AP Calculus - AB Syllabus Course Overview Textbook(s ...

Course OutlineIntroduction to Calculus (1 week)A. An intuitive approach to calculus will be developed using the classic motion problemviewed from several approaches.1. Finding speed from the position (the derivative)2. Finding distanced traveled from the speed (the integral)3. Understanding the relationship between the two processes (Fundamental Theorem ofCalculus)Unit 1: Limits and Continuity (3 - 4 weeks)A. Rates of Change1. Average Speed2. Instantaneous SpeedBefore beginning a formal look at limits, students will develop an intuitive sense of limits by exploringdiscontinuities and asymptotes of functions using the graphing calculator. Students will use the zoomfeature or tables of values to verbally explain the behavior of the graph as it approaches certain points.B. Limits at a Point1. 1-sided Limits2. 2-sided Limits3. Sandwich TheoremC. Limits involving infinity1. Asymptotic behavior (horizontal and vertical)2. End behavior models3. Properties of limits (algebraic analysis)4. Visualizing limits (graphic analysis)D. Continuity1. Continuity at a point2. Continuous functions3. Discontinuous functionsa. Removable discontinuity (0/0 form)b. Jump discontinuity (We look at y = int(x).)c. Infinite discontinuityE. Rates of Change and Tangent Lines1. Average rate of change2. Tangent line to a curve3. Slope of a curve (algebraically and graphically)4. Normal line to a curve (algebraically and graphically)5. Instantaneous rate of changeUnit 2: The Derivative (5 - 6 weeks)A. Derivative of a Function1. Definition of the derivative (difference quotient)2. Derivative at a Point3. Relationships between the graphs of f and f’4. Graphing a derivative from data