AP Calculus AB Curriculum Map

							                                                         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