Difference between revisions of "User:Geometry285"
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==Problem 1== | ==Problem 1== | ||
− | What value of <math>x</math> minimizes <math>|||2^|x^2| - 4|-4|-8|</math>? | + | What value of <math>x</math> minimizes <math>|||2^{|x^2|} - 4|-4|-8|</math>? |
<math>\textbf{(A)}\ -2\qquad\textbf{(B)}\ -1\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ 1\qquad\textbf{(E)}\ 2</math> | <math>\textbf{(A)}\ -2\qquad\textbf{(B)}\ -1\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ 1\qquad\textbf{(E)}\ 2</math> | ||
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==Problem 2== | ==Problem 2== | ||
− | Suppose | + | Suppose the set <math>S</math> denotes <math>S = {1,2,3,4 \cdots n}</math>. Then, a subset of length <math>1<k<n</math> is chosen. All even digits in the subset <math>k</math> are then are put into group <math>k_1</math>, and the odd digits are in <math>k_2</math>. Then, one number is selected at random from either <math>k_1</math> or <math>k_2</math> with equal chances. What is the probability that the number selected is a perfect square, given <math>n=4</math>? |
− | <math>\textbf{(A)}\ | + | <math>\textbf{(A)}\ \frac{1}{2}\qquad\textbf{(B)}\ \frac{3}{11}\qquad\textbf{(C)}\ \frac{6}{11}\qquad\textbf{(D)}\ \frac{7}{13}\qquad\textbf{(E)}\ \frac{3}{5}</math> |
[[G285 MC10A Problems/Problem 2|Solution]] | [[G285 MC10A Problems/Problem 2|Solution]] |
Revision as of 19:27, 11 May 2021
Posting here until I find a place for an upcoming mock I’m creating
Contents
Problem 1
What value of minimizes
?
Problem 2
Suppose the set denotes
. Then, a subset of length
is chosen. All even digits in the subset
are then are put into group
, and the odd digits are in
. Then, one number is selected at random from either
or
with equal chances. What is the probability that the number selected is a perfect square, given
?
Problem 3
Let be a unit square. If points
and
are chosen on
and
respectively such that the area of
. What is
?
Problem 4
What is the smallest value of for which