AP Calculus BC
Syllabus: St Joseph High School, Metuchen NJ 08840
Course Planner
Primary Textbooks
Finney, Ross L., Franklin Demana, Bert Waits, and Daniel Kennedy.
Calculus: Graphical, Numerical, Algebraic. Addison –Wesley.
Howard Anton.
Calculus with Analytic Geometry. Wiley
Review materials include
Multiple Choice and Free Response questions in Preparation for the AP Calculus (BC)
Examination. D&S Marketing Systems, Inc.
The sequence in which material is covered follows the sequence of chapters in the text,
Calculus: Graphical, Numerical, Algebraic.
A graphing calculator is used throughout the course although at times and on certain
assessments it is not allowed. The majority of students have Texas Instrument calculators
with the TI-89 becoming ever more the norm.
Chapter 1: Prerequisites for Calculus (approx. 5 days)
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Functions and Graphs
Parametric Equations
Solving Inequalities
Solving Trigonometric equations
Chapter 2: Limits and Continuity (approx 10 days)
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Limits (at a point and at infinity)
Continuity
Tangent Lines
Slope at a point on a curve
Chapter 3: Derivatives (approx. 15 days)
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Definition of the Derivative including various notations
Existence of the Derivative
Rules for Differentiation
Chain Rule
Implicit Differentiation
Derivatives of Exponential and Logarithmic Functions
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 Derivatives of Trigonometric and Inverse trigonometric Functions
Chapter 4: Applications of the Derivative (approx 15 days)
 Mean Value Theorem and Extreme Value Theorem
 Functional Analysis, increasing/decreasing, critical points, points of
inflection, and concavity
 Connecting a graph with its derivatives
 Optimization problems
 Linearization and Newton’s Method
 Related Rates
Chapter 5: The Definite Integral (approx 15 days)
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Sigma Notation
Rectangle Approximation Methods
Reimann sums and the Definite Integral
Definite Integrals and Antiderivatives
First Fundamental Theorem of Calculus
Trapezoidal Rule
Chapter 6: Differential Equations and Mathematical Modeling (15 days)
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Techniques of Integration
Integration by parts
Variable Separable differential equations
Euler’s Method
Slope Fields
Exponential Growth and Decay
Logistic growth
Chapter 7: Applications of the Definite Integral (approx. 15 days)
 Integral as Net Change
 Area, Volume (including Cylindrical Shells), Length of a Curve
 Work, Fluid Force
Chapter 8: L’Hopital’s Rule, Improper Integrals, Partial Fractions (approx 15 days)
 Indeterminate Forms and L’Hopital’s Rule
 Relative Rates of Growth
 Improper Integrals and Partial Fractions (revisited)
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Chapter 9: Infinite Series (approx 15 days)
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Geometric Series
Power Series
Taylor and Maclaurin Series
Lagrange Remainder
Tests for Convergence
o Divergence Test
o Integral test
o Comparison Test
o Ratio Test
o Root Test
o Limit Comparison Test
o Alternating Series test
o Ratio test for Absolute Convergence
 Radius and Interval of Convergence
Chapter 10: Parametric, Vector, and Polar Functions (approx 10 days)
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Parametric Functions, First and Second Derivatives
Length of a curve
Vector-Valued Functions
Polar Coordinates and Polar Graphs
Calculus of Polar Curves
Review for the AP Examination
The pacing of the material varies from class to class and from year to year but time
remains at the end of the year (approx 10 days) to review specifically for the examination
using the review book. Approximately six AP quality examinations are reviewed. The
students take this material in a variety of settings, stress-free and stress-full.
In the week prior to the examination the students take a “mock” AP examination to
familiarize them with the AP conditions.
Teaching Strategies
a. Topics are communicated using the rule of four, Numerically, Geometrically,
Symbolically, and Verbally.
b. Justifications and the “how” of solutions are expected. Students are required to
write responses in correct mathematical notation in order to validate their
responses.
c. The use of the calculator is strongly encouraged however at times it is removed
from the process.
d. Students are encourage to work on certain problems collaboratively.
e. “Extra” help sessions are available to students after school throughout the year.
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Assessment
Each chapter is assessed through corrected homework assignments, quizzes
(announced and unannounced) and in class tests, normally one per chapter.
Several weekend worksheet assignments are completed throughout the course of the
year.
At the mid point of the year an examination consisting of the first five chapters is
completed. At the end of the year a comprehensive final examination is given in the
form of a “Mock AP”
Note
My goal is to encourage a love of mathematic. I encourage questions and
investigation beyond the scope of the course. I encourage the students to answer the
“Why” and “How” of a solution, writing answers in correct mathematical notation.
Mathematics is a beautiful language of communication and I hope to develop this
skill among my students
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