What kind of math should I expect in first year chemistry?
Let's answer three ways:


Specific expected math  Important mathematical skills will include algebra (including understanding variables and constants conceptually), interpreting graphs, and logorithms. There is very little chance you will need to know calculus in first year chemistry. If you have specific concerns, like those described in the comments, your advisor or department assistant should be able to directly address those.
First year chem philosophy  A good goal for first year chemistry is to understand fundamental chemistry concepts so that you can apply them in future courses and work. To do this, you need to know enough math that it doesn't prohibit you from understanding the concepts.
Continuing Education This one is just my opinion and I'm sure many will disagree. If you want to work in chemistry, take more math and physics than the department requires. It will give you a more thorough and complete understanding of chemistry. It will give you an edge in the future in solving interesting problems. This can be done in parallel however- the department won't expect that you're doing this.


Bonus: As many people before me have suggested, go to 6-8 classes on syllabus day even if you're only signed up and intending to take 4. Its always better to know your options and theres no risk to going and seeing whats available. In this case, you'll learn if you've got the background the professor expects for this course and can compare it with other options.