AP
Calculus BC · AP · High school · Math
Full College Board Course and Exam Description framework for Calculus BC · AP, including course-scope topics not assessed on the AP Exam. Topics marked with an asterisk (*) are assessed on the exam. Click a topic for the full text and study materials.
Standards
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Unit 1: Limits and Continuity
- 1.1 * — Introducing Calculus: Can Change Occur at an Instant?
- 1.2 * — Defining Limits and Using Limit Notation
- 1.3 * — Estimating Limit Values from Graphs
- 1.4 * — Estimating Limit Values from Tables
- 1.5 * — Determining Limits Using Algebraic Properties of Limits
- 1.6 * — Determining Limits Using Algebraic Manipulation
- 1.7 * — Selecting Procedures for Determining Limits
- 1.8 * — Determining Limits Using the Squeeze Theorem
- 1.9 * — Connecting Multiple Representations of Limits
- 1.10 * — Exploring Types of Discontinuities
- 1.11 * — Defining Continuity at a Point
- 1.12 * — Confirming Continuity over an Interval
- 1.13 * — Removing Discontinuities
- 1.14 * — Connecting Infinite Limits and Vertical Asymptotes
- 1.15 * — Connecting Limits at Infinity and Horizontal Asymptotes
- 1.16 * — Working with the Intermediate Value Theorem (IVT)
Unit 2: Differentiation — Definition and Fundamental Properties
- 2.1 * — Defining Average and Instantaneous Rates of Change at a Point
- 2.2 * — Defining the Derivative of a Function and Using Derivative Notation
- 2.3 * — Estimating Derivatives of a Function at a Point
- 2.4 * — Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- 2.5 * — Applying the Power Rule
- 2.6 * — Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- 2.7 * — Derivatives of cos x, sin x, eˣ, and ln x
- 2.8 * — The Product Rule
- 2.9 * — The Quotient Rule
- 2.10 * — Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
Unit 3: Differentiation — Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
- 4.1 * — Interpreting the Meaning of the Derivative in Context
- 4.2 * — Straight-Line Motion: Connecting Position, Velocity, and Acceleration
- 4.3 * — Rates of Change in Applied Contexts Other Than Motion
- 4.4 * — Introduction to Related Rates
- 4.5 * — Solving Related Rates Problems
- 4.6 * — Approximating Values of a Function Using Local Linearity and Linearization
- 4.7 * — Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
Unit 5: Analytical Applications of Differentiation
- 5.1 * — Using the Mean Value Theorem
- 5.2 * — Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- 5.3 * — Determining Intervals on Which a Function Is Increasing or Decreasing
- 5.4 * — Using the First Derivative Test to Determine Relative (Local) Extrema
- 5.5 * — Using the Candidates Test to Determine Absolute (Global) Extrema
- 5.6 * — Determining Concavity of Functions over Their Domains
- 5.7 * — Using the Second Derivative Test to Determine Extrema
- 5.8 * — Sketching Graphs of Functions and Their Derivatives
- 5.9 * — Connecting a Function, Its First Derivative, and Its Second Derivative
- 5.10 * — Introduction to Optimization Problems
- 5.11 * — Solving Optimization Problems
- 5.12 * — Exploring Behaviors of Implicit Relations
Unit 6: Integration and Accumulation of Change
- 6.1 * — Exploring Accumulations of Change
- 6.2 * — Approximating Areas with Riemann Sums
- 6.3 * — Riemann Sums, Summation Notation, and Definite Integral Notation
- 6.4 * — The Fundamental Theorem of Calculus and Accumulation Functions
- 6.5 * — Interpreting the Behavior of Accumulation Functions Involving Area
- 6.6 * — Applying Properties of Definite Integrals
- 6.7 * — The Fundamental Theorem of Calculus and Definite Integrals
- 6.8 * — Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- 6.9 * — Integrating Using Substitution
- 6.10 * — Integrating Functions Using Long Division and Completing the Square
- 6.11 * — Integrating Using Integration by Parts
- 6.12 * — Using Linear Partial Fractions
- 6.13 * — Evaluating Improper Integrals
- 6.14 * — Selecting Techniques for Antidifferentiation
Unit 7: Differential Equations
- 7.1 * — Modeling Situations with Differential Equations
- 7.2 * — Verifying Solutions for Differential Equations
- 7.3 * — Sketching Slope Fields
- 7.4 * — Reasoning Using Slope Fields
- 7.5 * — Approximating Solutions Using Euler's Method
- 7.6 * — Finding General Solutions Using Separation of Variables
- 7.7 * — Finding Particular Solutions Using Initial Conditions and Separation of Variables
- 7.8 * — Exponential Models with Differential Equations
- 7.9 * — Logistic Models with Differential Equations
Unit 8: Applications of Integration
- 8.1 * — Finding the Average Value of a Function on an Interval
- 8.2 * — Connecting Position, Velocity, and Acceleration of Functions Using Integrals
- 8.3 * — Using Accumulation Functions and Definite Integrals in Applied Contexts
- 8.4 * — Finding the Area Between Curves Expressed as Functions of x
- 8.5 * — Finding the Area Between Curves Expressed as Functions of y
- 8.6 * — Finding the Area Between Curves That Intersect at More Than Two Points
- 8.7 * — Volumes with Cross Sections: Squares and Rectangles
- 8.8 * — Volumes with Cross Sections: Triangles and Semicircles
- 8.9 * — Volume with Disc Method: Revolving Around the x- or y-Axis
- 8.10 * — Volume with Disc Method: Revolving Around Other Axes
- 8.11 * — Volume with Washer Method: Revolving Around the x- or y-Axis
- 8.12 * — Volume with Washer Method: Revolving Around Other Axes
- 8.13 * — The Arc Length of a Smooth, Planar Curve and Distance Traveled
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- 9.1 * — Defining and Differentiating Parametric Equations
- 9.2 * — Second Derivatives of Parametric Equations
- 9.3 * — Finding Arc Lengths of Curves Given by Parametric Equations
- 9.4 * — Defining and Differentiating Vector-Valued Functions
- 9.5 * — Integrating Vector-Valued Functions
- 9.6 * — Solving Motion Problems Using Parametric and Vector-Valued Functions
- 9.7 * — Defining Polar Coordinates and Differentiating in Polar Form
- 9.8 * — Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
- 9.9 * — Finding the Area of the Region Bounded by Two Polar Curves
Unit 10: Infinite Sequences and Series
- 10.1 * — Defining Convergent and Divergent Infinite Series
- 10.2 * — Working with Geometric Series
- 10.3 * — The nth Term Test for Divergence
- 10.4 * — Integral Test for Convergence
- 10.5 * — Harmonic Series and p-Series
- 10.6 * — Comparison Tests for Convergence
- 10.7 * — Alternating Series Test for Convergence
- 10.8 * — Ratio Test for Convergence
- 10.9 * — Determining Absolute or Conditional Convergence
- 10.10 * — Alternating Series Error Bound
- 10.11 * — Finding Taylor Polynomial Approximations of Functions
- 10.12 * — Lagrange Error Bound
- 10.13 * — Radius and Interval of Convergence of Power Series
- 10.14 * — Finding Taylor or Maclaurin Series for a Function
- 10.15 * — Representing Functions as Power Series
* Assessed on the AP Exam (per the Course and Exam Description). All topics listed; unmarked topics are course scope only.
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AP Course and Exam Description (College Board)
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