AP CALCULUS AB / LEARN BY TOPIC

AP Calculus AB. Understand the change.

StudyGlitch AP Calculus AB Materials connects calculus concepts with the reasoning needed to use them. Start with a topic guide, study a short worked example, then practise with multiple-choice, numeric and written-response questions.

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WHAT YOU WILL LEARN

AP Calculus AB materials built around understanding

The learning map spans the eight AP Calculus AB units, from limits and continuity through differentiation, integration, differential equations and applications of integration. Its 81 AB topic entries follow the College Board framework; BC-only content is excluded.

Practise switching between equations, graphs, tables and verbal descriptions. Short explanations identify the concept and the solving steps. Written responses add a rubric for comparing your reasoning after submitting; they are self-reviewed rather than automatically marked as correct.

Independent AP Calculus AB learning resources. StudyGlitch is not affiliated with or endorsed by College Board.

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Submit your response, read the explanation and compare it with the supplied rubric. Your rubric self-review is saved, but it does not count as an automatically correct answer or raise scored mastery.

Are topics the same as mathematical practice skills?

No. Topic labels describe the calculus content. Mathematical practice tags describe the kind of reasoning a question uses. The topic map organizes learning; the tags add another way to understand the task.

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Sign in to save your progress. Continue learning resumes an unfinished question; Continue practice selects the next unanswered question in difficulty order. Once a skill or topic is covered, review your saved answers or choose another. Review due questions offers previously seen questions when their review time arrives. Completion, first answers, assisted practice and later reviews remain distinguishable; repeated answers do not create unlimited mastery evidence.

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YOUR LEARNING MAP

Eight units. Eighty-one topics.

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AP Calculus AB. Understand the change.

AP Calculus AB materials built around understanding

Eight units. Eighty-one topics.

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)

Differentiation: Definition and Fundamental Properties

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, sin x, 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

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

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 Introduction 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'Hospital's Rule for Determining Limits of Indeterminate Forms

Analytical Applications of Differentiation

5.1 Using the Mean Value Theorem

5.2 Extreme Value Theorem, Global Versus 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 of Functions over Their Domains

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

Integration and Accumulation of Change

6.1 Exploring Accumulations 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

6.14 Selecting Techniques for Antidifferentiation

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

7.6 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

Applications of Integration