• Classroom Information
     
    I teach Advanced Placement Calculus AB, Advanced Placement Calculus BC, and Precalculus Regents.  Homework can be accessed on schoology.
     

    CALCULUS AB SYLLABUS

     Unit One:        Prerequisites for Calculus                                              

    1.3                  Exponential, Absolute Value Functions

    1.4                   Parametric Functions         

    1.5                   Functions and Logarithms

    1.6                  Trigonometric Functions

                           Compositions with Functions

    Review and Test                                                                  

     

    Unit Two:       Limits and Continuity

     2.1                  Rates of Change and Limits

                           Evaluate limits analytically, one-sided limits

                           Trig limits      

    2.2                   Limits Involving Infinity

                           Vertical Asymptotes

    2.3                   Continuity   

    2.4                   Rates of Change and Tangent Lines

                            Intermediate Value Theorem

     Review and Test                                                               

     

    Unit Three:    Derivatives

    3.1                  Derivative of a Function

    3.2                   Differentiability        

    3.3                   Rules for Differentiation

    3.4                   Velocity and other Rates of Change

    3.5                   Derivative of Trigonometric Functions

    3.6                   Chain Rule

    3.7                   Implicit Differentiation

    3.8                   Derivatives of Inverse Trig Functions

    3.9                   Derivatives of Exponential and Logarithmic Functions

    Review and Test                                                           

     

    Unit Four:      Applications of Derivatives

    4.1                   Extreme Values of Functions

    4.2                    Mean Value Theorem

    4.3                    Connecting f’ and f” with the graph of f

    4.4                    Modeling and Optimization

    4.5                    Linearization and Differentials

    4.6                    Related Rates

    Review and Test                                                           

     

     

    Unit Five:       The Definite Integral

    5.1                    Estimating with Finite Sums

    5.2                     Definite Integrals    

    5.3                     Definite Integrals and Antiderivatives

    5.4                     Fundamental Theorem of Calculus

    5.5                     Trapezoidal Rule

    Review and Test                                                                 

     

     Unit Six:         Differential Equations and Modeling      

    6.1                      Antiderivatives and Slope Fields

    6.2                      Integration by Substitution

    6.3                      Integration by Parts

    8.4                      Partial Fraction and Completing the Square

                               Solving Differential Equations

    6.4                      Population Growth

                               Exponential Model

                               Logistic Model

    Review and Test                                                                

     

     Midterm Review and Exam after  section 6.1                

     

     

    Unit Seven:  Applications of the Definite Integral

    7.1                   Integral as Net Change

    7.2                    Areas in the Plane

    7.3                    Volumes

                             Volume by Revolution (Disk, Washer, Shell)

                             Volume by Cross Section

    7.4                     Lengths of Curves

    7.5                     Applications from Science

    Review and Test                                                                  

     

    Unit Eight:     L’Hopital’s Rule and Improper Integrals

     8.1                    L’Hopital’s Rule                            

     

    Review for the AP Exam                                                    

     

     

    Course Overview

                This course is designed to cover all of the topics included in the Calculus AB topic outline as described in Calculus AB Course Description published by the College Board.  In addition, Formal Definition of Limit,  Integration by Parts, Integration by Partial Fractions, L’Hopital’s Rule, and Length of a Curve are also included.

                The objective of this course is to have students come away with a very strong understanding of calculus concepts, strong skills in the mechanics of calculus, and the ability to use available technology to make them successful in both future pursuits in their mathematical course work and on the Advanced Placement Exam.

     

    Textbook and  Resources

     

    Finney, Demana, Waits, and Kennedy.   Calculus- Graphical, Numerical, Algebraic.  Menlo Park: Scott Foresman-Addison Wesley, 1999, 1st Ed. 

    Lederman, David.  Multiple Choice and Free Response Questions in Preparation for the AP Calculus (AB) Examination.  D&S Marketing, 2003, 8th Edition.

    McMullin, Lin.  Teaching AP Calculus.   D&S Marketing, 2002.

    Released AP Exams 

    AP Calculus Course Description