Chapter 1 Review Answers

NOTATION TIPS:
- I have written "squared" as ^2
- ( ) around part of a fraction just means that whole quantity is in the numerator or denominator--you don't need ( ) in your answer
- I have written "less than/greater than or equal to" as <= and >=

REMEMBER: We will not take time to discuss the review in class on the day of the test, so be sure your questions are answered before then! I will be available on Thursday in the morning and after 3:00, after school on Friday, and on Monday morning at 7:15.

1. 8
2. -6
3. 19
4. 7
5. 3x^2 + 4y
6. 13/2 a + 8b
7. $36.95
8. -4
9. 2.2
10. 2/3
11. 0


12. 2(b - y) - 5
13. 3y/(y-2), y is not equal to 2
14. (L - py)/(1 - u), u is not equal to 1
15. v/(pi r^2), r is not equal to 0
16. 13x = 104
16. 24, 32, 48
17. x + x + 22 = 85
17. $31.50 and $53.50
18. x <= -3


19. y <= 8
20. k < 2
21. x < -1 or x > 5
22. -5 <= t < 2
23. -1 <= x <= 4
24. x = 5, x = 4


25. y = 5
26. z <= -1/2 or z >= 2
27. -1/5 < x < 1

August 15

The previous post seems funny now--what I called "the bottle battle" has really become a battle. While she was here, Gretchen gave Nathan his daily bottle (part of the conditioning program); little did we know that it was his last--a few days later he absolutely refused to have anything to with the exact same bottle filled with the exact same liquid! Since then, every time Danial or I tries to give him a bottle, he has a complete meltdown until the offending imposter is removed. It is so frustrating because it's like he just turned it off! I plan to continue trying, with the hope that he will turn it back on one day, just as randomly. However, we think it will come down to the first day I am back at school--if Nathan wants to eat between 6:00am and 3:30pm, Nathan will have to give in and accept a bottle. How can a boy that cute be so stubborn? And where does this stubborn streak comes from...?

My Aunt Beth visited last week. We were out and about a little each day, including the midweek farmer's market downtown, the up-and-coming Alberta Arts neighborhood (which isn't much to see on a weekday afternoon), and the Japanese Garden and Rose Test Garden. It was unusually overcast that week (I know it's Portland, but we have hot, dry summers), but we caught a break on Friday and Mount Hood showed itself so that we could get a few photos. Again, it was really nice to have someone (an adult!) to hang out with and to share the challenge of going on outings. Hopefully the next time Aunt Beth visits we can take her to see some of the sights that require a little more time in the car.

We use the bouncy seat to entertain Nathan when we need some hands-free time (mostly bathroom breaks and when eating). We call it "the movie" because it has cheesy music and a water-filled display that pumps air bubbles through a scene with two fish and a starfish, making them move. Over the last few weeks Nathan has become aware of "the movie" and is much more willing to hang out and watch it while we take a break. Here he is watching pretty intently.



Doesn't this look like he's playing air guitar?










We are using the bjorn more and more instead of the stroller, which uses the car seat (you can see he likes this better!). Eventually we plan to get a jogging stroller, and probably a regular stroller for shopping and other indoor trips.






And here is the ever popular video...

August 7

Danial recognized that I was likely to go crazy if he didn't give me a break. The next morning we agreed that he'd work in the morning, and I'd have the rest of the day off. Woo-hoo! I didn't do anything exciting, but I did take a nap, run some errands, and go out to eat and have ice cream with a friend. And we both learned something very important. It would be nice if it were that Sarah needs a real break on a regular basis, but it was that Nathan doesn't really like taking a bottle. Who knew?!

We have given Nathan an occasional bottle over the last few weeks, and we assumed that he would accept multiple bottles in one day just as easily. This is where we were wrong. The first one was no problem, but he was not having anything to do with the second one a few hours later! This is a problem because in a few weeks he is going to have to take three or four bottles a day if he hopes to eat between 7 am and 4pm. So now we are trying behavioral conditioning on him: one bottle a day for a week or so, then two the next, then three, and so on. It could be rough, though, because I am the one who feeds him all day after 9 am--and who wants to take a lousy bottle when the real thing is just inches away? Cross your fingers for me!

In other news, Aunt Gretchen came to visit over the weekend. Danial craftily arranged for her to come this weekend because he knew he was leaving us to work in Tacoma for a few days. I made sure Gretchen got the full baby experience: change a few diapers, feed a bottle, push Nathan in the stroller, try to soothe a screaming baby in the car, playtime in "the jungle gym." I didn't make her get up in the middle of the night though (I do try to be a good person). I think she and Nathan hit it off, and I was really happy to have her here. For some reason, having a companion (be it my husband or my sister) makes me more confident about taking Nathan out in public. Maybe it's knowing that there are two of us to try to soothe him if things go wrong, or maybe it's that if you act like you're competent at something, people often believe you and it becomes the truth. Whatever the case, we went out several times and did just fine, and just had a really nice visit.


