# AP® Calculus AB Course Syllabus

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```					       AP® Calculus AB Course Syllabus

Course Overview

year of work in calculus and related topics comparable to courses in
colleges and universities. It is expected that students who take an AP course
in calculus will seek college credit or placement, or both, from institutions
of higher learning." * Taken from the Advanced Placement Course

Students taking AP Calculus AB will experience a college level calculus
course. Students are required to take the AP Exam in the spring. Students
will be expected to demonstrate their understanding of the concepts
graphically, numerically, analytically and verbally. Graphing Calculators
are essential in this course. Students will be given a summer packet
reviewing and/or reinforcing pre-calculus skills necessary for success in AP
Calculus with an assessment during the first week of classes.

Topics to be covered are dictated by the AP syllabus provided by the
College Entrance Examination Board. They include: Functions and Graphs,
Limits and Continuity, Differential Calculus, and Integral Calculus.

Primary Text:

Foerster, Paul A. Calculus: Concepts and Applications. 1 st ed. Berkeley:
Key Curriculum Press, 1998.

Supplemental Resources:

Technology Use:
Graphing Calculators ( TI-83+ or equivalent)
Excel
Course Outline:

Ch 1: Limits, Derivatives, Integrals ( weeks)
In this unit students are introduced to the concepts of limits, derivatives and
integrals.
• The Concept of Instantaneous Rate
• Rate of Change by Equation, Graph, or Table
• One Type of Integral of a Function
• Definite Integrals by Trapezoids, from Equations and Data
• Limit of a Function

Ch 2: Properties of Limits
The Limit Theorems (briefly)
Continuity
Limits Involving Infinity
The Intermediate Value Theorem and Its Consequences

Ch 3: Derivatives, Antiderivatives, and Indefinite Integrals
Difference Quotients, and One Definition of Derivative
Derivative Functions Numerically and Graphically
Derivative of the Power Function, and Another Definition of Derivative
Displacement, Velocity, and Acceleration
Introduction to Sine, Cosine, and Composite Functions
Derivatives of Composite Functions - The Chain Rule
Derivatives of Composite Functions - The Chain Rule
Proof and Application of Sine and Cosine Derivatives
Antiderivatives and Indefinite Integrals

Ch 4: Products, Quotients, and Parametric Functions
Derivative of a Product of Two Functions
Derivative of a Quotient of Two Functions
Derivatives of the Other Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Differentiability and Continuity
Graphs and Derivatives of Implicit Relations

Ch 8: The Calculus of Plane and Solid Figures, Part 1
Critical Points and Points of Inflection
Maxima and Minima in Plane and Solid Figures
Ch 5: Definite and Indefinite Integrals
Review of Antiderivatives; Linear Approximations and Differentials
Formal Definition of Antiderivative and Indefinite Integral
Formal Definition of Antiderivative and Indefinite Integral
Riemann Sums, and the Definition of Definite Integral
Riemann Sums, and the Definition of Definite Integral
The Mean Value Theorem and Rolle's Theorem
The Mean Value Theorem and Rolle's Theorem
The Fundamental Theorem of Calculus
Definite Integral Properties and Practice
A Way to Apply Definite Integrals
Numerical Integration by Simpson's Rule and Calculator

Ch 6: The Calculus of Exponential and Logarithmic Functions
Antiderivative of the Reciprocal Function
Natural Logarithms, and Another Form of the Fundamental Theorem
Derivatives of Exponential Functions - Logarithmic Differentiation
The Number e, and the Derivative of Base b Logarithmic Functions
The Natural Exponential Function, the Inverse of ln
Limits of Indeterminate Forms - L'Hospital's Rule
Derivative and Integral Practice for Transcendental Functions

Ch 7: The Calculus of Growth and Decay
Exponential Growth and Decay
Other Differential Equations For Real World Applications
Slope Fields

Ch 8: The Calculus of Plane and Solid Figures, Part 2
Area of a Plane Region
Volume of a Solid by Plane Slicing
Volume of a Solid of Revolution by Cylindrical Shells

Motion & Average Functions

Related Rates

AP Practice Exams
Remainder of Course - Projects

Teaching Strategies:
Collaboration
Use of graphing calculators
Exploration sheets provided with student text
Mini-Labs
Projects

Sample Student Activities:
Blog
Ball Bounce
Reimann sums
Mystery Curve
Final Project
Etc….
Assignments and Assessments

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