Application & Interpretations SL (AI SL):
Applications & Interpretations HL (AI HL):
Analysis & Approaches SL (AA SL):
Anslysis & Approaches HL (AA HL):
Note: Both AI HL, and AA HL have higher level math content studied usually in university, however AA HL gears you for the "analysis" as is in the name, while AI HL seems to have been built for "application", as is very evident in the textbooks and curriculum papers I have seen.
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AI SL: Old maths studies. Compared to maths studies, there are a few additions alike Voronoi diagrams, simple integration by hand or using trapezoidal rule, t-test, modelling using graphs, addition of sine graph, binomial, Spearman's rank correlation, bais clogs. The IA has also changed, now it is more like current maths SL/HL. Otherwise, it is good ol' maths studies.
AI HL: It is like old maths HL but with statistics option (MUCH harder than AI SL). There are a few things that have been removed compared to maths HL: hard integration (say by parts), some theoretical parts (say vector dot/cross properties or the way rational functions look). In addition it gets lots of statistics option, matrices (!!!) (including properties, eigenvalues/eigenvectors, determinants, Markov chains and other smaller bits and pieces) and solving differential equations using numerical Euler's method (up to second order differential equation). It also gets all the stuff from the AI SL (so say Voronoi diagrams and trapezoidal rule). ALSO: changes to exam. ALL papers have GDC. Paper 1 and 2 are 2 hrs long (P1 is lots of section A questions, P2 is lots of section B questions). Paper 3 is 1 hr long, some kind of extended response questions. No clue what is that exactly, read guide for further guidance.(modifié)
AA SL: old maths SL, but without vectors. That's all mostly. Very small changes otherwise.
AA HL: old maths HL, but with half of calculus option (excluding convergence/divergence series, Taylor series, Riemman sum, Rolle's/mean value theorem, integral with infinite boundaries and some smaller pieces). Also Poisson is gone now. In return it gets: integration by partial fractions, some more rational functions (with oblique asymptotes), a bit more theory on stats; and from calculus option it gets: L'hop, Maclaurian series, first order differential equations, Euler's method for first order. Exam for P1 and P2 is the same, but P3 is a new type: 1 hr long with GDC, where you answer 2 extended response questions. Again, no idea what exactly is that, check guide for further information.