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M 4/3/06
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Classes resume.
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T 4/4/06
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HW due:
§11-6 #25, 26; §11-7 #1, 3, 5, 9.
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W 4/5/06
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HW due:
First, finish up yesterday’s HW if you have not already done so. Make sure that
your answers follow the 3-step “formula/plug-ins/result” standard that we
discussed. If you did some of this during class yesterday, so much the
better. Then write §11-8 #2-24 even, 25, 26. Show work, but you may find your
calculator’s “!” symbol (found under MATH PRB 4) to be helpful for checking
your answers. Problems 17-23 odd are done below to help you see what is
required.
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Th 4/6/06
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HW due:
Read §11-10; write §11-10 #4-52 eoe, plus 53.
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F 4/7/06
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“Practice Test” on Chapter 11.
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weekend
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Please visit the following
links in order to learn from your mistakes and prepare for Monday’s test. Smart student hint: Use the other
period’s test to give yourself extra practice. Find a quiet room and work the
problems under time pressure. The format is similar, but you will notice that
the problems are switched around and altered a bit.
E period:
-- Blank copy
-- Answer key with statistics
F period:
-- Blank copy
-- Answer key with statistics
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M 4/10/06
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“Real Test” on Chapter 11. This test will be similar to Friday’s test and will
begin after 5-10 minutes of Q&A at the start of the period. The higher of
your two scores will be recorded. If you missed school on Friday, even for an
excused absence, then today’s test will be the one that counts. Please learn
as much as you can from Friday’s test!
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T 4/11/06
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No class (Diversity Day).
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W 4/12/06
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HW due:
Read §§12-1 and 12-2; write §12-1 #1-13 odd, §12-2 #1. Check your answers for
accuracy. Show work in the manner illustrated below.
2. P(total ³ 10) = P(total
= 10, 11, or 12) = P( (5, 5) or (4,
6) or (6,4) or (5, 6) or (6, 5) or (6, 6) ) = 6/36 = 1/6
8. P(3 < total < 7) = P(total = 4, 5, or 6) = P( (2, 2) or (1, 3) or (3, 1) or (1,
4) or (4, 1) or (2, 3) or (3, 2) or (3, 3) or (2, 4) or (4, 2) or (1, 5) or
(5, 1) ) = 12/36 = 1/3
10. P(total = 13) = P(impossible outcome) = 0
2(h) in second set: P(penny T or
nickel T) = 1 – P(complementary
event) = 1 – P(neither is tails)
= 1 – P(penny H and nickel H) = 1 –
(½ · ½) = 3/4
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Th 4/13/06
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HW due:
Read §12-3; write §12-3 #1-13 odd. You may show less writing this time than
you did yesterday. Hint: You can
use the symbols Ù, Ú, and ~ to stand for
“and,” “or,” and “not,” respectively. For example, in #4, you could show your
work as follows:
4a. # of ways(dog Ú cat) = #(dog) + #(cat) = 37 + 15 = 52
4b. #of ways(dog Ù cat) = #(dog) · #(cat) = 37 · 52 = 555
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F 4/14/06
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HW due:
Read §12-4 plus pp. 651-652 of §12-5; write §12-4 #9, 11, 15, 21, §12-5 #17,
20, 22, 26, 27.
Bonus (2 points): Compute the probability
of a full house on the deal in 5-card draw poker. Be prepared to explain your
work and your answer. Write your answer in terms of permutations and
combinations. For example, the earlier problem we analyzed could be written
as P(two pair) = 13C2 · 4C2 · 4C2 · 44C1/(52C5).
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M 4/17/06
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HW due:
Read §12-6; write §12-6 #1, 3, and the following probability problem.
Probability problem: A fair coin is
flipped 10 times. What is the probability that a run of at least 4 heads in
row or 4 tails in a row occurs? Write up your work and your answer. We will
compare answers in class.
Analytic solution to Friday’s bonus:
(13P2)(4C2)(4C3)/(52C5) = 3744/2,598,960 » .00144, approximately 3 times in every 2000 hands.
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T 4/18/06
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HW due:
1. Use a truth table to prove the tautology that ~(P Þ ~Q) Û (P Ù Q).
2. Read §13-1; write §13-1 #1-10 all. Extremely rough sketches are
acceptable, but be sure to label your axes with English description, variable letter, and units. Also show at
least one labeled tick mark on each axis.
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W 4/19/06
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HW due:
1. Read §13-2 twice and make reading notes that include questions. If you
have no questions, I will administer a short quiz to verify that you
understand everything. This assignment is required from everyone, since it
was mentioned in class that we would be proceeding into §13-2.
2. Use a truth table to prove that ~(A
Ú (B Ú ~C)) Û ~A Ù ~B Ù C. Since
this was not posted before 2:30, I will grant extra credit for those who do
this. Everyone should attempt it, however.
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Th 4/20/06
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HW due:
Read §13-3; prepare #13-#36 for quick oral presentation; show written work
for §13-3 #4-36 eoe. You will not
be able to use notes or calculator during the oral presentation of #13-#36.
