You are currently browsing the tag archive for the ‘paper 3’ tag.

**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**

**Teacher resources:**

If you are a teacher then please also visit my new site: **intermathematics.com** for over 2000+ pages of content for teaching IB mathematics including worksheets, mock exams, investigations, enrichment tasks, technology guides, exploration support and investigations.

**Student resources:**

I have made separate student packs for both Applications students and Analysis students. You can also see some free examples below.

**Exploring Curvature (Analysis)**

Download the question pdf **here**.

Download the full worked solutions pdf **here**.

Students explore a measure of curvature in an investigative context using a mixture of differentiation, L’Hopital’s rule and graphical skills.

**Rotating curves (Analysis)**

Download the question pdf **here**.

Download the full worked solutions pdf **here**.

Students explore the use of parametric and Cartesian equations to rotate a curve around the origin. You can see a tutorial video on this above. The mathematics used here is trigonometry (identities and triangles), functions and transformations.

**Approximating pi with polygons (Analysis)**

Download the question pdf **here** .

Download the full worked solutions pdf **here**.

Students follow in the footsteps of the great Greek mathematicians to derive approximations for pi using a mixture of trigonometry and calculus.

**Who killed Mr. Potato? (Analysis and Applications)**

Download the question pdf **here**.

Students explore Newton’s Law of Cooling to predict when a potato was removed from an oven. The mathematics used here is logs laws, linear regression and solving differential equations.

**Graphically understanding complex roots (Analysis)**

Download the question pdf **here**.

Students explore graphical methods for finding complex roots of quadratics and cubics. The mathematics used here is complex numbers (finding roots), the sum and product of roots, factor and remainder theorems, equations of tangents.

**Avoiding a magical barrier (Analysis and Applications)**

Download the question pdf **here**.

Students explore a scenario that requires them to solve increasingly difficult optimization problems to find the best way of avoiding a barrier. The mathematics used here is creating equations, optimization and probability.

**Life’s a Beach (Applications)**

Download the question pdf **here**.

**Purchase options**

It takes a lot of time to create these resources – so if you would like to support the site (and prepare well for the exams!) you can also purchase a full exam pack with full typed solutions below.

Please note that you do not need a PayPal account to purchase – simply click on the relevant card.

**HL Analysis students**

You can buy a student Paper 3 pack – which includes 8 full investigation questions (around 240 marks) and full worked solutions through the PayPal link below.

**Student Paper 3 Investigation pack for HL Analysis **

Questions include:

- Rotating curves
- Who killed Mr Potato?
- Graphically understanding complex roots
- Avoiding a magical barrier
- Circle packing density
- A sliding ladder investigation
- Exploring the Si(x) function
- Volume optimization of a cuboid

Buy the Student P3 Analysis pack [with MS]

This includes 8 investigation questions and full worked solutions (57 pages of content). You can pay below. If you don’t have a PayPal account please click the relevant credit card. Please note this is not an automatic download – I will email it to you the same day.

$8.00

**HL Applications students**

You can buy a student Paper 3 pack – which includes 6 full investigation questions (around 180 marks) and full worked solutions through the PayPal link below.

**Student Paper 3 Investigation pack for HL Applications**

Questions include:

- Investigating BMI
- Who killed Mr Potato?
- Life’s a Beach
- Hare vs. Lynx
- Rolling Dice
- Avoiding a Magical Barrier

Buy the Student P3 Applications pack [with MS]

This includes 6 investigation questions and full worked solutions (41 pages of content). You can pay below. If you don’t have a PayPal account please click the relevant credit card. Please note this is not an automatic download – I will email it to you the same day.

$8.00

**Super Bundle:**

You can also purchase a super bundle of Paper 3s and also a **168 page** Super Exploration Guide to help you get great marks in your coursework.

Exploration Guide + Analysis Paper 3s

Both the Exploration Guide and 8 Paper 3s for the Analysis course

$16.00

Exploration Guide + Applications Paper 3s

Both the Exploration Guide and 6 Paper 3s for the Applications course

$16.00