AP® Calculus BC
Course Overview
Everything in the Calculus BC topic outline as it appears in the AP® Calculus Course
Description is covered in this course. The primary textbook is Calculus – Early
Transcendentals 8th Edition by Howard Anton, Irl Bivens and Stephen Davis. The goal
of this course is to prepare students for the AP Calculus BC exam in May.
Throughout the course, the instruction and development of the AP Calculus concepts
model the techniques (graphical, numerical, analytical and verbal) and emphasize the
connections among all types of representations. These same techniques and connections
are the focus of the AP examination and are reflected in assessment throughout the
course. Students are given examples of AP Free Response as well as Multiple Choice
questions in the form of in-class work, homework, quiz and test questions. Every test
includes both Multiple Choice and Free Response questions. Students discuss Calculus
orally through group work and in-class discussions.
Students are expected to know the graphs of basic functions (basic trig functions, e x ,
ln x, simple polynomials) and use their familiarity of the graphs’ properties in order to
applications. Students will be able to evaluate limits, differentiate, and integrate
polynomial, trigonometric, exponential and logarithmic functions. Students are held
accountable for the processes as well as the conceptual meaning behind limits,
derivatives and integration.
Technology
The TI-83 Plus graphing calculator will be used for presentations. Students will use either
a TI-83 or TI-84 graphing calculator. Students will use their calculators to graph, find
zeros and points of intersection, evaluate derivatives at a point, and evaluate definite
integrals.
Student Evaluation
Marking period grades are computed using homework, quizzes, and tests. All students are
expected to take the AP exam. Tests include questions that are modeled after the AP
Exam. Each test is comprised of a calculator and non-calculator part. Both parts contain
multiple-choice questions as well as free response questions.
Course Plan
Below is the sequence of topics covered in the AP Calculus BC course.
The following are covered extensively in Honors Analysis and are reviewed briefly via a
summer packet and at the beginning of the school year.
Review (Chapter 1)
 Real Numbers and the Coordinate Plane
 Lines and Linear Functions
 Polynomials and Rational Functions
 Algebra of Exponentials and Logarithms
 Parametric Functions
 Polar Functions (11.1)
 Graphs
 Trigonometric Functions
Topic Outline for Calculus BC
Limits and Continuity
(Chapter 2)
6 days
 Computing Limits
 Limits at Infinity and End Behavior
 Continuity
 Continuity of Trigonometric and Inverse Functions
The Derivative
(Chapter 3)
16 days
 Rates of Change and Tangent Lines
 The Derivative Function
 Techniques of Differentiation
 Product and Quotient Rules
 Derivatives of Trigonometric Functions
 The Chain Rule
 Derivatives of Parametric Equations (11.2)
 Derivatives of Polar Equations (11.2)
Derivatives of Logarithmic, Exponential and Inverse Trig Functions
8 days
 Implicit Differentiation
 Second Derivatives
 Derivatives of Logarithmic Functions
 Derivatives of Exponential and Inverse Trigonometric Functions
 L’Hopital’s Rule
(Chapter 4)
The Derivative in Graphing and Applications (Chapter 5)
20 days
 Related Rates (3.7)
 Local linearization (3.8)
 Analysis of Functions (Increase, Decrease, Concavity, Relative Extrema)
 Curve Sketching
 Absolute minima and maxima and applied problems
 Newton’s Method
 Mean-Value Theorem
Integration
(Chapter 6)
14 days
 Overview of Area Problem
 Indefinite Integral
 U-substitution
 Definition of Area as a Limit
 Definite Integral
 Fundamental Theorem of Calculus
Principles of Integral Evaluation (Chapter 8)
11 days
 Integration by Parts
 Trigonometric Integrals and substitutions
 Partial Fractions
 Simpson’s Rule (numerical integration)
 Improper Integrals
Applications of the Definite Integral
(Chapter 7)
15 days
 Area between Two Curves
 Volumes by Slicing: Disks and Washers
 Volumes by Shells
 Average value of a function on an interval
 Lengths of Curves (7.4 and 11.2)
 Area in Polar Coordinates (11.3)
Mathematical Modeling
(Chapter 9)
6 days
 First-Order Differential Equations
 Slope Fields and solving equations graphically
 Euler’s Method and solving equation numerically
 Modeling – Population Growth and logistic equations
Infinite Series
(Chapter 10)
24 days
 Sequences
 Infinites Series
 Convergence Tests
 Comparison, Ratio and Root tests
 p series tests
 Conditional Convergence
 Taylor Series
 Power Series
 LaGrange remainder
Review and preparation for AP Exam – Approximately 4 weeks
Done both individually and in groups. Exams given and analyzed.
Teacher Resources
Primary Textbook
Calculus – Early Transcendentals 8th Edition by Howard Anton, Irl Bivens and Stephen
Davis
Supplementary Texts:
Calculus, 8th Edition, Houghton Mifflin Company, 2006 by Ron Larson, Robert P.
Hostetler, and Bruce H. Edwards.
Calculus: Graphical, Numerical, Algebraic, Prentice Hall, 2003 by Ross L Finney,
Franklin D. Demana, Bert K. Waits and Daniel Kennedy.
Additional Resources
AP Calculus Course Description
AP Released Exams
Technology Resources
Students are required to have a graphing calculator. The TI-83 or TI-84 is recommended
for Calculus BC.