Welcome
to the HappyCal Zone
(Honors
AP Calculus BC, Period A)
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) 


W 5/15/13 
(Relaxed start at 8:20
today, tomorrow, and Friday.) 

Th
5/16/13 
Friday schedule is in effect today. 

F 5/17/13 
Thursday schedule is in effect today. 

M 5/20/13 
15th Annual Field Trip to the National Cryptologic Museum, Fort Meade, MD. Bus departs at 8 a.m. from near the intersection of
Garfield St. and the service road near Grant Meadow. We will return at
approximately 1 p.m. after a guided tour of the museum and an interactive
lecture by a working NSA mathematician. Regular
school dress code is required. 

T 5/21/13 
7:25 a.m.: It’s JBAM
a at McDonald’s Week! 

W 5/22/13 
7:25 a.m.: It’s JBAM
b at McDonald’s Week! 

Th
5/23/13 
No additional HW due,
except for Ian, James, and Vasisht, who still need to pass the Excelcise. 

F 5/24/13 
Last day of classes. 

T 5/28/13 
Final Exam, Steuart
201202, 2:00 p.m. ·
This is not
supposed to be a regurgitation of a comprehensive treatment of the subject. In
other words, don’t try to emulate Wikipedia. ·
The purpose of
this exercise is to give you the
chance to think deeply on the connections you have formed in your own brain
over the course of the year. It is, therefore, a personal document. It should
be coherent, yes, but it’s less a “teaching someone else about the calculus”
document than it is a “documenting what you know and how you know it”
document. ·
Please write
legibly. It doesn’t need to be overly neat, and you should feel free to write
quickly so that your ideas flow well, but avoid sloppiness. Don’t be fussy:
the digit “1” is a simple downstroke, for example,
and you don’t need to label your x
and yaxes unless you switch them
for some unusual reason. ·
Good, clean,
focused content is better than large volumes of random thoughts. ·
Pencil is
preferred, but if your ideas flow better in ink, you may use a pen. ·
Here are a few
suggested topics you might want to include, since they give you a chance to
describe your personal thought process in some detail:  Integration by parts You can
write a perfectly good, highscoing essay without
hitting these topics. (Well, scratch that, I think we all know you need to
mention FTC at some point. But the other topics listed above are a matter of
personal taste. There are, of course, some major topics that nearly everyone
will want to include: variablefactor products, diff. eqs., limits, Riemann
sums, and the like.) ·
You will write
your exam without notes. You can’t even use a copy of this set of
instructions! You may use a calculator if you wish to include a few tables or
graphs, but that is not required. It’s mostly just you and your brain and a
pencil, working to produce a document that cements your knowledge of the
course for all time. 

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.com, a site that I
possibly shouldn’t tell you about . . .
Extra Help:
 Karl’s Calculus Tutor for
firstyear 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 tutorial 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, 2010, 2011, and 2012.
 Permitted features for
graphing calculators on the AP examination
 Actual
college tests from Mr. Hansen’s alma mater (great practice!) Note:
MATH 121 is the calculus course I took back in the (ulp!)
1970s.
 Multiple choice practice #1 with answer key
 Multiple choice practice #2 with answer key
 First semester recap
(recycled from my 200607 IntroCal class, for which
this handout served as a fullyear 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 §117 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 BaileyBorweinPlouffe 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: 28 May 2013