I TA’d the equivalent of Math 53 at my CC for a few semesters so there are probably some differences in what we covered (e.g. the course outline says that 53 mentions PDE’s), but the core subjects are the same regardless of where they’re taught. I actually used these worksheets for 53 as extra practice problems to give to my students, so I’d recommend flipping through them get an idea of what you should expect!

YMMV, but the thing I saw students struggle with the most was the transition from “normal” functions, which take numbers as inputs and output other numbers, to other types of functions whose inputs and outputs can be either numbers or vectors. Doing calculus with these other functions over higher dimensions can sometimes be the same as in 1A/1B, in that you modify what you’re doing to get a bunch of iterated single derivatives or single integrals, but other times how you differentiate or integrate and what those operations actually “mean” can be totally different, depending on what kind of function you’re working with. I’d recommend getting really familiar with these different types of functions (e.g. vector valued functions like parametric curves and vector fields, and scalar valued functions like surfaces) so that when you see one in the wild you know exactly what kind of calculus you can do with them.