(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.
|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:
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
|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
||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
||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
||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.
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).
||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?
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).
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.
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
||Write at least
two (explicit) questions on concepts for which you are still
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?
studying for Final Exam. (Optional but
||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
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
Your goal is to improve the Calculus Prep website in the following ways:
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
||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
||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.