"Make up" means to compensate for something lost or missed. To take a make up exam means to take an exam that was missed. Make-up refers to cosmetics such as lipstick or powder applied to the face. The joke is talking about a cosmetic student. The joke is playing on the word make up which sounds like "make-up". 
The cosmetic student was sick on the day of the final exam . Now she has to take a Make Up exam .