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M 4/4/011
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Classes resume after spring break. No additional HW
is due today.
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T 4/5/011
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HW due: Write §12-6 #13, 24, 26, §12-7 #1, 5, 8, 11,
14. Then log your points.
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W 4/6/011
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HW due:
1. Reread §12-7, especially the green boxes on pp. 634-635. You probably
already have reading notes for this section.
2. Read §12-8 (last reading assignment of the year; reading notes required,
as always).
3. Read the silly dialogue from 4/2/2009
(no reading notes required).
4. Redo §12-7 #11, 14 (rehash from yesterday, but the answers left on the
board were incorrect).
5. Write §12-7 #25-30 all. For these problems, you may use any resource you
wish to help you get the answers, as long as you document your source.
6. Finally, log your points.
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Th 4/7/011
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HW due: Correct your answers to §12-7 #25-30 using
the answers on the same web page as yesterday’s silly dialogue; then answer
questions 1 and 2 below and log your points.
1. Prove the “loose end” from yesterday’s class discussion, namely that  for any natural
number n beyond some point.
Precisely where is that point?
2. Consider the expression cos 2.4, which is approximately equal to −0.7373937.
Compute
(a) the Lagrange error bound after 5 nonzero terms
(b) the AST error bound after 5 nonzero terms
(c) the actual absolute error after 5 nonzero terms (using your calculator’s
value of cos 2.4 as a reference)
(d) your personal opinion of which is easier, (a) or (b). Remember, in (b),
you need to prove that the AST conditions are satisfied.
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F 4/8/011
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HW due: Read the 4/13/2009
calendar entry; write parts (a), (b), and (c) of the problem posed there;
read (do not write) §12-8 #21; write §12-8 #7, using the calendar entry as a
guide, but seeking accuracy to within 0.0000001, not to 7 decimal places as
originally requested. Then, log your points.
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M 4/11/011
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HW due:
6. Work problem
#6 from the 2009 alternate exam, without calculator. Set a timer for 15
minutes.
77. Work problem #77 below, with calculator. Allow about 25 minutes.
78. Correct your work for the AP problem by visiting here,
and then remember to log your points.
Problem 77: Let f be a function having derivatives of
all order, where  for any natural
number n, and let f (−2) = 1.
(a) Write the Taylor series for f (x), using a = −2 as the center of the expansion.
(b) Prove that the power series in part (a) converges for all real x.
(c) Write the Lagrange error term for f
(x), and use  to represent the
unknown value between a and x.
(d) Use the Lagrange error bound to determine the number of terms in part (a)
that would guarantee computation of  within 0.0001 of the
true value.
(e) Take advantage of the fact that you can compute  quite accurately on
your calculator, and see how many terms of the Taylor series in part (a) are actually needed in order to achieve
accuracy within 0.0001. The answer should be 3 fewer than the answer to part
(d).
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T 4/12/011
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HW due: Write at least 2 of the following 3
questions, and check your work against the scoring rubric provided in the
lower half of the sheet: 2009
AP exam #6, 2010
AP exam #6, 2010
AP alternate exam #6. Note: No
calculator is allowed for any of these. Remember to log your points.
In class: Review day.
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W 4/13/011
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Test (100
pts.), required for Form V at 8:00, optional for Form VI at 7:20.
This test will emphasize Chapter 12 but may contain any AP-type content from
the entire year. Names of famous mathematicians, rules of logic, and facts
about adaptive quadrature and chaos, although interesting, are not AP topics
and will therefore not be included on this test.
If you are in Form VI and would like to take this test, you may come in at
7:20 and work until about 8:15. Career Day normally does not begin until
about 8:30. If you take both tests, today and tomorrow, the better of the two
will be scored.
To assist you with studying for tomorrow’s test, here is a blank copy and a complete solution key with scoring rubric.
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Regarding
format . . .
