Saturday, December 19, 2009
Unit 3 test
Unit 3 test
Tuesday, December 15, 2009
Wednesday and Friday
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
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
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
Monday, December 7, 2009
Tyler's Late Post
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
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
Monday, November 30, 2009
Unit 3 logarithms, Scribe post, Collin Downs
1. log(a*b)=log(a) * log(b)
2. log a^n= n*log a
3. log a/b= log a - log b
These will be used in our homework tonight which is p. 243/11-45 odd, 61-67 odd.
Monday, November 23, 2009
example: log(27)^9, in words: "The power you raise 27 to to get 9"
Then we found the inverse of exponential: f(x)=b^x then: y=b^x, then inverse: x=b^y, then solve for y: y= log(b)^x. So f^(-1)(x)=log (b)^x
Monday, November 23rd, 2009
HW:
- p. 236/1-29 odd, 33, 39-44 all, 49-69 odd
- Be sure you are ready for the Supercorrection Follow-up Test (blank copy of the test available here)
Friday, November 6, 2009
Today we did a warm-up with rational functions. We reviewed graphing and simplifying, and molly wrote up a google-doc on 'steps to graph rational functions.' We also discussed the equation 0/0=0, and pondered whether or not the answer would be 1, or whether it would result in an error on your calculators. We calculated our asymptotes for our warm-up using division to find the end-behavior. We explored rational functions using grapher, and added extra x's on the numerator's using our previous equation's from our warm-ups. We also fooled around with adding 7x, 5x, 12x, etc. and 2x, etc. on the numerator and denominator (respectively) to change the horizontal asymptotes. What we ascertained is that when there is a larger power on the denominator than on the numerator, the end behavior reached closer and closer to 0, regardless of the numerator's behavior. We can find the end behavior of our graphs by using division if the numerator's power is higher than the denominator's power, if the powers are the same then the lead coefficient of the numerator divided by the lead coefficient of the denominator is the horizontal asymptote for the end behavior, and if the power in the denominator is higher than the highest power in the numerator, then the end behavior is y=0. We finished by graphing the functions with all of the above information. We then calculated f(x) is less than or equal to 0. We used molly's steps to solve and graph our second equation. We revised our steps by adding that you can cancel portions of equations if it is possible. We changed our equation from g(x)=(2-x)(2+x)/(x-2) =-x-2, x does not equal 2. Mr. O'Brien went over what to expect for the test, and gave us the revision problems for the test, and encouraged us to do extra problems if we wanted to. Mr. O'Brien corrected the notion that Juniors will be in class on the 17th when the Supercorrections are due, and we spent the rest of the class reviewing any homework problems we wanted to.
Wednesday, November 4, 2009
There is no quiz on Friday, but the Unit 2 test is on Tuesday.
Thursday, October 29, 2009
Friday, October 23rd
Before we refreshed on these two forms of division, we went over homework, which was composed of problems from section 2.1 and 2.2. since this was our first time looking over chapter two homework together, we refreshed on some basics, like finding the Axis of Symmetry (of quadratics) and and the roots of polynomial functions etc. This will be the material present on next class’ quiz.
Our lesson regarding Synthetic Division and Polynomial Long Division showed us that while both were effective, each had their time and place. Synthetic Division was more simple, but Polynomial Long division could be used regardless of what the polynomial is being divided by. We then saw how the remainder theorem can help one find function values.
Tuesday, October 27, 2009
Scribe Post 10/27/09
Monday, October 26, 2009
Homework for 10/27/09
- Molly W.
W-2 Pre-AP Calc
Tuesday, October 20, 2009
HWK assigned10/18
-Henry W-2
Monday, October 19, 2009
Pre-AP Calc 10/19/09
Tuesday, September 29, 2009
Scribe Post for 9/29/09
THE TEST will cover all assigned homework and content learned in chapter 1. When you come to class that day you should have all of your homework organized as specified on the class website so you can take a full eighty minutes to complete the test. You should study by: making sure you understand the points explained in the chapter summary, doing six questions of your choice from pgs. 117-122, and reviewing all hw, notes, and quizzes.
In the last ten minutes of class Mr. O'Brien answered the questions we had on today's homework which covered inverse functions. The questions included problems 21, 23, 27, 61, and 63 on page 99. If you still have any more questions on the homework or on any part of chapter 1 you should see Mr. O'Brien or email him. Good luck on the test!
