Regents exams are the state exams in New York State. These exams are necessary in order to graduate from high school. The ones that must be passed include biology, English, earth science, global history, American history and integrated algebra.egents are the tests you normally have to take to graduate high school. Sometimes your school may not need you to take them, but most of the time when you do, you graduate with a regents diploma. I know there's a regents for math and english, and a language.