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Plotting asteroids - will 2024 YR4 hit Earth?

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…

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Buffon's needle: Calculating pi

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…

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Lattice based cryptography

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…

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A completely new Paper 2 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.

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Predicted May 2025: SL Applications Paper 1

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.

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Predicted May 2025: SL Analysis Paper 2

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.

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Predicted May 2025: SL Analysis Paper 1

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.

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Paper 3s for HL Applications

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.

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Paper 3s for Analysis HL

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.

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Modelling Guide for IAs

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

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Statistics Guide for Explorations

Stats guide

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Exploration Guide for IB Maths Coursework

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

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Maths and Evolutionary Biology

  Maths and Evolutionary Biology Mathematics is often utilised across many fields – lets look at an example from biology, evolutionary biology and paleontology, in trying to understand the development of homo-sapiens.  We can start with a large data set which gives us the data for mammal body mass and brain size in grams (downloaded from here).  I then tidied up this to remove the rows with NA…

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A Cat and Mouse Game

A Cat and Mouse Game The Numberphile video above talks through an investigation in which a mouse is swimming in a pond, with a hungry cat prowling around the edge.  The cat can’t swim, but can run at a speed of 4m/s.  The mouse can swim at a speed of 1m/s and can run faster than the cat on the land.  The question is, can the mouse ever escape and run to safety? Modelling the cat The cat, C…

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Aliquot sequence: An unsolved problem

Aliquot sequence: An unsolved problem At school students get used to the idea that we know all the answers in mathematics – but the aliquot sequence is a simple example of an unsolved problem in mathematics.  The code above (if run for long enough on a super-computer!) might be enough to disprove a conjecture about this sequence.  Let’s look at this sequence and the associated conjecture. Aliquot…

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Time dependent gravity exploration

Time dependent gravity exploration In our universe we have a gravitational constant – i.e gravity is not dependent on time.  If gravity changed with respect to time then the gravitational force exerted by the Sun on Earth would lessen (or increase) over time with all other factors remaining the same. Interestingly time-dependent gravity was first explored by Dirac and some physicists have tried…

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Cowculus - the farmer and the cow

Cowculus – the farmer and the cow The Numberphile video above is an excellent starting point for an investigation – so I thought I’d use this to extend the problem to a more general situation.  The simple case is as follows: A farmer is at point F and a cow at point C. There is a river represented by the line passing through 𝐴𝐵. The distance 𝐴𝐹 is 2km, the distance 𝐵𝐶 is 6km and the distance 𝐴𝐵…