Testing out of a course used to generally be available for freshman level courses but rarely for anything more advanced than that. (The exception might be that one could generally test out of up to a year of calculus since some people don't consider calculus a freshman course - e.g., business majors, etc.) It was a cheaper option at some universities than the AP exams were for students that had taken AP courses, although AP courses were not required to test out of a course. The testing out option enabled high school students that had taken advanced courses to start university more in-line with their backgrounds rather than having to repeat courses for no reason.
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Edit: that was decades ago - don't forgo an AP exam thinking you can test out unless you already have admission and have verified the availability and costs of testing out of a course.
(A technician discovers how to do simple arithmetical calculations in a world where no remembers arithmetic since its all automated away.)
More information regarding the short story on its Wikipedia page: https://en.wikipedia.org/wiki/The_Feeling_of_Power
The short story itself can be found online.