2005 UIL Math questions

[sxk1693]

The problem are 36: Find the remainder of (4x^4-3x^3+2x^2-x)/(x^2-5)
I dont think the remainder theorem applies with quadratics in the denominator. Is there a trick instead of dividing it all out.

41. the sum of the digits of the number (2^2000)(5^2005)

42. This is the only one I missed and I still don't know why!!! How many critical numbers of the function f defined by
f(x) = x/(x^2-9)??? Did I mess up my derivative. I got that there is one critical number however the answers say there is none.

21. If x = .444... in base 5 and y = .333... in base four, then |x-y| in base three is:

29. Basically they gave you a 9 by 9 square and told you to find how many squares with various sizes were in the figure.

Help would be appreciated!!! My accuracy was nice on this test only missing 42, but I only got 31 questions right. I need to get faster with this.

[88bobcat]

[sxk1693]

But critical numbers also happen where the function is not differentiable too right? The function has asymptotes at x = -3 and 3.
There should be 2 critical numbers. The answer key still says there is no critical points though.
My derivative is: (-x^2-9)/(x^2-9)^2.
The numerator is never equal to zero but the denominator is at x=-3 and x=3

[007math]

Hmm, I agree with sxk1693. Maybe this question was thrown out?

EDIT: Ah, must be defined at -3 and 3. Thanks Capybara

[Capybara]

But one requirement for critical number is that the original function must be defined. So 3 and -3 dont count.

[88bobcat]

[88bobcat]

[88bobcat]