The great Indian mathematician Ramanujan discovered some amazing examples of these. Investigate some rocket science! Go to  this website to find examples of the Math Exploration Click on a specific paper and you will find three options: 1) the paper, 2) the paper with teacher annotations and 3) the score. The only real thing that I came up with is something to do with statistics and Pokemon, but those don't seem to work well because all the probabilities are already preprogrammed in the game. 24) Are you psychic? 9) Designing bridges – Mathematics is essential for engineers such as bridge builders – investigate how to design structures that carry weight without collapse. Hey everyone. 22) The Folium of Descartes. We can use a Poisson model and some Excel expertise to predict the outcome of sports matches – a technique used by gambling firms. HL Mathematics IA (18/20) Maths IA For the IA, I encourage you to start as soon as possible – the more time you spend on it, the more you think about the maths you’re putting into it and hence, there will be a lower chance of you making mistakes that will cost you marks. Check out these sample IAs. 13) Telephone Numbers – these are numbers with special properties which grow very large very quickly. 7) Quantum Mechanics – a statistical universe? Includes: Full revision notes for SL Analysis (60 pages), HL Analysis (112 pages) and SL Applications (53 pages). Useful websites for use in the exploration, A selection of detailed exploration ideas. What should I do with that topic? Quantum Mechanics – a statistical universe? 29) Classical Geometry Puzzle: Finding the Radius. Yes No 2. 37) Modelling a Nuclear War. Listen to the sounds that different sine waves make. 1) Traffic flow : How maths can model traffic on the roads. Arthur was literally the ONLY person in his HL Math Class that got a 7 on his Math IA. The twin prime conjecture states that there are infinitely many consecutive primes ( eg. Change ), You are commenting using your Facebook account. If you’ve never come across this site before, start by exploring the IB Maths SL/HL/Studies Videos tab at the top of the website. Mathematics HL Internal Assessment Student Checklist Student Name: _____ Date: _____ 1. The following are examples of HL/SL IAs based on the current mark scheme with grader comments. The IB wants to see you take an idea, explore what is interesting about it, and show how engaged you are with the topic. 20) Modelling infectious diseases – how we can use mathematics to predict how diseases like measles will spread through a population. His Math IA grade was the reason he got accepted into his top-choice university. A good use of your calculus skills. You can download these here. Regardless, the IA is all about EXPLORATION. Projectile!motion!is!the!motion!of!an!object!that!is!moving!in!air!and!experiences! 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. This investigates a generalized version of projectile motion – discover what shape is created. 14)The Poincare Conjecture and Grigori Perelman – Learn about the reclusive Russian mathematician who turned down $1 million for solving one of the world’s most difficult maths problems. ie 6 is a perfect number because 1 + 2 + 3 = 6. 4) Rocket Science and Lagrange Points – how clever mathematics is used to keep satellites in just the right place. Exponential and trigonometric regression. Algebra, Calculus etc) and each area then has a number of graded questions. Investigate the surprising correlation between finger ratios and all sorts of abilities and traits. 32) RSA code – the most important code in the world? Together this is around 120 pages of content. 30) Can you solve Oxford University’s Interview Question?. Ideas for Math HL IA? How do you even choose a topic? Change ). = -1/12 ? All rights reserved. Maths Books. Also, what is with “Does finger length predict mathematical ability?”? ibalasia. … 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. 6) Bullet projectile motion experiment – using Tracker software to model the motion of a bullet. Change ), You are commenting using your Google account. What is the minimum number of colours needed for any map? 23) Modelling music with sine waves – how we can understand different notes by sine waves of different frequencies. How can we find the area of any polygon? His Math IA grade was the reason he got accepted into his top-choice university. 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. The Past IB Exams section takes you to full video worked solutions to every question on every past paper – and you can also get a prediction exam for the upcoming year. IB Mathematics HL and SL IA Tips. Maths IA – Maths Exploration Topics. ( Log Out /  The Practice Exams section takes you to ready made exams on each topic – again with worked solutions. This topic links to graph theory. Go to first unread Skip to page: This discussion is closed. IB Physics 100 Concepts+tips. Goldbach?). Ideas for Math HL IA? 4) Genetics – Look at the mathematics behind genetic inheritance and natural selection. 