Practice questions on graphing parabolas

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B8MSB3tEywM5ZDhmYmI4ZWItZDA0MS00NzNhLWIwMDAtYjFiZTU5YTQ2MDg5&hl=en_US

Class Saturday, May 28th

Hi all - in the morning, we took the exam. How'd it go?

Then in the afternoon we discussed sections 11.5, 11.6 and the start of 11.7. Check out the homework for what I expect us to know and do.

The main secret is that logs undo exponential functions. So if I have b to the x equals y, that is the same equation as log-base-b of y equals x. It's confusing. The first problems, translate the log form into the exponential form and see how it looks that way - I might not know what log-base-5 of 125 is, but I know if I set up 5^x = 125 then x must be 3, and those are the same math object in different form.

Tomorrow (Monday) I'll post the first half of the practice for the final - on quadratics and graphing parabolas. We haven't discussed some of that yet, but we will next week (and this is the part tat I have the key already written for...) I'll post the rest of the final practice on logs, and the keys to both part, later in the week (certainly before class on June 4th).

Next week we'll finish up logs, talk about graphing parabolas, redo the exam we took today, and review for the final. It's bound to be a big exciting day!

Here's the homework for next week:

11.5: 1 - 5 all, 13 - 109 EOO

11.6: 1 - 5 all, 15 - 67 EOO

11.7: 17 - 37 odd

Key for second practice exam

Hi all:

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B8MSB3tEywM5MWE5OTIwYzQtZWJlNC00NDlkLTlmNmItM2Y3ZTAwOWViNjll&hl=en_US

It's not quite complete - I still need to add the graphs to the last question. I'll post an updated version tomorrow afternoon (all the material is there except for that one question - I can't get my laptop to do graphs anymore...)

Good luck, and see you Saturday!

-Dave

Practice exam for the second exam next week

Hi all - here's the link to the practice exam. I saved it as a pdf because of all the symbols and math stuff - let me know if you have any problems opening it and I can send you the word document. Woo hoo!

https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B8MSB3tEywM5NmU1ZWRkZTgtZjRlYi00N2E1LThiYzMtZjhiYzI1ZWE3NjU2&hl=en_US

I will post the key Wednesday afternoon. Look for it Thursday morning. Remember - our exam next week starts at 9am and goes until noon, and then we talk about a couple more sections from chapter 11 in the afternoon.

-Dave

Post for Saturday, May 21st

Hi all,

Today we covered sections 9.5 and 9.6, touched on section 10.1, and then sections 11.3 and 11.4.

Next week is the second exam, over sections 9.1-9.6, 10.1 and 10.2, and 11.1 - 11.4. In the afternoon we'll cover sections 11.5 and 11.6. That's May 28th.

The week after that we'll talk about graphing parabolas (the picture formed by quadratic equations) and solving exponential and log equations. That's June 4th.

The following Saturday is our last - we review for an hour (from 9am - 10am) and then start the final exam at 10. The final will cover mostly graphing parabolas and solving log and exponential equations; we use most of the material from the rest of the term to do those things.

I'll post the practice exam tomorrow - look for it in the evening, or Monday morning. I'll post the key to it Wednesday evening (you'll see it Thursday morning). I'll also have a practice exam and key for the final.

Look at the chapter 9 test on pages 889-890: 2 - 29 and 31 - 41 to start looking at the chapter 9 material. Do the section tests, or the homework from each section for more practice.

We'll need to be able to use the quadratic formula (the first question on next week's exam asks us what the quadratic formula is). Review sections 10.1 and 10.2 (don't worry about completing the square, though).

We'll also look at the first four sections of chapter 11 - combinations and compositions of functions, inverse functions, exponential functions and the number e as the base of exponential functions. Look at the chapter 11 test on pages 1079-1080, problems 1 - 20 to start (and again do more practice where you need to).

Good luck on the exam!

-Dave

Post for Saturday, May 14th

Hi everyone - sorry this is going up so late, and thank you to the two people who phoned me about this today! I THOUGHT I wrote and posted a log for the most recent class, but I don't see it up (or a saved draft).

So! In class we covered sections 9.3 and 9.4 on radical things (square and other roots), and then section 11.2 on inverse functions. In the afternoon we redid the first exam for partial credit - we'll get it back the next class (the 21st) with a score. The second project is also due this coming class period - have you started it?

Next week we'll cover the rest of chapter 9, some more sections of chapter 10, and sections 11.3 and 11.4 on exponential functions. Whatever we discuss will be the high-water mark for the exam in two weeks (May 28th); that afternoon we'll cover log functions. Log functions are Very Important and kinda tricky, so you really oughta plan for both the exam in the morning and the discussion in the afternoon.

