Welcome to the HappyCal Zone

(Honors AP Calculus BC, Period A)
Web address shortcut for this page: www.modd.net/1011hcal

Are you nervous when you see NCWEE? concerned when you see CIRC? perturbed when you see PBC? Visit Mr. Hansen’s fabled abbreviations page to make sense of those cryptic markings you see on your papers.


Schedule at a Glance (see archives for older entries)
Written assignments should follow the HW guidelines. Enter your scores here.


T 5/10/011

HW due: By the end of class today, each group must submit a project proposal and a list of proposed milestone dates. Working on this during class is permitted. Please arrive at or before 8:00 a.m. so that your group will have maximum benefit from your input.

Yesterday, we generated some ideas for “calculus projects,” i.e., projects that involve the calculus in some fashion. We discussed image stabilization, gravity- and motion-simulating computer games, spread of memes (rumors, fashions, etc.), and a few other concepts. The idea is that you should create a product of some type: software, a PowerPoint briefing, a short report, or something of that nature. Your group should also plan on giving an oral presentation either to the entire class or to Mr. Hansen in private (your choice) during the final week of school.

If you are completely unable to generate any project ideas, try Mr. Hansen’s random word generator (to be demonstrated in class).

Group 1: Steven, Austin, Jonathan                                  Fish Banks analysis
Group 2: Martin, Nicky, Miles                                           Java-based computer game
Group 3: Wil, Bobby, Taylor                                             Lanchester’s equations
Group 4: Michael, Alex, Bogdan                                       Volume and cost of a new Potomac River bridge
Group 5: Nathan, Sandy                                                     RC circuit analysis


W 5/11/011

HW due: Work on your group project.

In class: Most of the period will be devoted to your group project, with Mr. Hansen available to offer suggestions and guidance. But first, Miles and Mr. Hansen will summarize Mr. Stephen Swad’s investment talk from Tuesday afternoon! (Mr. Swad is CFO of language software developer Rosetta Stone Ltd.)


Th 5/12/011

HW due: Work on your group project.

In class: Again, most of the period will be devoted to your group project, with Mr. Hansen available to “add value” as much as possible.


F 5/13/011



M 5/16/011



T 5/17/011

Ditto. No penalty for tardiness (up to about 15 minutes) if you bring a McDonald’s receipt.


W 5/18/011

JBAM competition before school; no penalty for tardiness (up to about 15 minutes) if you bring a McDonald’s receipt.


Th 5/19/011

Save the date! Field trip to the NSA’s National Cryptologic Museum, Fort Meade, MD. Bus will depart at 8:00 a.m. and will return shortly before 1:00 p.m. If you attend, you will be excused from periods A-E and the first half of F period. If you do not attend, there will be a worksheet for you to work on during what would otherwise have been your HappyCal class period.

School dress is required, but you may leave your blazer on the bus during the tour if you wish. Snacks are available from vending machines at the museum, and a few snacks will be provided by Mr. Hansen.

Schedule at the museum:

  0900-1020 Museum tour
  1020-1040 Snack break
  1045-1155 Lecture/workshop conducted by a mathematician from the NSA (“MAGIC” conference room)
  1200 Bus returns to STA


F 5/20/011

BIG TRIG competition before school; no penalty for tardiness (up to about 15 minutes) if you bring a McDonald’s receipt.

Class meets in MH-103 today and Monday.


M 5/23/011

Class meets in MH-103 again today.


T 5/24/011

Group 4 presentation (Michael, Alex, Bogdan): 8:25 a.m.

Group leaders must prepare a 1-paragraph written report stating what each group member contributed to the effort. Be specific. Then, list what you believe a fair distribution of points should be. It is acceptable to request an equal point distribution (1/3, 1/3, 1/3) if that is supported by the facts.


W 5/25/011

Group 1 presentation (Steven, Austin, Jonathan): 8:25 a.m.


Th 5/26/011

Group 2 presentation (Martin, Nicky, Miles): 8:00 a.m.
Group 3 presentation (Will, Bobby, Taylor): 8:25 a.m.


F 5/27/011

Last day of school.

