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AP Calculus AB · Lessons

AP Calculus AB lessons

8 sections · 81 skills · work through the full outline skill by skill — read the long-form lesson or flip through the slide-style version.
Long-form lessonsSlide-style lessons

AP Calculus AB

Practice 81 skills across this outline.

Recommended next
Volumes with Cross Sections: Squares/Rectangles
Applications of Integration
Long-form lesson
Weighting distribution
8 categories
Applications of Integration
13%
Analytical Applications of Differentiation
13%
Integration and Accumulation of Change
13%
Contextual Applications of Differentiation
13%
Limits and Continuity
13%
Differential Equations
13%

Skills

The comprehensive taxonomy of ap calculus ab — drill into a card to work its skills.

Applications of Integration

12 core skills13% total weight
0/12 completed
12 skills to mastery
1
Volumes with Cross Sections: Squares/RectanglesRecommended
Long-form
2
Accumulation Functions, Definite Intervals, Applied ContextsAvailable
Long-form
3
Volumes with Cross Sections: Triangles/SemicirclesAvailable
Long-form
4
Area Between Curves with Multiple IntersectionsAvailable
Long-form
5
Area Between Curves: Functions of xAvailable
Long-form
6
Area Between Curves: Functions of yAvailable
Long-form
7
Average Value of Functions on IntervalsAvailable
Long-form
8
Disc Method: Revolving Around x/y AxesAvailable
Long-form
9
Disc Method: Revolving Around Other AxesAvailable
Long-form
10
Position, Velocity, and Acceleration Using IntegralsAvailable
Long-form
11
Washer Method: Revolving Around x/y AxesAvailable
Long-form
12
Washer Method: Revolving Around Other AxesAvailable
Long-form

Analytical Applications of Differentiation

12 core skills13% total weight
0/12 completed
12 skills to mastery
1
Mean Value TheoremAvailable
Long-form
2
Determining Intervals on Increasing, Decreasing FunctionsAvailable
Long-form
3
Candidates TestAvailable
Long-form
4
Concavity of Functions Over Their DomainsAvailable
Long-form
5
Connecting a Function and Its DerivativesAvailable
Long-form
6
Exploring Behaviors of Implicit RelationsAvailable
Long-form
7
Extreme Value Theorem, Extrema, Critical PointsAvailable
Long-form
8
First Derivative TestAvailable
Long-form
9
Introduction to Optimization ProblemsAvailable
Long-form
10
Second Derivative TestAvailable
Long-form
11
Sketching Graphs of Functions and DerivativesAvailable
Long-form
12
Solving Optimization ProblemsAvailable
Long-form

Integration and Accumulation of Change

11 core skills13% total weight
0/11 completed
11 skills to mastery
1
Fundamental Theorem of Calculus: Definite IntervalsAvailable
Long-form
2
Applying Properties of Definite IntegralsAvailable
Long-form
3
Approximating Areas With Riemann SumsAvailable
Long-form
4
Behavior of Accumulation Functions Involving AreaAvailable
Long-form
5
Exploring Accumulations of ChangeAvailable
Long-form
6
Finding Antiderivatives and Indefinite IntegralsAvailable
Long-form
7
Fundamental Theorem of Calculus: Accumulation FunctionsAvailable
Long-form
8
Integrating Using SubstitutionAvailable
Long-form
9
Integrating, Long Division, Completing the SquareAvailable
Long-form
10
Riemann Sums and NotationAvailable
Long-form
11
Selecting Techniques for AntidifferentiationAvailable
Long-form

Contextual Applications of Differentiation

7 core skills13% total weight
0/7 completed
7 skills to mastery
1
Rates of Change in Applied ConceptsAvailable
Long-form
2
Meaning of the Derivative in ContextAvailable
Long-form
3
Connecting Position, Velocity, and AccelerationAvailable
Long-form
5
L'Hospital's RuleAvailable
Long-form
6
Local Linearity and LinearizationAvailable
Long-form

Limits and Continuity

16 core skills13% total weight
0/16 completed
16 skills to mastery
1
Defining Continuity at a PointAvailable
Long-form
2
Introducing CalculusAvailable
Long-form
3
Algebraic Properties of LimitsAvailable
Long-form
4
Confirming Continuity over an IntervalAvailable
Long-form
5
Connecting Infinite Limits and Vertical AsymptotesAvailable
Long-form
6
Connecting Multiple Representations of LimitsAvailable
Long-form
7
Defining Limits and Using Limit NotationAvailable
Long-form
8
Determining Limits Using Algebraic ManipulationAvailable
Long-form
9
Determining Limits Using the Squeeze TheoremAvailable
Long-form
10
Estimating Limit Values from GraphsAvailable
Long-form
11
Estimating Limit Values from TablesAvailable
Long-form
12
Exploring Types of DiscontinuitiesAvailable
Long-form
13
Limits at Infinity and Horizontal AsymptotesAvailable
Long-form
14
Removing DiscontinuitiesAvailable
Long-form
15
Selecting Procedures for Determining LimitsAvailable
Long-form
16
Working With the Intermediate Value TheoremAvailable
Long-form

Differential Equations

7 core skills13% total weight
0/7 completed
7 skills to mastery
1
Finding General Solutions: Separation of VariablesAvailable
Long-form
2
Exponential Models with Differential EquationsAvailable
Long-form
3
Initial Conditions and Separation of VariablesAvailable
Long-form
4
Modeling Situations with Differential EquationsAvailable
Long-form
5
Reasoning Using Slope FieldsAvailable
Long-form
6
Sketching Slope FieldsAvailable
Long-form
7
Verifying Solutions for Differential EquationsAvailable
Long-form

Differentiation: Composite, Implicit, and Inverse Functions

6 core skills13% total weight
0/6 completed
6 skills to mastery
1
Chain RuleAvailable
Long-form
2
Calculating Higher-Order DerivativesAvailable
Long-form
3
Differentiating Inverse FunctionsAvailable
Long-form
4
Differentiating Inverse Trigonometric FunctionsAvailable
Long-form
5
Implicit DifferentiationAvailable
Long-form
6
Selecting Procedures for Calculating DerivativesAvailable
Long-form

Differentiation: Definition and Fundamental Properties

10 core skills13% total weight
0/10 completed
10 skills to mastery
1
Rate of Change at a PointAvailable
Long-form
2
Applying the Power RuleAvailable
Long-form
3
Connecting Differentiability and ContinuityAvailable
Long-form
4
Derivative NotationAvailable
Long-form
5
Derivative Rules of Constant, Sum, DifferenceAvailable
Long-form
6
Derivatives of Trigonometry and Logarithmic FunctionsAvailable
Long-form
7
Derivatives of Reciprocal Trig FunctionsAvailable
Long-form
8
Estimating Derivatives of a FunctionAvailable
Long-form
9
The Product RuleAvailable
Long-form
10
The Quotient RuleAvailable
Long-form