AP Calculus

Week 5
9-9-19 to 9-13-19

Overview of Topics

Links to Previous Weeks

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 Continuity Practice Worksheet

Additional Resources
​(For This Week)

Khan Academy

Other Websites

math is fun ​Magoosh ​Lumen

YOU Tube

Other Websites

Geogebra 

Desmos

FDWK Section 2.1 pp 66-67
FDWK 2.1 Assignment Links

Solutions

 

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