Topics include:

• Introducing Calculus: Can Change Occur at an Instant?
• Defining Limits and Using Limit Notation
• Estimating Limit Values from graphs
• Estimating Limit Values from tables
• Determining Limits Using Algebraic Properties of Limits
• Determining Limits Using Algebraic Manipulation
• Selecting Procedures for Determining Limits
• Determining Limits Using the Squeeze Theorem
• Connecting Multiple Representations of Limits
• Exploring Types of Discontinuities
• Defining Continuity at a point
• Removing Discontinuities
• Confirming Continuity over an Interval
• Connecting Infinite Limits and Vertical Asymptotes
• Connecting Limits at Infinity and Horizontal Asymptotes
• Working with the Intermediate Value Theorem (IVT)

On The Exam 10%–12% of exam score

Topics include:

• The Chain Rule
• Implicit Differentiation
• Differentiating Inverse Functions
• Differentiating Inverse Trigonometric Functions
• Selecting Procedures for Calculating Derivatives
• Calculating Higher Order Derivatives

On The Exam 9%–13% of exam score

Topics include:

• 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
• 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
• Introduction to Optimization Problems
• Solving Optimization Problems
• Exploring Behaviors of Implicit Relations

On The Exam 15%–18% of exam score

Topics include:

• 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

On The Exam 6%–12% of exam score

Topics include:

• 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
• Derivatives of cos x, sin x, ex, and ln x
• The Product Rule
• The Quotient Rule
• Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

On The Exam 10%–12% of exam score

Topics include:

• 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

On The Exam 10%–15% of exam score

Topics include:

• 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
• Integrating Using Substitution
• Integrating Functions Using Long Division and Completing the Square
• Selecting Techniques for Anti differentiation

On The Exam 17%–20% of exam score