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Posting here until I find a place for an upcoming mock I’m creating
Hello. This is Geometry285
{{G285 MC10A}}
[[G285 Mock MC Series|G285 Mock MC Series]]
==Problem 1==
What is the smallest value of <math>x</math> that 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>
[[G285 MC10A Problems/Problem 1|Solution]]
==Problem 2==
Suppose the set <math>S</math> denotes <math>S = \{1,2,3 \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 put 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)}\ \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]]
==Problem 3==
Let <math>ABCD</math> be a unit square. If points <math>E</math> and <math>F</math> are chosen on <math>AB</math> and <math>CD</math> respectively such that the area of <math>\triangle AEF = \frac{3}{2} \triangle CFE</math>. What is <math>EF^2</math>?
<math>\textbf{(A)}\ \frac{13}{9}\qquad\textbf{(B)}\ \frac{8}{9}\qquad\textbf{(C)}\ \frac{37}{36}\qquad\textbf{(D)}\ \frac{5}{4}\qquad\textbf{(E)}\ \frac{13}{36}</math>
[[G285 MC10A Problems/Problem 3|Solution]]
==Problem 4==
What is the smallest value of <math>k</math> for which <cmath>2^{18k} \equiv 76 \mod 100</cmath>
<math>\textbf{(A)}\ 2\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 20</math>
[[G285 MC10A Problems/Problem 4|Solution]]
==Problem 5==
Let a recursive sequence be denoted by <math>a_n</math> such that <math>a_0 = 1</math> and <math>a_1 = k</math>. Suppose <math>a_{n-1} = n+a_n</math> for <math>n>1</math>. Let an infinite arithmetic sequence <math>P</math> be such that <math>P=\{k+1, k-p+1, k-2p+1 \cdots\}</math>. If <math>k</math> is prime, for what value of <math>p</math> will <math>k_{2021} = k-2022p+1</math>?
<math>\textbf{(A)}\ 1011\qquad\textbf{(B)}\ \frac{1011}{2}\qquad\textbf{(C)}\ 2021\qquad\textbf{(D)}\ \frac{2021}{2}\qquad\textbf{(E)}\ 4042</math>
[[G285 MC10A Problems/Problem 5|Solution]]

Latest revision as of 09:47, 12 May 2021

Hello. This is Geometry285

G285 Mock MC Series

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