Welcome to the IntroCal Zone

(Introduction to the Calculus, Period B)
Web address shortcut for this page: www.modd.net/67intcal

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.


M 5/14/07

Triple HW due: Answer the following questions. Questions 1 and 2 are worth 4 points each, and questions 3 and 4 are worth 2 points each. That is a total of 12 points, which is why this is called a triple HW.

1. Using the window [–5, 5]
´ [–4, 4], sketch a high-resolution slope field for the diff. eq.

2. Explain mathematically what makes the diff. eq. in question #1 a guaranteed winner in the contest posed in the assignment due 5/7/2007. In other words, why is it that no initial condition more than 3 units from the origin can have a solution curve that passes within 1.5 units of the origin? Partial credit will be given for an explanation based on the shape of the slope field. For full credit, you need to write 2 or 3 sentences, and you need to think back to Algebra II or Precal in order to find a mathematically convincing explanation.

(If you have forgotten all your Algebra II and Precal knowledge, then state that, give an explanation based on the shape of the slope field, and move on.)

3. What is the deadline for submitting make-up homework assignments for partial credit? The answer can be found on the Web.

4. What are the date, time, and location for the final exam that the students with 12 or more absences in the second semester (or an average below 80%) will need to take?

Note: The official exam schedule posted on www.stalbansschool.org has not yet been corrected as of this writing. You will need to look elsewhere to find the answers to #4.


T 5/15/07

Field trip to the National Cryptologic Museum, Fort Meade, MD. Bus will load at 8:00 a.m. sharp behind Martin Gym. We will leave just a few minutes later, so don’t be late! You are excused from your A through E period classes but are expected to attend F period. Bobby will unfortunately be unable to join us, since he has a conflict with AP Chemistry.

Note: Today is the final deadline for submitting make-up homework assignments for partial credit.


W 5/16/07

HW due: Nothing new, but any previously assigned work may be rescanned.

Quiz (10 pts.) will cover various general topics from the year. All questions will be drawn from the IntroCal Saga handout. There may be a mixture of fill-in-the-blank, short essay, and mild computation.


Th 5/17/07

HW due: Same as yesterday.

Another Quiz (10 pts.) will be similar to yesterday’s.

Note: Today is the last day on which extra credit work, such as crossword puzzles, will be accepted.


F 5/18/07

Last day of school / teacher evaluation. Please do not skip today.

Guest speaker: Mr. Joe Morris ’62, Mitre Corporation.


M 5/21/07

Final Exam, Room S, 11:00 a.m. Seniors with at least a B average and fewer than 12 absences for the second semester are exempt (assuming there is no senior prank, of course).

Content of the final exam questions will be drawn almost entirely from the IntroCal Saga handout.

If you cannot take the exam at the scheduled time, or if you have more than two exams on the same day, you must contact me by May 15 to make alternate arrangements.


Essential Links:
STA School Handbook
-- College Board: AP Calculus AB Course Description
-- Eric Weisstein’s World of Mathematics, the Web’s most extensive mathematics resource (no kidding!)

Extra Help:
-- Karl’s Calculus Tutor for first-year students
-- Calc101.com, a site I really shouldn’t 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.
-- Another integral approximator tool 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 many sample problems and solutions

Links for AP Preparation:
-- Real sample AP questions from the College Board
-- AB Calculus Cram Sheet (courtesy of Will Felder and Mr. Hansen)
-- BC Calculus Cram Sheet from previous years
-- “Stuff you MUST know cold” (link to another AP calculus teacher’s site; requires Adobe Acrobat reader)
-- Review question logsheet (requires Microsoft Excel)
-- Permitted features for graphing calculators on the AP examination: you’ll definitely want to print this one out
-- 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

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

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Last updated: 12 May 2007