Both tests will have a 50-minute time limit and will use the same format,
which is as follows:
- Part I: Calculator allowed. Part I consists of
1 question similar to #77 due on 4/11. After 15 minutes, you will be
required to put your calculator away, and Part II will be distributed.
Therefore, you need to plan to do anything that requires use of the calculator
during this first 15-minute window.
- Part II: No calculator allowed. Part II
consists of 2 questions similar to the “AP #6” problems given for HW due
4/11 and 4/12. You should allow 30 minutes for Part II. You may work all
questions on the test during this time, but no calculator is allowed.
Regarding the time limit, please read below, since this has changed . . .
TIME LIMIT of 50 minutes will be
strictly enforced. Although Steven asked if he could start early, that is not
going to be permitted. Compensation for the extremely tight time limit is
that scoring will be based on AP criteria, with approximately 70% = A, 55% =
B, 40% = C, etc. Hopefully everyone will understand the need for uniform
timing, since otherwise the switchover from with-calculator to no-calculator
mode at the 15-minute mark would be too complicated.
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Th 4/14/011
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Test (100
pts.), required for Form VI, optional for Form V.
This test will have the same format as yesterday’s
test, although the numbers and the precise nature of the problems may
change somewhat. Today’s test is optional for Form V (since you have College
Night on Wednesday evening), but if you wish to take it anyway, the better of
the two will be scored.
Form V students who wish to “sleep in” should report for roll call sometime
before the end of the period.
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F 4/15/011
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No additional HW due today, after those dual tests.
Whew! (Yes, it would have been even better if this had been posted by 3:00
p.m. However, as you know, there is a general rule that if HW is not posted
by 3:00 p.m.—or by some reasonable hour on Friday evening, before the weekend
begins in earnest—then there is no HW assignment.)
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M 4/18/011
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HW due: Log your daily AP review on the AP review sheet.
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T 4/19/011
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HW due: Ditto. All this week, we will have “relaxed
start time” at 8:10, with grace provided up to a few minutes after that.
When logging your problems, please write a little more detail than merely a
checkmark: a page number and a problem number, for example.
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W 4/20/011
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HW due: Ditto.
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Th 4/21/011
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HW due: Ditto.
In class: Quizzes (10 pts. each) on standard
AP-type problems demonstrated in class.
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F 4/22/011
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HW due: Ditto.
In class: Ask-Backward Bingo? Maybe!
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M 4/25/011
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Optional full-scale
practice AP exam, 8:00 a.m.−12:00 noon, MH-313. If you attend, please try to arrive by about 7:50
at the Senior Circle entrance. If you do “reasonably well” on the practice
exam, that will give you an additional comfort factor going in to the real
exam. I know I had previously said I would also waive the final exam
requirement, but for administrative reasons that is not possible, and I
apologize.
Be sure to bring something to snack on during the break, since your glycogen
levels will need to be recharged. Spare batteries are strongly encouraged.
IMPORTANT: Just as on the day of the real exam, practice leaving your
cell phone in your car or in your locker. You are not permitted to use
telephones or computers of any type during the 4-hour exam period. If you use
a phone on exam day between 8:00 and 12:00, even if during the break, your
phone will be confiscated and your exam score will be canceled without a
refund.
Format is as follows:
Part IA: MC without calculator, 28 questions, 55 minutes.
Part IB: MC with calculator, 17 questions, 50 minutes
- - - Granola bar break - - -
Part IIA: FR with calculator, 2 questions, 30 minutes
Part IIB: FR without calculator, 4 questions, 60 minutes
You may, if you wish, continue to work on the Part IIA problems during the
time allocated for Part IIB. However, you cannot use your calculator during
the final 60 minutes.
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T 4/26/011
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“Relaxed start” continues. Keep working on your
review log, and feel free to count the time you spent yesterday. A little bit
of work each day is the key!
In class: Group work to solve the practice exam, 100%.
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W 4/27/011
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Ditto.
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Th 4/28/011
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Ditto.
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F 4/29/011
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Ditto.
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