Reminder: Mr. W offer to help with summer assignment expires at end of July.
If too many students wait until the last minute to seek help from me, my schedule will not accommodate everyone.
You deserve a break after AP Calculus AB!
I hope you enjoy at least a little bit of time not having to worry about school. However, at some point in the summer (perhaps midway?) you'll need to start making sure that all those skills you've acquired in recent years don't seep from your brain. Your summer assignment consists of two parts:
Parametric Curve project, Desmos link due via email BEFORE Day #1 of class begins, other materials due AT Day #1 class. This project plunges you into a PreCalc exploration of the first topic that we'll study in Calc BC. We'll wait until our opening weeks in August to get to get into the differential and integral Calculus of parametric curves, but this summer task should still provide you a worthy challenge. It reinforces a variety of topics that you've mostly learned already (function addition, function composition, function transformations), but you could probably benefit from some sharpening of your skills. I hope you find yourself taking personal interest in this project and finish with a creative work that you'll be proud to share.
Prepare for test on AP Calc AB content, to be given on Day #2 or Day #3 of class.
More details on both parts of this assignment follow.
As usual, I will gladly make myself available to offer assistance ALL JUNE AND JULY, except as follows:
Scoring AP Exams in Kansas City: June 5 - June 18
Personal travel: July 2 - July 9
Any assistance from me must be sought and received and received before August 4, when teachers return to campus.
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:
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 ~ ~ ~
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.
2025-26 projects
First project done over summer; Second project done in opening weeks of school and required animation and a mix of symmetry/asymmetry
__________ and __________ by Lola
__________ and __________ by Lucia
__________ and __________ by Olivia
__________ and __________ by Hannah
__________ and __________ by Adelaide
__________ and __________ by Owen
__________ and __________ by Tristan
__________ and __________ by Maddy
__________ and __________ by Caliste
__________ and __________ by Dia
__________ and __________ by Emma
Calculus Master ambigram by Mr. W.
If it helps to see, here are the Calculus Master graphs and Calculus Master equations.
Incoming BC students, remember that your summer project does NOT need to have animation and/or rotation!
2024-25 projects
First project done over summer; Second project done in opening weeks of school and required animation and a mix of symmetry/asymmetry
Big Dragon and Roblox by Felix
Tiana (Frog) and Avatar Aang by Melanie
Taj Mahal and Graduation Bear by Audrey
Chug Jug and Durr Burger by Larson
Baymax (Big Hero 6) and Hello Kitty by Ainsley
Beachin' and Pumpkin Patch by Sophia
Pete the Cat and Charlie Brown by Mia
Washington Quarter Eagle and Unicorn Fox by Toby
Avocado and Flower, Gleam and Glow by Larissa
Straw Hat Jolly Roger and Bart Simpson by Conor
Mystery Eye and B.O.B. by DeVonte'
propeller cap by Mr. W.
If it helps to see, here are the propeller cap graphs and propeller cap equations.
Incoming BC students, remember that your summer project does NOT need to have animation and/or a mix of symmetry and asymmetry!
2023-24 projects
First project done over summer; Second project done in opening weeks of school and required animation and a mix of symmetry/asymmetry
Black Jack and Media logos by Elijah
Route 11 and Kansas Interstate Exit by Nicolas
Bob the Minion and Diamondback by Will
Etihad Stadium and Walk the Plank by Elie
Fleur-de-lis and Angel by Sadie
Playing Card Box and Weird Bunny Cat Thing by Kella
Perry the Platypus and THX by Keiffer
OG Avengers and Caffeine Cup by Stella
Squid-ish and Pink Panther by Roy
Laughing Emoji by Graham
Sword and Superhero Hands by Cypress
Peter Dies and Peter Dies: Bigger and Bolder by Dominic
f-hole from double bass (in response to this tweet) and Goose Egg by Mr. W.
If it helps to see, here are Goose Egg X-Y graph, X(t) and Y(t) graphs, and X(t) and Y(t) equations.
Incoming BC students, remember that your summer project does NOT need to have animation and/or a mix of symmetry and asymmetry!
