My coursesAP Calculus AB

YOUR COURSE, ONE TOPIC AT A TIME

AP Calculus AB

Find your flow with limits, derivatives, and integrals.

Course outline

8 units in this preview

01UNIT 1Limits and Continuity16 topics

176 MCQs availableStart Practice

1.1Introducing Calculus: Can Change Occur at an Instant?Study topic Practice · 11 MCQs

1.2Defining Limits and Using Limit NotationStudy topic Practice · 11 MCQs

1.3Estimating Limit Values from GraphsStudy topic Practice · 11 MCQs

1.4Estimating Limit Values from TablesStudy topic Practice · 11 MCQs

1.5Determining Limits Using Algebraic Properties of LimitsStudy topic Practice · 11 MCQs

1.6Determining Limits Using Algebraic ManipulationStudy topic Practice · 11 MCQs

1.7Selecting Procedures for Determining LimitsStudy topic Practice · 11 MCQs

1.8Determining Limits Using the Squeeze TheoremStudy topic Practice · 11 MCQs

1.9Connecting Multiple Representations of LimitsStudy topic Practice · 11 MCQs

1.10Exploring Types of DiscontinuitiesStudy topic Practice · 11 MCQs

1.11Defining Continuity at a PointStudy topic Practice · 11 MCQs

1.12Confirming Continuity over an IntervalStudy topic Practice · 11 MCQs

1.13Removing DiscontinuitiesStudy topic Practice · 11 MCQs

1.14Connecting Infinite Limits and Vertical AsymptotesStudy topic Practice · 11 MCQs

1.15Connecting Limits at Infinity and Horizontal AsymptotesStudy topic Practice · 11 MCQs

1.16Working with the Intermediate Value Theorem (IVT)Study topic Practice · 11 MCQs

02UNIT 2Differentiation: Definition and Fundamental Properties10 topics

110 MCQs availableStart Practice

2.1Defining Average and Instantaneous Rates of Change at a PointStudy topic Practice · 11 MCQs

2.2Defining the Derivative of a Function and Using Derivative NotationStudy topic Practice · 11 MCQs

2.3Estimating Derivatives of a Function at a PointStudy topic Practice · 11 MCQs

2.4Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not ExistStudy topic Practice · 11 MCQs

2.5Applying the Power RuleStudy topic Practice · 11 MCQs

2.6Derivative Rules: Constant, Sum, Difference, and Constant MultipleStudy topic Practice · 11 MCQs

2.7Derivatives of cos x, sin x, eˣ, and ln xStudy topic Practice · 11 MCQs

2.8The Product RuleStudy topic Practice · 11 MCQs

2.9The Quotient RuleStudy topic Practice · 11 MCQs

2.10Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant FunctionsStudy topic Practice · 11 MCQs

03UNIT 3Differentiation: Composite, Implicit, and Inverse Functions6 topics

66 MCQs availableStart Practice

3.1The Chain RuleStudy topic Practice · 11 MCQs

3.2Implicit DifferentiationStudy topic Practice · 11 MCQs

3.3Differentiating Inverse FunctionsStudy topic Practice · 11 MCQs

3.4Differentiating Inverse Trigonometric FunctionsStudy topic Practice · 11 MCQs

3.5Selecting Procedures for Calculating DerivativesStudy topic Practice · 11 MCQs

3.6Calculating Higher-Order DerivativesStudy topic Practice · 11 MCQs

04UNIT 4Contextual Applications of Differentiation7 topics

77 MCQs availableStart Practice

4.1Interpreting the Meaning of the Derivative in ContextStudy topic Practice · 11 MCQs

4.2Straight-Line Motion: Connecting Position, Velocity, and AccelerationStudy topic Practice · 11 MCQs

4.3Rates of Change in Applied Contexts Other Than MotionStudy topic Practice · 11 MCQs

4.4Introduction to Related RatesStudy topic Practice · 11 MCQs

4.5Solving Related Rates ProblemsStudy topic Practice · 11 MCQs

4.6Approximating Values of a Function Using Local Linearity and LinearizationStudy topic Practice · 11 MCQs

4.7Using L’Hospital’s Rule for Determining Limits of Indeterminate FormsStudy topic Practice · 11 MCQs

05UNIT 5Analytical Applications of Differentiation12 topics

132 MCQs availableStart Practice

5.1Using the Mean Value TheoremStudy topic Practice · 11 MCQs

5.2Extreme Value Theorem, Global Versus Local Extrema, and Critical PointsStudy topic Practice · 11 MCQs

