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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.  

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.  

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.

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.

IB Maths Super Exploration Guide

Below you can download a comprehensive exploration guide that I’ve written to help students get excellent marks on their IB maths coursework.  The guide is suitable for both Analysis and also Applications students. Over the past several years I’ve written over 200 posts with exploration ideas and marked hundreds of IAs whilst working as an IB examiner.  It’s frustrating how many students throw away marks from not understanding the criteria correctly.  Hopefully this will make a big difference!

I have split the guide into 3 separate pdfs – focusing on (1) Exploration essentials (2) Statistical explorations (3) Modeling explorations.  The first part is completely free.

Content in the 3 guides includes:

1. The new marking criteria,
2. How to choose a topic,
3. Examples of around 70 topics that could be investigated,
4. Useful websites for use in the exploration,
5. A student checklist for completing a good investigation,
6. Common mistakes that students make and how to avoid them,
7. Regression techniques (polynomial, trigonometric, exponential etc) 
8. Non calculator methods for modelling (to show understanding)
9. Technology support – how to use Desmos, Tracker and Geogebra effectively
10. Pearson’s product and correlation investigation methods
11. Chi-squared and Spearman’s rank investigations 
12. Advanced statistical techniques (t-tests, Poisson, Bernoulli trials, normal distribution and more)
13. Non calculator methods for statistics (to show understanding)
14. And a lot, lot more!

Make sure you give yourself the best chance of doing well on your coursework.

Part 1: Exploration Essentials Guide (63 pages)

You can download this for free here

Part 2: Statistics for Explorations Guide (55 pages)

You can download a preview pdf here

Part 3: Modelling for Explorations Guide (50 pages)

You can download a preview pdf here

Purchase options

Please note – these will be emailed to you and are not an automatic download. You don’t need a PayPal account – simply click the relevant credit card to pay as a guest.

(1) Exploration Guide bundle.

(2) HL Paper 3 Bundle

If you are also doing Higher Level then you can purchase a bundle of both the Super Exploration Guide and also some Paper 3 questions with full worked solutions.