test or test-paper

[Clark]

You made a few mistakes in the test / in your test paper.

Which is a better option?

[David L.]

The 'test paper' is the sheet handed out by the teacher with the test questions on it. So, if there are errors, they are those of the person who wrote/typed the sheet. The sentence would be spoken to that person by some member of staff proofreading the test paper.
'test' as in 'You made a few mistakes in the test' refers to the students answers.

[Clark]

David, what's the word for the sheet that students hand in?

[philadelphia]

(Student) handbook?

[bhaisahab]

David, what's the word for the sheet that students hand in?

It's "the answer sheet."

[David L.]

Or, at Uni with essay-type answers, 'answer booklet'