# AP Calculus AB Curriculum Map

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```							                                                         AP Calculus AB Curriculum Map
Freeport Public Schools

Time              Topics                                                          Skills
Line                                                    (Use of graphing calculator is required on a regular basis)
Students will:
First         Pre-Calculus     • Simplify expressions containing absolute value
Quarter                        • Graph: a) y = l f (x) l
Limits                      b) y = F l x l
Derivative       • Solve absolute value equations
• Graph and solve F (x) s a
• Graph and solve lF (x) l s a
• Determine whether a function is odd, even or neither
• Determine which, if any, symmetries a relation has
• Find limits of a function algebraically, graphically, and numerically
• Determine whether or not a function is continuous
• Be able to graph functions
• Find the derivative of a function using the definition
• Be able to find derivative graphically, algebraically, and numerically
• Be able to use the calculator to evaluate derivatives numerically
• Be able to do velocity problems algebraically and graphically
• Apply the chain rule
• Find the equation of a line tangent to the curve
• Find the equation of a line that best approximates the curve

Second        Application of   •   Find the global and local extreme of a function
Quarter       Derivatives      •   Be able to do application of Rolle’s and mean value theorem
•   Be able to graph derivative given, function, and graph function given derivative
Integration      •   Be able to determine where a function is increasing and decreasing
•   Be able to determine the concavity of a function and its points of inflection
•   Do related rates and problems
•   Be able to do initial condition problems
•   Use the right approximation method and left approximation method
•   Make a connection between differential and integral calculus
•   Find antiderivative of appropriate functions
•   Be able to do velocity problems

AP Calc AB 09-10.doc                                                                                                  FPS 2009-2010
Page1
AP Calculus AB Curriculum Map
Freeport Public Schools

Time              Topics                                                           Skills
Line                                                     (Use of graphing calculator is required on a regular basis)
Students will:
Third         Integration
Quarter                        •   Find the approximation to an integral by using trapezoidal rite
Application of   •   Find area using integrals
Integration      •   Find volume
•   Find derivative of natural log
Functions        •   Integrate with ⊥
•   Differentiate and integrate with e
•   Do exponential growth and decay problems
•   Find derivatives and integrals of “a”
•   Be able to differentiate inverse trig functions and do antiderivative problems with inverse trig in answer
•   Know when and how to use L’Hospital’s rule in a limit problem
•   Be able to find the derivative of the inverse of a function without finding the inverse

Fourth        Review           •   Be able to do Part I questions with and without a calculator
Quarter                        •   Be able to do Part II with and without calculator

Final Exam

AP Calc AB 09-10.doc                                                                                                                           FPS 2009-2010
Page2

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