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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.


For students taking their exams in 2021 there is a big change to the IB syllabus – there will now be 4 possible strands: IB HL Analysis and Approaches, IB SL Analysis and Approaches, IB HL Applications and Interpretations, IB SL Applications and Interpretations.

IB Applications and Interpretations

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There is a reasonable cross-over between the current Studies course and the new Applications SL course.  However there is quite a lot of new content – and as such the expectation is that this course could be quite a bit more challenging that the current SL course.   The HL Applications course is a rather odd mix of former Maths Studies topics, former SL topics and former IB HL Statistics topics.

Some key points:

  1. The SL Applications course will be a complete sub-set of the HL Applications course, and the HL exam will include some of the same questions as the SL exam.
  2. Both SL and HL will only have calculator papers (and have no non-calculator papers like Analysis)
  3. Both SL and HL will have Paper 1 consisting of short questions and Paper 2 with longer style questions (similar to the current Maths Studies course).
  4. HL students will do an investigation style Paper 3 – potentially with the use of technology.  This will lead students through an investigation on any topic on the syllabus.
  5. The Exploration coursework will remain – however the guidance is now that it should be 12-20 pages (rather than 6-12 previously).

What does this all mean for Applications SL?

If the IB follow through with their stated plan to have both new SL courses (Applications and Analysis) the same difficulty then either:

(a) The Analysis course will remain at the same level of difficulty as the current Maths SL and therefore many students who up until now have taken Maths Studies will find the new Applications course extremely challenging.

(b) The Analysis course will be made easier than the current Maths SL course, so that the new Applications course is also a little more accessible – though still harder than the current Maths Studies course.

I would predict that (b) is the more likely of these two – otherwise there will be a significant cohort of IB students (around 30%) who fail to get even a Level 4 in their maths.  At the moment I would advise that all weaker students should definitely take this course (IGCSE Grade C and below), but it may be the case that it is a good option for more stronger students who have traditionally taken SL rather than Studies.

What does this all mean for Applications HL?

This is really hard to work out – if Applications SL remains accessible for students with low IGCSE grades, and Applications HL contains a subset of these questions, then that would suggest that the Applications HL would be significantly easier than the current HL course.  However, there are a number of challenging topics on the Applications HL syllabus which could well be used to stretch top students.  Again the stated aim of the IB is for the two HL courses to be the same difficulty – so this is one we will really have to wait and see with.

Based on the current information I would advice only students with an A* in IGCSE to take this course. It would appear to be aimed at students who need some mathematical skills for their university courses (such as biology, medicine or business) but who do not want to study mathematics or a field with substantial mathematics in it (such as engineering, physics, computer science etc).

Resources for teachers and students

This will be a work in progress – but to get started we have:

General resources

  1. A very useful condensed pdf of the Applications and Interpretations formula book for both SL and HL.
  2. An excellent overview of the changes to the new syllabus – including more detailed information as to the syllabus changes, differences between the two courses and also what 10 of the leading universities have said with regards to course preferences.
  3. University acceptance.  Information collated by a group of IB teachers on university requirements as to which course they will require for different subjects (this may be not be up to date, so please check).

Investigation resources for Paper 3 [Higher Level]

  1. Old IA investigations

Standard Level

[Links removed – hopefully the IB will provide these resources elsewhere]

(a) All SL IA investigations from 1998 to 2009 : This is an excellent collection to start preparations for the new Paper 3.

(b) Specimen investigations: These are 8 specimen examples of IA investigations from 2006 with student answers and annotations.

(c) SL IA investigations 2011-2012: Some more investigations with teacher guidance.

(d) SL IA investigations 2012-2013: Some more investigations with teacher guidance.

(e) Koch snowflakes: This is a nice investigation into fractals.

Higher Level 

(a) All HL IA investigations from 1998 to 2009:  Lots more excellent investigations – with some more difficult mathematics.

(b) HL IA investigations 2011-2012: Some more investigations with teacher guidance.

(c) HL IA investigations 2012-2013: Some more investigations with teacher guidance.

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

New website for International teachers

I’ve just launched a brand new maths site for international schools – over 2000 pdf pages of resources to support IB teachers.  If you are an IB teacher this could save you 200+ hours of preparation time.

Explore here!

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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