As promised earlier this week, here's my experience with the ASTB:
I have covered a lot of stuff on the ASTB in recent college courses (mostly physics courses) and honestly just reviewed the night before using the ACCEPTED ASTB STUDY GUIDE.
That being said, I have stalked all the ASTB posts on here relentlessly and looked over and grew familiar with the contents of the ASTB through about 3 months of browsing. Of course whenever someone posted their study guide, I would attempt to familiarize myself with all the contents.
Here are my tips for studying for each section:
Math: khanacademy.org was an awesome site for brushing up on the math concepts that I had forgotten over the years. Look through the ASTB forums and use the math website to review the concepts brought up by all the other guys on the forum (matrices, fractional exponents, etc...) I am assuming you have some sort of background of up to algebra 2 for this test. If not, study, study, study. Khan academy is a good resource for beginning to work through Algebra 2 level problems.
Reading: Just like some of the other guys said, the reading gets very dense very quickly. It is a ton of thick Navy jargon. Something I found that was helpful was that I used scratch paper, wrote out A, B, C, D on the page and would then after reading the passage would attempt to permanently eliminate answers. I would then cross out that letter and attempt to focus on the remaining answers. Without my sheet method, I would simply scan the answers and get a little overwhelmed trying to eliminate them mentally. Just take your time on this, I probably only answered 15 questions and did not finish before time ran out.
Mechanical: The ACCEPTED guide was kind of helpful here. I had an early edition of the book and it was very poorly made. Review simple machines (levers, wedges, pulleys, fulcrums), review acceleration, velocity, and acceleration due to gravity (G's and definition of G forces). There are some study guides posted on here that really hit the nail on the head. All in all, my background studies in physics really came to the rescue here. I am not familiar with any great basic physics websites with practice problems but they're probably out there.
Aviation: The ACCEPTED guide helped a little bit here. Know nautical terms, know parts of an airplane. I believe it was Notorious Nate who started the APEX ASTB thread and in his post he said to review the classification system for planes (know the letter designations for planes/helicopters because it comes in handy here). This section is pretty straightforward. I remember I needed to know the first man to fly faster than the speed of sound (Charles Yeager).
NATFI: This was actually the most mind blowing part of the test. Made me feel like a lazy, selfish bastard who hates working with others and mouths off to his superiors. Haha just try to go for the lesser of two evils on these questions.
PBM: I actually was laughing by the end because how bad I thought I was doing. Honestly just relax and PAY ATTENTION to which ear they say is your "target" ear. The first time around, I was confused about which ear I was supposed to be listening to at first but picked things back up toward the end. The joystick sucks and the throttle sucked even more. Things will get embarrassing but do your best and try to focus all the way through.
Final tips: To be perfectly honest, I was laughing at how awful I thought I was doing the whole time. I let the whole "computer adaptive" test get in my head so that I analyzed the difficulty of the next question and thought I must have answered the previous question incorrectly. My advice is: Don't psyche yourself out! I literally was playing mind games with myself. So I would get a relatively easy question and think to myself "Shit, I missed the last one." With this mindset I actually thought I was failing for a majority of the test. Eventually I convinced myself to just take each question as it was and not think about how I was doing overall. I ended up not finishing the reading section before time ran out and I ended up doing okay so don't freak out if time is running out and start guessing C on the remaining questions. You can be pretty confident if you just try to cover all your bases and keep calm throughout the test.
Hope this helps! Sorry for the novel.
Cheers,
Tyler