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AP Calculus BC · Lessons

AP Calculus BC lessons

10 sections · 111 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 BC

Practice 111 skills across this outline.

Recommended next
Local Linearity and Linearization
Contextual Applications of Differentiation
Long-form lesson
Weighting distribution
10 categories
Contextual Applications of Differentiation
10%
Differentiation: Composite, Implicit, and Inverse Functions
10%
Applications of Integration
10%
Integration and Accumulation of Change
10%
Parametric, Polar, and Vector Functions
10%
Differentiation: Definition and Fundamental Properties
10%

Skills

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

Contextual Applications of Differentiation

7 core skills10% total weight
0/7 completed
7 skills to mastery
1
Local Linearity and LinearizationRecommended
Long-form
2
Connecting Position, Velocity, and AccelerationAvailable
Long-form
4
L'Hospital's RuleAvailable
Long-form
5
Meaning of the Derivative in ContextAvailable
Long-form
6
Rates of Change in Applied ConceptsAvailable
Long-form

Differentiation: Composite, Implicit, and Inverse Functions

6 core skills10% total weight
0/6 completed
6 skills to mastery
1
Selecting Procedures for Calculating DerivativesAvailable
Long-form
2
Calculating Higher-Order DerivativesAvailable
Long-form
3
Chain RuleAvailable
Long-form
4
Differentiating Inverse Trigonometric FunctionsAvailable
Long-form
5
Differentiating Inverse FunctionsAvailable
Long-form
6
Implicit DifferentiationAvailable
Long-form

Applications of Integration

13 core skills10% total weight
0/13 completed
13 skills to mastery
1
Area Between Curves with Multiple IntersectionsAvailable
Long-form
2
Accumulation Functions, Definite Intervals, Applied ContextsAvailable
Long-form
3
Arc Length of Smooth, Planar CurveAvailable
Long-form
4
Area Between Curves: Functions of xAvailable
Long-form
5
Area Between Curves: Functions of yAvailable
Long-form
6
Average Value of Functions on IntervalsAvailable
Long-form
7
Disc Method: Revolving Around Other AxesAvailable
Long-form
8
Disc Method: Revolving Around x/y AxesAvailable
Long-form
9
Position, Velocity, and Acceleration Using IntegralsAvailable
Long-form
10
Volumes with Cross Sections: Squares/RectanglesAvailable
Long-form
11
Washer Method: Revolving Around x/y AxesAvailable
Long-form
12
Washer Method: Revolving Around Other AxesAvailable
Long-form
13
Volumes with Cross Sections: Triangles/SemicirclesAvailable
Long-form

Integration and Accumulation of Change

14 core skills10% total weight
0/14 completed
14 skills to mastery
1
Behavior of Accumulation Functions Involving AreaAvailable
Long-form
2
Riemann Sums and NotationAvailable
Long-form
3
Applying Properties of Definite IntegralsAvailable
Long-form
4
Approximating Areas With Riemann SumsAvailable
Long-form
5
Evaluating Improper IntegralsAvailable
Long-form
6
Exploring Accumulations of ChangeAvailable
Long-form
7
Finding Antiderivatives and Indefinite IntegralsAvailable
Long-form
8
Fundamental Theorem of Calculus: Accumulation FunctionsAvailable
Long-form
9
Fundamental Theorem of Calculus: Definite IntervalsAvailable
Long-form
10
Integrating, Long Division, Completing the SquareAvailable
Long-form
11
Integrating Using SubstitutionAvailable
Long-form
12
Integrating Using Integration By PartsAvailable
Long-form
13
Selecting Techniques for AntidifferentiationAvailable
Long-form
14
Using Linear Partial FractionsAvailable
Long-form

Parametric, Polar, and Vector Functions

9 core skills10% total weight
0/9 completed
9 skills to mastery
1
Motion Problems, Parametric, Vector-Valued FunctionsAvailable
Long-form
2
Arc Lengths of Curves: Parametric EquationsAvailable
Long-form
3
Area Bounded By Two Polar CurvesAvailable
Long-form
4
Area of a Polar RegionAvailable
Long-form
5
Defining and Differentiating Parametric EquationsAvailable
Long-form
6
Defining and Differentiating Vector-Valued FunctionsAvailable
Long-form
7
Integrating Vector-Valued FunctionsAvailable
Long-form
8
Polar Coordinates and DifferentiationAvailable
Long-form
9
Second Derivatives of Parametric EquationsAvailable
Long-form