Finally, due to popular demand, here is another video. But beware--as you can see, he's in the carseat. Don't let the pacifier fool you--keep your finger on the volume control (it's also a little long)!

July 29

One can never have too many pictures of a naked or semi-naked baby! (The daddy in the background is not naked, just shirtless.)


On Saturday we went to a street fair and intended to stop for a bite to eat, but the service was so bad we ended up staying there for several hours. The chicken salad sandwich (that we didn't really order) was really good, but we were not impressed with the mac and cheese (even Danial!).


When Nathan doesn't want to be put down and I or we need to kill some time to put off a feeding, a good thing to try is taking a little walk. It could be around the block, or just from front yard to back yard.







He periodically throws back his head to put his face in the sun (or the drizzle) as if to say, "Bring it on! I love it!"

The first video (I didn't know I could post them)! Nathan spends some time in the "jungle gym" every day, cooing at the baby in the mirror and enjoying the hanging toys. We can't decide if he's hitting them on purpose yet or if it's just random.
The video is not exciting, but the baby is cute.

Three Weeks Old

In case anyone is checking back here for updates and more photos... Here they are!







My mom has been here for three weeks, although she has not appeared on this page yet.

She has been a cleaning machine, and has given us valuable advice, particularly on how to bathe the baby.

Not much of interest has happened lately--on most days we run through the same cycle of tasks every two to three hours:
feed Nathan,













burp and change Nathan,










put Nathan to sleep.












I try to get some sleep during the last phase of the cycle between about 7pm and 7am, and try to get in at least one nap during the day, too. When I'm awake I feel pretty good and not really "sleep deprived," but I cry often enough to indicate that I'm probably getting less than I need. The cats agree.My husband, as always, loves to cuddle with Nathan whenever possible.
He has also been good about trying to get us out of the house on an errand or for a walk at least once a day. This is a good thing, and we get lots of "oohs" and "ahhs" while we're out.Soon we hope to be able to use the carrier to get around outside, too.
Isn't he the cutest thing ever?

One Week Old

Things are going pretty well so far, and we are getting established in our roles.

My husband is our diaper-changing specialist, and he enjoys reading the newspaper out loud to Nathan to "entertain" him.

I, of course, am the feeding specialist. We go through the cycle--feeding, a little burping, a diaper change, more feeding, then wrap tightly and put to bed--about every 2 to 3 hours. He makes the cutest little faces after his belly's all full and he's lying there passed out like a little drunkard.























Also, I finally got the last of my school work out of the way. Funny how I thought I was going to be able to take the Memorial Day weekend to get all of the loose ends tied up!

As always, more photos are posted at snapfish.com. Use sarahko99@hotmail.com as the login, and "photos" as the password .

The Pictures and The Story

Starting on Friday morning and all through the afternoon and evening, I had short, 30-second contractions. We decided to go to sleep that night and call in to the hospital the next morning. But at about 11:15 pm I felt a big kick and my water broke and we decided NOT to wait until the morning to call the hospital.

But when I called, they were full!!

They told me everything sounded okay, and that I should wait for a few more hours when they would have a room available. Over the next two hours, my contractions got really intense, longer, and much closer together, and we arrived at the hospital at about 2:00 am. Just after a discussion with the midwife about pain medication, the baby's heartrate began to slow down when I had a contraction, but it didn't rebound like it was supposed to between contractions. So there were suddenly about 6 people in my tiny little delivery room, they put an oxygen mask on me, and turned me over and over until they found a position that kept the heart rate as normal as possible.

I will spare you the rest of the gory details, but the baby was born at 4:41 am--less than three hours after we arrived at the hospital. Because of the heart rate issue, everyone seemed to forget about the pain medication, and I never did get any--so I was really happy that it was all over quickly!

We came home on Monday afternoon, then had to go back to the hospital on Tuesday afternoon. Jaundice is pretty normal in babies, but it can be dangerous beyond a certain level. Nathan's level got a little high, so we took him in to hang out in the nursery under the special lights that help relieve the jaundice. It wasn't too bad--I got to feed him every 2-3 hours like usual, but got to go back to my room to sleep in between (at home, he often cries for some of the time between feedings and no one can sleep).Now we are home again and trying to figure out a routine and how to make this all work. It's a good thing he's so cute!

Baby is EARLY! It's HERE!

The baby was born at 4:41 am on Saturday morning. HIS name is Nathan Alexander (are you surprised it's a boy?), and I will try to post some pictures and more info back here tomorrow.

