I believe "Put a mark on an exam" would make sense in British English.
In American English: 'Grade a test.' or, less common, 'Give/Assign a grade for/to a test.'
"I'd give it (the test) an 8, or a score of 8."
A score of 8 wouldn't make sense in America. We assign a score of 100, or a letter grade of 'A,' when someone gets every response right, and subtract points from that perfect score for each incorrect answer given (or a percentage is calculated). The score/percentage roughly corresponds to a letter grade. One college posts their grading criteria as documented in the table below.
Percent | Letter Grade |
94-100 | A |
90-93 | A- |
87-89 | B+ |
83-86 | B |
80-82 | B- |
77-79 | C+ |
73-76 | C |
70-72 | C- |
67-69 | D+ |
63-66 | D |
60-62 | D- |
<60 | F |