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# 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 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.

• 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

• 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

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

• 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

• 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

• 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

• 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

• 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

• 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

• 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

## 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.

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## 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.

#### AP Calculus Course at a Glance

Excerpted from the AP Calculus AB and BC Course and Exam Description, the Course at a Glance document outlines the topics and skills covered in the AP Calculus courses, along with suggestions for sequencing.

PDF

#### 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.

PDF

#### AP Calculus AB and BC CED Scoring Guidelines

This document details how each of the sample free-response questions in the course and exam description (CED) would be scored.

PDF

#### The Difference Between AP Calculus AB and AP Calculus BC

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

Article

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