Thursday Morning at the Hospital

My husband and I went down to the hospital at 8:00 this morning, and headed to Labor and Delivery. Right away they weighed me on this big walk-on scale like they use for dogs and other large animals at the vet, which I thought was a really sensitive thing to do (did you hear the sarcasm?). I got a room and they did an ultrasound to make sure the baby was still in the wrong position, then put on some monitors to check its heartbeat.


They want to be ready for an emergency c-section in case something goes wrong, so the nurse put an IV-lead in my hand, and gave me a shot of a muscle relaxer to keep me from having contractions. Then the doctor covered my belly with ultrasound goo to make it slick, got one hand behind the baby's head and the other behind its butt, and started turning. The only pain was from the pressure of her fingers on my skin, and although it wasn't comfortable, it was definitely not as bad as I had expected. Halfway around she was going to stop for a few seconds, but I told her I was okay, and she turned him/her all the way around.

We are officially head down and feet up! The nurse told me it was one of the fastest and easiest ones she has seen.

Of course, right after all of the hard stuff was over, I started to feel like I was going to pass out or get sick (for anyone who knows, my blood pressure was down to 80 over 32!). Ice chips, a cold cloth, and some fanning took care of it though, so they just hooked me up to the baby monitor again for another hour and sent me home.

I am off to take a nap and relax, and maybe grade some tests later. I'll keep you posted.

How was the first day with Mrs. Martin? I hope you were nice to her!

This Is Why Your Tests Are Not Graded

This is me on the couch in my living room Monday night, which my cats actually enjoyed. As you can see, grading was not really an option.

Baby Shower Photos: May 18

Thanks, girls! I had no idea that you were planning this, so I was really surprised! All of the gifts were very cute, but the best part was really having all of you together to celebrate with me!

Chapter 8 Review Answers

1A. Points include: (-2, .014), (-1, .05), (0, .2), (1, .76), (2, 2.9)
1B. Points include: (-2, 48), (-1, 12), (0, 3), (1, .75), (2, .19)

2A. y = .0015 (10)^x
2B. y = 1 (1/3)^x

3A. y = 12500(.91)^x, and y = $7800 after 5 years
3B. y = 50 (1.03)^x and y = $57.96 after 5 years

4A. translation shifts down 5 from the parent
4B. translation shifts 2 to the right and up 3 from the parent

5A. log (base 6) 36 = 2
5B. log (base 3) 27 = 3

6A. log (base 2) .125 = -3
6B. log .001 = -3

7A. 6
7B. 0

8A. -2
8B. -3

9A. log 192
9B. log (base 3) (7x^4)

10A. log (base 2) (5/3)
10B. log (y^3/z)

11A. 2log (base 2) x + 3 log (base 2) y
11B. log 6 + 4 log s - log t

12A. log (base 3) 2 - log (base 3) x
12B. 5 log (base 6) x + 10 log (base 6) y - 2 log (base 6) z

13A. 2.3774
13B. 3.0589

14A. .6599
14B. .6658

15A. 10/3
15B. 8

16A. 5.1962
16B. 500

17A. 18.19 hours
17B. 28.21 years

18A. .8283
18B. 3.7726

19A. 4.307
19B. 1.82 x 10^-4

20A. $301.11
20B. $1169.82

Period 2 Chapter 6 Retake Review

degree 2: quadratic, degree 3: cubic
degree 4: quartic, degree 5: quintic

1 term: linear, 2 terms: binomial, 3 terms: trinomial

1A. x^5 - x^3 + x, quintic, trinomial

1B. 4x^3 + 2x^2 + 2x, cubic, trinomial

2A. y = (2.04x10^-4)x^3 + .26 x^2 - 3.62 x + 29.3

2B. $414.93

Imaginary zeros/roots come in pairs called CONJUGATES.

3A. x^3 - 4 x^2 - 11 x + 30

3B. x^3 + 6 x^2 + 9 x + 54

To find the zeros of a function, FIRST MAKE IT EUQAL TO ZERO, then SOLVE FOR x.

Multiplicity: THE NUMBER OF TIMES A FACTOR OR ZERO APPEARS

4A. x = -1 (mult. of 2), x = 3/5 (mult. of 1)

4B. x = 0 (mult. of 1), x = 2 (mult. of 3), x = -1/2 (mult. of 1)

FACTORING CHECK LIST:
1. Check for a GREATEST COMMON FACTOR. Continue factoring.

