♾️AP Calculus AB/BC study guides

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AP Calculus AB/BC Exams →

Multiple-Choice Questions (MCQ)

Free Response Questions (FRQ)

Unit 1 – Limits and Continuity →

1.0

Unit 1 Overview: Limits and Continuity

1.1

Introducing Calculus: Can Change Occur at An Instant?

1.2

Defining Limits and Using Limit Notation

1.3

Estimating Limit Values from Graphs

1.4

Estimating Limit Values from Tables

1.5

Determining Limits Using Algebraic Properties of Limits

1.6

Determining Limits Using Algebraic Manipulation

1.7

Selecting Procedures for Determining Limits

1.8

Determining Limits Using the Squeeze Theorem

1.9

Connecting Multiple Representations of Limits

1.10

Exploring Types of Discontinuities

1.11

Defining Continuity at a Point

1.12

Confirming Continuity over an Interval

1.13

Removing Discontinuities

1.14

Connecting Infinite Limits and Vertical Asymptotes

1.15

Connecting Limits at Infinity and Horizontal Asymptotes

1.16

Working with the Intermediate Value Theorem (IVT Calc)

Unit 2 – Fundamentals of Differentiation →

2.0

Unit 2 Overview: Differentiation

2.1

Defining Average and Instantaneous Rates of Change at a Point

2.2

Defining the Derivative of a Function and Using Derivative Notation

2.3

Estimating Derivatives of a Function at a Point

2.4

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

2.5

Applying the Power Rule

2.6

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

2.7

Derivatives of cos x, sinx, e^x, and ln x

2.8

The Product Rule

2.9

The Quotient Rule

2.10

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

Unit 3 – Composite, Implicit, and Inverse Functions →

3.0

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

3.1

The Chain Rule

3.2

Implicit Differentiation

3.3

Differentiating Inverse Functions

3.4

Differentiating Inverse Trigonometric Functions

3.5

Selecting Procedures for Calculating Derivatives

3.6

Calculating Higher-Order Derivatives

Unit 4 – Contextual Applications of Differentiation →

4.0

Unit 4 Overview: Contextual Applications of Differentiation

4.1

Interpreting the Meaning of the Derivative in Context

4.2

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

4.3

Rates of Change in Applied Contexts other than Motion

4.4

Intro to Related Rates

4.5

Solving Related Rates Problems

4.6

Approximating Values of a Function Using Local Linearity and Linearization

4.7

Using L'Hopitals Rule for Determining Limits in Indeterminate Forms

Unit 5 – Analytical Applications of Differentiation →

5.0

Unit 5 Overview: Analytical Applications of Differentiation

5.1

Using the Mean Value Theorem

5.2

Extreme Value Theorem, Global vs Local Extrema, and Critical Points

5.3

Determining Intervals on Which a Function is Increasing or Decreasing

5.4

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

5.5

Using the Candidates Test to Determine Absolute (Global) Extrema

5.6

Determining Concavity

5.7

Using the Second Derivative Test to Determine Extrema

5.8

Sketching Graphs of Functions and Their Derivatives

5.9

Connecting a Function, Its First Derivative, and its Second Derivative

5.10

Introduction to Optimization Problems

5.11

Solving Optimization Problems

5.12

Exploring Behaviors of Implicit Relations

Unit 6 – Integration and Accumulation of Change →

6.0

Unit 6 Overview: Integration and Accumulation of Change

6.1

Integration and Accumulation of Change

6.2

Approximating Areas with Riemann Sums

6.3

Riemann Sums, Summation Notation, and Definite Integral Notation

6.4

The Fundamental Theorem of Calculus and Accumulation Functions

6.5

Interpreting the Behavior of Accumulation Functions Involving Area

6.6

Applying Properties of Definite Integrals

6.7

The Fundamental Theorem of Calculus and Definite Integrals

6.8

Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

6.9

Integrating Using Substitution

6.10

Integrating Functions Using Long Division and Completing the Square

6.11

Integrating Using Integration by Parts

6.12

Integrating Using Linear Partial Fractions

6.13

Evaluating Improper Integrals

6.14

Selecting Techniques for Antidifferentiation (AB)

