Due
Date |
Homework
from the textbook |
Preparation
for Certification Exam |
Class
Projects |
|
8/29 |
p.
203: 19(a-c) p.
214: 16, 18 p.
243: 2, 3, 6, 9, 10, 19(a) |
For this and all future reviews, you can choose which 5 exercises to do. Please submit a total of 5 exercises only; the grader will be instructed to only grade the first 5 solutions that are submitted. Warning: If a problem looks too easy to be true, it might not be. So be careful and check for subtleties. At the top of your write-up, you must also write a statement attesting that you have at least thought about all assigned problems. Points will be deducted if you do not write this statement. (This does not mean that you solved all of the problems --- just that you gave some thought about how to solve every problem.) |
None. All presentations will be peer-graded. |
The
class project concerns various ideas that could be
used to engage students with topics in the secondary mathematics curriculum. Topics
will be assigned on a first-come, first-served basis. You are welcome to sign
up by e-mail, but please suggest about 5-10 different topics (in priority
order) in case your first choice is no longer available. Be
sure to title your file in the form John_Doe_15.docx, as indicated in the
instructions. |
9/5 |
p.
244: 20, 22, 33, 37, 43, 48, 51 Hints: #22: Ignore the part about the
Euclidean algorithm since we didn’t cover that in class. Just get the
answers. #33: It’s false. So you just
need to find one counterexample. #48: Argue by contradiction.
Suppose that p is a prime that
divides bd. Show that p can’t divide ad+bc. FYI: This theorem is a
follow-up to p. 203 19(a-c) from last week. |
Group
1 will be responsible for Questions 1-10. |
Part
1 (Pre-Algebra and Probability/Statistics) is due. |
|
9/12 |
p. 244: 25, 30, 31, 32 p. 251: 3, 4, 5, 6, 10, 15, 16 Hints: #31: Of course, 12 = 22
* 3 and 120 = 23 * 3 * 5. So how much flexibility does that give
you with the prime factorization of x? #32: Try x = 10p, where p is a prime greater than or equal to
7. |
Group
2 will be responsible for Questions 11-20. |
||
9/19 |
p. 253: 2, 4, 6, 9 p. 254: Let’s Go 4 p. 263: 10, 31 Hints: p. 253 #9: Remember that to show a
proposition is false, you only need one counterexample. p. 263
#31: I’m not necessarily looking for a formal proof; finding aceeptable values of y
via trial-and-error is perfectly fine. Problem 4.1: Here's a popular magic trick for children: (a)
Take any
3-digit number in which the first and last digits differ by 2 or more. (b)
Reverse the
number, and subtract the smaller of the two numbers from the larger (e.g.
782-287=495). (c)
Then reverse
the result and add (thus 495+594=1089). Prove that you always end up with 1089. Problem 4.2: (a)
Here's a
second magic
trick. Cut out the six numbered cards, read the instructions, and perform
this trick (either by yourself or for a friend). Write a statement attesting
that you actually did do this. (b)
Use binary
numbers to explain why this magic trick works. Hint: Find the binary representation of the first few numbers on
each of the six cards. Do you see a pattern? |
Group 3 will be responsible
for Questions 21-30. |
Part
2 (Algebra I and Algebra II) is due. |
|
9/26 |
None. EXAM #1 Remember that the test
starts at 8:00. Please talk to Dr. Q to make alternate arrangements if
you’re not able to arrive at class by 8:00. The
review questions should help prepare you for the
exam. There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. Also,
I don’t claim infallibility. If you think I made an inadvertent mistake
while recording these videos, please let me know so I can take a look at it. |
Group 1 will be responsible
for Questions 31-40. |
|
|
10/3 |
p.
254: Let’s Go 3 p.
264: 18, 19, 20(a-d), 23, 24, 26, 27, 28, 33(a) |
Group
2 will be responsible for Questions 41-50. |
||
10/10 |
p.
229: 2, 3(cd), 5, 6, 7, 8 p.
347: 2, 5 Notes: p. 230 #2 and #3: Your
answers should have the form (something) + (something else) i. Also, your
answer for #2 should match the answer to #3(a) if a = 3 and b = 2. p. 230 #6 and #7, the expressions
were given in class and in the class notes. You need to prove that these
expressions are true. Don't just state them without proof. Regarding p. 347 #2 and #5:
We will not cover Section 12.1 in class. So I just expect you to (1) experiment
with a graphing calculator until you find cubic polynomials that meet the
given criteria, and then (2) once you have your polynomial, then you should
explain why it meets the given criteria. You may need to use factoring and/or
calculus to produce an adequate explanation. (It is possible to construct such polynomials more
systematically, and you are welcome to try to find out how to do these
problems without blindly guessing.) |
Group
3 will be responsible for Questions 51-60. |
Part 3 (Geometry)
is due. If
you haven't selected a question from all five areas yet, I encourage you to
select questions from the remaining area(s) for this week's submission. |
|
10/17 |
p.
