I am a bit astonished that a pre-calculus class includes all these topics.
You and me both.
I recall seeing complex numbers in high school, all right-- but not really WORKING with them in polar coordinate systems until Physics, P-Chem, and DiffEQ. Certainly I first encountered polar coordinate systems in college material relating to analytic geometry. Not in this class, which is effectively the same material as is (theoretically) covered in MTH 112.
This is where I think trying to plan an education for our children who we piece bits and pieces together from different sources due to lack of anything that truly fits their needs gets really challenging. My first thought when I read the list of topics was that my math classes in high school covered almost *all* of them before my AP Calculus class in high school. That doesn't mean I had a better or more thorough math curriculum - it just means they were on our list of things that needed to be covered before you got to Calculus. Curriculum simply varies so much from learning institution to learning institution, even in "classic" things that would seemingly be a straightforward progression such as math.
I don't know if it's something your dd would want to use as an approach to filling in the gaps, but if she's not opposed to working with a tutor, that's an option. I think you're in a college town, right Howler? If you can find a college math major who enjoys tutoring that might be one way to go which would allow you to quickly cover what's missing.
Good luck with it all -
polarbear