Group 5 presentation (Nathan, Sandy): 8:00 a.m.
This will be followed by several minutes of reminiscences and final thoughts to send you on your way. Seniors will be wished a fond farewell.


Th 6/2/011

Final Examination, 2:00 p.m., Steuart 201-202.

The examination will consist of one question: “Write, in your own words, the story of the calculus.” This is your opportunity to tie the themes of the course into one coherent collection of thoughts. The value for your long-term memory is enormous. You will have one hour. No notes are allowed, but you may use a calculator if you wish.

Here is an example of an essay I wrote (for IntroCal) that ties together all the major themes. Nothing this elaborate is expected, of course, since you have only one hour and will be writing in longhand, but I thought you might want to see the example anyway. Your essay should incorporate some second-semester topics as well: things like variable-factor products, related rates, solids of revolution, solids by plane slicing, techniques of integration, and, of course, power series.

Seniors with a B average (80%) or above in the second semester are not required to take the final exam. The exam is required for everyone else and will count as 20% of the semester grade. In most cases, it should be a grade-boosting opportunity. Seniors who wish to take the exam as a way to boost their grade are welcome to attend, and for those people, the exam will be counted only if it helps.


Essential Links:
STA School Handbook
-- College Board: AP Calculus BC Course Description
-- Eric Weisstein’s World of Mathematics, the Web’s most extensive mathematics resource (no kidding!)
-- WolframAlpha, a site that I possibly shouldn’t tell you about . . .

Extra Help:
-- Karl’s Calculus Tutor for first-year students
-- Calc101.com, another site I might not want to tell you about (click it and you’ll see why)
-- Temple University: Calculus on the Web (COW)

Links Based on Class Discussions:
-- Troy’s Integral Approximation Thingy: a neat JavaScript application for Midpoint Rule, Trapezoid Rule, Simpson’s Rule, etc.
-- The “RiemannSums Applet” found by John S. (actually shows you the rectangles or trapezoids)
-- Chris and Andrew’s proof that Simpson’s Rule is a weighted average of the Midpoint and Trapezoid Rules
-- Braxton’s direct proof of FTC2
-- Proof that FTC1 implies FTC2 and conversely
-- Related rates tutorial and practice problems
-- Partial fraction decomposition with sample problems and solutions, courtesy of the University of California at Davis

Links for AP Preparation:
-- Real sample AP questions from the College Board
-- AB Calculus Cram Sheet
-- BC Calculus Cram Sheet (courtesy of Will Felder and Mr. Hansen)
-- “Stuff you MUST know cold” (link to another AP calculus teacher’s site; requires Adobe Acrobat reader)
-- Review question logsheet (requires Microsoft Excel); also available are old versions for 2003, 2009, and 2010
-- Permitted features for graphing calculators on the AP examination
-- Actual college calculus tests from Mr. Hansen’s alma mater (great practice!)
-- Multiple choice practice #1 with answer key
-- Multiple choice practice #2 with answer key
-- First semester recap (recycled from my 2006-07 IntroCal class, for which this handout served as a full-year recap)

Fun Links:
-- Homemade “Segway”-like balancing scooter uses a fair amount of calculus!
-- Mathematicians as depicted in the movies (Good Will Hunting, etc.)
-- An Algebra II problem that has a calculus flavor to it. (This is problem #26 from §11-7 of Foerster’s Algebra and Trigonometry: Functions and Applications.) The problem is to determine which sweepstakes prize is better: a $20,000 lump sum or $100 a month for life. Assume 4% annual interest compounded monthly. In part (d), the challenge is to determine how the answer changes if the interest rate changes to 7%.
-- The Mt. Sinai problem and two variations
-- The astonishing Bailey-Borwein-Plouffe algorithm for calculating pi to any desired decimal place
-- Sound wave analysis (harmonics, Doppler shift, etc.) / excellent site developed by students at TJHSST in Virginia
-- Good problems (some calculus, some not)
-- More fun links on Mr. Hansen’s home page

Serious Links:
-- Summer math camps for talented high school students
-- Click here for other serious links

Return to Mr. Hansen’s home page

Return to Mathematics Department home page

Return to St. Albans home page

Last updated: 27 May 2011