5 and 7 are consecutive primes). Projectile!motion–!Mathematics!IA!!! 10) Envelope of projectile motion. Together this is around 120 pages of content. ( Log Out /  Some ideas may be to: Consider more about the fundamentals about "squaring the circle". Check out our math videos! Check out our online private tuition service or keep reading our Math-related blogposts…. Maths is closely connected with astronomy – see how we can work out the distance to the stars. Within each topic listed below, we include the basic reasons for investigating each topic, what the possible independent variables and dependent variables are as well as the basic experimental setup! 19) Elliptical Curves– how this class of curves have importance in solving Fermat’s Last Theorem and in cryptography. There has been a recent breakthrough in this problem. 19) Introduction to Modelling. Circular measure. I have been struggling since quite a while to choose a math hl topic, your topic seems quite interesting. This topics provides a fascinating introduction to both combinatorial Game Theory and Group Theory. A 60 page pdf guide full of advice to help with modelling and statistics explorations – focusing in on non-calculator methods in order to show good understanding. Advice on using Geogebra, Desmos and Tracker. 15) Julia Sets and Mandelbrot Sets – We can use complex numbers to create beautiful patterns of infinitely repeating fractals. 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. 27) Volume optimization of a cuboid  – how to use calculus and graphical solutions to optimize the volume of a cuboid. Fourier transforms have an essential part to play in modern life – and are one of the keys to understanding the world around us. 10) Pythagorean triples: A great introduction into number theory – investigating the solutions of Pythagoras’ Theorem which are integers (eg. 25) Palindrome numbers: Palindrome numbers are the same backwards as forwards. For example, Mod 3 means the remainder when dividing by 3. Here is a list of 20 interesting topics to help you get inspiration: 1. I would strongly recommend students use this as a resource during the course. 1a) Non-Euclidean geometries: This allows us to “break” the rules of conventional geometry – for example, angles in a triangle no longer add up to 180 degrees. Maths of Global Warming – Modeling Climate Change, Circular Motion: Modelling a Ferris wheel, Predicting the UK election using linear regression, Modelling the spread of Coronavirus (COVID-19), Finding the volume of a rugby ball (or American football). The formula given to us was: =∫ 2 Hence, I wondered if there was a similar way in which the surface area of a … Meet Aaryan today by clicking below! Here is a geometric proof. Explore the maths behind code making and breaking. What is the Mordell equation and how does it help us solve mathematical problems in number theory? 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. What is your best way of surviving the zombie apocalypse? A chance to look at some statistics with surprising results. 9) Optimization of area – an investigation. 1) The Monkey and the Hunter – How to Shoot a Monkey – Using Newtonian mathematics to  decide where to aim when shooting a monkey in a tree. Feeling cool about maths but nervous about TOK? 2) How to Design a Parachute – looking at the physics behind parachute design to ensure a safe landing! --> Source 4: Inspiring Mathematics Online --> Source 5: Famous and Interesting Math Problems --> Source 6: Sample IAs by Syllabus Topic The best way to get a feeling for how SL math topics can be used to explore is to see great examples of IAs! Can we find a function that plots a square? If you are asking, “what is a good topic for a Math IA”, we can help you brainstorm. Still feeling confused? extremely helpful as my teacher is super vague! 43) Narcissistic Numbers – what makes a number narcissistic – and how can we find them all? 10) Is there a correlation between Premier League wages and league position? Find your group chat here >> start new discussion closed. 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? What is the geometric shape of soap bubbles? 8) Change in a person’s BMI over time – There are lots of examples of BMI stats investigations online – see if you can think of an interesting twist. 9) Does finger length predict mathematical ability? 6) Logarithmic scales – Decibel, Richter, etc. 46) Ramanujan’s Taxi Cab and the Sum of 2 Cubes. 11) The One Time Pad – an uncrackable code? – An essential component of JPEG, DNA analysis, WIFI signals, MRI scans, guitar amps – find out about the maths behind these essential technologies. This also has some harder exams for those students aiming for 6s and 7s. Useful Links: An Interactive Maths Dictionary. You can also model everything from Angry Birds to stunt bike jumping. Need help with your math IA? 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. Pay us to Get an Excellent and Original IA! 25) Reaction times – are you above or below average? 7) Sierpinksi triangle: a fractal design that continues forever. NOTE: These topics are purely meant as inspiration and are not to be chosen blindly. If you are watching this video now, you seem serious about boosting your IB grade. = -1/12 ? Look at the inherent probabilistic nature of the universe with some quantum mechanics. Some nice examples of using polar coordinates to create interesting designs. Continuous random variables. Quiz 5. These are beautifully  handwritten and of a very high quality. Continuous random variables. If you are watching this video now, you seem serious about boosting your IB grade. 8) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. 17) Graphing Stewie from Family Guy. 3) Projectile motion: Studying the motion of projectiles like cannon balls is an essential part of the mathematics of war. 3) Galileo: Throwing cannonballs off The Leaning Tower of Pisa – Recreating Galileo’s classic experiment, and using maths to understand the surprising result. Fully updated for the new syllabus. Why e is base of natural logarithm function: Fourier Transforms – the most important tool in mathematics? Can you solve Oxford University’s Interview Question? Surprisingly maths can help! 3) Stacking cannonballs – solving maths with code – how to stack cannonballs in different configurations. How all our digital communications are kept safe through the properties of primes. 11) Flatland by Edwin Abbott – This famous book helps understand how to imagine extra dimension. 8) Log Graphs to Plot Planetary Patterns. New II: Paper 3 Practice Questions for HL. Friendly numbers, Solitary numbers, perfect numbers. Investigate what changes the condition of numbers, 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) Continued fractions: These are fractions which continue to infinity. Bivariate Statistics. Use Tracker software to create a Sine wave. Why do magic squares work? 3,4,5 triangle). 35) Fermat’s Theorem on the sum of 2 squares – An example of how to use mathematical proof to solve problems in number theory. 30) Maths of Global Warming – Modeling Climate Change – Using Desmos to model the change in atmospheric Carbon Dioxide. 12) Four colour map theorem – a puzzle that requires that a map can be coloured in so that every neighbouring country is in a different colour. Can we use a mixture of pure maths and computing to solve this problem? Qualified Writers in: Math, Biology, Physics, ESS, History, Economics, Chemistry, Geography, Music, Computer Science or even Design and Technology! 12) Magic squares and cubes: Investigate magic tricks that use mathematics. Even though many of these topics led to high scores for some of our graduates in the past, it is important that you listen to the advice of your subject teacher before choosing any topic! Check out our. What does it show regarding rational and irrational numbers? Investigate how binary is used – link to codes and computing. I’ve teamed up with Mr Mac to provide full class revision notes fully updated for the new syllabus. There’s a really great website been put together to help IB students with topic revision both for during the course and for the end of Year 12 school exams and Year 13 final exams. 7) Möbius strip: An amazing shape which is a loop with only 1 side and 1 edge. It is now used as a saying to represent something impossible. 17) Does sacking a football manager affect results? 3) Benford’s Law – using statistics to catch criminals by making use of a surprising distribution. IB math HL IA/ Exploration ideas Watch. Over 300 examples of maths IA exploration topics and ideas for IB mathematics. 3) Gambler’s fallacy: A good chance to investigate misconceptions in probability and probabilities in gambling. Sections. 4) Bluffing in Poker: How probability and game theory can be used to explore the the best strategies for bluffing in poker. Use the binomial distribution to test your ESP abilities. 16) Graphing polygons investigation. Which times tables do students find most difficult? 2. Posted by. Proof doesn’t always have to be algebraic. 7) When do 2 squares equal 2 cubes? 6) Impact Earth – what would happen if an asteroid or meteorite hit the Earth? I would really recommend these resources for all IB students – it takes a lot of skill to successfully condense a syllabus into the essential content – and these notes really are of the highest quality. 4) Bad maths in court – how a misuse of statistics in the courtroom can lead to devastating miscarriages of justice. I’ve just put together seventeen full investigation questions – each one designed to last around 1 hour, and totaling around 40 pages and 600 marks worth of content. I would really recommend everyone making use of this – there is a mixture of a lot of free content as well as premium content so have a look and see what you think. 6) Batman and Superman maths – how to use Wolfram Alpha to plot graphs of the Batman and Superman logo. 2. 4) Bad maths in court - how a misuse of statistics in the courtroom can lead to devastating miscarriages of justice. You can download these notes on my site. Some classic physics – which generates some nice mathematical graphs. Here is a list of over 200 ideas with links to further reading for your maths exploration! An interesting insight into the mathematical field of Number Theory. 9) Modeling with springs and weights. 19) Natural logarithms of complex numbers. 40) Modelling the spread of Coronavirus (COVID-19). 36) Predicting the UK election using linear regression. 22) Modelling Zombies – How do zombies spread? Can all fractions with a numerator of 2 be written as 2 Egyptian fractions? Fourier Transforms – the most important tool in mathematics? Full length rough draft submitted prior to winter break for review. Bivariate Statistics. Maths Exploration (IA) ideas. 