I fully agree with Willie Wong in that algebra-precalculus is the appropriate tag. Many US based students (think they) have taken a course in algebra in high school, and have problems tagging here. A couple years back the tag `algebra' was blacklisted and split into algebra-precalculus and abstract-algebra to make the distinction between high school/freshman algebra and higher algebra.
I also think that your suggested solutions are not good. However, I upvoted your question for reminding us all about this persisting problem. It might be a good idea to give more tips about tagging in the relevant section of the Help Center. The current one looks like it is copy/pasted from SO. It might benefit the newcomers to have a few rules of thumb layed down there - together with an assembly of links to the common tag wikis. If the mods are too busy, and this is judged helpful, I might volunteer to make the above changes. Of course, some other people who 1) know the American high school better, 2) know the English language better, and 3) have even more time, would do an even better job, so I won't stand in their way :-)