I always say study what you don't know. Someone like me studying television trivia is a waste of time, but I do need to study on art & literature.
Of all the Jeopardy tests I've taken, when trying to place all the questions into the classic 6 Trivial Pursuit categories, I find the tests are top heavy on A&L. If that's your strong point, you've got a good start.
Things to memorize:
Presidents, elements, world capitals.
All three are manageable lists and come up often.
Shakespeare also tends to come up, so if you're lacking in that category, it's good to get a small list of the popular shows with characters and a brief synopsis of each.
this is about all i can suggest on the short-term you have a month to go study strategy, but if you pass this test, I would suggest doing what I've done and read the World Almanac cover-to-cover.
On a side note, I thought Jeopardy had already been to NYC in April, does anyone here know if that's true (I just find it interesting if they came twice, and heartbreaking if they came twice and I still didn't get randomly pulled to go test there this year).