AP Calculus BC
Course Syllabus
Course Overview
Our primary textbook is Calculus: Early Transcendentals Single Variable, 8th edition by Howard Anton, Irl
Bivens, and Stephen Davis (John Wiley & Sons, Inc., 2005). We cover all of the topics in the Calculus BC
topic outline as it appears in the AP Calculus BC Course Description. The two main objectives of the course
are that students do well on the AP Exam and that they are prepared to succeed in future math courses. There is
a focus on creating a balance of understanding, skills, and the use of technology.
Course Planner
AP Calculus BC
Section
CHAPTER 1
1.1
1.3
1.4
Appendix A
1.5
1.6
1.8
CHAPTER 2
2.1
2.2
2.3
2.5
2.6
CHAPTER 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
CHAPTER 4
4.1
4.2
4.3
4.4
Topics
Timeline
FUNCTIONS
Functions
New Functions from Old
Families of Functions
Trigonometry Review
Inverse Functions
Exponential and Logarithmic Functions
Parametric Equations
LIMITS AND CONTINUITY
Limits (intuitively)
Computing Limits
Computing Limits: End Behavior
Continuity
Continuity of Trig & Inverse Functions
THE DERIVATIVE
Tangent Lines, Velocity, and General Rates of Change
The Derivative Function
Techniques of Differentiation
The Product and Quotient Rules
Derivatives of Trig Functions
The Chain Rule
Related Rates
Local Linear Approximation
EXPONENTIAL, LOGARITHMIC, & IVERSE
TRIGONOMETRIC FUNCTIONS
Implicit Differetiation
Derivatives of Logarithmic Functions
Derivatives of Exponential and Inverse Trig Functions
L’Hopital’s Rule
8 DAYS
1 day
1 day
1 day
1 day
1 day
1 day
1 day
12 DAYS
1 day
1 day
2 days
1 day
3 days
21 DAYS
1 day
3 days
2 days
1 day
2 days
3 days
3 days
2 days
10 DAYS
2 days
2 days
2 days
1 day
Section
CHAPTER 5
5.1
5.2
5.3
5.4
5.5
5.7
5.8
CHAPTER 6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
CHAPTER 7
7.1
7.2
7.6
CHAPTER 8
8.2
8.5
8.7
8.8
CHAPTER 9
9.1
9.2
9.3
CHAPTER 10
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
CHAPTER 11
11.2
11.3
AP EXAM
REVIEW
Topics
THE DERIVATIVE IN GRAPHING AND
APPLICATIONS
Analysis of Functions I
Analysis of Functions II
More on Curve Sketching
Absolute Maxima and Minima
Applied Max and Min Problems
Rolle’s Theorem; Mean-Value Theorem
Rectilinear Motion
INTEGRATION
The Area Problem
The Indefinite Integral
Integration by Substitution
Sigma Notation; Area as a Limit
The Definite Integral
The Fundamental Theorem of Calculus
Rectilinear Motion and Average Value
Evaluating Definite Integrals by Substitution
APPLICATIONS OF THE DEFINITE INTEGRAL IN
GEOMETRY
Area Between Two Curves
Volumes by Slicing; Disks and Washers
Average Value
PRINCIPALS OF INTEGRAL EVALUATION
Integration by Parts
Integration using Partial Fractions
Numerical Integration
Improper Integrals
DIFFERENTIAL EQUATIONS
1st Order Differential Equations and Applications
Slope Fields; Euler’s Method
Modeling with 1st Order Differential Equations
INFINITE SERIES
Sequences
Monotone Sequences
Infinite Series
Convergence Tests
The Comparison, Ratio, and Root Tests
Alternating Series; Conditional Convergence
Maclaurin and Taylor Polynomials
Maclaurin and Taylor Series; Power Series
Differentiating and Integrating Power Series
ANALYTIC GEOMETRY IN CALCULUS
Tangent Lines for Parametric and Polar Curves
Area in Polar Coordinates
Timeline
19 DAYS
2 days
3 days
3 days
1 day
2 days
1 day
2 days
19 DAYS
1 day
1 day
2 days
2 days
1 day
3 days
2 days
2 days
9 DAYS
1 day
4 days
1 day
6 DAYS
2 days
1 day
1 day
1 day
6 DAYS
2 days
2 days
1 day
14 DAYS
1.5 days
1.5 days
1 day
1 day
2 days
1 day
1 day
2 days
1 day
3 DAYS
2 days
1 day
12 days
Technology
A TI-83 or TI-83 plus graphing calculator is required for this course. Students learn how to use their calculators
to solve problems, interpret results, and support conclusions. For example, students use their calculators to
evaluate definite integrals, to approximate unfamiliar irrational answers, or to graphically confirm conclusions
they reached on paper algebraically.
Teaching Strategies
I try to establish a classroom atmosphere where the students see me as their coach. We work together towards
the common goal of doing well on the AP Exam. I try to help them see deeper mathematical connections by
stressing four different approaches to topics – graphical, numerical, analytical, and verbal. I feel that
understanding these connections is the key to understanding Calculus. As far as the verbal component is
concerned, I often have questions on assignments, tests, and quizzes where students must explain concepts or
solutions by writing in full sentences. I often have students working together in small groups (especially on
large review assignments) where I encourage discussion and explanation of procedures and solutions. I spend a
considerable amount of time going over previous AP Exams so students become familiar with the question
types and the grading methods.
Student Evaluation
Quarter grades are computed using homework, quizzes, and tests as individual categories. Each quarter grade
represents 40 percent of the semester grade with the final exam representing the remaining 20 percent.
Homework is generally graded based on effort with the exception of review assignments where students are
strongly encouraged to use one another as resources. Quizzes and tests often have both calculator and noncalculator sections.