Explore differential and integral calculus across all ten BC units, from limits and derivatives to parametric and polar curves, vector-valued functions, and infinite series.
At a glance
Connect the AB foundation to the full BC curriculum
BC develops the differential and integral calculus shared with AB, then extends the methods and the kinds of functions students can analyze. Lessons connect symbolic calculations with graphs, tables, models, and written explanations. Students learn to select a method, state its conditions, and check whether the result makes sense.
Units 1–8 build the shared calculus foundation and introduce additional BC methods. Units 9–10 focus on curves described in different forms and on infinite sequences and series.
Bring confidence with algebra, factoring, rational expressions, exponents, logarithms, function composition and inverses, and radian trigonometry. Work comfortably with equations, graphs, tables, and coordinate geometry. Familiarity with sequences, parametric descriptions, and polar coordinates also helps prepare for BC’s later units.
The additional methods include integration by parts, linear partial fractions, improper integrals, Euler approximations, logistic models, and arc length. BC also analyzes parametric and polar curves, vector-valued motion, convergence, Taylor approximations, and power series.
Sessions follow the student’s current unit and strengthen earlier ideas that the new work depends on. We connect a concept to a worked example, compare methods, and ask students to explain the conditions behind their choices. Calculator-supported investigation is paired with exact work and written justification.
