For calculus, I'd recommend you know how to deal functions, basic trig and geometry and pretty much most of the stuff in pre-calc.
Calculus is all about instantaneous changes and adding these changes, and the real thing you need to be aware of as you learn are what the changes actually correspond to.
When you understand what the changes mean intuitively and can relate them to the equations, then your job will be a lot easier.
In mathematics there are three main things: representation, transformation, and constraints.
Representation is the structure (so numbers, vectors, matrices, functions, sets, etc), transformations is how you change something (you can change something to another equation and both before and after are the same or you can make an approximation which you will see a lot of engineering where they aren't the "same" but "close enough" for what you need to do) and the other are constraints (which you can think of the amount of variability of variation or how "general" or "abstract" something is).
This is what all mathematics is about even if it's pure, applied, or statistics.
In calculus, you'll have the conceptual stuff, the intuitive stuff, and the linguistic stuff.
The conceptual stuff are just the concepts and the biggest one is changes and how to relate integrals to derivatives.
The intuitive stuff is relating specific kinds of changes and mathematics to something non-mathematical that you can visualize and see what those things are intuitively.
Finally, the linguistic stuff is the stuff that relates purely to the symbols. You will do a lot of symbol shuffling with algebra and use the mathematical tricks to solve problems, and while this is a big part of your learning (especially in the beginning) it isn't the whole story.
So yes, to prepare look at your pre-calculus material and if you aren't confident, you may want to do a few exercises or watch a few videos, and if you aren't satisfied then maybe you should get advice from the lecturers (I think you'll be ok though).