So I took business calculus for to fulfill the math requirement at Cal Poly SLO. If I wanted to apply
to a UC, say UCB, who require Calc 1A/B, would I still have a chance of gaining admission?
UCB Math 1A and 1B are calculus for math, physics, chemistry, and engineering majors. A calculus for business majors course would probably be considered equivalent to Math 16A and 16B. So if your intended major requires Math 1A and/or 1B but you have calculus for business majors, you may not fulfill the requirement.
Check http://www.assist.org to see if your courses are accepted for your major at UCB, assuming that you are currently at a California community college.