High School Killer who loves Classical music

I must have seen this in the early 1990s, but it seemingly involved a high school popular kid (maybe?) who ends up being “the killer,” but we don’t know that until the end?  We only know who the killer is because, apparently, a certain classical music piece or something is played during the killings, and then at the end of the movie, the “guy who we never would’ve expected” plays the same piece in his snazzy car tape deck.

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