Since the χ2 value 7.03535 is greater than 5.991, I reject the null hypothesis and accept the alternative hypothesis, concluding that eye color and hair color are dependent variables. 13) Different number systems – Learn how to add, subtract, multiply and divide in Binary. 8) Log Graphs to Plot Planetary Patterns. 30) Can you solve Oxford University’s Interview Question?. 6) Continued fractions: These are fractions which continue to infinity. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL). 11) Understanding the fourth dimension: How we can use mathematics to imagine (and test for) extra dimensions. 11) Mersenne primes: These are primes that can be written as 2^n -1. The regression section includes detailed regression techniques (linear, quadratic, cubic, trigonometric, exponential, linearization using log scales. There is a $1 million prize for solving the Riemann Hypothesis and $250,000 available for anyone who discovers a new, really big prime number. What is the geometric shape of soap bubbles? 11) Is there a correlation between stock prices of different companies? Zeno’s paradox of Achilles and the tortoise, The Poincare Conjecture and Grigori Perelman, The Monkey and the Hunter – How to Shoot a Monkey, Galileo: Throwing cannonballs off The Leaning Tower of Pisa. Can we find a function that plots a square? Cesaro Summation: Does 1 – 1 + 1 – 1 … = 1/2? Useful websites for use in the exploration, A selection of detailed exploration ideas. This is a lovely construction using just compasses and a ruler. Here is a geometric proof. 32) Soap Bubbles, Wormholes and Catenoids. 46) Ramanujan’s Taxi Cab and the Sum of 2 Cubes. 4) Genetics – Look at the mathematics behind genetic inheritance and natural selection. Is there a correlation between arm span and foot height? 18) Hyperbolic geometry – how we can map the infinite hyperbolic plane onto the unit circle, and how this inspired the art of Escher. 10) Mathematical card tricks – investigate some maths magic. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. 15) Birthday paradox: The birthday paradox shows how intuitive ideas on probability can often be wrong. This is a fantastic 70 page booklet explaining different modelling methods from Moody’s Mega Maths Challenge. Chi Squared Test for Independence compares two catagorical variables to test for independence. 10) Is there a correlation between Premier League wages and league position? 22) Diophantine application: Cole numbers. Studies have shown that bilingual students have better “working memory” – does this include memory recall? 17) Does sacking a football manager affect results? Most of the people I interviewed were Caucasian, and because of this I should have only tested Caucasian students. 31) The Shoelace Algorithm to find areas of polygons. 14) Bayes’ theorem: How understanding probability is essential to our legal system. 20) Modelling infectious diseases – how we can use mathematics to predict how diseases like measles will spread through a population. 9) Maths and football – Do managerial sackings really lead to an improvement in results? Really useful! How many people need to be in a room for it to be at least 50% likely that two people will share the same birthday? Essential knowledge for future astronauts. 28) How to avoid a Troll – an example of a problem solving based investigation, 29) The Gini Coefficient – How to model economic inequality. Revision Village is an exceptional resource for all IB maths students which I would strongly recommend all students make use of during their course. Can we use a mixture of pure maths and computing to solve this problem? Observed Values (Total observations from the students of both TOK teachers). Are the IB maths test scores normally distributed? 1) Radiocarbon dating – understanding radioactive decay allows scientists and historians to accurately work out something’s age – whether it be from thousands or even millions of years ago. 5) Project Euler: Coding to Solve Maths Problems. This conclusion shows that people with brunettes are more likely to have brown eyes than blue or green eyes and that there is proportionately a greater diversity of eye color evident in blondes than brunettes. Fourier Transforms – the most important tool in mathematics? Zeno’s Paradox – Achilles and the Tortoise, Normal Numbers – and random number generators, Ramanujan’s Taxi Cab and the Sum of 2 Cubes, A geometric proof for the arithmetic and geometric mean, Classical Geometry Puzzle: Finding the Radius. 3) Chinese postman problem – This is a problem from graph theory – how can a postman deliver letters to every house on his streets in the shortest time possible? What I like about this is that you are given a difficulty rating, as well as a mark scheme and also a worked video tutorial. 27) Volume optimization of a cuboid – how to use calculus and graphical solutions to optimize the volume of a cuboid. The eye color and hair color Asian or black students would have misrepresented the data, since most Asians and blacks have black hair and brown eyes. 12) How to win at Rock Paper Scissors. Using the SIR model to understand epidemics. Make sure to download a copy! You can also sign up for free to access their exams secrets emails their revision notes and predictions for the November 2020 and May 2021 papers. 17) Medical data mining – Explore the use and misuse of statistics in medicine and science.
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