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I can't figure out your DD's skill level from your post but a teacher auditioning a new student will have that student play a couple of pieces, which I presume your DD would do from memory. Since she can read music (both treble clef and bass clef?), it might make sense to see how she sight-reads written music from beginning level piano books (I, II).

You know, she knows bass clef somewhat because her band teacher teaches music fully with tests/theory, but she isn't used to playing in it. She'd have to learn. She may have done this already. I really don't know how she learned to play all the little bits and songs she knows. I know that some of them she learned by ear (pop songs she wanted to play). How unusual is this ability?

It's a good idea to buy some beginning books. Can anyone recommend a cheap one??