Due
Date |
Homework
from the textbook |
Preparation
for Certification Exam |
Class
Projects |
|
8/28 |
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. You
are welcome to request all four topics for the whole semester if you wish, or
you can request your topics one at a time. Be
sure to title your file in the form John_Doe_15.docx, as indicated in the
instructions. |
9/4 |
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. |
Tuesday,
9/1 in GAB 473 Group
1 will be responsible for Questions 1-12. |
Part
1 (Pre-Algebra and Probability/Statistics) is due. The project should be submitted through
Blackboard. |
|
9/11 |
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. |
Friday,
9/11 in GAB 473 Group
2 will be responsible for Questions 13-24. |
||
9/18 |
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 looking for a formal proof; finding acceptable 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? |
Monday, 9/14 in GAB 317 Group 3 will be responsible
for Questions 25-36. |
Part
2 (Algebra I and Algebra II) is due. |
|
9/25 |
None. |
Tuesday, 9/22 Group 1 will be responsible
for Questions 37-48. |
|
|
Monday, 9/28 |
EXAM #1 THIS IS A CHANGE The
exam will be held in the Sage Hall Testing Center, located in Suite C330. I
will be there between 8-10:50. You may arrive at any
time between 8 and 9, and you will have 1 hour, 50 minutes from the time of
your arrival to complete the exam. Please
talk to Dr. Q to make alternate arrangements if you’re not able to
block off 1 hour, 50 minutes on this morning. 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. |
|||
10/2 |
p. 254: Let’s Go 3 p. 264: 18, 19, 20(a-d),
23, 24, 26, 27, 28, 33(a) |
Friday,
10/2 Group
2 will be responsible for Questions 49-60. |
||
10/9 |
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.) |
Monday,
10/5 in GAB 317 Group
3 will be responsible for Questions 61-72. |
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. |
|
10/16 |
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. |
Tuesday,
10/13 Group
1 will be responsible for Questions 73-84. |
|
|
10/23 |
None. EXAM #2 The
exam will be held in the Sage Hall Testing Center, located in Suite C330. I
will be there between 8-10:50. You may arrive at any
time between 8 and 9, and you will have 1 hour, 50 minutes from the time of
your arrival to complete the exam. Please
talk to Dr. Q to make alternate arrangements if you’re not able to
block off 1 hour, 50 minutes on this morning. 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. |
Friday,
10/23 Group
2 will be responsible for Questions 85-96. |
|
|
10/30 |
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. |
Monday,
10/26 in GAB 317 Group
3 will be responsible for Questions 97-108. |
||
11/6 |
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) |
Tuesday,
11/3 Group
1 will be responsible for Questions 109-120. |
|
|
11/13 |
p. 288: 1, 3, 12(ab) p. 291: 3, 4, 6, 16 p. 307: 1, 2, 5(ac) p. 317: 6 For p. 307 #5(c), ignore the instruction that says "If
a product is required within an exponentiation problem, compute it via
logarithms." For p. 317
#6(b), you just need a value of h, not the largest value of h that meets the
condition. |
Postponed
until next week. |
Postponed until next week. |
|
11/20 |
p. 129: 6, 7, 8 p. 231: 15, 23(abde), 25 p. 328: 4, 6 Notes: For p. 231 #23(de), only answer
the parts involving 1-i. For p. 328 #6, be sure to consult
Section 9.3.1 (pp. 281-283) before answering. NOTE: Please complete the
SPOT by November 22. If you were not able to complete the SPOT in class on
November 13, here is the link to do so: https://unt.iasystem.org/survey/4051.
|
Monday,
11/16 in GAB 317 Group
3 will be responsible for Questions 133-144. Friday,
11/20 Group
2 will be responsible for Questions 121-132. |
Part 4 (Precalculus) is due. |
|
Monday, 11/23 |
EXAM #3 --- the date has changed, as discussed in class. The
exam will be held in the Sage Hall Testing Center, located in Suite C330. I
will be there between 8-10:50. You may arrive at any
time between 8 and 9, and you will have 1 hour, 50 minutes from the time of
your arrival to complete the exam. Please
talk to Dr. Q to make alternate arrangements if you’re not able to
block off 1 hour, 50 minutes on this morning. 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. |
|||
Wednesday 11/25 |
NONE. |
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Thursday, 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. |
You
can also submit the optional course survey and one copy of the consent form at
any time up to and including the date of the final. These surveys and consent
forms were distributed in class on Monday, November 30. Completion
of the survey is worth an extra 100 on both the homework problems and the
certification review problems. |