The week after that (June 4th) we'll cover the rest of the material from chapters 10 and 11, and redo the exam. The week after THAT (June 11th) is our final - 9am, in our regular classroom. It's been quite a wild ride, yes?

Also on this next Saturday (the 21st) we'll do course evaluations - your chance to give me (and the textbook, and the course in general) a grade.

Homework for May 21st:

Finish project 2

Section 9.3: 13 - 113 EOO

Section 9.4: 11 - 51 EOO

Section 11.2: 15 - 33 odd; 35 - 67 EOO.

See you Saturday!

-Dave

Second Project

Froemke – Math 95 – Spring 2011 – Project 2 – Project is due May 21

1. If f(x) = 1/(x + 1) and g(x)= x² . Give the following compositions:

a. f(g(x))

b. g(f(x))

c. f(f(x))

d. g(g(g(x)))

2. Use the table to find the following:

t	f(t)	g(t)	p(t)
0	0	-2	-10
1	2	5	-5
2	4	10	0
3	6	13	2
4	8	16	4
10	-20	22	22
12	-10	15	25
15	-3	8	28

1. f(2)
2. f(15) – g(15)
3. (f-g+p)(3)
4. (g*p)(1)
5. (f/p)(2)
6. g(f(2))
7. (f o g)(2)
8. f(p(0))
9. p(f(1))

3) The DaveCo monthly revenue on car-painting robots is 5 million dollars per robot. The cost is (x² + 6) million dollars, where x is the number of robots produced in a month. Remember: Profit is Revenue minus Cost.

a) What’s the DaveCo monthly profit on robots?

b) What’s the best number of robots to produce?

4) The number N of bacteria in a refrigerated food is given by

N(T)=20T² - 80T+500; 2 < T < 14

where T is the temperature of the food (in degrees Celsius). When the food is removed from refrigeration, the temperature is given by

T(t)=4t+2; 0 < t < 3

where t is the time (in hours).

a) Find the composition of N(T(t)) and interpret its meaning in context of the problem.

b) Find the number of bacteria in the food when t=2 hours.

c) Find the time when the bacterial count reaches 2000.

5) One of the two functions below has an inverse:

f(x) = (x-1) / 2

g(x) = x² – 5x + 6

a) Which one does not? Justify your answer.

b) Find the inverse of the one that does.

c) Verify that you’ve found the correct inverse by composing functions.

Post for Saturday, May

Hey all - how'd the exam go?

In the afternoon we covered sections 10.2 (the Quadratic Formula) and 11.1 (Operations using functions, and Composition of Functions.) It was awesome.

Next week we'll cover sections 9.3 and 9.4, 10.1 (those are all related, about simplifying roots and solving square root equations) and then section 11.2 (inverse functions). In the afternoon we'll redo this week's exam for partial credit on missed problems.

I'll post the second project soon - it's due week after next (May 21st).

Homework for Saturday:

Section 10.2: 1 - 11, 13-27 odd, 37-41 odd, 45, 49, 57, 59, 65, 69-87 odd

Section 11.2: 9-12, 13-77 odd

Link to the Key to the first practice exam

Hi all - here's the link:

https://docs.google.com/document/d/14GPj3PN5-4R0HBa7W3ly4Gh3lyBfPokzHDd1v-jpJks/edit?hl=en

Again, please let me know if you have any errors. Everything looks good from my end, on a few different computers and Operating Systems that I checked it on, but weird things can happen.

Also - I apologize for the three non-factorable quadratics hidden in here - one in the story problem about the river, and two in big fraction equations. On the actual exam, we'll be able to factor any quadratic - next exam we'll have another tool to use. I changed the two rational problems to what I WANTED, not the typos that gave non-factorable quadratics; if you got the equation I did and stopped for the problem where I visited Susan on the river - well, that's okay.

Remember - we get to use a page of notes and a calculator. We'll come in Saturday morning, talk about any last-minute questions we might have, and then take the exam for the rest of the morning half. Then in the afternoon we'll work through the start of chapters 10 and 11. Whee!

-Dave

Practice Exam the First

Hi everyone - here's the link to the practice exam that I uploaded to Google docs.

https://docs.google.com/document/d/1YHGHsKkNKOUv8Tt4_mtDlFV_1XWKUvgilxNHPQCm8IM/edit?hl=en

Please let me know if you have trouble seeing or accessing it. I'll post a key to it - also to google docs - sometime Wednesday evening (or Thursday early early morning). The key will be more than just answers, but a huge thing with most of the questions worked out. Good luck!

-Dave