Uhhuh... What is there to figure out? Like I said many posts ago, there's no way this wouldn't be public knowledge. It's the most prestigious hero academy. How on Earth would none if these people try to prepare at all before going to the entrance exam? The most obvious part would be to read about the basics of the exam. What happened here equals to taking the entrance exam of a regular university faculty without checking out which books you are supposed to study and merely reading some random books or trusting that maybe by sheer luck your high school covered the stuff. Not to mention this is Japan and people go to those cram schools.

There's no figuring out anything. This plot was purely artificial, and, like Shinta said, it's 100% generic shounen.