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?

## 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…