So anything you find interesting. 14) Circular inversion – what does it mean to reflect in a circle? Medical Test Accuracy and Statistics IB Mathematics SL . How to use graphic software to make art from equations. Friendly numbers, Solitary numbers, perfect numbers. 15) Modelling epidemics/spread of a virus – what is the mathematics behind understanding how epidemics occur? (pdf). 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. In some geometries triangles add up to more than 180 degrees, in others less than 180 degrees. 4) Rocket Science and Lagrange Points – how clever mathematics is used to keep satellites in just the right place. 21) Projective geometry – the development of geometric proofs based on points at infinity. Using the SIR model to understand epidemics. 26) Fermat’s little theorem: If p is a prime number then a^p – a is a multiple of p. 28) Recurrence expressions for phi (golden ratio): Phi appears with remarkable consistency in nature and appears to shape our understanding of beauty and symmetry. Change ). 16) Are a sample of student heights normally distributed? So there we have it, 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! 6) Square Triangular Numbers. The percentages shows that the dominant eye color is brown in people with brunette hair, and the dominant eye color for blondes is blue. 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? Expected Values (Predicted amount of students with specific hair and eye color based on Probability Law) and rounded to three significant figures. 37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur. 10) Is Intergalactic space travel possible? 23) Perfect Numbers: Perfect numbers are the sum of their factors (apart from the last factor). View Math_IA_sample1.pdf from MATH ENG 111 at ESSEC. This is also a potential opportunity to discuss the Golden Ratio in nature. 12) Towers of Hanoi puzzle – This famous puzzle requires logic and patience. They offer a Physics course, a Chemistry course and a Biology course. 5) Diophantine equations: These are polynomials which have integer solutions. IB Maths Resources from British International School Phuket, The best IB science online revision is definitely provided by. You can now download a Exploration Guide to the entire IA coursework process for the new syllabus (first exam 2021) to help you get excellent marks in your maths exploration. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL). All content is written with the exploration in mind – and shows non-calculator methods where possible to help demonstrate understanding. Can we use a mixture of pure maths and computing to solve this problem? Explore this famous number theory puzzle. This website works best with modern browsers such as the latest … In this case, r=2 and c=3, therefore: By looking at a table of critical values of the χ2 distribution, the critical value for two degrees of freedom and 5% level of significance is 5.991. What is the geometric shape of soap bubbles? Use modeling and volume of revolutions. Scroll down this page to find over 300 examples of maths IA exploration topics and ideas for IB mathematics students doing their internal assessment (IA) coursework. You can now download a Statistics and Modelling Guide full of advice to help with modelling and statistics explorations. Algebra, Calculus etc) and each area then has a number of graded questions. Both of the charts will look like this: I will then set out to each of the classes to obtain my data in tally marks until all 83 students have been studied. 9) Optimization of area – an investigation. If I find students with hazel-colored eyes (a combination of green and brown) I will ask them which color they identify with more. The planets follow a surprising pattern when measuring their distances. 35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory. This is a nice way to link some maths history with studying an interesting function. Why does the twin paradox work? 11) Zeno’s paradox of Achilles and the tortoise: How can a running Achilles ever catch the tortoise if in the time taken to halve the distance, the tortoise has moved yet further away? Investigate the surprising correlation between finger ratios and all sorts of abilities and traits. Maths and Time: Exploring ideas regarding time dilation; Plotting Planets: Using log functions to track planets! 6) Batman and Superman maths – how to use Wolfram Alpha to plot graphs of the Batman and Superman logo. This is an nice example of how you can investigation optimization of the area of different polygons. This is a function which is used in Quantum mechanics – it describes a peak of zero width but with area 1. 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. 6) Continued fractions: These are fractions which continue to infinity. 5) Knight’s tour in chess: This chess puzzle asks how many moves a knight must make to visit all squares on a chess board. 16) Euler’s identity: An equation that has been voted the most beautiful equation of all time, Euler’s identity links together 5 of the most important numbers in mathematics. There has been a recent breakthrough in this problem. 7) Fibonacci sequence and spirals in nature – There are lots of examples of the Fibonacci sequence in real life – from pine cones to petals to modelling populations and the stock market. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. 3) Their Practice Exams section takes you to ready made exams on each topic – again with worked solutions. The following are examples of HL/SL IAs based on the current mark scheme with grader comments. 