le 24 de novembre

HAPPY BIRTHDAY, MR. O'BRIEN!!

Schedule:
- QUIZ!
- Homework questions
- In class questions

Today in class:
Today, we took a homework quiz that everyone loved doing. The questions focused on logarithms and their properties, as well as some nifty tricks we've learned along the way. We then began to work on the in class questions in small groups, just to make things easier. In case you forgot to write them down, here they are:
[Descending order signifies the difficulty]
Page #253: 101, 97, 95, 91, 87, 59, 55, 53, 39, 33.

However, we DID take a short break to go over some homework problems. Mainly, we reviewed how to do logarithms algebraically using the properties of exponents. Here are some notes!

1. If two things are equal, you may log them.

You can do this:


Ding ding ding! That means that you can them do the properties of logs to get through this one, which should really come in handy.

2. Substituting a variable for a series of computations is WAY easier. For example, if you have you can say . Ta-da! This helps when doing equations such as number fifty-seven on the homework [phew] since you could in theory do this:

Let .



Isn't that so much nicer?

3. You can use the quadratic formula in conjunction with the One-to-One or the Common Sense property! Yay! This is sort of obvious, but it's a good thing to remember when you're stuck & can't decide what to do.

After we finished reviewing some homework [#'s 27, 57, 65, 81, & 99], we began to work on our in class problems again. Please note: if any of these are not finished during class, they ARE NOT homework over vacation! However, they do need to be done for class on TUESDAY. It is also good to remember that quarter two projects are posted & available for review. DON'T FORGET!

Have a great Thanksgiving!

[Happy scribing, Annie!]

HW:

• p. 253/101, 97, 95, 91, 87, 59, 55, 53, 39, 33 (whichever are not finished in class)
• Read the Second Quarter Project
  

Post for Class on 11/20/09

We began class by looking at a few blogs created by other math classes. One was from a precalc class similar to ours, and theirs was far superior to what we have done so far. The web address for this blog is: http://pc40sw09.blogspot.com/search/label/Exponents%20and%20Logarithms, in case anyone is interested. We also went over the new rubric for second quarter blogging and talked about how we are planning on moving away from the wikispace and onto the blog.

Getting into the math, we went over the Supercorrection followup tests. Most of the mistakes people made were small, so it seems like we finished strong on that unit. We moved onto logarithms, and started off by looking at the website listed at the bottom of this post. This post goes over the four basic properties of logs and is a very helpful tool. However, this post as well as what Mr. O'Brien said in class goes to prove that y = log_bx if and only if b^y = x,

where x > 0, b > 0, and b 1 is the most important equation used in logarithms. After this, we did the problems p. 243/ 47-59 odd, 69-79 odd, and 80 in class with our groups. Although these problems could look a bit complicated to begin with, by using the four big properties we were able to break them down into a simpler form. Mr. O'Brien also showed us how working vertically instead of horizontally can make problems easier to solve and let us make fewer mistakes. Mr. O'Brien demonstrated how to simply break down problems by solving the problems p. 253/12, 14, 30, 56, 86, and 94 as practice problems.

Main lesson of the day: Even the most complex problems can be broken down into the four basic log properties.

Homework for next class:

p. 253/9-23 odd, 27, 29, 35, 49, 57, 65, 81, 93, 99

If you miss class, be sure to do p. 243/47-59 odd, 69-79 odd, 80 and p. 253/12, 14, 30, 56, 86, 94 as these will be included on homework quizzes for this unit.

Look over your homework in preparation for the quiz next class

Link to four properties: http://www.andrews.edu/~calkins/math/webtexts/numb17.htm

Scribe Post: 11/18/2009

Today, we started off class by taking the Supercorrection Follow-up Test for 25 minutes. Then, we proceeded to explore the value and nature of the number ‘e’ (aka 2.718281828459045...). We discovered the y=ex is the same as y=logex which is also the same as ln x. “Logmn is the power you raise m to to get n.”
Next, we went over last night’s homework discussing ‘log’ and ‘ln’, putting questions on the board and going over them as a class as usual. We took a look at the Mystery Function, leading into the Big Three Log Properties.

Big Three Log Properties:

logn(a•b)=logn(a)+logn(b)
logn(a/b)=logn(a)-logn(b)
logn(am)=m•logan

Next, we covered the Powerful Change of Base Formula.

Powerful Change of Base Formula:

logn x = logbx / logbn

Homework: p. 243 #11-45 odd, 61-67 odd

Monday, November 16, 2009

We started out class with the warm-up worksheet on the Lift-Off Function - we explored the properties of exponents leading to lift-off function is gb(x). We also did some graphing for the warm-up. Then, we went over the homework problems, 55 and 59 --- Both these questions were compound interest problems. After going over homework questions, we briefly went over the mystery function...which we found out is actually logarithms, and then we also reviewed the lift-off function which was also the logarithm function. We learned in class, that logarithms will be the inverse to exponential functions! So, when you get a logarithm problem, you don’t even have to deal with it as a logarithm, you can just convert it back to a exponential.

*Note: On your calculator, ln, is how you can solve for natural log.
Remember that, g(x) = log1 x, does not exist!

We ended class early, and were able to start our homework!
HW for next class:
* p. 236/1-29 odd, 33, 39-44 all, 49-69 odd
* Be sure you are ready for the Supercorrection Follow-up Test

Next Scribe: Julia

11/12/09

Today we spent the first half of class working on our supercorrections that are due on Friday. Then we began talking about the properties of exponents. We went over basic rules such as a power times a power you add the exponent; a power divided by a power you subtract the exponents; and a power to a power you multiply the exponents. Using these properties we then revised the homework on the board. Then we took a look at the exponential Function: f(x)=a^x. Then using both grapher and our GDC's, we graphed the exponential functions a= 1/2, 2, e, 3. Then using GeoGebra we graphed a family of exponential function. We figured out that A must be greater than zero and cant be equal to one, because one to any power is one which graphs as a line. Other properties we found were that the Y intercept is 1, when 0 < a < 1 a > 1 it's increasing.


Homework
Finnish supercorrections for Friday 11/13/09
Finnish Mystery Function for Monday 11/16/09
Do the following book problems for Monday 11/16/09
P. 226/ 7-11, 15, 19, 27, 33, 45-51 odd, (55, 59 formula on page 224)

Next Scribe Anna

11/3/09

We began the class with two warm up problems. The object of this exercise was to graph the problems and solve for inequalities values without using the aid of a calculator or computer. After working one these problems at our tables, we then went over the first problem as a class and we used it to create our class “Steps to Graph Rational Functions”. Then we went over the second problem and used our steps to solve it. As we were solving it we remembered to add two more steps. We also went over how to solve for the inequalities on both problems. Then we went over problematic homework questions. We also discussed “volcano asymptotes”.

Test next class.
All home works due.

HW:

* p. 208/5, 19, 37, 51, 55, 71, 77, 105, 129, 141
* Review for Unit 2 test
* Organize your homework- make sure each assignment is completely checked and corrected and that each has your name, date, and the assignment at the top. The grading rubric is available here: homework.pdf. Stack your homework ordered from oldest to newest with the homework cover page on top. Staple your stack in the lower right hand corner. You will hand in your homework on the day of the test before you take your test.

next scribe, mr. pieri