IB Maths is a struggle for most people going through their diploma. 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! Where do you even begin such a task? How do you even choose a topic? We’re compiled 50 common Maths IA topics that may spark some creative juices and set you on your way to conquering one of the hardest assignments of the diploma!

1-10

  • Pascal’s triangle: Discovering patterns within this famous array of numbers
  • Pythagorean triples: Can you find patterns in what numbers form a pythagorean triple?
  • Monty Hall problem: How does Bayesian probability work in this real-life example, and can you add a layer of complexity to it?
  • The Chinese Remainder Theorem: An insight into the mathematics of number theory
  • Sum of all positive integers is -1/12? Explore this fascinating physics phenomenon through the world of sequences and series
  • Birthday paradox: Why is it that in a room of people probability dictates that people are very likely to share a birthday? 
  • Harmonic series: Explore why certain notes/chords in music sound dissonant, and others consonant, by looking at the ratios of frequencies between the notes.
  • Optimizing areas: Optimizing the area of a rectangle is easy, but can you find a way to do it for any polygon?
  • Optimizing volumes: Explore the mathematics of finding a maximum volume of a cuboid subject to some constraint
  • Flow of traffic: How does mathematics feed into our traffic jams that we endure every morning?

11-20

  • Football statistics: Does spending a lot of cash during the transfer window translate to more points the following year? Or is there a better predictor of a team’s success like wages, historic performance, or player valuation?
  • Football statistics #2: How does a manager sacking affect results? 
  • Gini coefficient: Can you use integration to derive the gini coefficient for a few countries, allowing you to accurately compare their levels of economic inequality?
  • Linear regressions: Run linear regressions using OLS to predict and estimate the effect of one variable on another.
  • The Prisoner’s Dilemma: Use game theory in order to deduce the optimal strategy in this famous situation
  • Tic Tac Toe: What is the optimal strategy in this legendary game? Will my probability of winning drastically increase by some move that I can make?
  • Monopoly: Is there a strategy that dominates all others? Which properties should I be most excited to land on?
  • Rock Paper Scissors: If I played and won with rock already, should I make sure to change what I play this time? Or is it better to switch? 
  • The Toast problem: If there is a room of some number of people, how many toasts are necessary for everyone to have toasted with everyone?
  • Cracking a Password: How long would it take to be able to correctly guess a password? How much safer does a password get by adding symbols or numbers?

Need help with your math IA? Check out our math videos!

21-30

  • Stacking Balls: Suppose you want to place balls in a cardboard box, what is the optimal way to do this to use your space most effectively?
  • The Wobbly Table: Many tables are wobbly because of uneven ground, but is there a way to orient the tables to make sure they are always stable?
  • The Stable Marriage Problem: Is there a matching algorithm that ensures each person in society ends up with their one true love? What is the next best alternative if this is not viable?
  • Mathematical Card Tricks: Look at the probabilities at play in the famous 3 card monte scam. 
  • Modelling the Spread of a Virus: How long would it take for us all to be wiped out if a deadly influenza spreads throughout the population?
  • The Tragedy of the Commons: Our population of fish is dwindling, but how much do we need to reduce our production by in order to ensure the fish can replenish faster than we kill?
  • The Risk of Insurance: An investigation into asymmetric information and how being unsure about the future state of the world may lead us to be risk-averse
  • Gabriel’s Horn: This figure has an infinite surface area but a finite volume, can you p
    rove this?
  • Modelling the Shape of an Egg: Although it may sound easy, finding the surface area
    or volume of this common shape requires some in-depth mathematical investigation
  • Voting Systems: What voting system ensures that the largest amount of people get the official that they would prefer? With 2 candidates this is logical, but what if they have more than 2?

31-40

  • Probability: Are Oxford and Cambridge biased against state-school applicants?
  • Statistics: With Tokyo 2020 around the corner, how aboutmodelling change in record performances for a particular discipline?
  • Analysing Data: In the 200 meter dash, is there an advantage to a particular lane in track? 
  • Coverage: Calculation of rate of deforestation, and afforestation. How long will our forests last?
  • Friendly numbers, Solitary numbers, perfect numbers: Investigate what changes the condition of numbers
  • Force: Calculating the intensity of a climber’s fall based upon their distance above where they last clamped in
  • Königsberg bridge problem: Using networks to solve problems. 
  • Handshake problem: How many handshakes are required so that everyone shakes hands with all the other people in the room? 
  • The mathematics of deceit: How con artists use pyramid schemes to get rich quick!
  • Modelling radioactive decay: The maths of Chernobyl – when will it be safe to live there?

41-50

  • Mathematics and photography: Exploring the relationship between the aperture of a camera and a geometric sequence
  • Normal Distribution: Using distributions to examine the 2008 financial crisis
  • Mechanics: Body Proportions for Track and Field events
  • Modelling: How does a cup of Tea cool?
  • Relationships: Do BMI ratings and country wealth share a significant relationship?
  • Modelling: Can we mathematically model musical chords and concepts like dissonance?
  • Evaluating limits: Exploring L’Hôpital’s rule
  • Chinese postman problem: How do we calculate shortest possible routes?
  • Maths and Time: Exploring ideas regarding time dilation
  • Plotting Planets: Using log functions to track planets!

So there we have it, 50 IB Maths IA topic ideas to give you a head-start for attacking this piece of IB coursework! Still feeling confused? Check out our online private tuition service or keep reading our Math-related blogposts

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