Finding focus with Archimedes Hard as it is to imagine now, for most of the history of mathematics there was no coordinate geometry system and therefore graphs were not drawn using algebraic equations but instead were constructed. The ancient Greeks such as Archimedes made detailed studies of conic sections (parabolas, ellipses and hyperbola) using ideas […]
Finding the average distance between 2 points on a hypercube This is the natural extension from this previous post which looked at the average distance of 2 randomly chosen points in a square – this time let’s explore the average distance in n dimensions. I’m going to investigate what dimensional hypercube is required to have an […]
Find the average distance between 2 points on a square This is another excellent mathematical puzzle from the MindYourDecisions youtube channel. I like to try these without looking at the answer – and then to see how far I get. This one is pretty difficult (and the actual solution exceptionally difficult!) The problem is to […]
Generating e through probability and hypercubes This is a really beautiful solution to an interesting probability problem posed by fellow IB teacher Daniel Hwang, for which I’ve outlined a method for solving suggested by Ferenc Beleznay. The problem is as follows: On average, how many random real numbers from 0 to 1 (inclusive) are required […]
Have you got a Super Brain? Adapting and exploring maths challenge problems is an excellent way of finding ideas for IB maths explorations and extended essays. This problem is taken from the book: The first 25 years of the Superbrain challenges. I’m going to see how many different ways I can solve it. The problem […]
You can download all 17 of the Paper 3 questions for free here: [PDF]. The full typed mark scheme is available to download at the bottom of the page. Seventeen IB Higher Level Paper 3 Practice Questions With the new syllabus just started for IB Mathematics we currently don’t have many practice papers to properly […]
