Sorry, but as a professional musician I had to correct the idea that a dance exam sounds odd. Exams in the performing arts are common. Auditions are usually to get a job, or a place on a course. Exams are to gain a qualification showing your attainment of a certain level of skill. Violin, drama, singing, ballet... you can 'have to take an exam' in any of them. Same with other practical skills - woodworking, upholstery, driving - practical exams are part of the qualification process. For anyone who works in dance, the phrase 'I have to take a dance exam tomorrow' sounds as natural as 'I have to go to the bank tomorrow'. More 'natural' English, though, is probably to omit 'to take': 'I have a dance exam tomorrow and I've lost my ballet shoes!'