It's actually called the "Uniform Bar Exam" because it's anything but universal. Only five states do/will soon accept UBE scores, and you can look at the list here: http://www.ncbex.org/single-news-item/article/58/27/
What you need to study for the exam is materials geared at the Multistate Bar Exam, the Multistate Essay Exam, and the Multistate Performance Test.
Here is a list of topics tested on the MEE:
Business Associations (Agency and Partnership; Corporations and Limited Liability Companies), Conflict of Laws, Constitutional Law, Contracts, Criminal Law and Procedure, Evidence, Family Law, Federal Civil Procedure, Real Property, Torts, Trusts and Estates (Decedents’ Estates; Trusts and Future Interests), and Uniform Commercial Code (Negotiable Instruments (Commercial Paper); Secured Transactions). Some questions may include issues in more than one area of law.
You can find more info about the MEE here: http://www.ncbex.org/multistate-tests/mee/
The old books you have will cover all of these topics.