K&B is one of the well rounded book for SCJP preparation, the book covers all the API necessarily to know about SCJP exam with the type of questions expected to as in real exam. So my suggestion would be to prepare the basic usage of those API from book and to study the rest method in exam, the JavaDocs comes handy. Also you need some practice of those methods.
Look there are some really important API to learn for exam, like Collections API, String, StringBuffer and Parsing, etc. But there may be few or limited number of important methods of those classes which are more focused. But it ain't a waste of time if you prepare all the methods.