock exams, investigations, enrichment tasks, technology guides, exploration support and investigations.

**Exploration 1: Rotating curves: **

Students explore the use of parametric and Cartesian equations to rotate a curve around the origin

Question download. Markscheme download.

**Exploration 2: Who killed Mr. Potato?**

Students explore Newton’s Law of Cooling to predict when a potato was removed from an oven.

Question download. Markscheme download.

**Exploration 3: Graphically understanding complex roots **

Students explore graphical methods for finding complex roots of quadratics and cubics.

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**Exploration 4: Avoiding a magical barrier **

Students explore a scenario that requires them to solve increasingly difficult optimization problems to find the best way of avoiding a barrier.

Question download Markscheme download.

**Exploration 5 : Circle packing density **

Students explore different methods of filling a space with circles to find different circle packing densities.

Question download. Markscheme download.

**Exploration 6: A sliding ladder investigation**

Students find the general equation of the midpoint of a slipping ladder and calculate the length of the astroid formed.

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**Exploration 7: Exploring the Si(x) function **

Students explore methods for approximating non-integrable functions and conclude by approximating pi squared.

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**Exploration 8: Volume optimization of a cuboid **

Students start with a simple volume optimization problem but extend this to a general case of an m by n rectangular paper folded to make an open box.

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**Exploration 9: Exploring Riemann sums **

Students explore the use of Riemann sums to find upper and lower bounds of functions – finding both an approximation for pi and also for .

Question download. Markscheme download.

**Exploration 10 : Optimisation of area **

Students start with a simple optimisation problem for a farmer’s field then generalise to regular shapes.

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**Exploration 11: Quadruple Proof **

** **Students explore 4 different ways of proving the same geometrical relationship.

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**Exploration 12: Circumscribed and inscribed polygons **

Students explore different methods for achieving an upper and lower bound for pi using circumscribed and inscribed polygons.

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**Exploration 13: Probability Generating function **

Students explore the link between algebra and probability through generating functions and model the eruption of a volcano.

Question download. Markscheme download.

If you are a teacher and find these useful, then please also visit my new site: intermathematics.com for over 3000+ pages of content for teaching IB mathematics including worksheets, mock exams, investigations, enrichment tasks, technology guides, exploration support and investigations – thanks!

Andrew