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There is a term 'marking' regarding an exam in Korea.

But, I don't think that's a proper word in English.

From some years ago, exam answers were transfered from the exam paper; exam paper itself is not collected to be marked but a extra sheet of answer paper(OMR card?) is given so students transfer their answers from exam paper to it.

I think this is the same in overseas countries too.

What verb do you use?

1. I marked(ticked) my answer in OMR card?

2. Mark(tick) your answer in OMR card?

3. Should I give him an extra marking time?(e.g,. he didn't finish marking so the teacher considers to give him an extra time for him to finish.)
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Perhaps "transferring answers".

"Mark" is appropriate for multiple choice - fill in the bubble answer sheets.
Comments  
Students: We have free audio pronunciation exercises.
Thank you.

Ah.. so 'mark' is still used for multiple choice on the 'bubble answer sheets'?

So the verb choice can be:

1. Transfer your answers in your answer sheet.(if questions are short answer or essay question)

2. Mark your answers in your answer sheet.(if questions are multiple choice)

3. Giving him an extra time for marking is not fair( is this correct?)
1: Looks fine

2: I would only use "mark" if there were bubbles or check-marks. "Write" would be more appropriate if a multiple-choice letter (A,B,C,D) were to be given as an answer.

3: Use the word for the situation. For written answers, use "transfer" instead.