You've just turned 16, and are suffering from exam anxiety and as such you tried faking a sickness. You'll have to face it head on, and simply head to class. While you're in your father's office, you can also collect the Medicine bobblehead.
Outside the exam room, the tunnel snakes are bothering Amita. While you can head into the class to take the goat, you can gain karma for stopping the tunnel snakes. The easiest way is to claim a lackey is following orders from Butch, but you can also attempt a speech check against Butch himself (i.e. overseer will crack down) or engage in combat (a good way to practice the meele interface if you haven't already.) If you want, you can lose karma simply by telling them that she's sensitive about her weight.
At the exam room, answer the questions honestly to the best of your ability (or as an alternative, choose the options you believe give you the best character.) To review the selections, talk to Mr. Brotch about the results - you can change them to whatever you want.