Looking for manga

Okay, I read this one a while ago so i'ma try and sum up what I remember
mc is a dude
gets his magic power tested
he's powerful I think(?)
he chooses tamer
goes to a school and has to take some sort of entrance exam
he manages to take this big wolf thing?
and then later in the series there's like an arena scene to see which section of the school gets funding and he wins it
I think he learns some other type of magic too later on, like a shadow thing? that part is fuzzy.