Short answer: They're similar, but Calculus AB covers a bit more (and goes more in-depth) than Calculus 1.
Long answer:
The AP Calculus AB test covers differentiation (taking derivatives) and early integration (taking antiderivatives), including the concept/applications of an integral and integration by substitution. In college, Calculus 1 covers mostly differentiation and Calculus 2 covers additional strategies for integration and series.
I like to think of it like this:
A = Differentiation
B = Integration
C = Series
So Calculus AB covers differentiation and integration and Calculus BC covers integration and series.
College is more like:
Calc 1 = A
Calc 2 = B&C
Of course, this depends on how much you cover in high school and college.
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