AP Calculus

AP Calculus AB Syllabus

 

Instructor:  Cassie Skaggs

Time:  5th and 6th periods ( 11:45 – 2:00)

Textbook: Calculus Larson, Hostetler, Edwards 7th edition *Most material used in the class will come from Master Math Mentor and worksheets provided by A+ College Ready.

Course Overview

This course covers every concept in the Calculus AB topic outline as it appears in the AP Calculus Course Description n, including integration by-parts and finding volume of revolved regions using the shell method.  Students enter this course knowing that it will be challenging and they are expected to work together to solve problems and communicate about calculus concepts.  We will explore concepts verbally, numerically, analytically and graphically.

We will meet at least 4 hours each month outside of class time for extra help.  There are 2 study sessions and 1 mock exam on weekends that students are strongly encouraged to attend.

Course Planner

Unit1: Precalculus Review (1 week)

  1.  Basic Function sand Domain, Range, and Symmetry
  2. Families of functions
  3. Vertical and Horizontal Asymptotes, Holes and End Behavior
  4. Piecewise Functions
  5. Trig Functions and Unit Circle
  6. Appropriate window for a graph on a graphing calculator

Unit 2:  Limits and Continuity (2 weeks)

  1.  Graphical Limits
  2. Limits at a point algebraically
  3. Limits involving infinity algebraically
  4. Limits of piecewise functions graphically and algebraically
  5. Use of table feature of graphing calculator to determine limits
  6. Continuity graphically and as defined by limits

Unit 3:  The Derivative (2 weeks)

  1.  Definition of Derivative
  2. Differentiability and continuity
  3. Derivatives of polynomial functions using the power rule
  4. Product and quotient Rules
  5. Derivatives of trigonometric, exponential and logarithmic functions
  6. The chain rule
  7. Applications to velocity and acceleration

Unit 4:  Applications of the Derivative part 1 (3 weeks)

  1.  Implicit Differentiation
  2. Derivative of inverse trigonometric functions
  3. Logarithmic differentiation and derivative of a”
  4. Related Rates

Unit 5:  Applications of the Derivative Part 2 (2 weeks)

  1.  Analysis of graphs using the first and second derivatives
    1.  Local and Global Extrema
    2. Intervals of increasing and decreasing
    3. Points of inflection
    4. Intervals of concavity
  2.  Making the connections betwe4en f, f