IB Maths Exploration Guide (for Applications and Interpretations, Analysis and Approaches) You can download a 27-page pdf guide to the entire IA coursework process for the new syllabus (first exam 2021). The guide talks you through An introduction to the essentials about the investigation, The new marking criteria, How to choose a topic, Examples of around […]
The Martingale system The Martingale system was first used in France in 1700s gambling halls and remains used today in some trading strategies. I’ll look at some of the mathematical ideas behind this and why it has remained popular over several centuries despite having a long term expected return of zero. The scenario You […]
This carries on our exploration of projectile motion – this time we will explore what happens if gravity is not fixed, but is instead a function of time. (This idea was suggested by and worked through by fellow IB teachers Daniel Hwang and Ferenc Beleznay). In our universe we have a gravitational constant – […]
Projectile Motion III: Varying gravity We can also do some interesting things with projectile motion if we vary the gravitational pull when we look at projectile motion. The following graphs are all plotted in parametric form. Here t is the parameter, v is the initial velocity which we will keep constant, theta is the angle […]
Projectile Motion Investigation II Another example for investigating projectile motion has been provided by fellow IB teacher Ferenc Beleznay. Here we fix the velocity and then vary the angle, then to plot the maximum points of the parabolas. He has created a Geogebra app to show this (shown above). The locus of these maximum points […]
Envelope of projectile motion For any given launch angle and for a fixed initial velocity we will get projectile motion. In the graph above I have changed the launch angle to generate different quadratics. The black dotted line is then called the envelope of all these lines, and is the boundary line formed when I […]