Unit 7 – Differential Equations →

7.0

Unit 7 Overview: Differential Equations

7.1

Modeling Situations with Differential Equations

7.2

Verifying Solutions for Differential Equations

7.3

Sketching Slope Fields

7.4

Reasoning Using Slope Fields

7.5

Approximating Solutions Using Euler’s Method

7.6

Finding General Solutions Using Separation of Variables

7.7

Finding Particular Solutions Using Initial Conditions and Separation of Variables

7.8

Exponential Models with Differential Equations

7.9

Logistic Models with Differential Equations

Unit 8 – Applications of Integration →

8.0

Unit 8 Overview: Applications of Integration

8.1

Finding the Average Value of a Function on an Interval

8.2

Connecting Position, Velocity, and Acceleration of Functions Using Integrals

8.3

Using Accumulation Functions and Definite Integrals in Applied Contexts

8.4

Finding the Area Between Curves Expressed as Functions of x

8.5

Finding the Area Between Curves Expressed as Functions of y

8.6

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

8.7

Volumes with Cross Sections: Squares and Rectangles

8.8

Volumes with Cross Sections: Triangles and Semicircles

8.9

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

8.10

Volume with Disc Method: Revolving Around Other Axes

8.11

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

8.12

Volume with Washer Method: Revolving Around Other Axes

8.13

The Arc Length of a Smooth, Planar Curve and Distance Traveled

Unit 9 – Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only) →

9.0

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

9.1

Defining and Differentiating Parametric Equations

9.2

Second Derivatives of Parametric Equations

9.3

Finding Arc Lengths of Curves Given by Parametric Equations

9.4

Defining and Differentiating Vector-Valued Functions

9.5

Integrating Vector-Valued Functions

9.6

Solving Motion Problems Using Parametric and Vector-Valued Functions

9.7

Defining Polar Coordinates and Differentiating in Polar Form

9.8

Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

9.9

Finding the Area of the Region Bounded by Two Polar Curves

Unit 10 – Infinite Sequences and Series (BC Only) →

10.0

Unit 10 Overview: Infinite Series and Sequences

10.1

Defining Convergent and Divergent Infinite Series

10.2

Working with Geometric Series

10.3

The nth Term Test for Divergence

10.4

Integral Test for Convergence

10.5

Harmonic Series and p-Series

10.6

Comparison Tests for Convergence

10.7

Alternating Series Test for Convergence

10.8

Ratio Test for Convergence

10.9

Determining Absolute or Conditional Convergence

10.10

Alternating Series Error Bound

10.11

Finding Taylor Polynomial Approximations of Functions

10.12

Lagrange Error Bound

10.13

Radius and Interval of Convergence of Power Series

10.14

Finding Taylor or Maclaurin Series for a Function

10.15

Representing Functions as Power Series

Frequently Asked Questions →

What is U-Sub and how do I use it?

What to Know Before Taking AP Calculus AB

What Calculator Functions Will Save Your Life?

Is AP Calculus AB/BC Hard? Is AP Calc Worth Taking?

What are Riemann Sums?

How Can I Get a 5 in AP Calculus AB/BC?

Unit 1 Review - Limits & Continuity

Best AP Calculus AB/BC Quizlet Decks By Unit

How do I take a derivative?

What is U-Substitution?

What Memes Are Perfect for AP Calculus AB/BC?

Unit 2 Review - Differentiation: Definition & Fundamental Properties

How do you defining and taking derivatives?

What is a Limit?

What is implicit differentiation and how do I do it?

Exam Skills →

AP Calculus Multiple Choice Questions

AP Calculus AB/BC Multiple Choice Help (MCQ)

AP Calculus Free Response Question (FRQ) Overview

Score Higher on AP Calculus 2024: MCQ Tips from Students

Score Higher on AP Calculus 2024: FRQ Tips from Students

Frequently Asked Questions

What does AP Calculus AB/BC cover?

AP Calculus AB/BC covers limits, derivatives, integrals, applications of those ideas, and BC-only topics like series and advanced accumulation methods.

How should I use these AP Calculus study guides?

Review the main concept first, then work practice problems right away so the formulas and reasoning stick. Topic guides help most when you pair them with active problem-solving.

Where can I find AP Calculus FRQ practice?

Use Fiveable's AP Calculus FRQ practice for AP-style free-response questions with AI-supported scoring on setup, notation, calculator use, and mathematical reasoning.

Should I study by unit or by skill in AP Calculus?

Start by unit if you are following class material, and switch to skill-based review closer to the exam. That makes it easier to connect related ideas like derivatives, integrals, and their applications.

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