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

Essential resources for IB students:

Revision Village has been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams. I would strongly recommend students use this as a resource during the course (not just for final revision in Y13!) There are specific resources for HL and SL students for both Analysis and Applications.

There is a comprehensive Questionbank takes you to a breakdown of each main subject area (e.g. Algebra, Calculus etc) and then provides a large bank 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 a large number of ready made quizzes, exams and predicted papers. These all have worked solutions and allow you to focus on specific topics or start general revision. This also has some excellent challenging questions for those students aiming for 6s and 7s.

Each course also has a dedicated video tutorial section which provides 5-15 minute tutorial videos on every single syllabus part – handily sorted into topic categories.

2) Exploration Guides and Paper 3 Resources

I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations. The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.