I personally would be extremely hesitant to recommend that someone take AoPS pre-algebra based only on the ability to pass that screening test.
Why? I mean, content-wise it seems fine; if what you mean is that content knowledge isn't really the limiting factor for most people doing AOPS, yeah.
Really, it's the full year of math in 3 weeks that worries me. If you're covering a chapter a day (which, according to the syllabus and the textbook, they are), there's no time to get up to speed.
This would bother me a bit too, but not so much because it's too fast as because it seems a bit of a waste of a chance to spend three solid weeks on maths, in most circumstances. Wouldn't it be bound to end up rushing through material with no chance to actually absorb and use it? I could see this making sense if the kid knew most of it already and needed a certificate to be allowed to avoid spending a whole year on it, or maybe as a dollop of new material for a kid who won't get it otherwise (DS is lolloping through ALEKS precalculus this holiday for this reason; his teacher is giving him problems in class which is great but he wanted a bit more " stuff").
If DD is currently keener on the history one, I think I'd go with that... Any particular reason not to? Oh, you said; maybe not rigorous enough. Hmm; wonder to what extent she could self-differentiate by e.g. reading different books?
