AP Calculus BC



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)

➢ Functions and Graphs

➢ Parametric Equations

➢ Solving Inequalities

➢ Solving Trigonometric equations

Chapter 2: Limits and Continuity (approx 10 days)

➢ Limits (at a point and at infinity)

➢ Continuity

➢ Tangent Lines

➢ Slope at a point on a curve

Chapter 3: Derivatives (approx. 15 days)

➢ Definition of the Derivative including various notations

➢ Existence of the Derivative

➢ Rules for Differentiation

➢ Chain Rule

➢ Implicit Differentiation

➢ Derivatives of Exponential and Logarithmic Functions

➢ 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)

➢ 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)

➢ 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)

Chapter 9: Infinite Series (approx 15 days)

➢ 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)

➢ 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.

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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