All shinigami looking to graduate must pass the exam. You may take the exam any time, but you may not take it again for another week. Passing the exam is based on how much training you have completed (your current reiryoku). Here is a list of what you must get on your success rate if you wish to pass.
1,000 Reiryoku- you must roll higher than a 66.
2,000 Reiryoku- you must roll higher than a 33.
3,000 Reiryoku- you can only fail if you receive a 1 on your success rate.
Every roll is final and absolute. I don't care if you have over 3k reiryoku and roll a 1, you won't get a second chance for another week. Each roll is completely random and is unchangeable, making it completely fair.
-Bleach New Edge Staff