Categorical Imperative and Cheating?

According to Kant’s Categorical Imperative Theory everyone should act in a way that their actions could be used as a universal Law. Kant shows us that categorical “oughts” are possible because we have reason, which makes categorical Oughts rational. For example, cheating on a test, if a person cheated on the test to get a better grade, and his maxim was made into universal law. Then everyone would cheat on the Test to get a better grade. But that law would actually defeat the purpose of giving the test because everyone who took the test would have similar grades, making the law contradictory to itself. But in fact to get a better grade on a test a person should study to get a better grade.