They don't care, as long as they will propel you to do well in the general courses. You obviously don't want to do badly in the remedial courses though, as they'll drag your GPA down and you won't have an adequate grasp of the material to do well in the prerequisites. So put in work. They don't have to come naturally easily to you, because everything is a progression. Algebra II can be hard to someone taking it for the first time, but talk to the same guy who's in Differential Equations and Algebra II material will be a piece of cake. It's all about developing yourself cognitively and in terms of a skill set.
A good system of note taking is active note taking, where you only put down the relevant information. You can also do Cornell notes, as they allow you to easily study via question/answer method (so you're testing yourself).
Make sure you're listening while writing and actively thinking about what you write. I've heard that reviewing the material right after the class (if you can) boosts retention, but it's not required to do well.
Good luck, man. I think you'll do just fine. Just take small, consistent steps and soon you'll see that you can do a lot better than you think. There's a psychological property out there that states that people that tend to consider themselves better than their peer tend to overestimate their actual intellect/abilities, whereas people that tend to consider themselves not to be as intelligent or skilled may be underestimating their intellect and skills.
This is what I'm talking about: http://en.wikipedia.org/wiki/Dunning–Kruger_effect