I was just interviewed on January 19th, and this was my experience:
I was interviewing for NR engineer and as a senior in college, I have taken almost all courses that I need to graduate. Since I am majoring in mechanical engineering and physics, I studied difficult integration problems (partial fractions, u substitutions, integration by parts), proving various surface area and volume formulas for geometric shapes, mechanical/electrical oscillators and the differential equations that describe them, RC, RL, and RLC circuits, and everything else from the NUPOC study guide that I could.
Come interview day, these were the sorts of questions I was asked:
Parabolic motion
Friction forces
Combining resistors in series and parallel
How do you find maxima/minima of functions
One fluids/heat transfer problem (qualitative, not quantitative though)
In short, virtually all of the questions I was asked I could have answered in high school. In addition, all of the interviewers were extremely nice to me and seemed genuinely enthusiastic that I was there interviewing.
On the other hand, other people interviewing were asked these sorts of questions (especially those going for subs it seemed):
Here is a circuit design problem that usually takes about an hour and a half. You have five minutes.
Complex geometric proof problem that I didn't even understand upon hearing it (and this was asked of a chemical engineering major)
In other words, I believe that the difficulty and sorts of questions you will be asked is very hard to predict. It is very dependent on who is interviewing you, what your major is (it seems electrical engineers may have had a more difficult time with their problems), and what your grades were in those classes. As a previous poster mentioned, if you got a bad grade in a class, study that especially. If you're going over the study guide and see a problem you think is easy, still do it. One person who was interviewing with me had a terrible interview because he had skipped over what he thought was an easy problem in the study guide, then couldn't do it when it was asked of him. Finally, rely on your fellow applicants when studying. Everyone knows something better than someone else, don't spend hours trying to figure out a problem when a fellow applicant can teach the concept to you in five minutes.
When you're interviewing, I have only one piece of advice: smile. The interviewers all want to see how you perform under pressure. In fact, they may ask you questions that they know are beyond your understanding just to see how you react and at least try to solve them. If you look enthused to be there interviewing and seem to be having a good time, even if you are struggling with the material and not getting questions right, it looks much better than staring at the problem with a sad face, hoping for a tip. The most useful words I uttered during any of my interviews were, "well, I DO know...."
In short, be confident. Be prepared. Look happy. And whatever you do, NEVER say the words "I don't know."
