MAT1575 Calculus II Spring 2020

Fall 2018 | Professor Kate Poirier

Final Exam Checklist

See this post for more final exam information. You have all day Tuesday and all day Wednesday to complete your exam. Your final exam score = 2/3 written work + 1/3 interview.

  1. Read the Math Department Academic Integrity Policy
  2. Final exam interview signup:
    • Sign up for an interview now.
    • One third of your final exam grade will be based on your interview.
    • Sign up for an available interview time ASAP.
    • You’re under no obligation to schedule your interview on the weekend; those time slots are available just in case anyone wants them.
    • If there are no time slots that work for you, send me an email and we’ll schedule your interview for a different time.
  3. Final exam WeBWorK access:
    • Your final exam will be available in WeBWorK starting late Monday night (really Tuesday at 12:00am) and will be open until Wednesday at 11:59pm. This is a different WeBWorK link from the one you used all semester. This one is just for final exams (and practice exams, which you should take before Monday).
    • Log in now if you haven’t already. You should have received an email from “WeBWorK Administrator” last week with your username and password. Even though it’s a brand new account, your username and password might be the same as they were for your other WeBWorK account, so you can try username: firstname.lastname and password: EMPLID.
    • Let me know before Monday if you have any trouble logging in.
  4. Written work file upload:
    • You will have 2 hours to complete the WeBWorK component and then 30 minutes to send me a your written work.
    • Don’t forget:
      • Check all antiderivatives by differentiating.
      • State the name of any convergence test you use.
    • Submit a single PDF of all your written work.
    • Don’t forget to include your student ID in the pictures of your hand-written work.
    • Use the link above; don’t use email.
  5. Interview meeting links will be sent to your email address.
    • Make sure you understand everything that you’re writing down and can explain it!
    • Practice explaining your work out loud before the interview.
    • Make sure you can answer questions like, “Why? How did you know to write that?”
      • “Because I saw a guy on YouTube do it,” is not an acceptable answer.
      • “Because that’s the rule,” is not an acceptable answer.

Final exam information

As promised, your final exam will follow a structure similar to the one we’ve been using for term tests since our class moved online.

WeBWorK component

Your final exam will be given over WeBWorK; the 2-hour test will be open from 12:00am on Tuesday, May 19 until 11:59pm on Wednesday, May 20. If you take a version of the exam on Tuesday, you’ll be able to take another version of it 24 hours later on Wednesday.

The WeBWorK part of the exam will NOT be given in our usual WeBWorK account. You should have already received an email from “WeBWorK Administrator” with the new link that’s just for exams, along with your login information. You should log in now so you don’t have a last-minute emergency, and so you can start taking practice exams (one practice exam every 24 hours).

Written work

You will have 30 minutes after your 2-hour WeBWorK timer ends to submit your written work (I will give you the link). Late submissions will incur a penalty: 10 points off the final exam score for every 30 minutes late.

Oral interview

Your WeBWorK score will not count toward your final exam grade and will only be used to determine which of your two written submissions will be graded. Your exam score will be calculate as:

  • 2/3 written work + 1/3 oral interview.

A sign-up sheet for oral interviews will be posted soon. We’ll try to get them done as quickly as possible after the 20th.

Other details

I’ll share other exam details and create an exam checklist shortly. For now, please read the student memo linked below and let me know if you have any questions. CityTech Math Final Exams – Student Memo

Participation points

A few of you have asked me how many participation points you currently have. I don’t have an easy answer, because there are several things I’m not keeping track of during the semester, because they’re easier to add up at the end of the semester. But hopefully I can help you get an idea of where you stand.

Remember that you need 20 participation points for full participation credit. Participation will count for 5% or 15% of your overall grade, depending on which grading scheme gives you a higher grade.

