Mr. Germanis' Class Website

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Change Requests
Entry Task
(Insert between current 4/17 and 4/20. Re-date subsequent dates)
Set-up and integral that will provide the volume of the sphere below.
Below is a front view of the given sphere.
Complete JR from 4/17

Compare disk method to washer method.

Pg. 361 #27, 28

Practice drawing regions: Pg 360-361 #2, 6, 12, 16, 17, 41

JR: Suppose you find the area under the function y = 2 between x = 2 and x = 8, then you revolve this shape around the line y = 1.
  1. Draw a graph of this scenario
  2. write an expression that will give the volume of this object.
Pg. 361 #23, 24, 43
(move current 4/27 content to 4/28)
Discuss with your table group the multiple ways of calculating volumes. Prepare an example of each for your group to present.
Problem demonstrations by group:
  • Calculating volumes of objects using calculus.
  • Review Geometric Volumes
  • Calculating area between curves.

JR: Consider problem 1 of Geometric Volumes (volume of a pyramid). How is the method for calculating the volume of a pyramid similar to calculating the volume of a cone? (Hint: setting up an equation may be helpful)

Complete at least 5 of the exercises on Khan Academy, use your judgement for what you need most work on. View  the supporting videos if needed.

Optional Resource: College Board Guide to Solids of Revolution.

An elevator has stopped between the first and second floors. The cable attached to the car weighs 5 pounds per foot and is 50 feet long. The car itself weighs 1000 pounds, including two 100-pound students who are trapped inside. To rescue the students, the car must be lifted 5 feet by manually winding the cable onto a pulley at the top of the building. How much work must be done? Pg. 371 #5, 9, 21, 30

JR: A particle is moved along the x-axis by force that measures 5x points at a point x feet from the origin. Find the work done in moving the particle from the origin to a point 4 feet from the origin.

Complete the problems assigned in class.
Use the method of cylindrical shells to compute the volume of the region bounded by y = x2; x = 1; x = 2; and, y = 0 when rotated about the y-axis.  Repeat for discs.
Quiz 5.1 Review

JR:  Explain how "area between two curves" relates to volume.
Review calculating solids of revolution by shell method, and cylindrical disk. Complete one of each problem to prepare for tomorrow's Quiz
Set up the integral that computes the volume resulting from rotating about the x-axis the region bounded by x = -y3 + y and the y-axis.
Homework Demonstrations.

Quiz 5.2 (Solids of Revolution)

JR:  Explain how to compute cross-section areas of a solid of revolution.  Include a diagram.
Pg. 378 select at least one problem from each section (there are five on this page).
As is
As is
Show your notes and work in your homework notebook when viewing the following videos. Pause the videos and attempt the problem first before viewing the solution. Check your solution by viewing the video.
A farmer has 2400 ft of fencing and wants to fence off a rectangular field that boarders a straight river. He needs no fence along the river. What are the dimensions of the field that have the largest area?
Continue Final Exam Prep Jigsaw.

JR: Explain the process for finding the extrema of a function that is defined on a closed interval (recall there are local and absolute extrema).
After today's class, a document will be posted HERE that contains your work from the Jigsaw activity. Complete four problems from topics you have not created or already completed. Be sure to detail your process.
Review the list of expected questions for the Final Exams. Write down the topics you need to review the most.
Expert Panels

Based on your response to the entry task, divide into 2 person groups for where you need to most improve.

Within your group, you will select a test-like problem and find the solution. You will become an expert on the topic and present your solution to the class tomorrow. Be sure to address potential problems other students may encounter.

Your demonstration need not be more than 5 minutes.

JR: Explain what you have already done to prepare for and what you will do to continue preparing for the final exam.
Complete ALL of the following:
  1. Prepare for your problem demonstration.
  2. Select another testable topic you are struggling with.
  3. Attempt at least two problems from that section of the text book.
  4. Prepare questions for the expert groups.
Write at least two (explicit) questions on concepts for which you are still uncertain.
Expert Demonstrations

Selected groups will present their problem and solution to the class.

Audience members should take notes about the presentation and ask questions to the expert groups.

Mr. G will answer any residual questions about the final.

JR: Reflect on your work during this semester. How has that impacted your confidence for the final? What will you do to maintain or improve your calculus confidence for the final?
Continue studying for Final Exam.  (Optional but Highly-Recommended)
  • Rewrite the correct solution to old quizzes and tests.
  • Attempt additional practice problems for chapter 3, 4 and 5.
Form a study group.
Get ready for the test!  Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Final 2.2, Free response: you may use two 3 x 5 note cards and YOUR calculator.  Expect questions on
  • Compute the area bounded by the given curves.
  • Compute the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis or line.
Reminder: you will not be allowed to do "corrections" on the final exams!

JR: What were the essential topics of knowledge that you needed to know to succeed in Calculus? What per-requisite skills would you have liked to know better?
Go to the following Calculus Prep website and list the major topics.
Collaborate with others in the class to create a Google Google Doc that begins to outline the essential prerequisites for Calculus
Website Project
Your goal is to improve the Calculus Prep website in the following ways:
  1. Better organize the topics (add or delete as needed).
  2. Each topic must clearly state a self assessment (you can find this on the internet if needed).
  3. Each topic must include concrete steps for improving the skill.
It is okay (encouraged actually) to borrow information from the Calculus Prep site from last year, however, you should not haphazardly copy all of the material, be selective and thoughtful when creating this webpage.

Your results will be posted on the website for summer homework for future Calculus students, make this something you are proud of!

JR: Write next steps you need to do tonight to make improvements on the website during the block period on Thursday. Be as clear and specific as possible.
From your JR response today, complete the self-assigned task. You must come with some product that positively contributes to your improvement of the class website.
Write about the number 1 thing you wish you knew before you took calculus. What would you say to an incoming student about calculus class?
Continue the project from yesterday.

JR: How much time will you realistically devote to preparing yourself over the Summer for next year's mathematics class? In what ways can you improve your likelihood of success?
Complete the finishing touches on the Calculus Prep website. Proofread your work before submitting; you do not want a sub-par piece of work published for all to see.

Rocket Science with Dr. Edge.

JR: No more JR's

6/14 Discuss any lingering tasks needed for the website.
Finalize content and organization of website
Continue working on the background necessary to ensure success in calculus next year.

*Unless otherwise noted, homework is due the next class day.