Studying for the exam or for learning? Is there time later?
In my experience (which has been both as a student and a professor), the best way to do well in theoretical physics graduate school is to get a really good understanding of the material.  That will give you the best path forward.  If you try to memorize a bunch of recipes for solving all different kinds of exam problems, you are missing the forest for the trees.  Moreover, once you are done with courses and exams, you will need to put what you have learned to use in a research context.  In doing research, it's how well you really understand the underlying physics that is going to matter the most.

To solve particular problems in E&amp;M or quantum mechanics, you may learn a lot of mathematical techniques, which can seem unrelated or disconnected at first.  However, many of them are really variations on the same underlying methodology.  For example, the solution of the Schroedinger equation using energy eigenstates is really a form of separation of variables, like that used in E&amp;M.  Similarly, separation of variables in spherical coordinates is really the same as a multipole expansion.  The best way to see these connections is to work examples problems, and most good textbooks at the graduate level have problems that are specifically designed to illustrate the deeper connections between the different techniques you have learned.

So my advice to you (and to the students I teach) is to go for deeper understanding of the physics and why certain strategies work in certain situations.  If you master that, you will also learn how to apply various techniques as a necessary corollary.