Here's a blank copy of the Unit 3 test to use as practice before Tuesday's follow-up test:
Unit 3 test
Saturday, December 19, 2009
Tuesday, December 15, 2009
Wednesday and Friday
You have all class to work on Supercorrections and prepare for the follow-up test next Tuesday. Please feel free to use this document to discuss problems:
http://etherpad.com/HwRSczyOkJ
If you'd like me to jump into a discussion, just let me know with an email.
Although I will be in London for the rest of the week, I am available via email. Just shoot me your questions!
Update: I'm now in the UK (Wednesday)- if you use the Etherpad link above, I can contribute to your discussion.
http://etherpad.com/HwRSczyOkJ
If you'd like me to jump into a discussion, just let me know with an email.
Although I will be in London for the rest of the week, I am available via email. Just shoot me your questions!
Update: I'm now in the UK (Wednesday)- if you use the Etherpad link above, I can contribute to your discussion.
Thursday, December 10, 2009
Scribe Post for 10/10/09
Mr. O'Brien passed the Unit 3 Quiz #2 tests back today, and we went over them for the first part of class. While going over the test, Mr. O'Brien stressed the importance of considering the order of operations while condensing logarithms. He also explained some of the simplifying, and explained why an expression such as
is not fully simplified, and should be further simplified to:
Mr. O'Brien also emphasized that we should use "=" only when the equation is completely equal, and "≈" if the equation is approximately equal. For example, if you have the equation x = 12/13, the equals sign is appropriate. But if you make 12/13 a decimal, it should be written as x ≈ .923 because the decimal is being rounded. He also pointed out that people were losing points for not following directions (for example, rounding to four decimal places when the problem specified to round to three decimal places).
He also explained problem #9 in detail, as follows:
ln 4x = 14/13 can be rewritten as
either by thinking of it as just directly translating it into this form, or by making each side of the equation raised to a power of e, like this:
He then explained checking it without a calculator. He also said to beware of extraneous solutions for our test. A problem can be done perfectly correctly, but then the solutions can be extraneous. This means we should be careful to check our answers by substituting the values back into the equations. He later said how we need to use common sense in checking our answers. For example, if we're doing a carbon dating problem and we get a negative answer for the time, there's obviously a problem with our math.
We then went to p. 270 of the textbook, which went over all of the things we're expected to know for the test. The themes of the test are the basics, as well as real-life problems. Note: we do not have to "recognize the five most common types of models involving exponential and logarithmic functions". We have to be able to use things from section 3.5, but we don't have to have them memorized.
After this, we reviewed homework questions. Mr. O'Brien talked about how, in order to minimize the amount of time we spent on problems during math tests, we should go through the problems to see if there are things we can recognize. For example, repeated calculations can use the "function machine" on our calculators. (Enter the function into the y= on our calculator, and then use a table that's set to ask for the independent variables.)
He also reviewed the correlation between
with the first equation being used for daily, monthly, yearly, etc. compounding, and the Pert equation being used for continuous compounding. (We will not need to have these equations memorized for the test).
Then we reviewed using the [STO→] key to store long values to letters in our calculators. To store a value (for example .56273) to a letter (or example A), type [.56273][STO→][ALPHA][A]. Then to recall the value, simply type [ALPHA][A].
Remember that % decrease is (amount of decrease/total amount). The amount of decrease is the difference of the two values.
For homework, we have to correct all our homework to turn in next class, do 8 problems from the Chapter 3 Review Test to include with our homework packet, and revise for the test next class. Mr. O'Brien said that the test will have a lot of word problems.
Scribe for next class is Andy.
is not fully simplified, and should be further simplified to:
Mr. O'Brien also emphasized that we should use "=" only when the equation is completely equal, and "≈" if the equation is approximately equal. For example, if you have the equation x = 12/13, the equals sign is appropriate. But if you make 12/13 a decimal, it should be written as x ≈ .923 because the decimal is being rounded. He also pointed out that people were losing points for not following directions (for example, rounding to four decimal places when the problem specified to round to three decimal places).
