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Tuesday, April 14, 2009

Chapter 9 Pretest Mania...

Today's class was dedicated to the pretest. It was pretty straightforward and we are capable of getting nearly 100% on questions like these. I mean, I can say for at least myself that I seem to be over thinking things. Or if not, my mistakes seem to come from errors... that shouldn't really be errors. Most of my other mistakes are a result from not continuing my work. I'd have the right idea or I'd have the right concept, but I wouldn't think it through. The steps of these questions are like putting ideas from different units together. I'd get stuck somewhere.....but hey.. this isn't a BOB, or maybe I should just merge it in. Meh...I'll probably do one later.

Anyhow, I guess I'll explain the pretest. If you can explain something, your understanding of it can be deeper.

In this question, an equation is given for acceleration. As well as that, initial values are given to help determine the equations for velocity and position.

The objective of the question is to find an equation that follow the conditions of the initial values and to help find the correct equation, it's important to remember, that acceleration is the second derivative of position. Ergo, the method of finding the position under these circumstances is antidifferentiating; once to get the velocity and another time, to get the position. C is the correct answer.

Here, a derivative is given and it's asking for the AVERAGE rate of change. As soon as this is indicated, so is the pattern. The general formula of the average rate of change is 1/b-a multiplied by the integral of the function from a to b, with respect to x. From there, it's as easy as "plug and chug" to get the answer which happens to be A.
This is the multiple choice question that confused me. Here, it really helps to write down the information that the question is giving you and think of other ways to skin a cat. One of the things the class learned was why Leibniz notation is very much appreciated. The question tells us that the slope of the tangent line [derivative] of y is equal to ey.

From there, we separate the variables and antidifferentiate, of course, not forgetting the "plus C" for the constant. In order to determine what value the constant is, we plug in the initial value to find the constant and it results in finding a general differentiable equation-- the answer for this question; letter c.

This is the last of the multiple choice questions. Another question that is easier to solve in Leibniz notation. This may look like a mini monster of a question, but one of the first things to do is to algebraically massage the equation to separate the x's on one side and the y's on the other.

Then, anti-differentiate both sides and find y. Again, to determine the constant, plug in the initial values given in the question and plug in that constant in order to determine a specific function, rather than settling with a family of functions caused by that "plus C".

Finally, there was the three part open response question.

For the first part, I was ashamed of myself... I spent ten more minutes on this part of the question than I should have. All of the needed information was already given in the question. All I needed was to plug the values in.

In part B, I got the right idea but I didn't get the right variables for Leibniz notation and I felt like i was going in circles. But I HAD IT!!! This question is following a very similar pattern to those questions from the multiple choice. Isolate variables, integrate each side to get the parent function... or the family of parent functions and solve for the constant to get the explicit equation.
Another way of checking if the equation is correct is to plug in the initial values and see if they are equal to each other.
Finally, since we've found the parent function in part B, all we have to do for this question is plug in the time it takes and determine the velocity.

There's the pretest for you. A quick reminder that Mr. K mentioned that he will not be here tomorrow and on our test day.. which is the next day after tomorrow. There isn't going to be a class tomorrow so.... enjoy.. your hour? haha.

The rest of the slides are question that are probably homework/review questions in preparation for the test.

Also.. our assignment.. Claim your wiki-questions soon!

Next scribe is....Kristina.

ZOMG>>>!! I almost forgot about our youtube tradition [that was broken...]

This one is really.. just.. incompetent.. but I love this movie.. it's been so long.. since I've seen this.

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