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CoursesCG1 Math and Computer Science

AP course · CG1 Math and Computer Science

AP Calculus BC.

The whole course, unit by unit. Build your understanding with the published lessons and resources, and keep your progress as you go.

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Introducing Calculus: Can Change Occur at an Instant?

Limits and Continuity

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Course progressQuestion bank ↗

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— of 111 lessons complete

Limits and Continuity
Differentiation: Definition and Fundamental Properties
Differentiation: Composite, Implicit, and Inverse Functions
Contextual Applications of Differentiation
Analytical Applications of Differentiation
Integration and Accumulation of Change
Differential Equations
Applications of Integration
Parametric Equations, Polar Coordinates, and Vector-Valued Functions
Infinite Sequences and Series

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111/111

01

Limits and Continuity

16 lessons · 1 unit

Unit 01

Limits and Continuity

—/16

Introducing Calculus: Can Change Occur at an Instant?Lesson
Defining Limits and Using Limit NotationLesson
Estimating Limit Values from GraphsLesson
Estimating Limit Values from TablesLesson
Determining Limits Using Algebraic Properties of LimitsLesson
Determining Limits Using Algebraic ManipulationLesson
Selecting Procedures for Determining LimitsLesson
Determining Limits Using the Squeeze TheoremLesson
Connecting Multiple Representations of LimitsLesson
Exploring Types of DiscontinuitiesLesson
Defining Continuity at a PointLesson
Confirming Continuity over an IntervalLesson
Removing DiscontinuitiesLesson
Connecting Infinite Limits and Vertical AsymptotesLesson
Connecting Limits at Infinity and Horizontal AsymptotesLesson
Working with the Intermediate Value Theorem (IVT)Lesson

02

Differentiation: Definition and Fundamental Properties

10 lessons · 1 unit

Unit 01

Differentiation: Definition and Fundamental Properties

—/10

Defining Average and Instantaneous Rates of Change at a PointLesson
Defining the Derivative of a Function and Using Derivative NotationLesson
Estimating Derivatives of a Function at a PointLesson
Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not ExistLesson
Applying the Power RuleLesson
Derivative Rules: Constant, Sum, Difference, and Constant MultipleLesson
Derivatives of cos x, sin x, e^x, and ln xLesson
The Product RuleLesson
The Quotient RuleLesson
Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant FunctionsLesson

03

Differentiation: Composite, Implicit, and Inverse Functions

6 lessons · 1 unit

Unit 01

Differentiation: Composite, Implicit, and Inverse Functions

—/6

The Chain RuleLesson
Implicit DifferentiationLesson
Differentiating Inverse FunctionsLesson
Differentiating Inverse Trigonometric FunctionsLesson
Selecting Procedures for Calculating DerivativesLesson
Calculating Higher Order DerivativesLesson

04

Contextual Applications of Differentiation

7 lessons · 1 unit

Unit 01

Contextual Applications of Differentiation

—/7

Interpreting the Meaning of the Derivative in ContextLesson
Straight-Line Motion: Connecting Position, Velocity, and AccelerationLesson
Rates of Change in Applied Contexts Other Than MotionLesson
Introduction to Related RatesLesson
Solving Related Rates ProblemsLesson
Approximating Values of a Function Using Local Linearity and LinearizationLesson
Using L’Hospital’s Rule for Determining Limits of Indeterminate FormsLesson

05

Analytical Applications of Differentiation

12 lessons · 1 unit

Unit 01

Analytical Applications of Differentiation

—/12

Using the Mean Value TheoremLesson
Extreme Value Theorem, Global Versus Local Extrema, and Critical PointsLesson
Determining Intervals on Which a Function Is Increasing or DecreasingLesson
Using the First Derivative Test to Determine Relative (Local) ExtremaLesson
Using the Candidates Test to Determine Absolute (Global) ExtremaLesson
Determining Concavity of Functions over Their DomainsLesson
Using the Second Derivative Test to Determine ExtremaLesson
Sketching Graphs of Functions and Their DerivativesLesson
Connecting a Function, Its First Derivative, and Its Second DerivativeLesson
Introduction to Optimization ProblemsLesson
Solving Optimization ProblemsLesson
Exploring Behaviors of Implicit RelationsLesson

