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It would indeed be impressive if she self-derived, but in AOPS this is Algebra I and not II. Do check what they are doing in their math class.

I wondered this, but it wouldn't be much like her to "fake" this to impress us. She is not a pleaser in any way. Still, you do have a point. She is doing Common Core Pearson Alg 1. It may well be that she was not taught THIS, but something that suggested it somehow.

She has fooled around some with math contests etc. Her scores are not bad, but not worthy of going further, if you know what I mean (as in, she can kinda hang at MATHCounts at a gifted magnet school, but there are also those kids who are doing much better) and anyway she doesn't want to. She doesn't really like *problems.* It's a fascination with discovering patterns...always has been.