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By popular request, here is the multiple-choice
answer key for last week’s practice AP exam:
Without calculator (#1-28): ECAEC DBEEE DBEAC DDAEE DEDBC CBA
With calculator (#76-92): ECBCE ECEAB CBCDE EB
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M 5/3/010
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Class will start at 8:00 a.m. today. (Reason: You
need to practice getting up and being alert by 8:00 a.m.) However, I will not
start deducting for tardiness until a few minutes later.
HW due: Each superpod group leader should pick up the photocopied
free-response answers posted under the letter “S” in my paper sorter outside
my office door. Distribute the papers as you see fit among the other group
members. Each group will be scored on the accuracy of its rubric scoring,
with the same score for everyone in the group. To clarify, that means that
if you have divided up the grading work reasonably, each person has only a
problem or two to grade. (Of course, you should also do a few AP review
problems for your log sheet over the weekend.)
Example: Your superpod scores your 6 problems as 4, 5, 8, 7, 4, 5. The actual
scores are 4, 5 ,8, 7, 4, 4. That’s pretty good! Your homework score would be
4 out of 4, even though your free-response score might not be high enough to
beat the other superpods.
Note: If your superpod leader was
not able to visit the paper sorter, or if you were unable to make contact
with your leader to get your pages to grade over the weekend, you can find
them here:
Superpod 1: Andrew B., Roberto, Tommy,
Justin, Austin
Superpod 2: Tim, Barun, Michael, Sunil,
Hank
Superpod 3: Alec, Andrew D., Jamie,
Joseph, Duncan, Chen
If you have lost your rubric sheets that were distributed Friday in class,
rubrics (or at least answers) for all problems can be readily found online.
Simply do a Google search for a series of words within the question.
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T 5/4/010
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No additional HW due.
In class: Interesting problems to prepare you for the AP exam. Roberto and
Duncan, copies for you are in the paper sorter outside my office,
alphabetically by last name.
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W 5/5/010
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AP
Examination, 8:00 a.m., Trapier Theater. Bring pencils, calculator, spare batteries, a snack
for the break, and a pen with blue
or black ink for the few places where a signature is required. Leave cell
phone, scratch paper, PDAs, notes, etc. in your locker or car.
There are 45 students (29 from AB, 16 from BC) who will be taking exams at
the same time. The first 20 or so to arrive will be able to claim a
full-sized desk to use as a work area. If you forget your snack, Ms. Dunn has
generously offered to provide snacks not only for her classes but for
HappyCal as well. Hurray!
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Th 5/6/010
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By suggestion of an anonymous e-mailer, class will
start at 8:15 today. As long as you arrive within a few minutes of the
designated start time, there will be no point penalty.
HW due: Your AP review log will be scanned one last time. Also, here is a solution to #92 from the practice exam. If
you can find a cleaner and/or faster solution, please let me know for extra
credit.
In class: Some interesting mathematical hoaxes.
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F 5/7/010
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Class today will begin at 8:20. I am still hoping
someone will find a faster or cleaner solution to #92 from the practice exam.
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M 5/10/010
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Class today will begin at
8:20 again. If you cannot find a faster or cleaner solution to #92 from the practice exam, then please help
me to design a class stunt that would equal or exceed this item from the
Snopes.com glurge gallery. Please see Mr.
Hansen’s Goals for a Class Stunt.
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T 5/11/010
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Class today will start
within a few minutes of 8:15.
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W 5/12/010
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Class today will start at
8:15 sharp. No AP exams today! Wheee!
In class: Stunt that was to have occurred today has been postponed until we
have 100% attendance. Instead, what we covered was a Whirlwind Introduction
to Statistics (1 of 2).
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Th 5/13/010
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Class today will start at 8:15
sharp again. Because of AP exams today and tomorrow, we will have to postpone
the stunt until sometime next week.
In class: Whirlwind Introduction to Statistics (2 of 2).
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F 5/14/010
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Class today will start at
8:15 sharp again. However, those who wish to start the quiz early may arrive
as early as 7:45 if desired.
Statistics Double Quiz (20 pts.).
Quiz makeups are not normally provided, but students who have morning or
afternoon AP exams today may take this quiz Thursday (5/13) during Math Lab or
at 7:45 a.m. today.
Since the quiz is short, the remainder of the class period will consist of a
preview of the field trip: overview of the U.S. intelligence community and
the NSA’s role.
