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 4–7% 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 8-9% 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 8–11% of exam score

Topics include:

• Modeling Situations with Differential Equations
• Verifying Solutions for Differential Equations
• Sketching Slope Fields
• Reasoning Using Slope Fields
• Approximating Solutions Using Euler’s Method BC ONLY
• Finding General Solutions Using Separation of Variables
• Finding Particular Solutions Using Initial Conditions and Separation of Variables
• Exponential Models with Differential Equations
• Logistic Models with Differential Equations BC ONLY

On The Exam 6–9% of exam score

Topics include:

• Defining and Differentiating Parametric Equations
• Second Derivatives of Parametric Equations
• Finding Arc Lengths of Curves Given by Parametric Equations
• Defining and Differentiating Vector Valued Functions
• Integrating Vector- Valued Functions
• Solving Motion Problems Using Parametric and Vector- Valued Functions
• Defining Polar Coordinates and Differentiating in Polar Form
• Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
• Finding the Area of the Region Bounded by Two Polar Curves

On The Exam 11–12% 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 4–7% 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 6–9% 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
• Integrating Using Integration by Parts BC ONLY
• Using Linear Partial Fractions BC ONLY
• Evaluating Improper Integrals BC ONLY
• Selecting Techniques for Anti differentiation

On The Exam 17–20% of exam score

Topics include:

• 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
• The Arc Length of a Smooth, Planar Curve and Distance Travelled BC ONLY

On The Exam 6–9% of exam score

Topics include:

• Defining Convergent and Divergent Infinite Series
• Working with Geometric Series
• The nth Term Test for Divergence
• Integral Test for Convergence
• Harmonic Series and p-Series
• Comparison Tests for Convergence
• Alternating Series Test for Convergence
• Ratio Test for Convergence
• Determining Absolute or Conditional Convergence
• Alternating Series Error Bound
• Finding Taylor Polynomial Approximations of Functions
• Lagrange Error Bound
• Radius and Interval of Convergence of Power Series
• Finding Taylor or Maclaurin Series for a Function
• Representing Functions as Power Series

On The Exam 17–18% of exam score