8) How to “Solve” Noughts and Crossess (Tic Tac Toe) – using game theory. All fully updated for the new syllabus. This particular problem was solved by Euler. For Parents. 21) Projective geometry –  the development of geometric proofs based on points at infinity. Any ideas for some not-so-generic Math IA topics? But no matter what the topic is about and whether you are super good and interested in math or not, you can get at least a mark 6/7, if you follow certain guidelines, including but not limited to perfect presentation, clear formulae, exact structure, logical development of the ideas, personal approach to the work(i.e. Thank you! 32) Soap Bubbles, Wormholes and Catenoids. ( Log Out /  but these range from quite easy (modular arithmetic, at least at the basic level) to impossibly hard (GRH? 5) The mathematics of cons – how con artists use pyramid schemes to get rich quick. Straight lines are not straight, parallel lines meet and angles in a triangle don’t add up to 180 degrees. Aaryan is one of our many tutors who smashed their Maths IA. Using the physics of travel near the speed of light to see how we could travel to other stars. A post which looks at the maths behind this particularly troublesome series. 39)Modeling hours of daylight – using Desmos to plot the changing hours of daylight in different countries. Premier League wages and league position? You can download these notes on my site here. 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? 5) Königsberg bridge problem: The use of networks to solve problems. 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. Quiz 2. 6) Square Triangular Numbers. Completely Free. So there we have it, 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! I'm completely lost and can't think of any ideas. Find out how! Maths Books. 7) Explore the Si(x) function – a special function in calculus that can’t be integrated into an elementary function. Look at some of the maths (and psychology behind winning this game. Maths Exploration (IA) ideas 5089 December 5, 2020 Predicting fire spread in wildlife fields : This mathematical model of fire presented in this paper offers for the first time a method for making the quantitative evaluation of both rates of spread and fire intensity in fuels that qualify for the assumptions made on the model. Quiz 3. ( Log Out /  22) Diophantine application: Cole numbers. The planets follow a surprising pattern when measuring their distances. In this post, we give you 50 IB Biology IA Ideas to help you speed up your research process. Pascal’s triangle patterns: Fibonacci sequence. 12) How to win at Rock Paper Scissors. It involves understanding the modulo operation. How strange things happen when we start to manipulate divergent series. New III:  Full class revision notes for SL and HL Analysis and SL Applications. Massive library of useful links and videos. Hi everyone, I need a math IA topic pretty soon and Ive been struggling to find something that I both like and can find an appropriate application of math to. I want to spend the last 3 weeks of the summer applying everything I learnt … Each exploration is assessed against the following five criteria. 2) Goldbach’s conjecture: “Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics. 3) Minimal surfaces and soap bubbles: Soap bubbles assume the minimum possible surface area to contain a given volume. It’s quite funny how (almost) everyone doing the IB would have the thought process of the following when finding a topic for their Math IA: 1. Use computer graphing to investigate. Math IA Ideas (Geometry (Using trigonometry to identify the structural…: Math IA Ideas (Geometry, Other, Functions, Statistics, Other ) Explore this famous number theory puzzle. 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. 38) Modelling a football season. 10) Codes and ciphers: ISBN codes and credit card codes are just some examples of how codes are essential to modern life. Arthur was literally the ONLY person in his HL Math Class that got a 7 on his Math IA. 18) Which times tables do students find most difficult? Copyright 2020 Lanterna Education ltd, not affiliated with the IBO. To make matters worse, on top of just doing the dreaded maths exam, we’re also expected to write a Maths IA exploration into a topic of our choice! Applications of differentiation. 23) Measuring the Distance to the Stars. 10) Is Intergalactic space travel possible? Look at the Bayesian logic behind the argument that we are living in a computer simulation. I have chosen math hl and economics hl as well. A great introduction to some of the ideas behind non-euclidean geometry. love this! You can, The IB Analysis and Approaches SL notes are a 60 page pd, the HL notes are a 112 page pdf and the SL Applications notes are 53 pages. A must for all Analysis and Applications students! 42) Normal Numbers – and random number generators – what is a normal number – and how are they connected to random number generators? 