All nineteen sub-topics, Standard and Higher Level, each with a student page and a teacher page.
4.1 to 4.9 are shared almost word for word between Applications and Interpretation and Analysis and Approaches, and Higher Level students take all of them too. 4.10 and 4.11 are Applications and Interpretation only and are marked, so nobody revises a test they will never sit.
Each student page has one thing you can move, and it is there to break a specific claim students get wrong rather than to look busy. Where a sentence would do the job better, the page has the sentence.
Eight more sub-topics for Applications and Interpretation Higher Level. All of them sit on top of the pages above, so do those first.
4.12 · Asking a question that does not answer itself HL Survey design, the faults worth naming, reliable against valid, and choosing categories before you test. A broken scale is perfectly reliable. That is what makes it dangerous. 4.13 · When a line is the wrong shape HL Fitting curves, the sum of squared residuals, and why a better number is not always a better model. Four models on the same data. The best fit predicts the coffee freezes. 4.14 · Transforming a random variable HL E(aX + b) and Var(aX + b), why a is squared, why b vanishes, and the absolute value a negative a needs. Slide b: the curve moves right across the screen and the width bar never changes length. 4.15 · The central limit theorem HL What actually becomes normal, the standard error, and the square root that makes precision expensive. Two graphs at once. The population stays skewed at every n; only the sample mean becomes a bell. 4.16 · Confidence intervals HL Computing one with t, what makes it narrower, and the interpretation that loses marks every session. A hundred intervals, five of which miss a mean that never moves. 4.17 · The Poisson distribution HL Scaling to the interval, adding independent Poissons, telling it from the binomial, and when it is the wrong model. Stretch the window to two hours and lambda becomes 6, not 3. 4.18 · Type I and Type II errors HL The two mistakes, power, why beta needs a specific alternative, and which error a context should protect against. Try to find a line that makes both errors small. You cannot, and then more data does it for you. 4.19 · Transition matrices and steady states HL Reading a transition matrix the right way round, powers of T, the steady state, and when there is not one. Three towns start completely differently and all three end at 0.6.Most courses start Topic 4 at probability and never come back. A student can then produce a regression line on a calculator without being able to say what r is measuring, estimate a mean from grouped data without saying the word estimate, and delete an inconvenient value because a rule called it an outlier.
Those are not hard ideas. They are just the ones nobody taught, because they sit at the front of a topic everyone is in a hurry to get through. The Higher Level pages above all depend on them, which is why 4.1 to 4.4 are first and not an appendix.
These pages are free and stay free, but they are general and your IA is not. Send me your research question, or whatever exists so far, and I will tell you in writing whether the topic has a ceiling on it, where the marks are going, and what to change first. That costs nothing and it comes back within 24 hours.
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.