Paper 3 investigations

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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 download a 41 page pdf with 17 Paper 3 questions here.  I have also provided the full worked solutions below which can be purchased for a small cost.

Individual questions

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.

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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.

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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.

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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.

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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. 

Analysis Students

(1) Analysis HL Paper 3 pack ($7.50)

17 full Paper 3 investigations and full worked solutions with typed markscheme.  Please note this is not an automatic download and will be emailed to you within a day.

 

(2) Analysis HL Paper 3 pack + Super Exploration Guide ($12)

17 full Paper 3 investigations and full worked solutions with typed markscheme and also 3 pdf guides to support students in achieving excellent marks in their explorations.  The guides take you through exploration essentials, technology support, common mistakes, statistical methods, regression techniques and lots more.  Written by an experienced IB Mathematics coursework moderator. Please note this is not an automatic download and will be emailed to you within a day.

 

Applications Students

(1) Applications HL Paper 3 pack ($6.50)

6 full Paper 3 investigations and and full worked solutions with typed markscheme.  Please note this is not an automatic download and will be emailed to you within a day.

 

(2) Applications HL Paper 3 pack + Super Exploration Guide ($12)

6 full Paper 3 investigations and full worked solutions with typed markscheme and also 3 pdf guides to support students in achieving excellent marks in their explorations.  The guides take you through exploration essentials, technology support, common mistakes, statistical methods, regression techniques and lots more.  Written by an experienced IB Mathematics coursework moderator.  Please note this is not an automatic download and will be emailed to you within a day.