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Your AP Calculus AB Resource Center

Overview of AP Calculus AB

AP Calculus AB 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 135,458 students in 2023 as it is one of the preferred AP courses. The subject was given a difficulty rating of 5.5 out of 10 by class alumnae on a reddit survey. AP Calculus AB is known for its challenging curriculum and rigorous exams.The course covers a broad range of topics in calculus, including derivatives, integrals, and the fundamental theorem of calculus.

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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 using Riemann Sums
  • Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
  • Antiderivatives and indefinite integrals
  • Properties of integrals and integration techniques

  • Interpreting verbal descriptions of change as separable differential equations
  • Sketching slope fields and families of solution curves
  • Solving separable differential equations to find general and particular solutions
  • Deriving and applying a model for exponential growth and decay

  • 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

Exam Date

AP Calculus AB Exam

Will be conducted on

Mon, May 13, 2024 | 12 PM Local

AP Calculus AB Exam Guide

AP Calculus AB is known for its challenging curriculum and rigorous exams. In the AP Calculus AB exam guide, we provide you with the exam structure, topics, study resources, and student performance over the past 10 years of AP Calculus AB exams to put together the comprehensive AP Calculus exam guide.

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AP Calculus AB Course Resources

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AP Calculus AB Course

The College Board website offers a variety of extra resources to help AP Calculus AB 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 AB exam, we have provided a list of extra resources below.

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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.



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. 



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.



The Difference Between AP Calculus AB and AP Calculus BC

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


AP Calculus AB Free Response Questions

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