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AP®︎ Calculus AB Study Guides

Prepare for your quiz, test, or the AP exam with comprehensive study guides that cover everything you need to know. Select a unit or topic to begin.

Unit 1: Limits and Continuity

All Topics
Complete Unit Review

Topic 1.1
Introducing Calculus: Can Change Occur at an Instant?

Topic 1.2
Defining Limits and Using Limit Notation

Topic 1.3
Estimating Limit Values from Graphs

Topic 1.4
Estimating Limit Values from Tables

Topic 1.5
Determining Limits Using Algebraic Properties of Limits

Topic 1.6
Determining Limits Using Algebraic Manipulation

Topic 1.7
Selecting Procedures for Determining Limits

Topic 1.8
Determining Limits Using the Squeeze Theorem

Topic 1.9
Connecting Multiple Representations of Limits

Topic 1.10
Exploring Types of Discontinuities

Topic 1.11
Defining Continuity at a Point

Topic 1.12
Confirming Continuity over an Interval

Topic 1.13
Removing Discontinuities

Topic 1.14
Connecting Infinite Limits and Vertical Asymptotes

Topic 1.15
Connecting Limits at Infinity and Horizontal Asymptotes

Topic 1.16
Working with the Intermediate Value Theorem (IVT)

Unit 2: Differentiation: Definition and Fundamental Properties

All Topics
Complete Unit Review

Topic 2.1
Defining Average and Instantaneous Rates of Change at a Point

Topic 2.2
Defining the Derivative of a Function and Using Derivative Notation

Topic 2.3
Estimating Derivatives of a Function at a Point

Topic 2.4
Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

Topic 2.5
Applying the Power Rule

Topic 2.6
Derivative Rules: Constant, Sum, Difference, and Constant Multiple

Topic 2.7
Derivatives of cos x, sin x, e^x, and ln x

Topic 2.8
The Product Rule

Topic 2.9
The Quotient Rule

Topic 2.10
Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

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

All Topics
Complete Unit Review

Topic 3.1
The Chain Rule

Topic 3.2
Implicit Differentiation

Topic 3.3
Differentiating Inverse Functions

Topic 3.4
Differentiating Inverse Trigonometric Functions

Topic 3.5
Selecting Procedures for Calculating Derivatives

Topic 3.6
Calculating Higher-Order Derivatives

Unit 4: Contextual Applications of Differentiation

All Topics
Complete Unit Review

Topic 4.1
Interpreting the Meaning of the Derivative in Context

Topic 4.2
Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Topic 4.3
Rates of Change in Applied Contexts Other Than Motion

Topic 4.4
Introduction to Related Rates

Topic 4.5
Solving Related Rates Problems

Topic 4.6
Approximating Values of a Function Using Local Linearity and Linearization

Topic 4.7
Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

Unit 5: Analytical Applications of Differentiation

All Topics
Complete Unit Review

Topic 5.1
Using the Mean Value Theorem

Topic 5.2
Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

Topic 5.3
Determining Intervals on Which a Function Is Increasing or Decreasing

Topic 5.4
Using the First Derivative Test to Determine Relative (Local) Extrema

Topic 5.5
Using the Candidates Test to Determine Absolute (Global) Extrema

Topic 5.6
Determining Concavity of Functions over Their Domains

Topic 5.7
Using the Second Derivative Test to Determine Extrema

Topic 5.8
Sketching Graphs of Functions and Their Derivatives

Topic 5.9
Connecting a Function, Its First Derivative, and Its Second Derivative

Topic 5.10
Introduction to Optimization Problems

Topic 5.11
Solving Optimization Problems

Topic 5.12
Exploring Behaviors of Implicit Relations

Unit 6: Integration and Accumulation of Change

All Topics
Complete Unit Review

Topic 6.1
Exploring Accumulations of Change

Topic 6.2
Approximating Areas with Riemann Sums

Topic 6.3
Riemann Sums, Summation Notation, and Definite Integral Notation

Topic 6.4
The Fundamental Theorem of Calculus and Accumulation Functions

Topic 6.5
Interpreting the Behavior of Accumulation Functions Involving Area

Topic 6.6
Applying Properties of Definite Integrals

Topic 6.7
The Fundamental Theorem of Calculus and Definite Integrals

Topic 6.8
Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

Topic 6.9
Integrating Using Substitution

Topic 6.10
Integrating Functions Using Long Division and Completing the Square

Topic 6.14
Selecting Techniques for Antidifferentiation

Unit 7: Differential Equations

All Topics
Complete Unit Review

Topic 7.1
Modeling Situations with Differential Equations

Topic 7.2
Verifying Solutions for Differential Equations

Topic 7.3
Sketching Slope Fields

Topic 7.4
Reasoning Using Slope Fields

Topic 7.6
Finding General Solutions Using Separation of Variables

Topic 7.7
Finding Particular Solutions Using Initial Conditions and Separation of Variables

Topic 7.8
Exponential Models with Differential Equations

Unit 8: Applications of Integration

All Topics
Complete Unit Review

Topic 8.1
Finding the Average Value of a Function on an Interval

Topic 8.2
Connecting Position, Velocity, and Acceleration of Functions Using Integrals

Topic 8.3
Using Accumulation Functions and Definite Integrals in Applied Contexts

Topic 8.4
Finding the Area Between Curves Expressed as Functions of x

Topic 8.5
Finding the Area Between Curves Expressed as Functions of y

Topic 8.6
Finding the Area Between Curves That Intersect at More Than Two Points

Topic 8.7
Volumes with Cross Sections: Squares and Rectangles

Topic 8.8
Volumes with Cross Sections: Triangles and Semicircles

Topic 8.9
Volume with Disc Method: Revolving Around the x- or y-Axis

Topic 8.10
Volume with Disc Method: Revolving Around Other Axes

Topic 8.11
Volume with Washer Method: Revolving Around the x- or y-Axis

Topic 8.12
Volume with Washer Method: Revolving Around Other Axes

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