2011 Regional

[chrishuff]

There are just some things I did not write down how to do/solve before the website went down back in December-Early January. As a result, I am asking questions over the same subjects. And also a couple of challenging ones

What does it mean when it is "closed" or "open" again?

6. The set of Prime numbers is closed under which one of the following four basic operations?
[Addition, Subtraction, Multiplication, Division]
A. +, -, *, /
B. +, -
C. *, /
D. +
E. Not closed under any of these

22. The eccentricity of the conic given by the equation [unparseable or potentially dangerous latex formula] is
A. [unparseable or potentially dangerous latex formula]

B. [unparseable or potentially dangerous latex formula]

C. [unparseable or potentially dangerous latex formula]

D. [unparseable or potentially dangerous latex formula]

E.[unparseable or potentially dangerous latex formula]


23. If [unparseable or potentially dangerous latex formula], then dy/dx = dx/dy when x = ?


30. Let p and q be the roots of [unparseable or potentially dangerous latex formula] Find [unparseable or potentially dangerous latex formula]

40. Which of the following is an inflection point of the function f(x) = [unparseable or potentially dangerous latex formula]

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Now for some challenging ones:

44. Find the midpoint of the domain of the real valued function f(x) = [unparseable or potentially dangerous latex formula]


Triangular numbers, factoring, and odds all crammed in one question!

25. What are the odds that a factor of the triangular number 276 is a triangular number?
A. 1:2
B. 1:3
C. 1:4
D. 3:1
E. 2:1

[nsguy1350]

6. A set is closed under an operation if performing the operation on any on the elements yields another one of the elements under any circumstance.

Addition: 3+5 is not a prime number, so any answer with addition is wrong.
Multiplication: multiplying two primes gives a non-prime. Therefore any answer with multiplication is wrong.
Subtraction: 3-2 is not prime.
Division: 5/3 is not prime.
Therefore E.

22. Eccentricity = c/a. For a hyperbola, a^2 + b^2 = c^2, with a being the major axis, and b being to transverse axis. c is the focal length.
Standard form: [unparseable or potentially dangerous latex formula] a = [unparseable or potentially dangerous latex formula], c = [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula], so C.

23. [unparseable or potentially dangerous latex formula]

30. Find [unparseable or potentially dangerous latex formula]. By the sum of the roots formula, p + q = -2, so 16.

40. Find the second derivative, find when this equals zero, then make a sign chart or some way to find the intervals of the signs of the second derivative, to see if the sign changes. If the sign changes, there is an inflection point.

44. Defined from [2/3, 9]. Solve where the inner root is zero, then where the outer root is zero (where the inner root is 5). Midpoint = 29/6.

25. :(
Prime factorization of 276: [unparseable or potentially dangerous latex formula]. # of positive integral divisors = 3 x 2 x 2 = 12. They are:
[unparseable or potentially dangerous latex formula]
1,3,6,276 are triangular.

Odds are 4/8 = 1/2.

I don't know any faster way, that would take me a while, especially to list every factor.

[chrishuff]

It's all ringing a bell in my head! :D

Thanks a lot! I guess #25 would be a true "Do you really know what your doing" kind of question where you must figure out all of that within "40 seconds" unless you save time on previous questions by answering them faster than 40 seconds.

If I could bring a silent timer into the test, I would have a quick set button to 40 seconds and for it to automatically count down. When it hits zero, I move onto the next question regardless of how close I came to solving the question.

[nsguy1350]

The actual test, with a 40 sec timer? I think that's a bad idea to continue no matter what, even if you're a second away, because then, you will be wasting precious time. Plus, if you don't know how to do a question, do you wait on it for 40 sec? Maybe a timer to keep track of the total time, but nothing else.

[chrishuff]

Yeah, you have a great point. I only based this strategy off of scoring a 360, which I am no where near achieving. I guess it would be most reasonable to keep track of time, especially if there is not a clock in the testing room.