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About the Course

It’s been said that change is the only true constant. Calculus helps make sense of change by grappling with questions that inspire thinkers from around the globe, across time, and in many disciplines. Can change occur in an instant? When is the next solar eclipse or the turning point for an economy? In AP Calculus BC, you’ll cover many of the mathematical principles in AP Calculus AB and build upon them. AP Calculus BC helps you prepare for further study in mathematics and other disciplines, such as engineering, computer science, or economics.

Skills You'll Learn

Determining expressions and values using mathematical procedures and rules
Connecting representations
Justifying reasoning and solutions
Using correct notation, language, and mathematical conventions to communicate results or solutions

Equivalency and Prerequisites

College Course Equivalent

A first-semester college calculus course and the subsequent single-variable calculus course

Recommended Prerequisites

You should have successfully completed courses in which you studied algebra, geometry, trigonometry, analytic geometry, and elementary functions. In particular, you should understand the properties of linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions, as well as sequences, series, and polar equations. You should know how to graph these functions and solve equations involving them. You should also be familiar with algebraic transformations, combinations, compositions, and inverses for general functions.

Exam Date

Mon, May 12, 2025

8 AM Local

AP Calculus BC Exam

This is the regularly scheduled date for the AP Calculus BC Exam.

Details Add to Calendar

About the Units

The course content outlined below is organized into commonly taught units of study that provide one possible sequence for the course. Your teacher may choose to organize the course content differently based on local priorities and preferences.

Course Content

Unit 1: Limits and Continuity

You’ll start to explore how limits will allow you to solve problems involving change and to better understand mathematical reasoning about functions.

Topics may include:

How limits help us to handle change at an instant
Definition and properties of limits in various representations
Definitions of continuity of a function at a point and over a domain
Asymptotes and limits at infinity
Reasoning using the Squeeze theorem and the Intermediate Value Theorem

On The Exam

4%–7% of exam score

Unit 2: Differentiation: Definition and Fundamental Properties

You’ll apply limits to define the derivative, become skillful at determining derivatives, and continue to develop mathematical reasoning skills.

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

You’ll master using the chain rule, develop new differentiation techniques, and be introduced to higher-order derivatives.

Unit 4: Contextual Applications of Differentiation

You’ll apply derivatives to set up and solve real-world problems involving instantaneous rates of change and use mathematical reasoning to determine limits of certain indeterminate forms.

Topics may include:

Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
Applying understandings of differentiation to problems involving motion
Generalizing understandings of motion problems to other situations involving rates of change
Solving related rates problems
Local linearity and approximation
L’Hospital’s rule

On The Exam

6%–9% of exam score

Unit 5: Analytical Applications of Differentiation

After exploring relationships among the graphs of a function and its derivatives, you'll learn to apply calculus to solve optimization problems.

Topics may include:

Mean Value Theorem and Extreme Value Theorem
Derivatives and properties of functions
How to use the first derivative test, second derivative test, and candidates test
Sketching graphs of functions and their derivatives
How to solve optimization problems
Behaviors of Implicit relations

On The Exam

8%–11% of exam score

Unit 6: Integration and Accumulation of Change

You’ll learn to apply limits to define definite integrals and how the Fundamental Theorem connects integration and differentiation. You’ll apply properties of integrals and practice useful integration techniques.

Topics may include:

Using definite integrals to determine accumulated change over an interval
Approximating integrals with Riemann Sums
Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
Antiderivatives and indefinite integrals
Properties of integrals and integration techniques, extended
Determining improper integrals

On The Exam

17%–20% of exam score

Unit 7: Differential Equations

You’ll learn how to solve certain differential equations and apply that knowledge to deepen your understanding of exponential growth and decay and logistic models.

Topics may include:

Interpreting verbal descriptions of change as separable differential equations
Sketching slope fields and families of solution curves
Using Euler’s method to approximate values on a particular solution curve
Solving separable differential equations to find general and particular solutions
Deriving and applying exponential and logistic models

On The Exam

6%–9% of exam score

Unit 8: Applications of Integration

You’ll make mathematical connections that will allow you to solve a wide range of problems involving net change over an interval of time and to find lengths of curves, areas of regions, or volumes of solids defined using functions.

Topics may include:

Determining the average value of a function using definite integrals
Modeling particle motion
Solving accumulation problems
Finding the area between curves
Determining volume with cross-sections, the disc method, and the washer method
Determining the length of a planar curve using a definite integral

On The Exam

6%–9% of exam score

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

You’ll solve parametrically defined functions, vector-valued functions, and polar curves using applied knowledge of differentiation and integration. You’ll also deepen your understanding of straight-line motion to solve problems involving curves.

Topics may include:

Finding derivatives of parametric functions and vector-valued functions
Calculating the accumulation of change in length over an interval using a definite integral
Determining the position of a particle moving in a plane
Calculating velocity, speed, and acceleration of a particle moving along a curve
Finding derivatives of functions written in polar coordinates
Finding the area of regions bounded by polar curves

On The Exam

11%–12% of exam score

Unit 10: Infinite Sequences and Series

You’ll explore convergence and divergence behaviors of infinite series and learn how to represent familiar functions as infinite series. You’ll also learn how to determine the largest possible error associated with certain approximations involving series.

Topics may include:

Applying limits to understand convergence of infinite series
Types of series: Geometric, harmonic, and p-series
A test for divergence and several tests for convergence
Approximating sums of convergent infinite series and associated error bounds
Determining the radius and interval of convergence for a series
Representing a function as a Taylor series or a Maclaurin series on an appropriate interval

On The Exam

17%–18% of exam score

Course Resources

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AP Classroom Resources

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AP Calculus AB and BC Course and Exam Description

This is the core document for the course. It clearly lays out the course content and describes the exam and AP Program in general.

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The Difference Between AP Calculus AB and AP Calculus BC

Learn the similarities and differences between these two courses and exams.

AP Calculus BC

Not a Student?

AP Calculus BC

About the Course

Skills You'll Learn

Equivalency and Prerequisites

College Course Equivalent

Recommended Prerequisites

Exam Date

AP Calculus BC Exam

About the Units

Course Content

Unit 1: Limits and Continuity

Unit 2: Differentiation: Definition and Fundamental Properties

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Unit 4: Contextual Applications of Differentiation

Unit 5: Analytical Applications of Differentiation

Unit 6: Integration and Accumulation of Change

Unit 7: Differential Equations

Unit 8: Applications of Integration

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Unit 10: Infinite Sequences and Series

Search AP Credit Policies

Course Resources

AP Classroom Resources

AP Calculus AB and BC Course and Exam Description

The Difference Between AP Calculus AB and AP Calculus BC

Additional Information

AP Calculus BC

Not a Student?

AP Calculus BC

About the Course

Skills You'll Learn

Equivalency and Prerequisites

College Course Equivalent

Recommended Prerequisites

Exam Date

AP Calculus BC Exam

About the Units

Course Content

Unit 1: Limits and Continuity

Unit 2: Differentiation: Definition and Fundamental Properties

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

Unit 4: Contextual Applications of Differentiation

Unit 5: Analytical Applications of Differentiation

Unit 6: Integration and Accumulation of Change

Unit 7: Differential Equations

Unit 8: Applications of Integration

Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Unit 10: Infinite Sequences and Series

Search AP Credit Policies

Course Resources

AP Classroom Resources

AP Calculus AB and BC Course and Exam Description

The Difference Between AP Calculus AB and AP Calculus BC

See Where AP Can Take You

Additional Information