# User:Geometry285

Posting here until I find a place for an upcoming mock I’m creating

## Problem 1

What is the smallest value of that 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 put 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

## Problem 5

Let a recursive sequence be denoted by such that and . Suppose for . Let an infinite arithmetic sequence be such that . If is prime, for what value of will ?