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Second Semester AP Calculus 2019-2020


Topics

  • Optimization Of Geometric Model 
Rectangle Optimization problems
Group Quiz/FA Rectangle Related Optimization
FA 1-10-20
3-wall fence problem
  • fence 500
  • fence 600
  • fence 800
  • fence 900
Box with no top square base
  • ​box no top square base 40
  • ​box no top square base 60
  • ​box no top square base 80
  • ​box no top square base 90
Can with a top given SA max Volume
  • can with top sa = 200
  • can with top sa = 1200
  • can with top sa = 1800
  • can with top sa = 3200
  • can with top sa = 5600
Goals
  • Be able to set up and optimize a volume of a basic solid based on given information and given constraints
  • Be able to use calculus to optimize a surface area of a basic solid based on given information and given constraints 
  • Be able to build and optimize a cost model based on a constrained box, rectangle, or can.
  • Be able to optimize distance or travel time based on given information and basic right triangle information 
  • Be able to build and optimize constrained operations of two or more numbers
  • Be able to build and optimize combined areas based on a fixed perimeter for both component areas
Practice 

1-8-20
  • Pauls's Online Notes  First Optimization Problems
    • ​​Link to solutions
  • ​Paul's Online Notes Optimization Assignment 
1-9-20
  • Optimization Practice Part 1
    • ​Link to solutions ​
1-10-20
  • Paul's Online Notes More Optimization Practice 
    • ​​Link to solutions
  • Paul's Online Notes More Optimization Assignment 
  • Optimization Practice Part 2 
  • Optimization Practice Part 3
  • Group Quiz/FA Rectangle Related Optimization

1-17-20
  • Group Formative Assessment on Optimization related to cylinders or cans ​
1-24-20
  • Quiz 1 Optimization of Cost, Surface Area, and Volume related to Boxes, Cans, and Rectangles
    • Maximize Parabola Rectangle Area Problem
    • Maximize Existing Wall Rectangle Area Problem
    • Maximize Box Volume based on Given Surface Area
    • Maximize Box Volume based on given rectangle of material and OPEN TOP
    • Maximize Can Volume based on Given Surface Area
    • Minimize Box Cost based on Given Surface Area, two rates for side and bottom
    • Minimize Can Cost based on Given Surface Area, three rates for side, top, and bottom
    • Minimize Can Cost based on Given Surface Area, two rates for side and bottom OPEN TOP

1-27-20
  • Building Models Related to Right Triangles
  • Building Models Related to Distance
  • Building and Optimizing Constrained Operations of two or more numbers
  • Optimization problems: Distance between a curve and number properties optimization problems 

1-30-20
  • Building Distance Models related to a fixed point to a curve
  • Using technology to confirm location of point that will guarantee minimum distance from a fixed point to a given curve (square root function)
  • FA Minimize Distance to a fixed point and a square root function with solutions 

2-6-20
  • Optimization beyond just rectangular shapes and distance 
  • Building area models related to circles and ellipses
    • Largest Rectangle bounded by an Ellipse
  • "The Gutter" problem
    • Rain Gutter problem ​
  • "The pipe in an L problem"
    • Cooridor Pipe Problem
  •  4.9  PAUL'S ONLINE Notes Practice & Assignment 
Links and Resources
Paul's Online Notes for Calc 1
Optimization Resources
Picture
  • Optimization links 
Picture
  • Optimization links
  • Professor Leonard video
  • Minimize Perimeter given an area
  • Maximize an area of a rectangle bounded by the x axis and a function
  • Rain Gutter problem 
  • Fencing Problem with a missing side 
  • Box Problem 
  • Can Problem
  • Wire Cutting Problem 
  • Cooridor Pipe Problem
  • Largest Rectangle bounded by an Ellipse
Picture
​Mr Hickman's Resources
  • 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