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F 4/21/06
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Quiz (possibly written, possibly oral) on §13-3. For example, if you were asked to compute sec 5p/3, you would say, “Hmmm, that’s asking for the
reciprocal of the cosine of 5p/3. Since the angle’s in the fourth quadrant, just a little past
270º, the cosine would be .5 and the reciprocal would have to be 2.”
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M 4/24/06
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Phi Beta Kappa Day (no
school).
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T 4/25/06
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Quiz Redux.
Anyone who did not earn a score of 10 last Friday will have another shot today
or tomorrow.
HW due: Read blue box on p. 731,
changing the word “An” to “The” in each case; read §13-5; write §13-3 #47,
64; write §13-4 #16-18 all, #21-31 odd.
Important: For the problems in
§13-4, show estimations before beginning, and show at least as much detail in
your work as is shown below. (A circle sketch is also recommended.)
5. sec 12.3º = 1/(cos 12.3º)
Estimate: Since 12.3º is a small
angle, cos 12.3º is close to 1. A good guess is .95, since we know that the
cosine decreases very slowly until we get past about 30º. Take reciprocal to
estimate 1/.95 » 1.05 as the answer.
Approx. by calc.: 1/(cos 12.3º) » 1/.977 » 1.023.
28. q = cot–1
1.452 = the angle whose tangent is 1/1.452
Estimate: Since 1.452 » 1.5, we are talking about an angle whose tangent is
approx. 2/3. Since tangent means “slope,” we have an angle somewhat less than
45º. (Remember, 45º gives a slope of 1.) I would guesstimate about 35º,
which is about .6 radians.
Approx. by calc.: tan–1
(1/1.452) » .603 in radian mode,
or approx. 34.555º. Then hit 2nd ANGLE 4 ENTER to convert to 34º33'.
[DMS stands for Degrees, Minutes, Seconds. This is a fast way to convert an
answer in “plain degrees” to degrees, minutes, and seconds.]
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W 4/26/06
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HW due:
Patch up any missing problems in your old homework. Then work problems on pp.
703-704 #T1abcd, T3ab, T4 all, T6a; p. 795 #C1, p. 798 #T1.
Note: On the test tomorrow, you
will be required to solve the problems like those on p. 795 and p. 798 without
a calculator. Practice your speed and accuracy.
In class: Review for test.
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Th 4/27/06
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Test on Chapter 12 (first 6 sections only), Truth
Tables, and Circular Function Basics.
Here are the answers to yesterday’s review problems to help you study:
pp. 703-704
T1a. 8P8 = 40320
b. We could have GBGBGBGB or BGBGBGBG. Either way,
there are 4 · 4 · 3 · 3 · 2 · 2 · 1 · 1 = 576 ways to fill the slots. Total =
1152.
c. 8P5
= 6720
d. You must choose 3 boys and then 2 girls to be part
of the line, then permute those children. This is a 3-step process, where
choosing 3 boys can be done in 4C3 = 4 ways, choosing 2 girls can be done in 4C2 = 6 ways, and permuting
the chosen children can be done in 5P5 = 120 ways. Total = 4 · 6 · 120 = 2880.
T3a. P(kid 1 muddy Ù kid 2 muddy Ù kid 3 muddy Ù . . . Ù kid 8 muddy) = P(kid
1 muddy) · P(kid 2 muddy) · P(kid 3 muddy) · . . . · P(kid 8 muddy) = (0.3)8 » 0.00006561.
b. P(kid 1
not muddy Ù kid 2 not muddy Ù . . . Ù kid 8 not muddy) = (0.7)8 » 0.0576. The reasoning is exactly the same as
in part (a), except that we use 0.7 instead of 0.3, since P(kid does not get a muddy shirt) = 1
– P(kid gets muddy shirt) = 1 – 0.3
= 0.7.
T4a. 0.8
b. 0.7
c. 0.56
d. P(~mudface
Ú ~mudshirt) = P(~(mudface Ù mudshirt)) by DeMorgan’s Law. The second
probability is 1 – P(mudface Ù mudshirt) = 1 – (0.2)(0.3) = 1 – 0.06 = 0.94.
e. 0.06
T6ai. 0.98
ii. 0.97
iii. (0.98)(0.97) = 0.9506
iv. (0.02)(0.03) = 0.0006
pp. 795, 798
C1a. –(Ö3)/2
b. –1
c. –1
d. –2
e. DNE
f. 3p/4
g. 5p/6
h. p/3
i. DNE
j. 2.5
T1a. (Ö3)/2
b. –(Ö3)/3
c. p/3 (same problem as C1h)
d. 5p/6 (same problem as C1g)
e. –(Ö74)/7, since this is like a geometry problem with
hypotenuse of Ö74
f. Solve proportion p/180 = 3/(no. of deg.) to get no. of degrees = 540/p.
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F 4/28/06
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HW due:
Write §14-1 #3-23 eoo, 28; §14-2 #1-5 odd. Reading notes are optional, since
the material in the text is duplicative of information already covered in
class. However, if you are stuck, you should certainly read over the text
and/or examples in order to help get “unstuck.”
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