You need a third table for this (possibly a fourth, if there are multiple grades).
I would like somehow for each STUDENT to then have a separate record of these grades, but linked to the "master" exam.
That's exactly how it needs to be organized. To take a simple case of one grade per student/exam, you would have a Grades table with fields for:
and it would be related to both Students (via StudentID) and to Exams (via ExamID).