Subject and exam are separate (if related) concepts, so you should not try to represent them within the same table. Also, the fact that an exam has been held for the given subject is separate from the fact that any particular student took that exam. Split all these concepts into their own tables, and the model becomes more natural, for example:
Representing a student that took the same exam several times is just a matter of adding multiple rows to the STUDENT_EXAM table.
NOTE: STUDENT_SUBJECT just records the fact that the student has enrolled in the subject, but not when (which year/semester). Keeping semester-specific information may require additional tables and more complicated relationships within the model.
NOTE: There is a diamond-shaped dependency in this model. Since SUBJECT_ID was passed from the "top" (SUBJECT), down both "sides" (STUDENT_SUBJECT, EXAM) and then merged at the "bottom" (STUDENT_EXAM) of the diamond, a student cannot take an exam on a subject (s)he has not enrolled in.