A Journey in Maths

Pi appears again – a probability problem This is a nice maths problem which has a surprising result: If you take 2 randomly generated numbers between 0 and 1 (lets call them x and y), then divide y by x, what is the probability that the resultant number will round to an even number? The obvious answer would be 50% – i.e if the 2 numbers are randomly generated then surely there will be an equal…

Cardioids in Coffee Cups Numberphile have just done a nice video on how a cardioid shape is formed when a light is shone against the side of a mug. You can see this effect above (from the Numberphile video here). So, I decided to recreate this using Geogebra to get to understand some of the maths behind this shape. What is a cardioid? Cardioids can be formed by tracing a fixed point on a…

Looking for a pre-Ice Age civilisation? An interesting thought experiment is to consider the rise of modern civilisation and to ask whether civilisations could have risen in the long distant past. Let’s look at some graphs to see the plausibility of the climatic side of this. Firstly we can see on this graph (source here) that there was a rapid change in temperature following the end of the…

FOBISIA Code Breaking Competition 2025 Back by popular demand – we’re going to run the FOBISIA Code Breaking Maths Challenge again.  Last year we had close to 120 schools taking part with over 22,000 students completing at least one code level.  We hope that this year’s event will be equally successful.   The dates will be: Between Monday 22nd and Friday 26th September 2025. If you are a teacher…

Solar Gravitational lens: Seeing alien planets Let’s say in the future we pick up a signal from Proxima Centauri b – an exoplanet which is orbiting the star Proxima Centauri around 4.2 light years away.  It would be nice to jump in a spaceship to explore further – but even travelling at 61,500km/h (the speed of Voyager 1) this would take a depressingly long 74,000 years.  So, would the mysteries…

Plotting asteroids – will 2024 YR4 hit Earth? According to current estimates there is approximately a 1.6% chance of a collision between asteroid 2024 YR4 and Earth.  This would not be an extinction level event – but could be enough to flatten a city.  So I thought I’d work backwards from the calculated orbital paths calculated above by NASA above (citation) to arrive at an estimation for this…

Buffon’s needle: Calculating pi The following problem, first posed in the 1700s by the Comte de Buffon has a surprising solution which can be used to generate pi.  This is a nice example of probability games which can generate mathematical results over repeated trials (the Monte Carlo method). Here is the original problem: “Suppose we have a floor made of parallel strips of wood, each the same…

Lattice based cryptography With the growing possibility of quantum computing being able to crack RSA encryption (the encryption technique which currently secures most banking and digital communications), the search is underway to find quantum-computing proof encryption.  One potential possibility is lattice based cryptography – so I will explore the basics of this below! Creating a lattice To…

A completely new Paper 1 for SL Applications students – this is my prediction for the May 2025 paper based on the style and trends for the questions currently being asked by IB examiners.  This includes both a full question paper and full typed markscheme.

A completely new Paper 2 for SL Analysis students – this is my prediction for the May 2025 paper based on the style and trends for the questions currently being asked by IB examiners.  This includes both a full question paper and full typed markscheme.

A completely new Paper 1 for SL Analysis students – this is my prediction for the May 2025 paper based on the style and trends for the questions currently being asked by IB examiners.  This includes both a full question paper and full typed markscheme.

Six original Paper 3 investigations to support problem solving skills to prepare for the Paper 3 Higher Level paper.  These investigations also are excellent for coursework explorations.  Full markschemes also included.

Eight original Paper 3 investigations to support problem solving skills to prepare for the Paper 3 Higher Level paper.  These investigations also are excellent for coursework explorations.  Full markschemes also included.

A 60 page modelling guide to support students through all aspects of modelling tasks for the IB exploration.

Stats guide

A 65 pdf guide to support students and teachers through the process of the IB coursework