AP Calculus AB
Course Syllabus
Course Overview
Our primary textbook is Calculus: Early Transcendentals Brief Edition, 8th edition by Howard Anton,
Irl Bivens, and Stephen Davis (Anton Textbooks, Inc., 2005). We cover all of the topics in the
Calculus AB topic outline as it appears in the AP Calculus Course Description, as well as several other
topics such as integration by parts and the shell method. 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 AB
Section
Appendix A
CHAPTER 1
1.1
1.3
1.4
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
Trigonometry
FUNCTIONS
Functions
New Functions from Old
Families of Functions
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
5 days
13 DAYS
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10 DAYS
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29 DAYS
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14 DAYS
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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
8.7
CHAPTER 9
9.1
9.2
9.3
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 of a Function and Applications
PRINCIPALS OF INTEGRAL EVALUATION
Numerical Integration
DIFFERENTIAL EQUATIONS
1st Order Differential Equations and Applications
Slope Fields; Euler’s Method
Modeling with 1st Order Differential Equations
Timeline
20 DAYS
2 days
4 days
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3 days
1 day
2 days
24 DAYS
1 day
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3 days
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1 day
3 days
3 days
2 days
10 DAYS
2 days
5 days
1 days
1 DAY
1 day
6 DAYS
2 days
1 day
1 day
13 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 non-calculator sections.