I just graduated from high school. We hosted our
own tournament for high school teams every year and
wrote our own questions. We also wrote questions to
sell to other tournaments as ours were seen as
exceptionally good. Opera and other forms of classical music,
as well as philosophy and art were always included
in the questions. Sure, these things aren't
typically covered in high school curriculum to a great
extent, but the teams that are willing to work outside of
what is required for classwork will learn the material
out of necessity, if not simple want of knowledge.
These are the good high school teams. The bad teams
won't work to learn the stuff, and so won't get the
questions on those topics. From that it follows that they
don't deserve to win your tournament anyways.