NSA field trip for Form VI and a few
other students will depart at 10:30 sharp from the Martin Gym area and
will return by lunchtime. If you have a conflict on May 25, which is when
most of the Form III, IV, and V students will be going, you may wish to go on
the May 14 trip instead. The May 14 trip is a tour of the museum only. The
May 25 trip will include both a tour of the museum and a hands-on
codebreaking workshop conducted by an NSA mathematician.
Form VI cannot go on May 25 because of the Snowpocalypse-induced rescheduling
of Career Day. Normal STA dress code will be in effect during our time at the
museum.
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M 5/17/010
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Please come to JBAM Monday
morning at 7:30. Full details and rules are at jbam.net.
I hope to see everyone there!
Don’t worry about being a little late to class. Remember, class does not
start until I get back from McDonald’s.
Double
Quiz Solution
As for the last question from Friday’s quiz, many answers are possible. (You
were supposed to construct an example showing that P(A|B) may equal P(B|A)
even though events A and B are not independent.) Perhaps the simplest
solution is to sketch a Venn diagram for mutually exclusive events A and B,
each of which has probability 0.5. For example, A could be the event that a
single coin flip is “heads,” while B could be the event that the single coin
flip is “tails.”
Since the events are mutually exclusive, P(A
and B) = 0, but P(A) · P(B) = 0.25. Thus we have proved that
the events are not independent, since the joint probability (namely, 0) does
not equal the product of probabilities (namely, 0.25).
However, since the events are mutually exclusive, P(A|B) is clearly 0, since if B occurs, A cannot. Similarly, P(B|A) = 0. Thus the conditional
probabilities are equal as required. 
Alternate
Solution
One of the many possible alternate approaches might look like this:
Here, P(A)
= P(B) = .2,  = .08,  = .32,  = .68, and so on.
The letter U in the upper right
corner represents the universe of all possible outcomes.
Since P(A | B) =  , we know that events A and B are not independent.
Another, perhaps easier, way of proving A and B to be not independent is to
check whether P(A) · P(B) equals . Let’s do that: P(A)
· P(B) = (.2)(.2) = .04, and that
is not the .08 that would be
required for independence.
However, the conditional probabilities satisfy the conditions of the problem:
P(A | B) =  = P(B | A).
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T 5/18/010
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Please come to McDonald’s
Week, day 2 (Big Trig competition). Class
starts when I get back from McDonald’s.
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W 5/19/010
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Class will start at 8:15
a.m. Seniors will be sleeping in, most likely.
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Th 5/20/010
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Class today meets in MH-313. A quiz on the Lagrange form of the error is highly
likely. Class (and the quiz) will begin at about 8:15 a.m., after the Big Trig Classic competition at McDonald’s.
Prizes will be ridiculous and will include screwdrivers this time.
Remember, today’s period ends at 8:40 since we are on a Friday schedule. You
will need to work relatively quickly.
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F 5/21/010
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Class today meets again in MH-313. We will start at about 8:15 a.m., after everyone
has returned from McDonald’s.
People who did well on yesterday’s quiz
will be able to leave early. Everyone else will have another shot, not to
replace the earlier score, but simply as another chance to have a better
grade stirred into the quarter average. The answer
key is now available, and hopefully you can learn from your mistakes and
do better this time.
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M 5/24/010
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HW due: Please carefully
review the blank quiz from last Friday and
the answer key.
Class today will begin as close to 8:00 a.m. as possible. If you are a couple
of minutes late, leniency will be provided. However, we need to practice
getting up earlier so that we will all be on time for tomorrow’s events (bus
trip for most of us, Career Day for Form VI).
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T 5/25/010
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NSA field trip, 8:00 a.m. to 1:00 p.m. We will depart from the Martin Gym area at 8:00
sharp and will return to campus halfway through F period. Normal STA dress
code will be in effect during our time at the museum.
Note: Form VI will not be in class
today because of Career Day, which was rescheduled to today as a result of
the Snowpocalypse.
If you have a conflict on this date, you may wish to go on the May 14 field
trip instead. The May 14 trip is a tour of the museum only. The May 25 trip
will include both a tour of the museum and a hands-on codebreaking workshop
conducted by an NSA mathematician.
Students (other than Form VI) who miss both field trips will be required to
complete a worksheet during
what would have been your class period. The worksheet will be collected on
Wednesday, 5/26.
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W 5/26/010
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HW due: In-class worksheet from yesterday. (This
assignment is required only if you are a Form IV or Form V student who missed
both field trips on May 14 and May 25.)
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