A difficult, prestigious math competition for the students with the top AMC + AIME schools in the United States. Simply qualifying for the exam means that you're among the best in the nation.
Usamimi is a Japanese word that has combined two others; "usagi" which means rabbit, and "mimi" which is ears. As you can guess, usamimi really just means "rabbit ears".
The act of removing all of one's belongings from someone's home after house/pet sitting for a prolonged period of time. Especially if the house/pet sitter is named Amoreena.