"Elementary" in the sense of "introductory", not in the sense of "taught in elementary school".

I understand that, but elementary quantum physics is still grossly past the level of the students and required more advanced theory just to get to that elementary level understanding of the subject.

Right, but this is elementary mathematics that is specifically chosen so that university-level mathematics is not required. (And rarely helps.)

Well, maybe not elementary school, but in highschool you should encounter those, especially second part. Non-degenerate in that case is fancy word for saying that those point cannot form a line (or a single point) - just that triangle is actually a triangle. This is pretty common term when it comes to math Olympiad so in would be extremely unlikely that someone can get to imo without encountering that in the past during training