CURRICULUM:     The Ontario Curriculum Grades 11 and 12: Mathematics 2007

AP Calculus AB program.

TEXT:                    Calculus Graphical, Numerical, Algebraic; Finney, Demana, Waits, Kennedy

COURSE

DESCRIPTION:     This is a university-level course in Differential and Integral Calculus, equivalent to one semester of Calculus at most universities. The AP Calculus course is designed to develop the student’s understanding of the concepts of Calculus and to provide experience with its methods and applications. The course emphasizes a multi-representational approach to Calculus with concepts, results, and problems expressed geometrically, algebraically, numerically, analytically, and verbally. Successful completion of the AP Calculus Course also provides the student with an MCB4UI credit.   Math is a subject that builds upon itself; attending class, being on time, and participating in class are not only essential for good progress, but are sometimes essential for survival of the class.  Unexcused absences result in no make up for the work.

EVALUATION:    70% is based on tests, quizzes, assignments.

                         30% is based on the summative assessment, which includes the June exam.

                          AP Credit is solely based on a successful 3.25 hour exam.

 AP Books            KAPLAN AP Calculus  AB and BC 2008   (required Chapters)

                              Harcourt Brace Calculus  (ISBN: 0-15-601556-0)  (optional)
 

OUTLINE

C1       Pre-Calculus (Summer) 8 lessons                 

             C1.1    Functions

            C1.2    Linear Equations

            C1.3    Parametric Equations

            C1.4    Factor and Remainder Theorem

            C1.5    Trigonometric Functions

            C1.6    Exponential Equations

            C1.7    Logarithmic Functions

            C1.8    Geometry and Similar Triangle

C2       Limits and Continuity                        7 lessons        

             C2.1    Rate of Change and Limits

            C2.2    Indeterminate Forms

            C2.3    Limits involving Infinity

            C2.4    Continuity

            C2.5    Rates of Change and Tangent Lines

            C2.6    Epsilon and Delta

            C2.7

C3       Derivatives                                         16 lessons      

             C3.1    Limit Definition of Derivative

            C3.2    Differentiability

            C3.3    Power Rule

            C3.4    Proof of Power Rule

            C3.5    Chain Rule

            C3.6    Product Rule

            C3.7    Proof of Product Rule

            C3.8    Quotient Rule

            C3.9    Proof of Quotient Rule

            C3.10  Velocity and Acceleration

            C3.11  Derivatives of Trigonometric Functions

            C3.12  Derivatives of Inverse Trigonometric Functions

            C3.13  Derivatives of Exponential and Logarithmic Functions

C3.14  Implicit Differentiation

            C3.15  Review

            C3.16  Review            

C4       Applications                                        14 lessons      

             C4.1    Extreme Values of Functions

            C4.2    Mean Value Theorem

            C4.3    Connecting  and  with and graphing (1) – Large Lesson

            C4.4    Connecting  and  with and graphing (2)

            C4.5    Connecting  and  with and graphing (3)

            C4.6    Optimization (1)

            C4.7    Optimization (2)

            C4.8    Optimization (3)

            C4.9    Linearization and Newton’s Method

            C4.10  Estimating Change and Rolle’s Theorem

            C4.11  Related Rates (1)

            C4.12  Related Rates (2)

            C4.13  Related Rates (3)

            C4.14  Review

C5       The Definite Integral                         14 lessons      

             C5.1    Estimating with Finite Sums

            C5.2    Riemann Sums

            C5.3    Definite Integrals

            C5.4    Definite Integrals and Antiderivatives (1)

            C5.5    Definite Integrals and Antiderivatives (2)

            C5.6    Definite Integrals and Antiderivatives (3)

            C5.7    Fundamental Theorem of Calculus (1)

            C5.8    Fundamental Theorem of Calculus (2)

            C5.9    Fundamental Theorem of Calculus (3)

            C5.10  Trapezoidal Rule

            C5.11  Simpson’s Rule

            C5.12  Review (1)

            C5.13  Review (2)

            C5.14  Review (3)

C6       Differential Equations and Modelling                      12 lessons      

             C6.1    Slope Fields (1)

            C6.2    Slope Fields (2)

            C6.3    Integration by Substitution (1)

            C6.4    Integration by Substitution (2)

            C6.5    Integration by Parts (1)

            C6.6    Integration by Parts (2)

            C6.7    Exponential Growth and Decay

            C6.8    Population Growth

            C6.9    Numerical Methods

            C6.10  Review

            C6.11  Review

            C6.12  Review

C7a     Applications of Definite Integrals                 7 Lessons      

             C7.1    Integral as Net Change

            C7.2    Areas in the Plane (1)

            C7.3    Areas in the Plane (2)

            C7.4    Volumes (1)

            C7.5    Volumes (2)

            C7.6    Volumes (3)

            C7.7    Review

 Practice exams           2 Weeks

 AP EXAM

The following units are for the AP Calculus BC Program

C7b     Applications of Definite Integrals                 4 Lessons

           C7.7    Lengths of Curves

C7.8    Applications from Science and Statistics (1)

            C7.9    Applications from Science and Statistics (2)

            C7.10  Review

C8       4 lessons

C9       5 lessons

C10     6 lessons