Course description
What students will do
This is Semester I of a two-semester AP Calculus BC sequence. It builds a rigorous, exam-ready command of limits, derivatives, and the beginnings of integration, with emphasis on conceptual understanding rather than mechanical procedure.
Instruction draws on a Berkeley graduate background in applied mathematics and data science. Students work through limits and continuity, then differentiation rules and their applications—related rates, optimization, and curve sketching—before turning to accumulation: Riemann sums, the definite integral, and the Fundamental Theorem of Calculus.
Students also practice free-response strategy and timed problem sets to build the stamina and precision the AP exam rewards. Small-group discussion helps surface misconceptions before they compound—particularly important in BC, where Semester II leans hard on the derivative and integral fluency established here. Semester II is coming soon; the topics it covers are outlined below.
Semester I · This course
Limits, Derivatives & Intro to Integration
- Limits and continuity
- Derivatives: rules, implicit differentiation, and the chain rule
- Applications: related rates, optimization, curve sketching
- Introduction to integration: Riemann sums, the definite integral, and the Fundamental Theorem of Calculus
Semester II Coming soon
Advanced Integration, Series & Polar/Parametric
- Advanced integration techniques: integration by parts, partial fractions, improper integrals
- Sequences and series: convergence tests, Taylor and Maclaurin series
- Polar and parametric relations, including vector-valued functions
AP Calculus BC Semester II is coming soon. Contact Bayview to be added to the interest list and hear first when dates are announced.
Who this is for
Students currently taking or preparing for AP Calculus BC who want a deeper conceptual foundation and stronger exam readiness. AB students are also well served—Semester I covers the AB core.