I would limit the memorization of method signatures to only those specifically mentioned in the
objectives. You will also need to know what you can pass to the constructors of the wrapper classes.
A typical exam question on wrappers will be designed to determine if you know what you can pass into a method and what is returned by the method. For example, does the wrapper method return an object or a primitive?
A typical question for the math class will verify that you know that the trigonometric methods accept radian values as arguments but not degrees.
A typical String question will try to invoke a StringBuffer method on a String object so you need to know which methods go with which class. Of course, there will be questions that
test your understanding of the immutability of String objects.