2022-23 projects
First project done over summer; Second project done in opening weeks of school and required animation and a mix of symmetry/asymmetry
LevelBall and Nodding Mutated Squirtle w/ tail by William
Ant and Car on NO roads by Serenella
Butterfly and Sleepy Face by Felicia
Guitar and Jazzy Jazz (the dog) by Sebastian
embrace and JKB (or JKB alt animation) by Jack
Kirby and Waddle Dee! by Kim
Carcharodon carcharias and YumMath by Elizabeth
Crying and Angry Bird by Theo
Silly Goose by Mr. W.
If it helps to see, here are Silly Goose X-Y graph, X(t) and Y(t) graphs, and X(t) and Y(t) equations.
2021-22 projects
First project done over summer; Second project done in opening weeks of school and required animation and a mix of symmetry/asymmetry
Pluto (The Whole Shebang) and IPRE (the thrilling sequel) (animated) by Corinna
Ice Cream Cone and Cat (animated) by Eleanor
UFO and Desmond the Bunny (animated) by Kara
Pig and Cartman (animated) by Aidan
Harold the Elephant and Dino Garden (animated) by Sisi
Tyler the Turtle and Dan the Dandelion (animated) by Emma
Cactus and Tea Kettle (animated) by Camille
Party BMO and Goomba (animated) by Julien
Fear Frog and The Homeowners (animated) by Owen
Untitled Graph and Black Armory (animated) by Jack
Pizza and Dancing stick figure (animated) by Evan
Wonder Woman logo and Gilbert (animated) by Atticus
Oliver the Bunny (animated) and House (animated) by Isabelle
Masked Face (animated) and The Batman 2022 by Mr. W
2020-21 projects
Projects done over summer. Unfortunately disruptions to school year due to pandemic prevented the assignment of a second project.
Black Lives Matter fist by Michael
Lighthouse by Lyle
Burger by Mikayla
Bee (big girl graph) by Ellen
Flower by Clara
TV by Benjamin
Owl by Greyson
Momo by Kaleb
King Me by Brandon
Ambivalent Cat by Mr. W
Flower in Vase by Mr. K. Thele from John Paul II H. S. in Plano, TX
Star by Patrick Ames, Boise State University
2019-20 projects
First project done over summer; Second project done in opening weeks of school and required animation and a mix of symmetry/asymmetry
pdf with all student work, including photos of wall displays & links
Bill Cipher and The Head of Sans, animated by Elijah
Rose and Grandpa Bat, animated by Natalie
Toilet and Airplane, animated by Colin
Route 66 and Clock, animated by Brynn
Ice Cream and Ponyo the Goldfish, animated by Kali
Spider Logo and Marshmallow Man, animated by Arshiya
Dragon and Shark, animated by Kaelyn
Spiderman Symbol and Sailboat by Jacob
Mickey Mouse and Ultimate by Athan
The Office and Ferb, animated by Nicco
Puzzle Ninja and Spiderman Logo and Singing Banana by Mr. W
2018-19 projects
First project done over summer; Second project done in opening weeks of school and required a mix of symmetry and asymmetry.
pdf with all student work, including graphs, equations, & links
Dragonborn Symbol and Philosopher's Stone by Miles H
Creepy Eyes and Bozo by Louis
Horcrux Ring and Audible Logo by Gus
King's Crown and Elephant by Benjamin
Nepalese Flag (top half) and Instagram Logo by Beni (Nepalese Flag, whole by Beni & Mr. W)
Angry Chicken and MAA logo by Mr. W
2017-18 projects
pdf with all student work, including graphs, equations, & links
Chinese Tower by Chenhui
Flamingo by Rion
Honda logo by Celeste
Soundcloud logo (modified) by Donald
Doggo by Gabrielle
Most beautiful dog in the world by Taya
Pineapple man by Callen
LRC (Learning Resource Center) logo and Batman Begins symbol and Batman, Dark Knight symbol and Fleur De Lis and Heisenberg sketch (Breaking Bad) and Superman symbol by Mr. W
Mr. W's collection of parametric curve projects in GeoGebra. These 3D models were created in GeoGebra by Mr. W, summer 2020.
Years later, recreated in Desmos3D. Click on each image to open the Desmos 3D versions.
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.