Hey,
How do teachers usually call that part of their job when they're checking students' answers on tests?
I found something like "grading exams" or tests, maybe just papers... I'm not sure which one they use more often.

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I call it 'marking'. I say,"I have some marking to do."

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From England I would say 'marking exams'.

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Grading papers is American terminology and in England we mark exams/tests

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I'm not an actual teacher so I'm probably not qualified to answer this. 
From my college days, my professors usually referred to it as "grading papers".
Checking/grading tests is another I would hear often. There are other phrases used but those three are the most common ones I recall hearing.