AP Calculus BC Topical Overview

1^st 9 weeks:

This term will primarily be a review and extension of concepts treated in AB; including the topics listed:

limits, continuity

l’Hopital’s Rule

definitions/interpretations of the derivative

differentiability

derivative rules

hyperbolic functions

linearization

Mean Value Theorem

relationship of derivatives and function

optimization

related rates

parametric equations

2^nd 9 weeks:

This term will include a review of integration rules and applications studied in AB with advanced techniques as listed:

definite integral and interpretations

Fundamental Theorem of Calculus

constructing antiderivatives

integration using substitution

integration by parts

integral tables

trigonometric substitutions

numerical approximations for integrals

approximation error

improper integrals and comparisons

area/volume

polar coordinates, functions

polar area

arc length

work and fluid force

3^rd 9 weeks:

This term will complete the BC content topics tested on the AP exam.

sequences

geometric series

convergence/divergence

tests for convergence

power series and intervals of convergence

Taylor polynomials

Taylor series

Lagrange Error Bound

differential equations

slope fields

Euler’s Method

growth/decay models

logistic models

4^th 9 weeks:

This term will be a 3-week review for the BC Calculus AP exam followed by independent investigations into mathematical modeling techniques and applications of mathematics.