(a) That's right. A is certainly bound by the terms that are expressly contained in the printed document she has signed. It does not matter that she did not read through the document before signing it. The law does not ask whether A was aware of all the terms, nor whether she actually assented to be bound by them. Instead, the law asks whether a reasonable observer would conclude, in the circumstances, that A appeared to consent to the terms in question.
There can be little doubt that when a person signs a document they know contains contractual terms, they objectively appear to be agreeing to be bound by those terms, and this is sufficient to bind them.