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 |