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I recently have taken the 2007 B releases and I can not find any solutions for the following problems:

13. Let f(x) = |x^2 - x| Find the sum of the critical points of the function. (answer: 1 1/2)

*and how do you find the critical points of a function, in general.

26. Megan Mony put $500 in a special account which earned 15% the first year, 50% the second year, and 40% the third year. What is Megan's average rate of return? (nearest whole %) ( answer: 37%)

*seems simple enough, but I am missing something obviously

36. Find the area of the quadrilateral. (picture given ) (answer: 31.5)
EDIT: Well I found out you could find the area of the big rectangle surrounding the figure and subtract the adjacent triangles. But is there an easier way to solve this?


That is all for now, I will be taking a few more tests this week as well, and will more than likely have some more questions for everyone :-D.

Thank you.

I apologize for the double post, but I had forgotten a couple more questions that I did not answer on that test.

29. *Would have to look at picture on test

also

52. The point P(3.-2) is translated vertically 3 unites down to point Q. Point Q is reflected across the line x = 0 to point R. Point R is translated 4 units to the left to point S. Point S is rotated clockwise about the orgin 120 (deg) to point T. Which quadrant or axis is point T in/on?

* I can follow it until you rotate the point 120 degrees, any explaination of rotating points on a graph a certain amount of degrees will be very helpful.


Thanks again!

13) the function would be a parabola with a vertex at x = 1/2 if it didnt have an absolute value in it. The absolute value flips it up over the y axis starting at 0 and going to 1.... so the tangent line has a slope of zero at x = 0, x = 1/2 (vertex), and x = 1 ----> 3/2

critical pts are where the tangent line has a slope of 0 - a critical pt exists at x = a when f'(a) = 0 .. put 'a' into the original equation f(x) to get the y coordinate of the critical point

26) I didn't like this question because it depends on if the new interest works on the original amount ($500) or the new amount but no one cares what I think.... the answer assuems that it goes on the new amount.

so 500(1.15)(1.5)(1.4) = 500* r^3
r = cube root of (1.15 * 1.5 * 1.4)

Sternhund, did you mean tangent instead of sine?


For #52, you can also do the problem (once you get to [unparseable or potentially dangerous latex formula]) by:

[unparseable or potentially dangerous latex formula]

But that is a first quadrant angle, so we need to add [unparseable or potentially dangerous latex formula] to that, since the point is in the third quadrant.

[unparseable or potentially dangerous latex formula]

Now, just subtract [unparseable or potentially dangerous latex formula] (subtract since it is a clockwise rotation), so your final point makes an angle with the x-axis of [unparseable or potentially dangerous latex formula], which means the point is in quadrant two.

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For #29, Find [unparseable or potentially dangerous latex formula] using sin, i.e.
[unparseable or potentially dangerous latex formula].
We can then easily find the associated angle with the rightmost triangle and find [unparseable or potentially dangerous latex formula] from that...I'll call that angle [unparseable or potentially dangerous latex formula].

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

my bad

stupid calculus

@ the problem about doing everything with the point (3,-2)... rotating clockwise, etc.

I hated this problem. I did everything right, except plotting the point (3,-2)... that is, somehow it ended up in the first quadrant ^_^

that's the only problem i missed on that test lol