I got an AP score of 3 in both AP Calculus AB and BC, should I take Engineering Calculus 1 or Engineering Calculus 2?
With a score of 3, I’d take Engineering Calculus 1.
Try the old final exams for your college’s engineering calculus 1 and engineering calculus 2 to see how your knowledge stacks up to the college’s standards. Then you can make a more informed placement decision between engineering calculus 1, engineering calculus 2, or engineering calculus 3.
In addition, here are some web based quizzes to check your readiness for calculus 1, 2, and 3 based on assumed prerequisite knowledge: http://www.math.buffalo.edu/rur_index.html
I would be surprised that a 3 gives you usable credit for either. Are you SURE you have that option?
Take Calc I, build a solid base. My daughter (also in engineering) took calc 1 because she’d not taken AP Calc in high school, and more than 1/2 her class had already taken calc in high school. Those students did not find it just a review course or an easy A. Those who expected the easy A either worked like crazy or they got a B. Or even a C.
Florida publics give credit for calculus 1 with a score of 3 on AB or BC. Credit for calculus 2 requires a 4 on BC. Private schools differ.
In Engineering? Surely this isn’t across the board of all schools for all majors?
Most likely the 3 that earns credit will be a null or void credit. An example of a void credit is this - The California UC system gives graduation credit for Calc 2 with a 3 in AP Calc BC. But for UC-Berkeley L&S, you need a 5 in order to get subject credit (4 for Engineering). So with a 3 in BC, you get the credit but in order for you to continue on with further Math classes, you need to take Calc 2 since you didn’t get subject credit for it. Once you take Calc 2, the credit you got from AP gets voided.
https://catalog.ufl.edu/UGRD/academic-advising/exam-credit/#examstext lists University of Florida AP credit. There does not appear to be any page saying that it is different for engineering majors (whose model schedules list MAC 2311 as the first math course, which the AP credit list shows a 3 on calculus AB or BC as fulfilling).
University of Florida conveniently has old MAC 2311 exams for the OP to try if s/he attends University of Florida: https://teachingcenter.ufl.edu/vsi/mac2311/