Limits → Derivatives → Integration → Series
Limit definition, evaluation techniques, Squeeze Theorem, continuity, IVT
Definition, power rule, product rule, quotient rule, higher-order derivatives
Chain rule, implicit differentiation, inverse trig derivatives
Related rates, linear approximation, Mean Value Theorem
Critical points, concavity, inflection points, optimization problems
Antiderivatives, Fundamental Theorem of Calculus, definite integrals
Substitution, integration by parts, partial fractions, trig integrals
Area, volume, arc length, accumulation functions
Slope fields, separable equations, Euler's method, logistic growth
Parametric equations, polar coordinates, vector-valued functions
Convergence tests, power series, Taylor & Maclaurin series
AP Calculus is two exams sharing most of one syllabus. Choosing between them, and knowing which units are shared, decides how you use these chapters.
BC covers everything AB covers and adds material — parametric and polar calculus, further integration techniques, and infinite series. The shared units are examined at the same standard on both papers. So a student on BC is not doing "harder limits"; they are doing the same limits plus more topics. If you are on AB, the later units here are enrichment rather than syllabus.
The unit order is not arbitrary. Limits underpin the definition of the derivative; the derivative underpins the Fundamental Theorem; the Fundamental Theorem underpins everything in integration. Students who jump to integration techniques because that is what the next test covers tend to be the ones who cannot explain why a substitution is allowed — and that gap shows up on the free-response section, where the reasoning earns marks.
Worked examples teach the method; past free-response questions teach what the examiner wants written down. These are not the same skill. On the free-response section, marks are awarded for setup and for the steps, so a correct answer with no visible work scores a fraction of what it should. Finish a chapter, then do the corresponding questions from a released paper and mark yourself against the published scoring guidelines.