How exactly do placement tests work for most colleges? Do you say "I want to take so-and-so upper math class", and they'll give you a specific test for that class to make sure you have knowledge of the prerequisites? Ex. If you want to place into a graduate-level analysis class, will they test your analysis skills? Or is there a general test for everyone? Let's say you're homeschooled and you've taken some of the classes from your local university, and some of them by yourself (using online notes, books, problem sets, exams, video lectures, etc.,)? What happens if you have studied mathematics at the rigorous undergraduate level before you leave high school? Let's also say that you're aware that what you study by yourself often is not as rigorous as what you would find in a university, and so you have consequently been very diligent in your studying, following online curricula strictly and using several books and sources to expand your knowledge so that you minimize your misconceptions about mathematics and don't learn it wrong? If you have already studied all of the degree requirements for a B.S. in math? Do you place into graduate classes, assuming you do well on the test? Do these graduate classes count towards your B.S. or a graduate degree? What happens when you get to grad school, then? Just a hypothetical situation.