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Year-Long AP Calculus Course
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Entire full year of powerpoint presentation lessons, notes, worksheets and google slides activities. Some things have answer keys and other don't.

AP Calculus Course Curriculum Content:

Unit 1 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)

Unit 2 Differentiation: Defining and Basic Derivative Rules

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, ex, 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

Unit 3 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

Unit 4 Contextual Applications of Differentiation

4.1   Interpreting the Meaning of the Derivative in Context

4.2   Straight-Line Motion; Connecting Position, Velocity, & Accelerations

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

Unit 5 Analytical Applications of Derivatives

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 Absolutes (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

Unit 6 Calculus 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 Notations

6.9     Integrating Using Substitution

6.10   Integrating Functions Using Long Division and Completing the Square

6.11   Integrating Using Integration by Parts (BC only)

6.12   Using Linear Partial Fractions (BC only)

6.13   Evaluating Improper Integrals (BC only)

6.14   Selecting Techniques for Antidifferentiation


Unit 7 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

7.5   Approximating Solutions Using Euler’s Method (BC only)

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

7.9   Logistic Models with Differential Equations (BC only)

Unit 8 Applications of Integration
8.1    Finding the Average Value of a Function on an Interval
8.2    Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3    Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4    Finding the Area Between Curves Expressed as Functions of x 
8.5    Finding the Area Between Curves Expressed as Functions of y
8.6    Finding the Area Between Curves That Intersect at More Than Two Points
8.7    Volumes with Cross Sections: Squares and Rectangles
8.8    Volumes with Cross Sections: Triangles and Semicircles
8.9    Volume with Disc Method: Revolving Around the x- or y-Axis
8.10  Volume with Disc Method: Revolving Around Other Axes
8.11  Volume with Washer Method: Revolving Around the x- or y-Axis
8.12  Volume with Washer Method: Revolving Around Other Axes
8.13  The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC only)


Everything is compressed to a zip file.

*Don't upload the whole zip file to google drive. To unzip a single file or folder, open the zipped folder, then copy & paste or drag the file or folder from the zipped folder to a new location. If you can't open a file and get an error telling you to change the zip file name, you have to right click and rename the whole zip file to a shorter name and it will open*

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Year-Long AP Calculus Course

Indian River School
6 Followers
$95.00

Highlights

Grades icon
Grades
9th - 12th
Subjects icon
Subjects
Teaching Duration
1 Year

Description

Entire full year of powerpoint presentation lessons, notes, worksheets and google slides activities. Some things have answer keys and other don't.

AP Calculus Course Curriculum Content:

Unit 1 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)

Unit 2 Differentiation: Defining and Basic Derivative Rules

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, ex, 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

Unit 3 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

Unit 4 Contextual Applications of Differentiation

4.1   Interpreting the Meaning of the Derivative in Context

4.2   Straight-Line Motion; Connecting Position, Velocity, & Accelerations

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

Unit 5 Analytical Applications of Derivatives

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 Absolutes (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

Unit 6 Calculus 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 Notations

6.9     Integrating Using Substitution

6.10   Integrating Functions Using Long Division and Completing the Square

6.11   Integrating Using Integration by Parts (BC only)

6.12   Using Linear Partial Fractions (BC only)

6.13   Evaluating Improper Integrals (BC only)

6.14   Selecting Techniques for Antidifferentiation


Unit 7 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

7.5   Approximating Solutions Using Euler’s Method (BC only)

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

7.9   Logistic Models with Differential Equations (BC only)

Unit 8 Applications of Integration
8.1    Finding the Average Value of a Function on an Interval
8.2    Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3    Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4    Finding the Area Between Curves Expressed as Functions of x 
8.5    Finding the Area Between Curves Expressed as Functions of y
8.6    Finding the Area Between Curves That Intersect at More Than Two Points
8.7    Volumes with Cross Sections: Squares and Rectangles
8.8    Volumes with Cross Sections: Triangles and Semicircles
8.9    Volume with Disc Method: Revolving Around the x- or y-Axis
8.10  Volume with Disc Method: Revolving Around Other Axes
8.11  Volume with Washer Method: Revolving Around the x- or y-Axis
8.12  Volume with Washer Method: Revolving Around Other Axes
8.13  The Arc Length of a Smooth, Planar Curve and Distance Traveled (BC only)


Everything is compressed to a zip file.

*Don't upload the whole zip file to google drive. To unzip a single file or folder, open the zipped folder, then copy & paste or drag the file or folder from the zipped folder to a new location. If you can't open a file and get an error telling you to change the zip file name, you have to right click and rename the whole zip file to a shorter name and it will open*

Report this resource to TPT
Reported resources will be reviewed by our team. Report this resource to let us know if this resource violates TPT's content guidelines.

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