This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
No, you don't have to know all the methods of all the classes, but it helps to know the common ones, especially in heavily used classes like Thread, String and StringBuffer. Use the published objectives as a guide. Bill