2. Check for a DIFFERENCE OF TWO SQUARES. Continue factoring.
Pattern: a^2 - b^2 = (a + b)(a - b)

3. Check for a SUM OR DIFFERENCE OF TWO CUBES.
Pattern: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Pattern: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

4. Check for a SUBSTITUTION TO MAKE A NICE QUADRATIC.

5A. 3x^2 (x - 2)(x + 1) =0
x = 0, x = 2, x = -1

5B. 4x (x + 5)(x - 2) = 0
x = 0, x = -5, x = 2

6A. 2 (x + 3)(x^2 - 3x + 9) = 0
x = -3, x = (-3 +/- 3i sqrt3) / 2

6B. (2x - 5)(4x^2 + 10x + 25) = 0
x = 5/2, x = (-5 +/-5i sqrt5) / 4

7A. (x + 10)(x - 10) = 0
x = -10, x = 10

7B. 3 (x + 4)(x - 4) = 0
x = -4, x = 4

8A. 2(x^2 - 14)(x^2 + 1) = 0
x = +/- sqrt14, x = +/- i

8B. (x^2 + 3)(x^2 + 5) = 0
x = +/- i sqrt 3, x = +/- i sqrt5

9A. (x + 1)(x - 3)(x - 4)

9B. (x - 3)(x - 3)(x + 2)

10A. complex roots: 3, possible real roots: 1, 3

10B. complex roots: 4, possible real roots: 0, 2, 4

11A. This is really tough! Don't even try p/q--it won't work because the last term is 36x. Instead, look for a GCF, then go through the rest of the factoring check list.
x = 0, x = +/- 3, x = +/- 2i

11B. This is also tough! Look for a GCF, then go through the rest of the factoring check list.
x = +/- sqrt14, x = +/- i

12A. x = -4, x = +/-i sqrt7

12B. x = -2, x = 1 +/- sqrt7

Chapter 6 Review

I have to warn you that the formatting is not as nice as if you were looking at a regular Word document--the post editor won't let me cut-and-paste from a Word document, and I couldn't find a way to type nice exponents.

Here's the best I could do:
"x squared" looks like "x^2"
"plus or minus" looks like +/-
"square root" looks like "sqrt"

Leave your name and a comment if you have a question, and I will reply by leaving a comment.

1A. x^5 - x^3 + x --> quintic trinomial

1B. 2x^2 + 2x --> quadratic binomial

2A. y = -.04x^3 + .65x^2 - 2.94x + 24.84 --> y=7.33 when x = 12

3A. y = x^3 - x^2 -25x + 25

3B. y = x^3 + 6x^2 + 12x + 8

4A. 3x^2 (x - 2)(x + 1)

4B. 4x (x + 5)(x - 2)

5A. x = -1 --> multiplicity 2 AND x = 3

5B. x = 0 & x = 2 -->multiplicity 3 AND x = -5

6A. x^3 + 3x^2 + 3x +4, R1

6B. 3x^2 - 7x + 7, R-8

7A. remainder = 0 --> yes, x - 3 is a factor

7B. remainder = 1 -->no, x-3 is not a factor

8A. P(-2) = 77

8B. P(3) = 153

9A. (x + 1)(x - 1)(x - 3)

9B. (x - 3)(x - 3)(x + 2)

10A. for periods 5, 7:
max = 3.08 (at x = -.15) AND min = -3.08 (at x = 2.15)

10A. for period 6:
The polynomial from 9A doesn't really have a relative max/min.
Instead, try x^3 - 3x^2 - x + 3 and check the answers for periods 3, 5

10B. for periods 5, 7:
max = 0 (at x =0) AND min = -1.26 (at x = .82) AND min = -45.1 (at x = -3.07)

10B. for period 6:
max = 18.5 (at x = -.33) AND min = 0 (at x =3)
Or try x^4 + 3x^3 - 5x^2 and check the answers for periods 3, 5

11A. factored: 2(x + 3)(x^2 - 3x + 9) = 0
solutions: x = -3 AND x = (3 +/- 3i sqrt3)/2

11B. factored: (2x - 5)(4x^2 + 10x + 25) = 0
solutions: x = 5/2 AND x = (-5 +/- 5i sqrt3)/4

12A. factored: (x + 10)(x - 10) = 0
solutions: x = -10 AND x = 10

12B. factored: 3(x + 4)(x - 4) = 0
solutions: x = -4 AND x = 4

13A. x = +/- sqrt14 AND x = +/- i

13B. x = +/- i sqrt3 AND x = i sqrt5

14A. 3 - 2i and 1 - sqrt2

14B. 2 + sqrt3

15A. y = x^3 - 2x^2 + x - 2

15B. y = x^4 -10x^3 + 39x^2 - 70x + 50

16A. complex: 3, real: 1 or 3
possible rational roots: +/- 1, +/-3, +/-5, +/-15

16B. complex: 4, real: 0, 2, or 4
possible rational roots: +/-1, +/-2, +/-4, +/-1/3, +/-2/3, +/-4/3

17A. x = 0, x = +/-3, x = +/- 2i

17B. x = +/-2 sqrt2, x = +/- i sqrt6

18A. x = 4, x = +/- i sqrt7

18B. x = -2, x = 1 +/- sqrt7

I told you I'd do it...

Check back here over the weekend for answers to the Chapter 6 Review!