2) Solving maths problems using computers – computers are really useful in solving mathematical problems. Go to  this website to find examples of the Math Exploration Click on a specific paper and you will find three options: 1) the paper, 2) … ... Maths Exploration (IA) ideas. The only real thing that I came up with is something to do with statistics and Pokemon, but those don't seem to work well because all the probabilities are already preprogrammed in the game. 1) Traffic flow: How maths can model traffic on the roads. Can we use a mixture of pure maths and computing to solve this problem? Some Qs … 2) Logistic function and constrained growth 3) Benford's Law - using statistics to catch criminals by making use of a surprising distribution. Also look at the finances behind Premier league teams. The following are examples of HL/SL IAs based on the current mark scheme with grader comments. Stuck for Ideas planning your Biology IA? I’ve put together this 63 page guide is which talks you through the essentials about the investigation, the new marking criteria, how to choose a topic, hand-picked examples of 70 excellent topics, useful websites, common student mistakes, advice on using software effectively and more. Beautifully written by an experienced IB Mathematics teacher, and of an exceptionally high quality. How to Prepare For Your IB English Individual Oral (IO)! Algebra and number. I would really recommend these resources for all IB students – it takes a lot of skill to successfully condense a syllabus into the essential content – and these notes really are of the highest quality. IB HL Math IA Topics (Mathematics in art~expolring the role of math in…: IB HL Math IA Topics 20) The Coastline Paradox – how we can measure the lengths of coastlines, and uses the idea of fractals to arrive at fractional dimensions. Applications of differentiation; Binomial Theorem; Bivariate Statistics; Circular measure; Complex Numbers; Continuous random … 3. Pros: IB specific. 34) Cesaro Summation: Does 1 – 1 + 1 – 1 … = 1/2?. 39) Zeno’s Paradox – Achilles and the Tortoise – A look at the classic paradox from ancient Greece – the philosopher “proved” a runner could never catch a tortoise – no matter how fast he ran. The IB Analysis and Approaches SL notes are a 60 page pd, the HL notes are a 112 page pdf and the SL Applications notes are 53 pages. 37) Mathematical proof and paradox – a good opportunity to explore some methods of proof and to show how logical errors occur. Investigate what makes a number happy or sad, or sociable! Make sure to download a copy! 13) The Watson Selection Task – a puzzle which tests logical reasoning. Here is a list of over 200 ideas with links to further reading for your maths exploration! Choose your own pattern investigation for the exploration. 27) Could Trump win the next election? ... Maths Exploration (IA) ideas. – Playing around with multiplicative persistence – can you break the world record? Use modeling and volume of revolutions. Can you find the loop of infinite sadness? The final mark for each exploration is the sum Pre-Diploma Quizzes Show sub menu. Based on my experience, a topic solely focusing on a single geometric problem will not earn good scores. 16) Are we living in a computer simulation? 10) Mathematical card tricks – investigate some maths magic. 5) Fourier Transforms – the most important tool in mathematics? IB Maths Resources from British International School Phuket, I’ve teamed up with Mr Mac to provide full class revision notes fully updated for the new syllabus. Still feeling confused? 1. If you are asking, “what is a good topic for a Math IA”, we can help you brainstorm. 28. 14) Circular inversion – what does it mean to reflect in a circle? The use of regression in polling predictions. All fully updated for the new syllabus. 7) Patterns in Pascal’s triangle: There are a large number of patterns to discover – including the Fibonacci sequence. This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. Close. Some of the Stats topics seem quite bizarre and wholly unmathematical in nature. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL). Please note that difference between HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently the HL and SL grades differ slightly. 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. We can analyse the data to find out. Cesaro Summation: Does 1 – 1 + 1 – 1 … = 1/2? Investigate how to solve them. 1) Modular arithmetic – This technique is used throughout Number Theory. 2) Gravity, orbits and escape velocity – Escape velocity is the speed required to break free from a body’s gravitational pull. 20 Math Internal Assessment Topic Ideas for SL Students Choosing the topic is usually the trickiest part which many IB students struggle with. Quiz 1. Does finger length predict mathematical ability? You choose your subject (HL/SL/Studies if your exam is in 2020 or Applications/Analysis if your exam is in 2021), and then have the following resources: The Questionbank takes you to a breakdown of each main subject area (e.g. Yes No 2. 40) Stellar Numbers – This is an excellent example of a pattern  sequence investigation. IB Exploration Modelling and Statistics Guide. This Math Class included two current UC Berkeley Students, an Oxford pupil, and a UPenn undergrad. 2. HL Mathematics IA (18/20) Maths IA For the IA, I encourage you to start as soon as possible – the more time you spend on it, the more you think about the maths you’re putting into it and hence, there will be a lower chance of you making mistakes that will cost you marks.

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