AP Calculus BC

Limits and Continuity

• Defining Limits and Using Limit Notation
• Estimating Limit Value from Graphs
• Determining Limits Using Algebraic Manipulation
• Exploring Types of Discontinuities
• Defining Continuity at a Point
• Removing Discontinuities
• Connecting Infinite Limits and Vertical Asymptotes
• Connecting Limits at Infinite and Horizontal Asymptotes
• Working with the intermidiate Vale Theorem (IVT)

Differentiation: Definition and fundamental properties

• Defining Average and Instantaneous Rates of Change at a Point
• Defining the Derivative of a Function
• Connecting Differentiability and Continuity
• Applying Power Rule
• Derivative of cos x, sin x, exp(x) and lnx
• The Product Rule
• The Quotient Rule
• Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Differentiation: Composite, implicit, and inverse functions

• The Chain Rule
• Implicit Differentiation
• Differentiating Inverse Functions
• Diffrentiating Inverse Trigonometric Functions
• Calculating Higher Order Derivatives

Contextual applications of differentiation

• Interpreting the meaning of the Derivative in Context
• Linear Approximation
• Straight Line Motion
• Introduction to Related Rates problems
• Using L’Hospital’s Rule for determining limits

Analytical applications of differentiation

• Using Mean Value Theorem
• Determining intervals on which a function is increasing or decreasing
• Using the First Derivative test to determine relative Extrema
• Test to determine Absolute Extrema
• Determine the Concavity
• Using the Second Derivative Test to Determine Extrema
• Sketching Graphs of Functions and their Derivatives
• Solving Optimization Problems 

Integration and accumulation of change

• Approximating Areas with Remann Sums
• Applying Properties of Definite Integrals
• Interpreting the behavior of Accumulation Functions Involving Area
• Selecting Techniques for Anti-differentiation
• Additional techniques of integration

Differential equations

• Modeling Situations with Differential Equations
• Verifying Solutions for Differential Equations
• Sketching Slope Fields
• Reasoning Using Slope Fields
• Finding General Solution Using Separation of Variables
• Finding Particular Solutions using initial conditions
• Exponential Models with Differential Equations
• Euler’s method and logistic models with differential equations

Applications of integration

• Finding the Average Value of a Function on an Interval
• Connecting Position, Velocity, and Acceleration using integral
• Finding the Area between Curves
• Volumes with Cross Sections: Squares and Rectangles
• Volumes with Cross Sections : Triangles and Semicircles
• Volume with Disc Method
• Volume with Washer Method
• Arc length and distance traveled along a smooth curve

• Parametric equations, polar coordinates, and vector-valued functions

• Infinite sequences and series