AP Calculus BC

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AP Calculus BC

Prerequisites
AP Calculus AB with a “C” or above
               OR
Honors Precalculus with an “A” AND Teacher Recommendation

Textbooks
– Finney, Demana, Waits, Kennedy (2011). Calculus: Graphical, Numerical, Algebraic. 4th Ed.:
   Pearson/Prentice Hall
– Barron’s AP Calculus, 11th Ed. (2012)

Course Description
In AP Calculus BC, students study functions, limits, derivatives, and integrals as well as
sequences, series, and vectors. Throughout the course students write and work with functions
represented by written descriptions, mathematical rules, graphs and tabular data. Throughout the
course, students are develop and exercise skills using the graphing calculator to solve problems,
experiment, interpret their results, and support their conclusions. Students learn the meaning of
the derivative and apply it to a variety of problems, while developing a deeper understanding of
the meaning of the solutions to those problems. Students study integrals and learn the
relationship between the derivative and the definite integral, using written work and graphing
technology to explore and interpret this relationship. Students learn how calculus is used to
model real-world phenomena by using functions, differential equations, integrals, and graphing
technology to solve problems, support their solutions, and interpret their findings. AP Calculus
BC is the equivalent of an introductory college-level calculus course and prepares students for
the AP Exam and further studies in science, engineering, and mathematics.

Course Content
Course content is directly in line with College Board’s Topic Outline for Calculus BC
– Prerequisites for Calculus
      – Linear, polynomial, exponential, logarithmic, and trigonometric functions
      – Parametric equations
– Limits and Continuity
– Derivatives and their Applications
     – Basic differentiation rules
     – Implicit differentiation
     – Derivatives of exponential, logarithmic, trigonometric, and inverse trigonometric functions
     – Velocity and rate of change
     – Extreme values of functions
     – Modeling and optimization
     – Linearization and differentials
     – Related rates
– Integrals and their Applications
     – Rectangular and trapezoidal approximations
     – Definite integrals and area
     – Fundamental Theorem of Calculus
     – Net change
     – Area, volume, and lengths of curves
     – Integrals in science and statistics
– Differential Equations and Mathematical Modeling
     – Slope fields and Euler’s Method
     – Integration by substitution and by parts
     – Exponential growth/decay and logistic growth
– Sequences, L’Hopital’s Rule, and Improper Integrals
– Infinite Series
– Parametric, Vector, and Polar Functions