347 #8(ab), 9 pp.
348-350 Your Turn 12(a), 14(a) p.
353 #1, 2, 4, 10 Hints: p. 347 #8, the local extrema and
point of inflection are found by solving f
'(x) = 0 and f ''(x) = 0, respectively. Then verify that
the x-coordinate of the point of
inflection is the average of the x-coordinates
of the two local extrema. p. 348 Your Turn 12(a): Do not use the Conjugate Root
Theorem (although your answer should match what you’d expect from the
Conjugate Root Theorem). Instead, begin by multiplying out (x – 5 – 3i)(x –a – bi). Then collect
the constant terms, the terms containing x,
and the terms containing x2.
Then figure out the values of a and b so that
the imaginary part of this product is equal to zero. p. 353 #10,
find both the possible number of positive roots and the possible number of
negative roots. |
Group
1 will be responsible for Questions 61-70. |
|
|
10/24 |
None. EXAM #2 Remember that the test
starts at 8:00. Please talk to Dr. Q to make alternate arrangements if
you’re not able to arrive in class by 8:00. The
review questions should help prepare you for the
exam. There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. |
Group
2 will be responsible for Questions 71-80. |
|
|
10/31 |
p.
266: Your Turn 34 p.
269: 1, 3(bc), 4 p.
347: 6 p.
353: 5 p.
365: 2, 3(a), 7(bcde) Notes: For p. 269 #4, let the following guide your thinking: You
can easily check that x = 2 is a
root of f(x) = x3 + 4x2 – 2x – 20 and that x = -2 is a root of g(x)
= -x3 + 4x2 + 2x – 20. So, let f(x) = an xn + … + a1 x + a0. If you know that f(a) = 0, is there a way to modify the
coefficients of f and create a new
polynomial g so that g(-a)
= 0? Once you see how to do this, then you’ll need to prove that your
idea actually works. Hint for p. 353 #5: Start
with f(x) = x2
– p, and argue by
contradiction. For p. 365 #2(c), it may also be helpful to also graph the
polynomial (with a calculator) on the interval [-2,3]. Hint for p. 366 #7(e): (1-a)(1+a+a2) = 1-a3. |
Group
3 will be responsible for Questions 81-90. |
||
11/7 |
p. 277 Your Turn 1 p. 278: 2, 3, 11, 12 p. 280: Your Turn 5(eg) p. 280: 1(a-d) p. 284: 3, 13 p. 319: 5, 7(abd) |
Group
1 will be responsible for Questions 91-100. |
|
|
Changed
to 11/17 because of PBI week (was
11/14) |
p. 288: 1, 3, 12(ab) p. 291: 3, 4, 6, 16 p. 307: 1, 2, 5(ac) For p. 307 #5(c), ignore the instruction that says
"If a product is required within an exponentiation problem, compute it
via logarithms." |
Group
2 will be responsible for Questions 101-110. |
Part 4 (Precalculus) is due. |
|
11/21 |
None. EXAM #3 Remember that the test starts at 8:00. Please talk to Dr.
Q to make alternate arrangements if you’re not able to arrive in class
by 8:00. The review questions should help prepare you for the exam.
There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. |
Group
3 will be responsible for Questions 111-120. |
. |
|
Monday,
12/1 (changed
from Wednesday 11/26
by request) |
p. 129: 6, 7, 8 p. 231: 15, 23(abde), 25 p. 317: 6 p. 328: 4, 6 Notes: For p. 231 #23(de), only answer
the parts involving 1-i. For p. 317 #6(b), you just need a
value of h, not the largest value
of h that meets the condition. For p. 328 #6, be sure to consult
Section 9.3.1 (pp. 281-283) before answering. |
A class survey was distributed in class on 11/26. Students who complete the survey will receive a free 100 on both the book homework and the certification reviews. |
The SETE should now be available by logging into http://my.unt.edu |
|
Thursday,
12/4 (changed
from Wednesday, 12/3) |
p. 328: 8, 9 p. 334: 1, 2, 3, 4(b), 6(bc), 8 p. 337: 1 The review
questions should help prepare you for the final. There are also solutions
for the review questions; I encourage you to watch these videos only
after attempting the review questions for yourself. Please remember to complete
the SETE. |
A
class survey was distributed in class on 11/26. Students who complete the
survey will receive a free 100 on both the book homework and the
certification reviews. |