The curriculum for AP Calculus (AB level) is taught in this course.  Students enrolled in this course are encouraged to take the AP Calculus exam at the end of the course.  The prerequisite for this course is a minimum of a B average in Precalculus/IB Methods 11 or IB Higher Level 11.

Learning Objectives
    The student will:
        Demonstrate the following skills
 

Properties of elementary functions
    The student will:
        Define and apply the properties of elementary functions, including algebraic, trigonometric, exponential, and composite functions and their inverses, and graph these functions using a graphing calculator.  The properties of functions will include:
              Domains
              Ranges
              Combinations odd even
              Periodicity
              Symmetry
              Asymptotes
              Zeros
              Upper and lower bounds
              Intervals where the function is increasing or decreasing

Properties of limits of functions
    The student will:
        Define and apply the properties of elementary functions. This will include limits of a constant, sum, product, quotient, one-sided limits, limits at infinity, infinite limits, and non-existent limits.
            *AP calculus BC will include the rigorous definitions of a limit.

Continuity
    The student will:
        State the definition of continuity and determine where a function is continuous or discontinuous.
          This will include:
              Continuity at a point.
              Continuity over a closed interval.
              Application of the Intermediate Value Theorem.
              Graphical interpretation of continuity and discontinuity.

Derivatives
    The student will:
        Find the derivative of an algebraic function by using the definition of a derivative.
          This will include:
              Investigate and describe the relationship between differentiability and continuity.
        Apply formulas to find the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses.
        Apply formulas to find the derivative of the sum, product, quotient, inverse, and composite (chain rule) of elementary functions.
        Find the derivative of an implicitly defined function.
        Find the higher order derivatives of algebraic trigonometric, exponential, and logarithmic functions.

Logarithmic differentiation
    The student will:
        Use logarithmic differentiation as a technique to differentiate non-logarithmic functions.

Mean Value Theorem
    The student will:
        State (without proof) the Mean Value Theorem for derivatives and apply it both algebraically and graphically.

Derivatives
    The student will:
        Apply the derivative to solve problems.
          This will include:
              Tangent and normal lines to a curve.
              Curve sketching
              Velocity
              Acceleration
              Related rates of change
              Differentials and linear approximations
              Optimization problems

Indefinite integral
    The student will:
        Find the indefinite integral of algebraic, exponential, logarithmic, and trigonometric functions.
        Use special integration techniques of substitution (change of variables)
        Use integration by parts.
            *AP Calculus BC will also include integration by trigonometric substitution and integration by partial fractions (only linear factors in the denominator).

Properties of the definite integral
    The student will:
        Identify the properties of the definite integral.  This will include the Fundamental Theorem of Calculus and the definite integral as an area and as a limit of a sum
          *AP Calculus BC will include composite functions defined by integrals,

Definite integral
    The student will:
        Apply the definite integral to solve problems.  These problems will include:
            Finding distance traveled on a line and velocity from acceleration with initial conditions.
            Growth and decay problems.
            Solutions of separable differential equations.
            The average value of a function, area between curves.
            Volumes of solids of revolution about the axes or lines parallel to the axes using disc/washer and shell methods.
            Volumes of solids with known cross-sectional areas.
            *AP Calculus BC will also include areas bounded by polar curves.

Approximate value
    The student will:
        Compute an approximate value for a definite integral.  This will include numerical calculations using Riemann Sums and the Trapezoidal Rule.
            *AP Calculus BC will also utilize Simpson's Rule.