The ways to earn participation points since we moved to online classes have been updated. You can keep earning participation points until midnight on Monday night. Points come from:

  1. sharing your work on the board during class
    • A few of you were able to accumulate a few of these points before we were sent home.
    • I’ve been keeping track of these.
  2. participating in OpenLab discussions
    • Every time you’ve submitted a post on the OpenLab, you’ve earned one participation point.
    • I’ll add these points up at the end of the semester.
    • You can find one of your posts and click your own name to see how many posts you’ve submitted.
    • You can continue to share your work on the OpenLab between now and Monday. I haven’t given you an official “Test #3 Solutions” assignment, but go ahead and submit a Test #3 solution if you like.
    • You can also submit posts for old assignments up until midnight on Monday.
  3. attending office hours
    • I’ve taken attendance at in-person and online office hours.
    • I have been keeping track of these points during the semester.
  4. attending the tutoring center (ask the tutor for a verification slip)
    • I collected verifications slips for in-person tutoring before we got sent home and I’ve received reports about your scheduled online tutoring sessions from the ALC.
    • I have been keeping track of these points during the semester.
  5. asking a question in the WeBWorK question/answer forum on the OpenLab
    • You can access the page for particular WeBWorK problems by clicking the “Ask for Help” button at the bottom of the page.
    • I’ll add these points up at the end of the semester.
  6. filling out the weekly check-in form (since moving online)
    • I’ll add these points up at the end of the semester.
    • You can submit one more before Monday night.
  7. Submitting the practice quiz or practice test when we transitioned t online classes.
    • I’ll add these points up at the end of the semester.
  8. Attending the pet party or review sessions held during the breaks between in-person and online classes.
    • I kept track of these points.
  9. Taking practice exams
    • You can earn one point for taking a practice exam in WeBWorK.
    • You can earn a second point for submitting your written work; see the post for instructions.
    • You can take one new practice exam every 24 hours between now and Monday night.
    • I’ll add up these points at the end of the semester.

I hope that helps!


Final exam WeBWorK login + practice exams

Final exam WeBWorK login

Last Friday, you received an email from “WeBWorK Administrator” with your final exam login information. It was sent to the email address that’s on file in CUNYFirst.

This is not your usual WeBWorK account; it’s new and just for your exam. You must log in this week to ensure that you have access. Your final exam will be available next Tuesday (really Monday night) to Wednesday. If you try to log in then and cannot, you may not be able to take your final exam.

If you did receive this email, you can try out the following login information. Let me know ASAP if you can’t log in.

Practice Exams

Once you’ve logged in, you can start taking practice exams. You can take a new practice exam after 24 hours. I suggest you take a practice exam every day until your final exam window opens next Monday night.

  • You will earn one participation point for every practice exam you take in WeBWorK.
  • You will earn a second participation point if you also send me your written work as a single PDF within 30 minutes at this link:
  • You will get a different link to submit your actual final exam.
  • The practice exams will not be graded.


Pre-class prep lesson for Wednesday, May 13

2.3 Volumes of Revolution: Cylindrical Shells 

P. 166: 120 – 131 all, 140-143 all, 145, 148, 158, 159
P. 271: 61

Webwork: Shells and Washers due 5/17

Notes from lecture and office hours:

Method of cylindrical shells

It will be helpful to remember the pictures from Monday’s lecture.

The method of cylindrical shells is another method for calculating volumes of solids of revolution. It differs from the methods discussed previously in that we’re no longer slicing to get areas of cross sections. (In some sense, though, we still are slicing; but the slices are no longer flat, they’re cylindrical). But the general principal is the same: we’ll integrate 2-dimensional areas to get the 3-dimensional volume.

Remember that vertical segment connecting the $x$-axis with the graph $y=f(x)$ at position $x$? When we rotated it around the $x$-axis, we got a disk. But what shape would we get if we rotate it around the $y$-axis (a line that’s parallel to the vertical segment instead of perpendicular to it)?

The visualization might take a bit of time if you haven’t tried to see it before. Hold your pencil vertically and then move your hand in a circle that’s parallel to the floor. Imagine you took a stop-motion video of this; what shape would your pencil sweep out?

Well, this method is called “cylindrical shells” because the answer to both of these questions is “a cylindrical shell.” Scroll to Figure 2.26 here. Your cylinder is hollow and has no top or bottom. The area we’re interested in is its surface area. Try cutting this cylinder vertically; what shape do you get?

How can you understand the formula:

$V = \int_a^b 2 \pi f(x) dx$?

  • This video (8 minutes) takes you through the formula and shows an example where the axis of rotation is the $y$-axis.
  • This video (9 minutes) does the same thing, but now the axis of rotation is the $x$-axis.  This approach tends to be helpful if your graph gives $x$ in terms of $y$: $x = f(y)$.
Which volume method when?

This is the big question. Part of the challenge in calculating volumes is knowing when to use which method. Following these segments through a rotation will help you determine the shape you’re dealing with; it will be a disk, a washer, or a cylindrical shell.

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