In the US, a lot of what is required for HS is decided by each state, so there are different requirements depending on where you live. Within those requirements there may be some flexibility - for example when I was in HS, everyone had to take biology in their second year, but there were 6-8 different 1-semester biology classes to choose from so we all picked two. Electives vary a lot depending on the individual school, its resources, etc. but there's usually some kind of music (usually at least band & choir) and foreign language (sometimes only one or two) and art; often there will be other classes like home economics, health, wood and/or metal shop, PE, and so on.
Within the rules set up by the state and by the local school districts, yes, students get to choose what classes they take.
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"[English] not only borrows words from other languages; it has on occasion chased other languages down dark alley-ways, clubbed them unconscious and rifled their pockets for new vocabulary."
-James Nicoll, can.general, March 21, 1992