Since the exact nature of what you need to know depends on exactly how your professor is running this class, the main thing I think can help is intensively studying with other students in the same class. Ask them lots of questions. Get them to explain things to you.

It'll help them learn the material better as well, since explaining and teaching helps people to learn and understand topics like this.

Also, with regards to the math, I hope you have a solid understanding of linear algebra. A lot of the math in intro quantum mechanics boils down to applied linear algebra.