IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
Anscombe's Quartet - the importance of graphs! Anscombe's Quartet was devised by the statistician Francis Anscombe to illustrate how important it was to not just rely on statistical measures when analyzing data. To do this he created 4 data sets which would produce nearly identical statistical measures. The scatter graphs above generated by the Python... Continue Reading →
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... Continue Reading →
Martingale II and Currency Trading We can use computer coding to explore game strategies and also to help understand the underlying probability distribution functions. Let's start with a simple game where we toss a coin 4 times, stake 1 counter each toss and always call heads. This would give us a binomial distribution with... Continue Reading →
Using Maths to model the spread of Coronavirus (COVID-19) This coronavirus is the latest virus to warrant global fears over a disease pandemic. Throughout history we have seen pandemic diseases such as the Black Death in Middle Ages Europe and the Spanish Flu at the beginning of the 20th century. More recently we have seen... Continue Reading →
https://www.youtube.com/watch?v=Zs2M7gWSbTg Simulating a Football Season This is a nice example of how statistics are used in modeling - similar techniques are used when gambling companies are creating odds or when computer game designers are making football manager games. We start with some statistics. The soccer stats site has the data we need from the 2018-19... Continue Reading →
https://www.youtube.com/watch?v=fcfQkxwz4Oo Quantum Mechanics - Statistical Universe Quantum mechanics is the name for the mathematics that can describe physical systems on extremely small scales. When we deal with the macroscopic - i.e scales that we experience in our everyday physical world, then Newtonian mechanics works just fine. However on the microscopic level of particles, Newtonian mechanics... Continue Reading →
Predicting the UK election using linear regression The above data is the latest opinion poll data from the Guardian. The UK will have (another) general election on June 8th. So can we use the current opinion poll data to predict the outcome? Longer term data trends Let's start by looking at the longer term trend... Continue Reading →
Modelling Radioactive decay We can model radioactive decay of atoms using the following equation: N(t) = N0 e-λt Where: N0: is the initial quantity of the element λ: is the radioactive decay constant t: is time N(t): is the quantity of the element remaining after time t. So, for Carbon-14 which has a half life of... Continue Reading →
Modeling Volcanoes - When will they erupt? A recent post by the excellent Maths Careers website looked at how we can model volcanic eruptions mathematically. This is an important branch of mathematics - which looks to assign risk to events and these methods are very important to statisticians and insurers. Given that large-scale volcanic eruptions... Continue Reading →
Are you Psychic? There have been people claiming to have paranormal powers for thousands of years. However, scientifically we can say that as yet we still have no convincing proof that any paranormal abilities exist. We can show this using some mathematical tests - such as the binomial or normal distribution. ESP Test You can... Continue Reading →
Statistics to win penalty shoot-outs With the World Cup nearly upon us we can look forward to another heroic defeat on penalties by England. England are in fact the worst country of any of the major footballing nations at taking penalties, having won only 1 out of 7 shoot-outs at the Euros and World Cup.... Continue Reading →
Which Times Tables do Students Find Difficult? There's an excellent article on today's Guardian Datablog looking at a computer based study (with 232 primary school students) on which times tables students find easiest and difficult. Edited highlights (Guardian quotes in italics): Which multiplication did students get wrong most often? The hardest multiplication was six times... Continue Reading →