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AP Calculus

Week 5

Picture
9-9-19 to 9-13-19

Overview of Topics

Links to Previous Weeks

  • Week 1: 8/14/19 to 8/16/19
  • Week 2: ​8/19/19 to 8/23/19​​​
  • Week 3: ​8/26/19 to 8/30/19​​​
  • Week 4: ​9/2/19 to 9/6/19

Exam Date for 2019-2020 School Year
​8:00 A.M. Tuesday May 5 
​


Schedule 9/9/19 to 9/13/19

monday
  • Review FA on HA VA and EBM
  • how to show positive and negative infinity from rational functions
  • review how to "creaate" a continuous function from a general piecewise function (unknown coefficients a, b problems)
  • Start IVT (intermediate value theorem) if time permits
tuesday
  • IVT theorem
  • review for quiz 2
  • Work on quiz 2 study guide
wednesday (Shortened Schedule Day Does NOT APPLY)
  • Quiz 2
thursday
  • Finish IVT
  • Writing equations of Normal Lines and Tangent lines for a variety of functions
  • Formative assessment on IVT and normal and tangent lines
friday
  • Review Activity for Quiz 3

Topics

Be able to use limit properties to show FORMALLY
  • that a function has a vertical asymptote
  • that a function has a horizontal asymptote
  • a function has the same Right End Behavior Model (REBM) as a simpler version of the original model
  • a function has the same Left End Behavior Model (LEBM) as a simpler version of the original model
  • limits of more advanced functions
Be able to establish the conditions of continuity
​​Be able to distinguish the different types and causes of discontinuities
  • jump/gap discontinuity
  • removable /point discontinuity
  •  infinite discontinuity
  • oscillating discontinuity
Be able to state and use the IVT (intermediate value theorem)
  • how to find "roots" of difficult to solve equations
  • how to find solutions to difficult to solve equations
  • connect IVT to Fundamental Theorem of Algebra 
  • review how to quickly use tables to show where a root would occur
    • hint sign change is important!
  • connect solutions to an equation is actually the location of a root of a similar function with a new constant
Be able to find slope of tangent and normal lines of polynomials 
  • Connect tangent slope to normal slope
  • Be able to write equations of lines in slope intercept form and point slope form

Applicable Learning Objectives from AP Central Calculus AB


Practice ​


Online Practice with Solutions

Paul's Online Practice Chapter 2


FDWK Textbook Assignments

FDWK Section 2.1 pp 66-67
  • assigned 8/19/19 to 8/23/19
  • See Desmos Solutions Below
​FDWK Section 2.2
  • assigned 8/26/19 to 8/30/19
​FDWK Section 2.3
  • assigned 9/2/19 to 9/6/19
​FDWK Section 2.4
  • assigned 9/2/19 to 9/6/19
​

Handouts and Formative Assessments

Sample Quiz and Study Guide for Quiz 1
  • ​assigned 8-19-19 to 8-26-19
  • Solutions to the sample quiz and study guide​
Continuity Practice Worksheet
  • related desmos file


Additional Resources
​(For This Week)


Khan Academy

  • IVT Intermediate Value Theorem
  • Limits and Continuity​

Other Websites

math is fun
  • IVT Definition
​Magoosh
  • IVT Definition
​Lumen
  • IVT Definition

YOU Tube

  • ​proof of special sine limit 1​
  • proof of special sine limit 2
  • ​finding limits through conjugates
  • ​limits and absolute value
​End Behavior Models
  • Left and right end behavior models 
  • Left and Right End Behavior Models 2
Limits at Infinity
  • Professor Leonard Video on limits at infinity
  • Limits at infinity HA and VA 
  • Limits at Infinity HA 
  • Limits at Infinity
  • ​Limits at infinity
  • Limits at Infinity with radicals​
Limits and Continuity Review
  • Limits and Continuity
  • Three Step Continuity Test
  • Continuity 
IVT
  • IVT video 1
  • IVT video 2
  • IVT video 3
  • IVT video 4
  • IVT video 5
  • IVT video 6
  • IVT video 7
​​Equations of Normal lines
  • Normal Line video 1
  • Normal Line video 2
  • Normal Line video 3
  • ​Normal Lines video 4

THIS Website

Topics Covered in AP Calculus AB

  • Limits and Continuity
  • ​Differentiation: Definition and Fundamental Properties
  • ​​Differentiation:: Composite, Implicit, and Inverse Functions
  • ​Contextual Applications of Differentiation
  • ​​Analytical Applications of Differentiation
  • ​Differential Equations
  • Integration and Accumulation of Change
  • Applications of Integration​