Differentiation: Definition and Fundamental Properties

10 core skills10% total weight
0/10 completed
10 skills to mastery
1
Derivatives of Reciprocal Trig FunctionsAvailable
Long-form
2
Applying the Power RuleAvailable
Long-form
3
Connecting Differentiability and ContinuityAvailable
Long-form
4
Derivative Rules of Constant, Sum, DifferenceAvailable
Long-form
5
Derivative NotationAvailable
Long-form
6
Derivatives of Trigonometry and Logarithmic FunctionsAvailable
Long-form
7
Estimating Derivatives of a FunctionAvailable
Long-form
8
Rate of Change at a PointAvailable
Long-form
9
The Quotient RuleAvailable
Long-form
10
The Product RuleAvailable
Long-form

Limits and Continuity

16 core skills10% total weight
0/16 completed
16 skills to mastery
1
Algebraic Properties of LimitsAvailable
Long-form
2
Confirming Continuity over an IntervalAvailable
Long-form
3
Connecting Multiple Representations of LimitsAvailable
Long-form
4
Connecting Infinite Limits and Vertical AsymptotesAvailable
Long-form
5
Defining Continuity at a PointAvailable
Long-form
6
Defining Limits and Using Limit NotationAvailable
Long-form
7
Determining Limits Using Algebraic ManipulationAvailable
Long-form
8
Determining Limits Using the Squeeze TheoremAvailable
Long-form
9
Estimating Limit Values from GraphsAvailable
Long-form
10
Estimating Limit Values from TablesAvailable
Long-form
11
Exploring Types of DiscontinuitiesAvailable
Long-form
12
Introducing CalculusAvailable
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

Infinite Sequences and Series

15 core skills10% total weight
0/15 completed
15 skills to mastery
1
Alternating Series Error BoundAvailable
Long-form
2
Alternating Series Test for ConvergenceAvailable
Long-form
3
Comparison Tests for ConvergenceAvailable
Long-form
4
Defining Convergent and Divergent Infinite SeriesAvailable
Long-form
5
Determining Absolute or Conditional ConvergenceAvailable
Long-form
6
Finding Taylor Polynomial Approximations of FunctionsAvailable
Long-form
7
Harmonic Series and p-SeriesAvailable
Long-form
8
Integral Test for ConvergenceAvailable
Long-form
9
Lagrange Error BoundAvailable
Long-form
10
Power Series: Radius, Interval of ConvergenceAvailable
Long-form
11
Ratio Test for ConvergenceAvailable
Long-form
12
Representing Series as Power SeriesAvailable
Long-form
13
Taylor and Maclaurin SeriesAvailable
Long-form
14
The nth Term Test for DivergenceAvailable
Long-form
15
Working with Geometric SeriesAvailable
Long-form

Analytical Applications of Differentiation

12 core skills10% total weight
0/12 completed
12 skills to mastery
1
Candidates TestAvailable
Long-form
2
Concavity of Functions Over Their DomainsAvailable
Long-form
3
Connecting a Function and Its DerivativesAvailable
Long-form
4
Determining Intervals on Increasing, Decreasing FunctionsAvailable
Long-form
5
Exploring Behaviors of Implicit RelationsAvailable
Long-form
6
Extreme Value Theorem, Extrema, Critical PointsAvailable
Long-form
7
First Derivative TestAvailable
Long-form
8
Introduction to Optimization ProblemsAvailable
Long-form
9
Mean Value TheoremAvailable
Long-form
10
Second Derivative TestAvailable
Long-form
11
Sketching Graphs of Functions and DerivativesAvailable
Long-form
12
Solving Optimization ProblemsAvailable
Long-form

Differential Equations

9 core skills10% total weight
0/9 completed
9 skills to mastery
1
Euler's MethodAvailable
Long-form
2
Exponential Models with Differential EquationsAvailable
Long-form
3
Finding General Solutions: Separation of VariablesAvailable
Long-form
4
Initial Conditions and Separation of VariablesAvailable
Long-form
5
Logistic Models with Differential EquationsAvailable
Long-form
6
Modeling Situations with Differential EquationsAvailable
Long-form
7
Reasoning Using Slope FieldsAvailable
Long-form
8
Sketching Slope FieldsAvailable
Long-form
9
Verifying Solutions for Differential EquationsAvailable
Long-form