--The scribe for next class will be Andy--
Friday, September 25, 2009
Scribe Post for 9/25/09
Scribe for the next class is Sean.
Wednesday, September 23, 2009
Scribe Post for 9/23/09
Monday, September 21, 2009
Scribe Post for 9/21/09
Sunday, September 20, 2009
Thursday, September 17, 2009
Tuesday's class
in class. Then, after all of this we went onto the symmetry sight off the class website, and downloaded the page. We then learned about symmetry proofs. And the ten problems on these pages was our homework.
Collin will be the next scribe.
Tuesday, September 15, 2009
How to find a line of best fit on TI-84 Plus
Linear Equation
To find the line of best fit for a linear equation, pretend we had the points: (-2, 5) (1, 11) (3,15)
Go to STAT > Edit... Under L1, enter all the x-coordinates. Under L2, enter all the y-coordinates. Then hit STAT > CALC > LinReg. Hit ENTER. You'll see something like this:
LinReg
y=ax+b
a=2
b=9
This means y=2x+9.
Quadratic Equation
Say you have a quadratic with these points: (-2, 3) (0,-5) (2, 11) (3, 28)
Go to STAT > Edit... Under L1, enter all the x-coordinates. Under L2, enter all the y-coordinates. Then hit STAT > CALC > QuadReg. Hit 2nd>1 (L1), then enter a comma, and then 2nd>2 (L2). Then hit ENTER. It will give you something like this:
QuadReg
y=ax²+bx+c
a=3
b=2
c=-5
This means that the equation is y=3x²+2x-5
Cubic Equation
For a cubic equation, enter the points. Pretend they're (-2, -8) (-1, -6) (0, -6) (1,4) (2, 36)
Go to STAT > Edit... Then enter all the x-coordinates under L1 and the y-coordinates under L2. Then hit STAT > CALC > CubicReg. Type 2nd>1 (L1), comma, then 2nd>2 (L2). Hit ENTER. You'll see something like this:
CubicReg
y=ax³+bx²+cx+d
a=2
b=5
c=3
d=-6
This means it's y=2x³+5x²+3x-6.
Good luck :)
Homework for 9/15
Thank you,
Henry W-2
Sunday, September 13, 2009
Friday September 11th's class
Wednesday, September 9, 2009
The Scribe List
This post can be quickly accessed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.
IMPORTANT: Make sure you label all your Scribe Posts properly (Your Name, Unit Title, Scribe Post) or they will not be counted.
Extra Credit: Tyler
Collin Sean Henry Miles Amber Marcel | Tyler Kyle Petra Andy Molly |
Katharine, Functions, Scribe Post
Overall the class believed that the homework went well and was a fair amount of problems. Some sections that the class had trouble with was pg. 49 (65, 75-78) The class seemed to not clearly understand domain. More importantly the class did not know how to find the domain easily, we were wondering if there was a equation to help solve the problem. On problems, 75-78, the class also wondered if there was a equation to find the solution, instead of simply guess and check. One of our class questions for the quiz next class is if we are able to have a note card to write the formulas on?
Hope your feeling better,
Katharine
Note: Tyler will be the next class scribe
Welcome
After each class, the scribe will post a synopsis of the day's events (Scribe Post). A student at another school described the role of a scribe as this:
A scribe post is basically like you are teaching the class again, but this time in your words in a way that other people can understand it. You can also recap other important things that we talk about in class (like Pi Day) so that if someone was away in our class, they would know what they missed. Also don't forget that when you scribe, you get the power to choose the next scribe.You will also use this blog to post your revision questions before a unit test revision (Revision), and you may make a posting to share at any time (On My Mind).
Your contributions to the class blog consist of a quiz grade (rubric on the class website). To ensure that you receive credit for your contributions, please ensure that any post you make has exactly three labels:
- Your first name.
- The unit of study, e.g. Functions
- The type of post: either Scribe Post, Reflection, or On My Mind.
Below are some guidelines for student bloggers that another teacher, Bud Hunt, came up with:
Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.
Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.
Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.
Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.To kick us off, add a brief comment to this post- thoughts or additions to the above discussion of privacy and blogging.
Note: This blogging model is courtesy of Darren Kuropatwa.