5.3Determining Intervals on Which a Function Is Increasing or DecreasingStudy topic Practice · 11 MCQs

5.4Using the First Derivative Test to Determine Relative (Local) ExtremaStudy topic Practice · 11 MCQs

5.5Using the Candidates Test to Determine Absolute (Global) ExtremaStudy topic Practice · 11 MCQs

5.6Determining Concavity of Functions over Their DomainsStudy topic Practice · 11 MCQs

5.7Using the Second Derivative Test to Determine ExtremaStudy topic Practice · 11 MCQs

5.8Sketching Graphs of Functions and Their DerivativesStudy topic Practice · 11 MCQs

5.9Connecting a Function, Its First Derivative, and Its Second DerivativeStudy topic Practice · 11 MCQs

5.10Introduction to Optimization ProblemsStudy topic Practice · 11 MCQs

5.11Solving Optimization ProblemsStudy topic Practice · 11 MCQs

5.12Exploring Behaviors of Implicit RelationsStudy topic Practice · 11 MCQs

06UNIT 6Integration and Accumulation of Change11 topics

121 MCQs availableStart Practice

6.1Exploring Accumulations of ChangeStudy topic Practice · 11 MCQs

6.2Approximating Areas with Riemann SumsStudy topic Practice · 11 MCQs

6.3Riemann Sums, Summation Notation, and Definite Integral NotationStudy topic Practice · 11 MCQs

6.4The Fundamental Theorem of Calculus and Accumulation FunctionsStudy topic Practice · 11 MCQs

6.5Interpreting the Behavior of Accumulation Functions Involving AreaStudy topic Practice · 11 MCQs

6.6Applying Properties of Definite IntegralsStudy topic Practice · 11 MCQs

6.7The Fundamental Theorem of Calculus and Definite IntegralsStudy topic Practice · 11 MCQs

6.8Finding Antiderivatives and Indefinite Integrals: Basic Rules and NotationStudy topic Practice · 11 MCQs

6.9Integrating Using SubstitutionStudy topic Practice · 11 MCQs

6.10Integrating Functions Using Long Division and Completing the SquareStudy topic Practice · 11 MCQs

6.14Selecting Techniques for AntidifferentiationStudy topic Practice · 11 MCQs

07UNIT 7Differential Equations7 topics

77 MCQs availableStart Practice

7.1Modeling Situations with Differential EquationsStudy topic Practice · 11 MCQs

7.2Verifying Solutions for Differential EquationsStudy topic Practice · 11 MCQs

7.3Sketching Slope FieldsStudy topic Practice · 11 MCQs

7.4Reasoning Using Slope FieldsStudy topic Practice · 11 MCQs

7.6Finding General Solutions Using Separation of VariablesStudy topic Practice · 11 MCQs

7.7Finding Particular Solutions Using Initial Conditions and Separation of VariablesStudy topic Practice · 11 MCQs

7.8Exponential Models with Differential EquationsStudy topic Practice · 11 MCQs

08UNIT 8Applications of Integration12 topics

132 MCQs availableStart Practice

8.1Finding the Average Value of a Function on an IntervalStudy topic Practice · 11 MCQs

8.2Connecting Position, Velocity, and Acceleration of Functions Using IntegralsStudy topic Practice · 11 MCQs

8.3Using Accumulation Functions and Definite Integrals in Applied ContextsStudy topic Practice · 11 MCQs

8.4Finding the Area Between Curves Expressed as Functions of xStudy topic Practice · 11 MCQs

8.5Finding the Area Between Curves Expressed as Functions of yStudy topic Practice · 11 MCQs

8.6Finding the Area Between Curves That Intersect at More Than Two PointsStudy topic Practice · 11 MCQs

8.7Volumes with Cross Sections: Squares and RectanglesStudy topic Practice · 11 MCQs

8.8Volumes with Cross Sections: Triangles and SemicirclesStudy topic Practice · 11 MCQs

8.9Volume with Disc Method: Revolving Around the x- or y-AxisStudy topic Practice · 11 MCQs

8.10Volume with Disc Method: Revolving Around Other AxesStudy topic Practice · 11 MCQs

8.11Volume with Washer Method: Revolving Around the x- or y-AxisStudy topic Practice · 11 MCQs

8.12Volume with Washer Method: Revolving Around Other AxesStudy topic Practice · 11 MCQs