AP Calc BC summer assignment

Parametric curve project

As discussed in final days of Calc AB, you may draw and graph an original design (suggested) or recreate an existing design.

Before applying symmetry, your final pair of X(t) and Y(t) parametric equations must include the following (both together, not individually):

• • ≥12 linear segments

  • ≥3 quadratic (or higher-degree) segments

  • ≥6 sinusoidal segments

  • ≥6 jump discontinuities

  • Even or odd symmetry for one or both equations

  • Note what is NOT required this time: (1) animation with a slider, and (2) a mix of symmetric and asymmetric design elements. Those will be required when we do this project one more time in the opening week(s) of school.

As an example of fulfilling the above requirements: Maybe before applying symmetry your X(t) has 2 sinusoidal segments and your Y(t) has 2 sinusoidal segments, giving 4 total. Will applying even/odd symmetry to those equations allow you to count this as 8 total sinusoidal segments? No! You need to add at least 2 more sinusoidal segments to the pre-symmetry total in order to meet the minimal requirement of 6 sinusoidal segments. I should see at least 6 instances of "sin" and/or "cos" across both your X(t) and Y(t) equations.

Of course you may add extra curves and features as you see fit to make your design appropriately fantastic. If you think some of your "extras" ought to count in place of some of the above requirements, negotiate any such alternatives with Mr. W BEFORE you move forward with a design.

Deliverables:

• • Final Desmos design on x-y plane -- Due BEFORE the start of Day #1 class meeting: Email the link to your finished Desmos creation to Mr. W. Notice that each time you "save" in Desmos, a new link is created. Therefore if you send a link and then make/save some changes, you'll need to send the new link. Mr. W will print the image in color to be used for the wall display.

  • Hand-drawn x-y, x-t, and y-t graphs -- Due AT Day #1 class meeting: Bring all sketches of the graphs you made along the way, most likely on graph paper. These do NOT need to be "pretty" enough to display, but nonetheless I want to see the evidence of your process. The x-t graph and y-t graph must be hand-drawn (I don't see how you would proceed otherwise). For the x-y graph only, if your design came from a digital image that you did not draw by hand, then you may alternately provide a print of a Desmos screen capture, annotated to show t-values at all the vertices. Here is a set of examples of such graphs. Notably this example does not include any jump discontinuities, which are now required:

• X(t) and Y(t) equations, including -c ≤ t ≤ c interval -- Due BEFORE or AT Day #1 class meeting: Simplify your equations as much as possible. (See examples of "simplifying" here.) This will be used for a display of your work outside Mr. W's classroom.
  Delivery options:

  • 1. Email me your equations BEFORE class on Day #1. Microsoft Word format strongly preferred so that Mr. W may adjust format if needed for display outside our classroom. If you don't have access to Word yourself, you are strongly advised to find someone who does so that you may use this method for copying/pasting equations from Desmos into Word. Please attach in an email as a Word file (.docx format). While you should find this method to be relatively quick/easy, Mr. W will not do this step for you.
       ~ ~ ~ OR ~ ~ ~

    2. If you reeeeeeally don't find access to Word, you may use Google Docs' equation editor and share the document with Mr. W. You'll have type in the entire equations from scratch (YUCK) because copy/paste won't work. Or you'll have to find some third-party extension that converts from the LaTeX format that gets copied from Desmos. If you happen to be familiar with some equation editor other than Word or Google Docs (MathType, LaTeX,...), I'm open to you using it, but just be sure to send the equations to me in a common file format such as PDF.
       
       

Resources:

• • Written how-to instructions that I printed and distributed before we left for the summer.
    Article viewable as PDF for students within the school network.
    Article available outside school network in NCTM Mathematics Teacher: Learning & Teaching PK–12, Volume 113, Issue 6 (June 2020).

  • Help from peers

  • Arrange meeting with Mr. W over summer, or email a Desmos link to a work-in-progress with a description of what problem(s) you're encountering

  • Here's a playlist of 11 instructional videos, working through the details of each step of the process. Link tinyurl.com/batmanmath redirects to this playlist.
    If you prefer, here is the original version all combined into  a single video, about 68 minutes long. When split into the 11 separate videos, a few minor changes were made, intended to clarify.

Exemplars:

Here are some finished projects created by previous BC rosters. I don't want to stifle ambition, but I suggest you be aware that many of these are MUCH more complicated than required to meet the project requirements. It might be a good idea to start modestly and add details when you get the hang of the process.

I tweak the requirements from year to year, so a previous year's project not meet all of the current year's criteria.

Test on AP Calc AB content

100-minute test on Day #2 or Day #3. All AP Calculus AB content is fair game.

• • Calculator allowed throughout entire test. You decide when it's appropriate to actually use it!

  • Multiple Choice: 22 questions, 50 minutes

  • Free Response Questions: Choose any 3 of the 4 that you'll be provided, 50 minutes

  • All questions are written by Mr. W, but half of all MC questions and FRQ from both sections are VERY similar to questions from the Official 2012 AP Calculus AB Practice Exam that CollegeBoard has released (including solutions) to the general public. Pretty much identical wording with just changes to the numbers/graphs. What a great study resource!

  • Barron's book is also still a good study resource.