He also explained problem #9 in detail, as follows:
ln 4x = 14/13 can be rewritten as
either by thinking of it as just directly translating it into this form, or by making each side of the equation raised to a power of e, like this:
He then explained checking it without a calculator. He also said to beware of extraneous solutions for our test. A problem can be done perfectly correctly, but then the solutions can be extraneous. This means we should be careful to check our answers by substituting the values back into the equations. He later said how we need to use common sense in checking our answers. For example, if we're doing a carbon dating problem and we get a negative answer for the time, there's obviously a problem with our math.
We then went to p. 270 of the textbook, which went over all of the things we're expected to know for the test. The themes of the test are the basics, as well as real-life problems. Note: we do not have to "recognize the five most common types of models involving exponential and logarithmic functions". We have to be able to use things from section 3.5, but we don't have to have them memorized.
After this, we reviewed homework questions. Mr. O'Brien talked about how, in order to minimize the amount of time we spent on problems during math tests, we should go through the problems to see if there are things we can recognize. For example, repeated calculations can use the "function machine" on our calculators. (Enter the function into the y= on our calculator, and then use a table that's set to ask for the independent variables.)
He also reviewed the correlation between
with the first equation being used for daily, monthly, yearly, etc. compounding, and the Pert equation being used for continuous compounding. (We will not need to have these equations memorized for the test).
Then we reviewed using the [STO→] key to store long values to letters in our calculators. To store a value (for example .56273) to a letter (or example A), type [.56273][STO→][ALPHA][A]. Then to recall the value, simply type [ALPHA][A].
Remember that % decrease is (amount of decrease/total amount). The amount of decrease is the difference of the two values.
For homework, we have to correct all our homework to turn in next class, do 8 problems from the Chapter 3 Review Test to include with our homework packet, and revise for the test next class. Mr. O'Brien said that the test will have a lot of word problems.
Scribe for next class is Andy.
HW
Purplemath.com log links (scribe?)
HW:
HW:
- Choose 8 problems from the Chapter 3 Review/Test. Include them with your homework packet.
- 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. 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.
- Revise for the test. Rest. Psych yourself up. Don't be late and don't be sick- Monday is game day...
Tuesday, December 8, 2009
Scribe Post 8.12.09
We started off with reviewing our Quiz from last class, and our Homework from last class. Then we took a Quiz regarding Log's. Our Quiz lasted for most of the class, but then we moved on to the next chapter.
We started off on pg.265, with problem #26 concerning the half-lives of Radon, and graphing the function y=ae^(-bt), where t is the length of time, b is the horizontal dilation, a is the vertical dilation, and y is the final value of the Radon. We subbed in values as t=1599, y=50, a=100, and then calculated for b, which was b=ln(1/2)/-1599. We then reversed our process, and calculated a with the values of 1.5=ae^-1000[ln(1/2)/-1599], which gave us the value of a=2.3g. We then filled in the values on TI-SmartView, which graphed the equation as a decaying function.
We then confirmed that the function did match the graph. Our homework deals with these functions tonight, but we don't have to memorize the functions for a test.
Next times scribe is Molly.
Monday, December 7, 2009
Tyler's Late Post
In class on Friday we took the first quiz on chapter 3 and then we went over our homework on pg. 253. The majority of the class time was consumed by the quiz. We did not go over any new materials, however we stressed a few laws of log to remember for the next quiz (which is tomorrow).
Notable Points:
1. The base property:
2. ln=e
I hope the class found everything else easy to follow with log. I apologize for the post being so late, most likely it wasn't any help to any of you. Homework for tomorrow is to study for the quiz. Review the HW from pg. 243, and 253 to study. There is also a HW assignment on pg. 253 due for tomorrow. Good luck to everybody on the test.
