IB Mathematics Internal Assessment
Scales, guitar strings, room acoustics, headphones, the beats in a track. Music is where many students already have real knowledge and real data, which is a head start on engagement. It is also a context where the mathematics is often quietly absent, because the interesting part is the sound. Here is how to keep the mathematics doing the work.
You can play it, record it and hear the difference, so the topic feels alive. The risk is that the listening carries the argument. A moderator cannot hear your recording. They read the page and ask what you calculated, what you decided and what you checked.
Keep one question in front of you the whole way through: what did the mathematics explain that my ears had already told me? If the answer is nothing, you have a description of music, not an exploration of it.
Time signatures as fractions, octaves as doubling, a mention of Pythagoras. Each point is true and none is investigated. It reads as a short essay with a few numbers in it, and no result in it could have come out differently.
A handful of classmates, two playlists and a mean score for each. The mathematics is a comparison of two averages, the sample is too small to say anything, and the real difficulties are about the experiment, not the number work. It rarely reaches course level, and at HL it falls well short.
The frequency of a string from its length, or of a pipe from its length, with the numbers substituted and a table at the end. Substitution is routine. The moment you have to justify why the formula applies to your instrument is where marks start, and most students skip it.
A free audio program draws the frequency chart. If you cannot say how the chart was calculated, what its limits are or why a peak is where it is, the software has done the mathematics and you have captured screenshots.
Pure ratios and equal temperament cannot both be exact, and the gap between them is a genuine piece of number theory. Work out for yourself what each system gives for the same intervals, measure how far they drift apart, and say what a musician loses with each choice. Keep your claims to what you can calculate and check.
Record your own instrument, find the frequencies that appear, and compare them with a model you have chosen and justified. Then look at where it fails. A real string is not ideal, and the size and direction of the error is the interesting result. This suits AA students who like trigonometry and functions, and AI students working from measured data.
A note from a violin and the same note from a flute differ because of the mix of waves inside them. Build a sound from simple waves, compare it with a recording and explain what you matched and what you could not. At HL this can lead naturally into Fourier ideas, but only take it as far as you can explain without borrowing someone else's derivation.
Two close notes produce a slow pulse, and two speakers produce quiet and loud places in a room. Predict where they will be, then go and measure with a phone app and a tape. The prediction can be checked against something you did not use to build it, which is exactly what makes it a result.
Why does loudness behave logarithmically, how quickly does a clap fade in your hall, and what does that do to speech? Collect decay measurements in more than one space, fit a model with a reason for its form, and compare the rooms. Logarithms and exponentials do real work here rather than being decoration.
Take "why does my guitar go out of tune" as a starting idea. Done as a list of causes it is a description. To turn it into an exploration, keep pushing.
None of that needs advanced mathematics. It needs a question you can defend and a willingness to report the result you actually got.
Reflection comes more easily here than in most contexts, because a real instrument or room will often disagree with your model. Record those moments properly: what you expected, what you found and what you changed. They are worth more than another clean chart.
Got a music or sound idea and not sure it can score?
Send me the question and what you plan to do with the mathematics. I read real submitted explorations every year, and I will tell you honestly whether it has enough to do, while there is still time to change direction.
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Written by a serving IB Diploma and Career-related Programme Coordinator and Head of Mathematics, who reads internal assessments across every subject group every year. If you then want the whole draft reviewed properly against all five criteria, that is the paid one, and it is refunded if it does not name at least three specific things to fix.
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I never write any part of it. Not a sentence, not a calculation, not your data. Under 18: a parent buys this and the thread is with them. I do not work with students at my own school.