In general, Applications and Interpretation covers a broad range of materials, but Analysis and Approaches covers a narrower range in greater depth. Below lists the main topics in each course, by color code from 2014-2020 syllabus Studies, SL and HL (including Further HL). New topics are italicized. HL includes all SL topics of the same course.
Common topics in all new Math courses:
Algebra: scientific notation, arithmetic/geometric progression, compound interest, annual depreciation, exponents/logarithms
Functions: lines, graph of a function, domain/range, definition of inverse, identifying extremas, intercepts, symmetry, zeros, asymptotes