<p>Just a belated comment that as a 30+ year faculty member in the sciences, I’ve seen lots of entering students who accepted the results of the math placement exam, and started where the university suggested, and a large number of students who thought they were beyond the recommended starting point. Generally, it did not go well for students to place themselves higher than the recommended class. The students who started where the placement exam results had suggested did much better overall. Granted, they had to take math longer–but a student who takes a higher-level course and has to drop it will also wind up taking longer. Taking the remedial class will also allow more time for work on other courses, rather than drowning in work in math.</p>