Second Semester AP Calculus 2019-2020

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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 

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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

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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

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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 

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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 

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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

• Optimization links 

• 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

​Mr Hickman's Resources

• optimization 2018-2019

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