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Paper 3 investigations

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Teacher resources:

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Student resources:

I have made separate student packs for both Applications students and Analysis students.  

To see the style of content you can download a pdf of the eight Analysis investigation here.

Examples of Analysis questions

Paper 1: Rotating curves: 

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.

Click to access rotate-curve.pdf

Paper 2: Who killed Mr. Potato?

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.

Click to access Who-killed-mr-potato.pdf

Paper 3:  Graphically understanding complex roots 

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.

Click to access graphically-understanding-complex-roots.pdf

Paper 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.  The mathematics used here is creating equations, optimization and probability.

Click to access Avoiding-a-magical-barrier.pdf

Purchase options

You can purchase the full exam pack and also 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:

  1. Rotating curves
  2. Who killed Mr Potato?
  3. Graphically understanding complex roots
  4. Avoiding a magical barrier
  5. Circle packing density
  6. A sliding ladder investigation
  7. Exploring the Si(x) function
  8. 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:

  1. Investigating BMI
  2. Who killed Mr Potato?
  3. Life’s a Beach
  4. Hare vs. Lynx
  5. Rolling Dice
  6. 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

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All content on this site has been written by Andrew Chambers (MSc. Mathematics, IB Mathematics Examiner).

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Free HL Paper 3 Questions

P3 investigation questions and fully typed mark scheme.  Packs for both Applications students and Analysis students.

Available to download here

IB Maths Super Exploration Guide

A Super Exploration Guide with 168 pages of essential advice from a current IB examiner to ensure you get great marks on your coursework.

Available to download here.

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