2013 ... 23 & 24

Two questions today include a very cool number theory/algebra reasoning question and a graph of a type to make them think.

Difficulty: Medium. My absolute favorite  question on the whole test. So cool how this works out.

Difficulty: Easy-Medium. Graphing piecewise functions with absolute value mixed in is not something that most students have had experience with. Easy enough to figure out from principles, but time pressure makes this harder than it really is.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest 2013

answer 23, answer 24. Published 4/29.