Mr Hickman's Class 2022-2023
Mr Hickman does NOT participate in social media!
  • Home
    • About
    • CC Math Standards Page >
      • CC Functions
    • VIDEOS 2020-2021
    • Desmos Library Directory >
      • Desmos How to VIDEOS 1
      • Desmos: How Do I Library
      • Desmos Coordinate Geometry
      • Desmos Geometry
      • Algebra Desmos Library >
        • Lines and Linear Functions
      • Quadratics 101 >
        • Parabola 101: Vertex Form Function
        • Parabola 101: Vertex Form Relations
      • Desmos: Advanced Algebra >
        • Non Linear Systems
      • Desmos Trigonometry
      • Desmos PreCalculus >
        • Desmos: Absolute Value Function
        • Desmos: Piecewise Functions
        • Desmos Polar Coordinate System
      • Desmos: AP Calculus
    • Digital Resources: >
      • Digital Resources: Number Line, Lines, and Linear Systems
      • Geogebra Library Directory
      • TI Nspire Library Directory >
        • TI Nspire How to VIDEOS 1
      • YOU Tube Library Directory
      • KHAN Academy Library Directory
      • "Other" Websites Library Directory
    • Technology Tutorials >
      • Building a Weebly Page >
        • How to Use a Template page to add pages quickly
      • MS Teams Technology Tutorials
      • MS Whiteboard Technology Tutorials
      • Flip Grid Technology Tutorials
      • One Note Technology Tutorials
      • Small PDF Technology Tutorials
    • What calculator should I get?
    • SAT Review 2019 >
      • Complex Number Review
  • ALGEBRA
    • Power Practice
    • Radical Practice
    • Exponential Practice
    • Logarithm Practice
    • Logarithmic Practice
    • Rational Functions
  • Geometry
    • Geometry File Library
    • BOY Review: Solve Equations 1
    • Week 4 Geometry Enriched
    • Week 5 Geometry Enriched
    • Enriched Geometry Semester 1 Archive
  • PRE-CALC
  • AP PRE-CALC
  • AP CALC AB
    • AP Calculus Objectives from AP Central
    • AP Calc AB Exam Details & Prep
    • AP CALC AB UNIT 1
    • AP CALC AB UNIT 2
    • AP CALC AB UNIT 3
    • AP CALC AB UNIT 4
    • AP CALC AB UNIT 5
    • AP CALC AB UNIT 6
    • AP CALC AB UNIT 7
    • AP CALC AB UNIT 8
    • CALC AB WK 4 GP4
    • AP Calculus Worksheets
  • Data Prob Stats

 AP Calculus AB: Unit 1 Section 1


Picture

Average Rate of Change

  • Finding AROC from a function over a specific interval
    1. find the related points
    2. determine slope between the two points
    3. the slope between the two points is the average rate of change from the given domain values from given intervals
Picture

Slope of a Secant Line

Finding slope of the secant line from a function over a specific interval
  1. find the related points
  2. determine slope between the two points
  3. the slope between the two points is the slope of the secant line
Picture

Instantaneous Rate of Change

Finding IROC of the tangent line from a function over at a specific given point point
  1. find the related point
  2. determine the limit of the function at the specific x coordinate of the given point
  3. OR determine the value of the derivative function at the specific x coordinate of the given point

This method of determining IROC has limitations 
  • can only be used for a particular value of a
  • It does help to be able to factor polynomials with this method
  • It does help to able to perform synthetic division of polynomials with this method
Picture

Both of these methods require tedious algebraic manipulation to complete.
  • It does help to be able to rewrite algebraic expressions with these methods 
  • These methods should be useful for all domain values of x not just one particular example
  • When algebra is done properly denominators h and delta x should be able to be canceled out
Picture
Picture

Slope of the Tangent Line

Finding slope of the tangent line from a function over at a specific given point point
  1. find the related point
  2. determine the limit of the function at the specific x coordinate of the given point
  3. OR determine the value of the derivative function at the specific x coordinate of the given point
Picture
Picture
Picture

Picture
  • Average Rate of Change AROC
  • Average Rate of Change (AROC), Secant Line, and Tangent Line & Instantaneous Rate of Change (IROC) 

Picture
  • ​GEOGEBRA AROC IROC BOOK
  • GEOGEBRA Calculus TB BOOK 

Picture
  • KA link: Average Rate of Change (AROC)
  • ​KA link: Instantaneous Rate of Change (IROC)

Picture
  • CK12 link: Average Rate of Change (AROC) 
  • CK12 link: Instantaneous Rate of Change (IROC) 
  • Calculus Directory​

Practice

These worksheets allows practice with 
AROC and Equations of Secants
  • KUTA 7.01 AROC Practice
    • DESMOS Related Graphs
  • KUTA 03 AROC Practice 2
    • ​DESMOS Related Graphs​​​
  • PON 2.1 PRACTICE
    • PON 2.1 PRACTICE Solutions
  • PON 2.1 ASSIGNMENT

Links and Resources

Picture
  • Paul's Online Notes for Calc 1​
  • PON NOTES: 2.1 Tangent Lines and Rates of Change ​

Picture
  • MIT Video: Rates of Change

Picture

Picture
  • PL Lecture 1.1: Intro to Limits (1:27:25)
  • PL Lecture 1.5: Slope of a Curve, Velocity, and Rates of Change (1:50:12)
  • ​PL Calculus Directory​

Picture
  • OCT Video: Intro to Limits (11:07)
  • ​​OC Calculus Directory 

Picture
  • PRB Video: Why are limits important in Calculus? (9:32)​
  • PRB Calculus Directory​​

Picture
  • PDE Video: Intro to Calculus (8:40)
  • PDE Video: The Slope of the Tangent Line (5:29)
  • PDE Video: Rates of Change (5:31)
  • ​PDE Calculus Directory​
Picture
  • MSMT Video: Average Rate of Change 1 (4:43)
  • MSMT Video: Average Rate of Change 2 (7:04)
  • MSMT Video: Average Rate of Change 3 (1:54)
  • MSMT Video: Average Rate of Change 4 (2:26)
  • MSMT Video: Average Rate of Change WORD Problem (2:54)
  • MSMT Video: Approximating Instaneous Rate of Change 1 (4:45)
  • MSMT Video: Approximating Instaneous Rate of Change 2 (8:08)
  • MSMT Video: Intro to Calculus (4:14)
  • ​​MSMT Calculus Directory​

Picture
  • DO Video: Intro Chapter Playlist 11 videos
  • ​​DO Calculus Directory​

Picture
  • Calculus Directory

Picture
  • MIF Intro to Calculus
  • MIF Calculus Directory

Picture

Picture
  • link to SH Desmos AP Calculus

Picture
​Mr Hickman's Resources
  • SH Calculus You Tube Channel 
  • optimization 2018-2019



Mr Hickman is available for assistance after school practically anytime.  Talk to me to be certain that I am aware you are coming and 99% of the time I will be able to help you