# Your AP Calculus BC Resource Center

## Overview of AP Calculus BC

AP Calculus BC is a college-level course offered by the College Board to high school students who are interested in studying biology at an advanced level. It was opted by 136,000 students in 2023 as it is one of the preferred AP courses. The exam’s difficulty rating stands at 5.5 out of 10 by class alumnae on a reddit survey. AP Calculus BC is known for its challenging curriculum and rigorous exams.The course covers a broad range of topics such as integration techniques, infinite series, and parametric equations.

## Course content

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.

- Defining the derivative of a function at a point and as a function
- Connecting differentiability and continuity
- Determining derivatives for elementary functions
- Applying differentiation rules

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.

- The chain rule for differentiating composite functions
- Implicit differentiation
- Differentiation of general and particular inverse functions
- Determining higher-order derivatives of functions

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.

- 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

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.

- 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

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.

- 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

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.

- 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

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.

- 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

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.

- 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

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.

- 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

## Exam Date

### AP Calculus BC Exam

Will be conducted on

##### Mon, May 13, 2024 | 12 PM Local

## AP Calculus BC Exam Guide

AP Calculus BC is known for its challenging curriculum and rigorous exams. In the AP Calculus BC exam guide, we provide you with the exam structure, topics, study resources, and student performance in AP Calculus BC exams to put together the comprehensive AP Calculus exam guide.

## Explore more in AP Calculus BC

## AP Calculus BC Course Resources

## AP Calculus BC Course

The College Board website offers a variety of extra resources to help AP Calculus BC students succeed on the exam. These resources include the AP Calculus Course at a Glance, the AP Calculus Course and Exam Description, the AP Calculus Scoring Guidelines, and more. To help students prepare for the AP Calculus BC exam, we have provided a list of extra resources below.

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#### AP Calculus AB and BC Course and Exam Description

This is the core document for this course. Unit guides clearly lay out the course content and skills and recommend sequencing and pacing for them throughout the year. The CED was updated in the summer of 2020 to include scoring guidelines for the example questions.

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