Maths IA
Math IA ideas: 40 IB Maths IA topics, guided
pick one, then make it yours ↓Forty topics that work for the Maths exploration. Open one to see the big idea, how to make it yours, a layout, a diagram, sample graphs and a step-by-step plan. Some use maths beyond your course: that's fine if you show you really understand it.
How the IB Maths IA is marked
- 20% of your grade
- 12 to 20 pages
- 20 marks
- AA and AI, SL and HL
- A. Presentation 4 marks A clear aim, a logical order and a conclusion.
- B. Mathematical communication 4 marks Correct notation, defined variables, labelled graphs.
- C. Personal engagement 3 marks Evidence that the choices are yours.
- D. Reflection 3 marks Thinking about what your results mean and what limits them.
- E. Use of mathematics 6 marks Maths at the right level for your course, used correctly.
Individual work: you write and submit your own exploration, using your own data or examples.
Math IA ideas to start with
- Bridge arch: is a cubic or quartic a real shape?Software will fit a cubic, a quartic, a degree-9 monster to your arch and give you a lovely R². The real question is which one deserves belief.
- Number bases: which base stores information best?Computers use base 2. We use base 10. Babylonians used base 60. Which one is best? You're going to find that the answer depends on what you count as cost.
- Tuner app: how does pitch change with string tension?Tighten a guitar string and the note rises. But by how much? You're going to turn a tuner app into a data logger, and let the data pick the function.
- Coin change: how fast does the count of ways grow?How many ways can you pay 50 cents? By hand it is easy, then hopeless. You're going to build a machine that counts for you, then ask how fast the count explodes.
- Chords in a circle: which formula counts the regions?Join points on a circle and count the regions. 1, 2, 4, 8, 16... you think you know what comes next. Draw one more point and check.
- Newton's method: how fast, and when does it fail?Your calculator finds roots in a blink. Newton's method is the idea inside. You're going to test how fast it works, and then go looking for the starting point where it breaks.
All 40 Maths IA topics
- Bridge arch: is a cubic or quartic a real shape?●○○
- Number bases: which base stores information best?●○○
- Tuner app: how does pitch change with string tension?●○○
- Coin change: how fast does the count of ways grow?●●○
- Chords in a circle: which formula counts the regions?●●○
- Newton's method: how fast, and when does it fail?●●○
- Repeating decimals: what is the pattern in the digits?●●●
- Roots of unity: a pentagon by ruler and compass?●●●
- Cans: the least metal for a given volume●○○
- Area under a curve: trapezium or Simpson?●○○
- When is the rate of change greatest in real data?●○○
- Best throwing angle when landing height differs●●○
- Vase or bowl: how close can integration get?●●○
- Maclaurin series: how many terms are enough?●●○
- Draining tank: predict the time to empty●●●
- Pursuit curves: does the chaser ever catch up?●●●
- Card and dice games: what is the best strategy?●○○
- Sleep and test scores: how strong is the evidence?●○○
- Screening tests: why a positive can still be wrong●○○
- Hot streaks: is a player streaky or just luck?●●○
- Waiting times: does a Poisson model fit?●●○
- Polls: how big a sample shrinks the margin of error?●●○
- Benford's law: does your data follow it?●●○
- Tie-breaks: do league rules change who wins?●●○
- Markov chains: what is the long-run weather?●●●
- Honeycomb: why do bees use hexagons?●○○
- Building height from angles: how accurate is it?●○○
- Golden ratio claims: do they hold up?●○○
- Shortest route: how good is a quick heuristic?●●○
- Orbits and ellipses: how well does an ellipse fit?●●●
- Fourier series: what is in a musical note?●●●
- Map projections: how do they distort the world?●●●
- Cooling drinks: does Newton's law of cooling fit?●○○
- Loans and savings: when does a plan break even?●○○
- Bouncing ball: how far does it travel in total?●○○
- Population: exponential or logistic for one country?●●○
- Setting a price: how to maximise profit from real data●●○
- Budget allocation: how does the best plan change?●●○
- Rumour spread: how does the contact rate matter?●●●
- Shop queue: predict its length from arrivals●●●
No topic matches. Try fewer words.
IB Maths IA guides
Official course page: the IB Maths pages on ibo.org. Check your teacher's guidance for the criteria that apply to you.
Make sure it's yours
This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.