If I want to know the mark my classmate got, can I say "How did you get?"

How much did you get?
would be fine, IMO.
Hmm I dont agree. For a start if you are asking about marks (a plural) it should be "How MANY did you get?"

This would make sense but in my opinion (im not an english teacher but i am a native speaker!) you should say "What did you get" as in what mark

hope that helps
Students: We have free audio pronunciation exercises.
Try: What did you get?
I did several Yahoo searches and indeed

How much did you get? is related more to money being paid.
What did you get? (suggested by GG) is related to grades.
Use either "what did you get?" if you are hoping your friend will tell you his exact mark, or "how did you do?" if you want a more general answer (pretty well, not very well, etc.)
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Good point Khoff. I was going to add to mine "But be prepared to hear 'None of your business!' because not everyone would share that information." But I think Khoff's alternative is a far better way to ask!