18) Hyperbolic geometry – how we can map the infinite hyperbolic plane onto the unit circle, and how this inspired the art of Escher. 41) Arithmetic number puzzle – It could be interesting to do an exploration where you solve number problems – like this one. 37) Modelling a Nuclear War. I’ve just put together thirteen full investigation questions – each one designed to last around 1 hour, and totaling around 30 pages and 450 marks worth of content. The best IB science online revision is definitely provided by Study Nova – set up by the excellent IB teacher Mitch Campbell, this has a wealth of both free and paid-for resources – from lecture videos, online tests, exam questions and worked solutions to IB past papers. How strange things happen when we start to manipulate divergent series. 13) Telephone Numbers – these are numbers with special properties which grow very large very quickly. Math ia's are tricky and frustrating especially the process of finding a good topic bug your teacher with q's bc your plan is rly important. This is a nice geometry puzzle solved using a variety of methods. it really good topics in math and i really like it and its new in math. Are there functions which plot any polygons? 14) Is there a correlation between stress and blood pressure? 35) Fun with Functions!. 5) Königsberg bridge problem: The use of networks to solve problems. 15) Is there a correlation between Premier League wages and league positions? Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. This action would have produced more accurate and consistent results. You can watch a short video on it here. Make sure to download a copy! 17) Graphing Stewie from Family Guy. 11) The One Time Pad – an uncrackable code? 13) Different number systems – Learn how to add, subtract, multiply and divide in Binary. 19) Natural logarithms of complex numbers. 32) Circular Motion: Modelling a Ferris wheel. 32) RSA code – the most important code in the world? Investigate some rocket science! Most of the people I interviewed were Caucasian, and because of this I should have only tested Caucasian students. This internal assessment showed that eye color is generally dependent on hair color. 2) Torus – solid of revolution: A torus is a donut shape which introduces some interesting topological ideas. 38) Friendly numbers, Solitary numbers, perfect numbers. 22) Diophantine application: Cole numbers. Once a relationship is established, Linear Regression can be used to create a linear model. 10) Mathematical card tricks – investigate some maths magic. 3) Galileo: Throwing cannonballs off The Leaning Tower of Pisa – Recreating Galileo’s classic experiment, and using maths to understand the surprising result. 10) Tangrams: Investigate how many different ways different size shapes can be fitted together. Is there a correlation between arm span and foot height? 28) Ford Circles– how to generate Ford circles and their links with fractions. This topics provides a fascinating introduction to both combinatorial Game Theory and Group Theory. Title: Using statistics, GDP per capita, income to know the affordability of immigration of Iranians IB MATHEMATICS SL IA 30) Time travel to the future: Investigate how traveling close to the speed of light allows people to travel “forward” in time relative to someone on Earth. A nice starting point for students good at coding – who want to put these skills to the test mathematically. χ 2 Test. 19) Introduction to Modelling. For this reason, I will travel during Learning Lab on a Monday to the two teachers of the TOK classes and again on the following day. 41) Finding the volume of a rugby ball (or American football). 16) Graphing polygons investigation. = -1/12 ? 9) Maths and football – Do managerial sackings really lead to an improvement in results? this website is a real reference for me, thanks! 7) When do 2 squares equal 2 cubes? I copied the name "i tried to copy the name “i tried to copy the name but it was too long” but it was too long" it wasnt too long. There is also a fully typed up mark scheme. 24) A geometric proof for the arithmetic and geometric mean. 18) Fermat’s last theorem: A problem that puzzled mathematicians for centuries – and one that has only recently been solved. – Playing around with multiplicative persistence – can you break the world record? 15) Julia Sets and Mandelbrot Sets – We can use complex numbers to create beautiful patterns of infinitely repeating fractals. 7) Black Swan events – how usefully can mathematics predict small probability high impact events? 11) Flatland by Edwin Abbott – This famous book helps understand how to imagine extra dimension. Look at some of the maths (and psychology behind winning this game. 6) Impact Earth – what would happen if an asteroid or meteorite hit the Earth? 8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. However, some factors in the research could have altered this conclusion. How can we find the area of any polygon? 25) Euler’s 9 Point Circle. 7) Sierpinksi triangle: a fractal design that continues forever. Chi Squared Test for Independence compares two catagorical variables to test for independence. 1b) The shape of the universe – non-Euclidean Geometry is at the heart of Einstein’s theories on General Relativity and essential to understanding the shape and behavior of the universe. 2) Their Questionbank takes you to a breakdown of each main subject area (e.g. This also has some harder exams for those students aiming for 6s and 7s. 26) Modelling volcanoes – look at how the Poisson distribution can predict volcanic eruptions, and perhaps explore some more advanced statistical tests.