# Difference between revisions of "User:Geometry285"

Geometry285 (talk | contribs) m |
Geometry285 (talk | contribs) m |
||

Line 4: | Line 4: | ||

==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> | ||

Line 11: | Line 11: | ||

==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