AP Central Website

Other Websites


Geogebra 


Desmos


FDWK Section 2.1 pp 66-67

FDWK 2.1 Assignment Links
  • ts and ContinuityLimits and ContinuityLimits and Continuity
  • ​Desmos #7-14 ​
  • ​Desmos #11
  • Desmos #11b
  • ​Desmos #15
  • Desmos #16
  • ​Desmos #17
  • ​Desmos #18
  • ​​Desmos #19​​
  • ​Desmos #20
  • ​Desmos #21
  • ​Desmos #22
  • ​Desmos #23
  • ​Desmos #24
  • ​Desmos #25
  • ​Desmos #26
  • ​Desmos #27
  • ​Desmos #28
  • ​​Desmos #29
  • Desmos #30
  • Desmos #31
  • Desmos #32
  • Desmos #33
  • Desmos #34
  • Desmos #35
  • ​Desmos #35b
  • ​Desmos #36
  • ​Desmos #37-40

Solutions


  • Solutions to the sample quiz and study guide

 


Topics throughout the semester


Week 1: 8/14/19 to 8/16/19
  • Basic Function Review
  • Domain and Range
  • Graphing functions and conic sections
  • Graphing Piecewise Functions
  • Properties and characteristics of inverse functions
  • Types of symmetry that functions may or may not have
    • symmetry about the origin
    • symmetry about the y axis
    • symmetry about the axis 
  • Types of reflections 
    • vertical (over x axis)
    • horizontal (over y axis)
    • both over x and y axis
    • over y = x
Week 2: ​8/19/19 to 8/23/19​​​​​
  • Be able to find the average rate of change between two specific points
  • Be able to connect the idea of a limit to the instantaneous rate of change
  • Be able to use a table to determine if a limit exists at a particular value of x
  • Be able to use a graph to determine if a limit exists at a particular value of x
  • Be able to use the properties of limits to determine one sided limits
  • Be able to use the properties of limits to determine two sided limits
  • Connect instantaneous rate of change to the slope of a tangent line to the function at the same point

Week 3: ​8/26/19 to 8/30/19​​​​​
  • Be able to find limits using a wide variety of methods
    • substitution
    • graphs
    • tables
    • properties 
    • algebraic manipulation
  • Be able to establish the conditions of continuity
  • Be able to distinguish the different types and causes of discontinuities
    • jump/gap discontinuity
    • removable /point discontinuity
    •  infinite discontinuity
    • oscillating discontinuity
Week 4: ​9/2/19 to 9/6/19
​​​Be able to use limit properties to show FORMALLY
  • that a function has a vertical asymptote
  • that a function has a horizontal asymptote
  • a function has the same Right End Behavior Model (REBM) as a simpler version of the original model
  • a function has the same Left End Behavior Model (LEBM) as a simpler version of the original model
  • limits of more advanced functions
Be able to establish the conditions of continuity
​​Be able to distinguish the different types and causes of discontinuities
  • jump/gap discontinuity
  • removable /point discontinuity
  •  infinite discontinuity
  • oscillating discontinuity

week 5
​Be able to use limit properties to show FORMALLY
  • that a function has a vertical asymptote
  • that a function has a horizontal asymptote
  • a function has the same Right End Behavior Model (REBM) as a simpler version of the original model
  • a function has the same Left End Behavior Model (LEBM) as a simpler version of the original model
  • limits of more advanced functions
Be able to establish the conditions of continuity
​​Be able to distinguish the different types and causes of discontinuities
  • jump/gap discontinuity
  • removable /point discontinuity
  •  infinite discontinuity
  • oscillating discontinuity
Be able to state and use the IVT (intermediate value theorem)
  • how to find "roots" of difficult to solve equations
  • how to find solutions to difficult to solve equations
  • connect IVT to Fundamental Theorem of Algebra 
  • review how to quickly use tables to show where a root would occur
    • hint sign change is important!
  • connect solutions to an equation is actually the location of a root of a similar function with a new constant
Be able to find slope of tangent and normal lines of polynomials 
  • Connect tangent slope to normal slope
  • Be able to write equations of lines in slope intercept form and point slope form


Additional Resources

Professor Leonard's You Tube Channel 

Libre Texts Online Calculus Books

Paul's Online Notes for Calc 1

Exam Date for 2019-2020 School Year 8:00 A.M. Tuesday May 5 

Overview of Topics


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