Here is a website that looks very useful for studying the rules of log: http://www.themathpage.com/aPreCalc/logarithms.htm
Notable Points:
1. The base property:
2. ln=e
I hope the class found everything else easy to follow with log. I apologize for the post being so late, most likely it wasn't any help to any of you. Homework for tomorrow is to study for the quiz. Review the HW from pg. 243, and 253 to study. There is also a HW assignment on pg. 253 due for tomorrow. Good luck to everybody on the test.
Here is a website that looks very useful for studying the rules of log: http://www.themathpage.com/aPreCalc/logarithms.htm
Friday, December 4, 2009
Wednesday, December 2, 2009
Unit 3 Logarithms, Scribe Post
Today we began class by a quick discussion of the mid-term, Mr. O’Brian mentioned that some of the questions on the test will be multiple choice. He also mentioned that students need to understand the concepts we have gone over so far this year.
Next we looked over the Unit 2 test, Mr. O’Brian stressed that students check all answers and make sure that you answer the question that is being asked. When your are supercorrecting pick apart the problem, see how many connections you can make, and show many different ways you can solve it. One note to make is anytime you have a test question concerning a function, you need to have a equal sign and function name with the solution. Mr. O’Brian explains that the questions on the supercorrection follow-up test are the problems he believes to be the most important, the problems he wants to “stick” in student’s minds.
Next, we took notes on the Big Three Log Properties. The first is
. The seconds is 
. The third is 
.
Next we created a proof for:.
Proof:
Let
and 
So:
Multiply:
Simplify:
Therefore:
Q.E.P.
We next proved the second of the Big Three Log Properties which is similar to the first proof but changes the multiplication and addition.
The third proof is almost similar to the second property applied multiple times. Mr. O'Brian said that for bonus, students should prove the third Log property.
Next, we looked at the other log properties on page 230 of our textbooks. Mr. O’Brian said that students should say the properties out loud in words to make sense of them.
We took notes on the Change of Base Formula which is
.
Proof:
Take the log of both sides:
Therefore:
Q.E.P
In the last 15 minutes of class Mr. O'Brian let us work on the homework problems.
Next Class: Mr. O’Brian noted that students should check their answers for the homework to prepare for the quiz because “there is no fudging with logs”. Quiz on friday will be non-calculator. Mr. O'Brian said that for bonus, students should prove the third of the Big Three Log Properties.
Tyler will be the next class scribe
Next we looked over the Unit 2 test, Mr. O’Brian stressed that students check all answers and make sure that you answer the question that is being asked. When your are supercorrecting pick apart the problem, see how many connections you can make, and show many different ways you can solve it. One note to make is anytime you have a test question concerning a function, you need to have a equal sign and function name with the solution. Mr. O’Brian explains that the questions on the supercorrection follow-up test are the problems he believes to be the most important, the problems he wants to “stick” in student’s minds.
Next, we took notes on the Big Three Log Properties. The first is
Next we created a proof for:
Proof:
Let
So:
Multiply:
Simplify:
Therefore:
Q.E.P.
We next proved the second of the Big Three Log Properties which is similar to the first proof but changes the multiplication and addition.
The third proof is almost similar to the second property applied multiple times. Mr. O'Brian said that for bonus, students should prove the third Log property.
Next, we looked at the other log properties on page 230 of our textbooks. Mr. O’Brian said that students should say the properties out loud in words to make sense of them.
We took notes on the Change of Base Formula which is
Proof:
Take the log of both sides:
Therefore:
Q.E.P
In the last 15 minutes of class Mr. O'Brian let us work on the homework problems.
Next Class: Mr. O’Brian noted that students should check their answers for the homework to prepare for the quiz because “there is no fudging with logs”. Quiz on friday will be non-calculator. Mr. O'Brian said that for bonus, students should prove the third of the Big Three Log Properties.
Tyler will be the next class scribe
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