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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Saturday, December 03, 2005

Friday's Pre-test

Like other unit before the test we had a Pre-test, in order for us to get ready for the test on Tuesday. The test is consist of 5 practice multiple type of questions and one Open response question. In today's pre-test we got this question:

The sides of this rectangle increase in such a way that dz/dt=1 and dx/dt=3dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt?

First we create a relationship in about this problem. and we got this z^2=x^2+y^2
then we find the derivative of that relationship.
2z dz/dt=2x dx/dt + 2y dy/dt. The two are reduces z dz/dt= x dx/dt + y dy/dt.
By the pythagorean theorem we found that z=5. So after that we just plug in the values.
(5)(1)=4(3)dy/dt+ 3 dy/dt
=15 dy/dt / 5
= 1/3 dy/dt
Since dx/dt= 3 dy/dt we got the value of dx/dt= 1.

Now our pre-test was done all we have to do is study for our test on Tuesday. Good Luck guys.... The next scribe is Steve....

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