06

Integration and Accumulation of Change

14 lessons · 1 unit

Unit 01

Integration and Accumulation of Change

—/14

Exploring Accumulations of ChangeLesson
Approximating Areas with Riemann SumsLesson
Riemann Sums, Summation Notation, and Definite Integral NotationLesson
The Fundamental Theorem of Calculus and Accumulation FunctionsLesson
Interpreting the Behavior of Accumulation Functions Involving AreaLesson
Applying Properties of Definite IntegralsLesson
The Fundamental Theorem of Calculus and Definite IntegralsLesson
Finding Antiderivatives and Indefinite Integrals: Basic Rules and NotationLesson
Integrating Using SubstitutionLesson
Integrating Functions Using Long Division and Completing the SquareLesson
Integrating Using Integration by PartsLesson
Integrating Using Linear Partial FractionsLesson
Evaluating Improper IntegralsLesson
Selecting Techniques for AntidifferentiationLesson

07

Differential Equations

9 lessons · 1 unit

Unit 01

Differential Equations

—/9

Modeling Situations with Differential EquationsLesson
Verifying Solutions for Differential EquationsLesson
Sketching Slope FieldsLesson
Reasoning Using Slope FieldsLesson
Approximating Solutions Using Euler’s MethodLesson
Finding General Solutions Using Separation of VariablesLesson
Finding Particular Solutions Using Initial Conditions and Separation of VariablesLesson
Exponential Models with Differential EquationsLesson
Logistic Models with Differential EquationsLesson

08

Applications of Integration

13 lessons · 1 unit

Unit 01

Applications of Integration

—/13

Finding the Average Value of a Function on an IntervalLesson
Connecting Position, Velocity, and Acceleration of Functions Using IntegralsLesson
Using Accumulation Functions and Definite Integrals in Applied ContextsLesson
Finding the Area Between Curves Expressed as Functions of xLesson
Finding the Area Between Curves Expressed as Functions of yLesson
Finding the Area Between Curves That Intersect at More Than Two PointsLesson
Volumes with Cross Sections: Squares and RectanglesLesson
Volumes with Cross Sections: Triangles and SemicirclesLesson
Volume with Disc Method: Revolving Around the x- or y-AxisLesson
Volume with Disc Method: Revolving Around Other AxesLesson
Volume with Washer Method: Revolving Around the x- or y-AxisLesson
Volume with Washer Method: Revolving Around Other AxesLesson
The Arc Length of a Smooth, Planar Curve and Distance TraveledLesson

09

Parametric Equations, Polar Coordinates, and Vector-Valued Functions

9 lessons · 1 unit

Unit 01

Parametric Equations, Polar Coordinates, and Vector-Valued Functions

—/9

Defining and Differentiating Parametric EquationsLesson
Second Derivatives of Parametric EquationsLesson
Finding Arc Lengths of Curves Given by Parametric EquationsLesson
Defining and Differentiating Vector-Valued FunctionsLesson
Integrating Vector-Valued FunctionsLesson
Solving Motion Problems Using Parametric and Vector-Valued FunctionsLesson
Defining Polar Coordinates and Differentiating in Polar FormLesson
Find the Area of a Polar Region or the Area Bounded by a Single Polar CurveLesson
Finding the Area of the Region Bounded by Two Polar CurvesLesson

10

Infinite Sequences and Series

15 lessons · 1 unit

Unit 01

Infinite Sequences and Series

—/15

Defining Convergent and Divergent Infinite SeriesLesson
Working with Geometric SeriesLesson
The nth Term Test for DivergenceLesson
Integral Test for ConvergenceLesson
Harmonic Series and p-SeriesLesson
Comparison Tests for ConvergenceLesson
Alternating Series Test for ConvergenceLesson
Ratio Test for ConvergenceLesson
Determining Absolute or Conditional ConvergenceLesson
Alternating Series Error BoundLesson
Finding Taylor Polynomial Approximations of FunctionsLesson
Lagrange Error BoundLesson
Radius and Interval of Convergence of Power SeriesLesson
Finding Taylor or Maclaurin Series for a FunctionLesson
Representing Functions as Power SeriesLesson

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