AP Calculus

Tim Brzezinski, Χρ.Έλληνας, Starla Negin, Mar 10, 2017

Contains applets that can be used to foster discovery learning, meaningful remediation, differentiation, and assessment within an AP Calculus-AB or Ap Calculus-BC class (Calculus 1 & Calculus 2 at most colleges and universities.)

Table of Contents

  1. Preliminary Review Topics
    1. Pythagorean Trigonometric Identity (1)
    2. Trig ID Movie (II)
    3. Trig ID Movie (III)
    4. Exponential Functions: Graphs
    5. Logarithmic Functions: Graphs
    6. Derivatives of Inverse Functions
    7. Oil Pipeline Optimization Problem
  2. Limits & Continuity
    1. Limits: Introductory Questions
    2. One CRAZY Limit !!!
    3. Cont in uity
    4. IVT Dynamic Illustrator
    5. Continuity Questions
    6. Vertical Asymptote (Defined as a Limit)
    7. Horizontal Asymptote (Defined as a Limit)
    8. One Special Limit
  3. Derivatives of Special Functions
    1. Derivatives (Intro)-2
    2. When does f'(x) = f(x)?
    3. Important Trig Limits
    4. Mean Value Theorem (Without Words)
  4. Derivatives & Differentation Techniques
    1. Average Velocity
    2. Average to Instantaneous (Intro)
    3. Constructing Graphs of Derivative Functions (Intuitively)
    4. Derivatives (Intro)-1
    5. Derivatives (Intro)-2
    6. 3-Way Color-Changing Derivative Grapher
    7. Sketch the Derivative (Warm Up)
    8. Graphing The Derivative of a Function
    9. Derivative of a Product
    10. Derivative of Sine & Cosine Functions (Quick Investigation)
    11. Derivative of Tangent Function (Investigation)
    12. Implicit Differentiation: Intro
    13. Folium of Descartes
    14. Implicit Differentiation (Quick Check)
    15. Derivative of Arcsine Function
    16. Derivative of Arccosine Function
    17. Derivative of Arctangent Function
    18. Derivatives of Inverse Functions
    19. Derivative of Natural Log Function
  5. Related Rates
    1. Related Rates (1)
    2. Related Rates (2)
    3. Falling Ladder !!!
    4. Related Rates (3)
    5. Related Rates: Adjustable Cone with dh/dt Constant
    6. Related Rates: Adjustable Cone with dV/dt Constant
    7. Related Rates (Rolling Carts Problem)
    8. Linearization Checker (Calculus)
  6. Linearization of Functions
    1. Linearization Illustrator (Calculus)
    2. Linearization Checker (Calculus)
  7. Closed Interval Method
    1. Critical Numbers & Critical Points of Functions (Intro)
    2. The Closed Interval Method (Application Problem)
  8. Optimization Problems
    1. Optimization Challenge 1
    2. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
    3. Critical Numbers & Critical Points of Functions (Intro)
    4. Honeybee Population (Growth Rate Question)
    5. Oil Pipeline Optimization Problem
    6. Distance From Point to Graph
  9. Riemann Sums; Indefinite and Definite Integrals
    1. Definite Integral Illustrator (I)
  10. Areas and Volumes
    1. Definite Integrals: Sum
    2. What Makes a Function Even?
    3. What Makes a Function Odd?
    4. Odd Functions: Another Look (Take 2)!
    5. U-Substitution (Definite Integrals)
    6. Areas Between Curves (Intro)
    7. Area Between Curves
    8. Area Between 2 Curves
    9. Disc Action!!!
    10. Washer Action!!! (1)
    11. Washer Action !!! (2) - Calculus
    12. Cylindrical Shell Action!!! (1)
    13. Cylindrical Shell Action!!! (2)
    14. V. of Solid NOT of Revolution
    15. Areas & Volumes: Culminating Activity
  11. Average Value and Arc Length
    1. Average Value of a Function
    2. Arc Length (Calculus)
  12. Integration Techniques
    1. Sine & Cosine of a Sum: Discovery
    2. Partial Fraction Decomposition Calculator

1.

Preliminary Review Topics

  • 1. Pythagorean Trigonometric Identity (1)
  • 2. Trig ID Movie (II)
  • 3. Trig ID Movie (III)
  • 4. Exponential Functions: Graphs
  • 5. Logarithmic Functions: Graphs
  • 6. Derivatives of Inverse Functions
  • 7. Oil Pipeline Optimization Problem

1.1.

