Mr. O'Brien's 2009-10 White Pre-AP Calculus: Katharine

Showing posts with label Katharine. Show all posts

Wednesday, March 10, 2010

Weds. March 10, Last Day of Unit 5

Today, we began class by finding the equations for two mystery graphs. The first one had the equation This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

which caused the graph to look like this:

The second graph's equation was This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

which caused the second graph to look like this:

After discovering the equations for the two mystery graphs; we turned our attention to number 21 and 22 of Francois and his Pedometer. For number one we noted that This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

. After evaluating number twenty two we discovered that his set for all distances was 2.42 + 2 This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

k where k is an integer but also at 3.86 + 2 This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

k where k is also an integer.

Following the warm-up, our class reviewed Quiz 4 of Unit 5. The two numbers that we paid special attention to were number 1 and 4. For number 1, we noted that if you take This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

and you added This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

you would get This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

, but if you added another This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

you would end up with This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

. This means, that all you have to do next is find the sin( This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

) which is This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

. For number 4, one thing to keep in mind is that in functions, there is an opposite order of operations. This means that the easiest way to solve the problem is by finding your a, b, and c value then plugging them into a equation which looks like this: This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

, the next step is to distribute your This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

which makes a=2, b= This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

and c=-

Once we finished going over the Unit 5 Quiz 4 and any questions students had trouble on, we took the review quiz. The quiz will only count towards your quarter grade if you want it to. The quiz questions were the exact same as the ones on the previous quizzes. Next class, there will be the unit test covering chapter four. Mr. O'Brien suggested to students that they should challenge themselves while studying for the test by working on more complex and conceptual questions than the basic review.

The next class Scribe will be Tyler.

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 $Log_{p} a\cdot b=Log_{p} a+Log_{p} b$ . The seconds is $Log_{p}\frac{a}{b} =Log_{p}a-Log_{p}b$ . The third is $Log_{p}a^{n}= n\cdot Log_{p}a$ .

Next we created a proof for: $Log_{p} a\cdot b=Log_{p} a+Log_{p} b$ .
Proof:
Let $u=Log_{p}a$ and $v=Log_{p}b$
So: $p^{u}=a$ $p^{v}=b$
Multiply: $p^{u}\cdot p^{v}=a\cdot b$
Simplify: $Log^{u+v} =a\cdot b$
$Log_{p}a\cdot b=u+v$
Therefore: $Log_{p}a\cdot b=Log_{p}a+Log_{p}b$
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 $Log_{p}a=\frac{Log_{b}a}{Log_{b}p }$ .
Proof:
$Log_{p}a=u$
Take the log of both sides: $Log_{b}p^{u}=Log_{b}a$
$u\cdot Log_{b}p=Log_{b}a$
$u=\frac{log_{b}a}{Log_{b}p }$
Therefore: $Log_{p}a=\frac{Log_{b}a}{Log_{b}p }$
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

Wednesday, September 9, 2009

Katharine, Functions, Scribe Post

Mr. O'Brian,
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

Mr. O'Brien's 2009-10 White Pre-AP Calculus

Wednesday, March 10, 2010

Weds. March 10, Last Day of Unit 5

Wednesday, December 2, 2009

Unit 3 Logarithms, Scribe Post

Wednesday, September 9, 2009

Katharine, Functions, Scribe Post

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