COURSE OBJECTIVES:

Students will . . .

• understand and interpret the behavior of functions using a variety of techniques. These techniques include limits, derivatives, and integrals.
• apply their knowledge to functions that are described as equations, as graphs, as verbal/written descriptions, and as numerical data.
• use numerical, analytical, and graphical techniques to arrive at solutions. Students will understand when and how technology (specifically a graphing calculator) can be used to arrive at a solution and when the technology can be misleading.
• communicate their knowledge and solutions verbally, graphically (using the graphing calculator), and in written responses.

CONTENT TOPICS

• Understanding limits graphically and numerically (using the graphing calculator)
• Understanding limits algebraically
• Limits involving infinity
• Asymptotes algebraically, graphically (using the graphing calculator), and as a limit
• Understanding continuity graphically (using the graphing calculator) and analytically
• Intermediate value theorem; extreme value theorem
• Rates of change
• Tangent, secant, and normal lines
• Defining the derivative as a limit and as the instantaneous rate of change
• Derivative at a point using the limit definition and “nDeriv” (using the graphing calculator)

CONTENT TOPICS

• The derivative function using the limit definition and graphically (using the graphing calculator and “nDeriv”)
• Finding the derivative from a graph or a table
• When the derivative doesn’t exist
• Continuity and differentiability
• Powers and polynomials
• Product and quotient rules
• Applying the rules to tangents
• Velocity and acceleration
• Trigonometric derivatives
• Chain rule
• Exponential and logarithmic derivatives
• Inverse trigonometric derivatives
• Implicit derivatives

CONTENT TOPICS

• Mean value theorem
• L’Hopital’s Rule; revisiting asymptotes
• Connecting 1^st and 2^nd derivatives with the graph of the function (using the graphing calculator)
• A closer examination of velocity and acceleration
• Discovering optimization
• Optimization and modeling techniques
• Related Rates
• Local linearity graphically (using the graphing calculator) and analytically

CONTENT TOPICS

Students are introduced to power functions and their characteristics. Students learn to write power functions, using direct and inverse variations, and also use power functions to model real world applications and solve for the created equations.

• Estimating area and volume
• Estimating the definite integral (Riemann sums and Trapezoidal rule)
• Applying and interpreting the definite integral
• Antiderivatives
• The exact value of a definite integral analytically (using anti-derivatives) and graphically (using the graphing calculator and “fnInt”)
• Fundamental theorem of calculus
• u-Substitution

CONTENT TOPICS

• Value and average value
• Growth and decay
• Differential equations
• Slope fields
• Growth and decay revisited
• Areas a
• Linear motion revisited
• Volume by known cross sections
• Volume by disk and washer methods

The AP Calculus AB exam is given in early May.