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Fermat’s Theorem – one of the most famous and long running puzzles in mathematics is a great way to introduce proof, the history of mathematics and also to show how apparent work on an entirely abstract concept can actually drive the development of techniques which have real world applicability.  The (much abridged!) story is that Fermat, a 17th century mathematician scribbled that he had a proof that the statement at the top of page was correct – ie. that whilst the equation holds when n = 2 (for pythagorian triples), for n greater than 2 there is no solution with positive whole numbers.  Mathematicians spent the next 358 years trying to find that same proof (and now believe that Fermat was actually mistaken), before Andrew Wiles finally proved it in 1995 using mathematics from elliptical curves.

A seemingly simple statement had occupied some of the best mathematical minds for over 3 centuries – everyone agreed that it probably was true – but to go from probably true, to 100% certainty – that knowledge gap required a monumental amount of effort.    How many other things can we genuinely say we are 100% certain of outside mathematics?

See the Horizon documentary on Fermat’s Last Theorem with Simon Singh and Andrew Wiles:

IB Revision

If you’re already thinking about your coursework then it’s probably also time to start planning some revision, either for the end of Year 12 school exams or Year 13 final exams. There’s a really great website that I would strongly recommend students use – you choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources:

The Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and each area then has a number of graded questions. What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial.  Really useful!

The Practice Exams section takes you to ready made exams on each topic – again with worked solutions.  This also has some harder exams for those students aiming for 6s and 7s and the Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year.

I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think.

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• 8,007,945 views

### IB HL Paper 3 Practice Questions (120 page pdf)

IB HL Paper 3 Practice Questions

Seventeen full investigation questions – each one designed to last around 1 hour, and totaling around 40 pages and 600 marks worth of content.  There is also a fully typed up mark scheme.  Together this is around 120 pages of content.

### IB Maths Exploration Guide

IB Maths Exploration Guide

A comprehensive 63 page pdf guide to help you get excellent marks on your maths investigation. Includes:

1. Investigation essentials,
2. Marking criteria guidance,
3. 70 hand picked interesting topics
4. Useful websites for use in the exploration,
5. A student checklist for top marks
6. Avoiding common student mistakes
7. A selection of detailed exploration ideas
8. Advice on using Geogebra, Desmos and Tracker.

### Modelling Guide

IB Exploration Modelling Guide

A 50 page pdf guide full of advice to help with modelling explorations – focusing in on non-calculator methods in order to show good understanding.

Modelling Guide includes:

Linear regression and log linearization, quadratic regression and cubic regression, exponential and trigonometric regression, comprehensive technology guide for using Desmos and Tracker.

### Statistics Guide

IB Exploration Statistics Guide

A 55 page pdf guide full of advice to help with modelling explorations – focusing in on non-calculator methods in order to show good understanding.

Statistics Guide includes: Pearson’s Product investigation, Chi Squared investigation, Binomial distribution investigation, t-test investigation, sampling techniques, normal distribution investigation and how to effectively use Desmos to represent data.