AP Calculus AB

Also covered in this plan

• Confirming Continuity over an Interval
• Removing Discontinuities
• Connecting Infinite Limits and Vertical Asymptotes
• Connecting Limits at Infinity and Horizontal Asymptotes
• Working with the Intermediate Value Theorem (IVT)
• Exam: Limits and Continuity
• Defining Average and Instantaneous Rates of Change at a Point
• Defining the Derivative of a Function and Using Derivative Notation
• Estimating Derivatives of a Function at a Point
• Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
• Applying the Power Rule
• Derivative Rules: Constant, Sum, Difference, and Constant Multiple
• Derivative Rules: Constant, Sum, Difference, and Constant Multiple
• Derivatives of cos x, sin x, e^x, and ln x
• The Product Rule
• The Quotient Rule
• Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
• Exam: Differentiation: Definition and Fundamental Properties
• The Chain Rule
• The Chain Rule
• Implicit Differentiation
• Differentiating Inverse Functions
• Differentiating Inverse Trigonometric Functions
• Selecting Procedures for Calculating Derivatives
• Selecting Procedures for Calculating Derivatives
• Calculating Higher-Order Derivatives
• Exam: Differentiation: Composite, Implicit, and Inverse Functions
• Interpreting the Meaning of the Derivative in Context
• Straight-Line Motion: Connecting Position, Velocity, and Acceleration
• Rates of Change in Applied Contexts Other Than Motion
• Introduction to Related Rates
• Solving Related Rates Problems
• Approximating Values of a Function Using Local Linearity and Linearization
• Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
• Exam: Contextual Applications of Differentiation
• Using the Mean Value Theorem
• Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
• Determining Intervals on Which a Function Is Increasing or Decreasing
• Using the First Derivative Test to Determine Relative (Local) Extrema
• Using the Candidates Test to Determine Absolute (Global) Extrema
• Determining Concavity of Functions over Their Domains
• Determining Concavity of Functions over Their Domains
• Using the Second Derivative Test to Determine Extrema
• Sketching Graphs of Functions and Their Derivatives
• Connecting a Function, Its First Derivative, and Its Second Derivative
• Solving Optimization Problems
• Exploring Behaviors of Implicit Relations
• Exam: Analytical Applications of Differentiation
• Exploring Accumulations of Change
• Approximating Areas with Riemann Sums
• Riemann Sums, Summation Notation, and Definite Integral Notation
• The Fundamental Theorem of Calculus and Accumulation Functions
• Interpreting the Behavior of Accumulation Functions Involving Area
• Applying Properties of Definite Integrals
• The Fundamental Theorem of Calculus and Definite Integrals
• Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
• Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
• Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
• Integrating Using Substitution
• Integrating Functions Using Long Division and Completing the Square
• Exam: Integration and Accumulation of Change
• Modeling Situations with Differential Equations
• Verifying Solutions for Differential Equations
• Sketching Slope Fields
• Reasoning Using Slope Fields
• Finding General Solutions Using Separation of Variables
• Finding Particular Solutions Using Initial Conditions and Separation of Variables
• Exponential Models with Differential Equations
• Exam: Differential Equations
• Finding the Average Value of a Function on an Interval
• Connecting Position, Velocity, and Acceleration of Functions Using Integrals
• Using Accumulation Functions and Definite Integrals in Applied Contexts
• Finding the Area Between Curves Expressed as Functions of x
• Finding the Area Between Curves Expressed as Functions of y
• Finding the Area Between Curves That Intersect at More Than Two Points
• Volumes with Cross Sections: Squares and Rectangles
• Volumes with Cross Sections: Triangles and Semicircles
• Volume with Disc Method: Revolving Around the x- or y-Axis
• Volume with Disc Method: Revolving Around Other Axes
• Volume with Washer Method: Revolving Around the x- or y-Axis
• Volume with Washer Method: Revolving Around Other Axes
• Exam: Applications of Integration