Is it permissible to pass the examinations required to obtain nominal certificates by utilizing circulated answers without attending courses, and what must be done to atone for having done so in the past?

The basic principle is that cheating is forbidden in all exams and academic assignments, whether or not obtaining the final certificate depends on it, and whether or not it results in an increase in grades. Therefore, it is not permissible to cheat in these exams, and whoever cheats must repent to Allah. As for relying on the answers of previous students for revision before an exam, this is permissible, provided that the exam is not limited to the same questions for which you obtained answers.