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AP Calculus

Week 4

Picture
9-2-19 to 9-6-19

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: ​9/2/19 to 9/6/19​​​

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


Schedule 9/2/19 to 9/6/19

monday
  • No School Labor Day
tuesday
  • Discuss QUIZ 1
  • Formative Assessment
    • VA and HA through Calculus methods
    • End Behavior Models
  • More Advanced Limit Properties
wednesday (Shortened Schedule Day Does NOT APPLY)
  • Work on quiz 2 study guide
  • Start on continuity 
thursday
  • Finish Continuity
  • Formative assessment on limit properties and basics of continuity
friday
  • Review Activity for Quiz 2

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

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

  • Limits and Continuity
  • proof of special sine limit
  • proof of special cosine limit

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 

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
  • 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
  • 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
  • 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
​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


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