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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Limits & Continuity

  • 1. Limits: Introductory Questions
  • 2. One CRAZY Limit !!!
  • 3. Cont in uity
  • 4. IVT Dynamic Illustrator
  • 5. Continuity Questions
  • 6. Vertical Asymptote (Defined as a Limit)
  • 7. Horizontal Asymptote (Defined as a Limit)
  • 8. One Special Limit

2.1.

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2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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3.

Derivatives of Special Functions

  • 1. Derivatives (Intro)-2
  • 2. When does f'(x) = f(x)?
  • 3. Important Trig Limits
  • 4. Mean Value Theorem (Without Words)

3.1.

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3.2.

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3.3.

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3.4.

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4.

Derivatives & Differentation Techniques

  • 1. Average Velocity
  • 2. Average to Instantaneous (Intro)
  • 3. Constructing Graphs of Derivative Functions (Intuitively)
  • 4. Derivatives (Intro)-1
  • 5. Derivatives (Intro)-2
  • 6. 3-Way Color-Changing Derivative Grapher
  • 7. Sketch the Derivative (Warm Up)
  • 8. Graphing The Derivative of a Function
  • 9. Derivative of a Product
  • 10. Derivative of Sine & Cosine Functions (Quick Investigation)
  • 11. Derivative of Tangent Function (Investigation)
  • 12. Implicit Differentiation: Intro
  • 13. Folium of Descartes
  • 14. Implicit Differentiation (Quick Check)
  • 15. Derivative of Arcsine Function
  • 16. Derivative of Arccosine Function
  • 17. Derivative of Arctangent Function
  • 18. Derivatives of Inverse Functions
  • 19. Derivative of Natural Log Function

4.1.

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4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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4.14.

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4.15.

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4.16.

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4.17.

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4.18.

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4.19.

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5.

Related Rates

  • 1. Related Rates (1)
  • 2. Related Rates (2)
  • 3. Falling Ladder !!!
  • 4. Related Rates (3)
  • 5. Related Rates: Adjustable Cone with dh/dt Constant
  • 6. Related Rates: Adjustable Cone with dV/dt Constant
  • 7. Related Rates (Rolling Carts Problem)
  • 8. Linearization Checker (Calculus)

5.1.

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5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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6.

Linearization of Functions

  • 1. Linearization Illustrator (Calculus)
  • 2. Linearization Checker (Calculus)

6.1.

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6.2.

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7.

Closed Interval Method

  • 1. Critical Numbers & Critical Points of Functions (Intro)
  • 2. The Closed Interval Method (Application Problem)

7.1.

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7.2.

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8.

Optimization Problems

  • 1. Optimization Challenge 1
  • 2. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
  • 3. Critical Numbers & Critical Points of Functions (Intro)
  • 4. Honeybee Population (Growth Rate Question)
  • 5. Oil Pipeline Optimization Problem
  • 6. Distance From Point to Graph

8.1.

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8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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9.

Riemann Sums; Indefinite and Definite Integrals

  • 1. Definite Integral Illustrator (I)

9.1.

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10.

Areas and Volumes

  • 1. Definite Integrals: Sum
  • 2. What Makes a Function Even?
  • 3. What Makes a Function Odd?
  • 4. Odd Functions: Another Look (Take 2)!
  • 5. U-Substitution (Definite Integrals)
  • 6. Areas Between Curves (Intro)
  • 7. Area Between Curves
  • 8. Area Between 2 Curves
  • 9. Disc Action!!!
  • 10. Washer Action!!! (1)
  • 11. Washer Action !!! (2) - Calculus
  • 12. Cylindrical Shell Action!!! (1)
  • 13. Cylindrical Shell Action!!! (2)
  • 14. V. of Solid NOT of Revolution
  • 15. Areas & Volumes: Culminating Activity

10.1.

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10.2.

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10.3.

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10.4.

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10.5.

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10.6.

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10.7.

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10.8.

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10.9.

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10.10.

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10.11.

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10.12.

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10.13.

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10.14.

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10.15.

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11.

Average Value and Arc Length

  • 1. Average Value of a Function
  • 2. Arc Length (Calculus)

11.1.

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11.2.

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12.

Integration Techniques

  • 1. Sine & Cosine of a Sum: Discovery
  • 2. Partial Fraction Decomposition Calculator

12.1.

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12.2.

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Information