Don't look at these tests the same way you look at a Coast Guard end-of-course test or a high school or college final exam. They have completely different purposes. The purpose of placement tests is to give your school a snapshot of your current skills in and knowledge of English and math so that the English and math courses you start with matches your ability to perform in them.
That being the case, I recommend you not study for these tests before taking them. Here's why.
If you study for a placement test, chances are you’ll do better on it than you would have done without studying. But the result of that will be that you’re placed in a course that’s more difficult than your current abilities justify and you’ll struggle to keep up with the course work. Your course work should be challenging, but it shouldn’t be so challenging that you fall behind, have to withdraw, or (worst) fail.
The best thing you can do to prepare for a placement test is relax. Get a good night’s sleep before the test so you can think clearly, but don’t consciously study for it. If you want to look over examples of the types of questions that will be on the test, that’s OK.
There are a number of web sites you can go to to check out the placement tests to see what you can expect. Aims Community College, in Colorado, is very good. Gray's Harbor College (WA), Housatonic Community College (CT), Montgomery College (MD), and many others also have helpful resources.
If you're pursuing a distance learning program, your ESO will almost certainly be authorized by your school to administer its placement tests. But even many schools in your geographic area will authorize your ESO to administer their placement tests. If your ESO hasn't already arranged to do so, ask him/her to contact the school to see if it can be done.