I just returned home from having taken my first ASTB. My score was an 8/8/8. To say that I'm pleased with my results would be an understatement, as I was positive that I bombing the PBM section throughout the duration of the exam. This forum and the study material it provides have been invaluable in my studies for the test, so here is my take on it. Hopefully it helps someone.
Math
This is the section that carries the most weight of the OAR parts regarding aviation, valuable to take note of that if you're trying to weigh your studying more heavily on certain sections under limited time.
Do all the practice problems you can get your hands on. And I do mean all of them, even the ones that seem immensely simple. Work through them all. I have taken one math class (CALC I) since graduating high school in '14. If you're in the same boat, brush up on everything covered in the review books and then some. Several people on here stated that their exams had logs, matrices, or binomials on their exam. For that reason, I studied all of these. The first two I already had knowledge of but I didn't have a damn clue as to how to write a binomial number. A matrices question did show up on my exam, not the latter two. Mostly simple questions other than those. There were a lot of percentiles and DRT. The average questions that I receiver were more complicated than your primary example in review books, such as "The average of the test scores was 80, the first four were 72 86 87 91, what was the fourth?". Mine were more along the lines of "X, Y and Z count for 30% of the final average, A is 40% of the final average, and B is 30% of the final average. B was 20units higher than Z. X,Y,A equal this amount, the final average is this amount. What is the value of B?" Super tedious stuff. I ended this section with plenty of time left.
Reading Comprehension
I actually did not study for this portion of the exam. You're either good at reading or your not. You have to pick one of the sentences that is correctly deducted from the passage, while the other three will be either blatantly wrong or just have a single detail wrong. I didn't take all the time on this section, although I wish I had. I felt like I was taking too long reading over my answer choices and rushed a little more than was necessary.
Mechanical
This section was very straight forward. Simple machines, a lot with air pressure/temp/volume, and some concepts that I had not covered. Barrons review book does a good job covering the majority of the things you will need to know for this section. Be sure to practice example problems, knowing the concept is entirely different form being able to apply it when given a problem. This is the section I actually studied the most for. I haven't had any college courses covering physics, only one simple class in high school. I was expecting this part of the exam to be brutal but I ended up being over prepared for it.
Aviation/Nautical
Study. Study. Study. If you are not in ROTC or prior enlistment, this section is where you should focus most of your time. Having not taken any courses pertaining to this section, I studied a lot. Unfortunately, I think studying on this section is hit or miss. Expand your history and terminology knowledge beyond what is found in the review books. They do not cover everything. Given, also know everything in the review books. I studied 4 ASTB prep books and not all of the material on this exam is in there, I'd say closer to 40%. I also went through every page of this thread that was posted in 2014 or later (because of the change of exams in 2013) and made sure I knew or would at least recognize answers to specific questions people said were on their exams. Know all the parts of an airplane and know how they work. DEFINITELY know what happens when you move the ailerons/rudder/elevators/flaps a certain way (ex. how to move them up/down or left/right and what it does to AOA/Camber/lift/drag/etc).
NATFI
ha ha
PBM
UAV: STUDY THE FLASH CARDS THAT EVERYONE ON THIS SITE RECOMMENDS. And then study them some more. Quite a good number of people suggested using the compass drawn on paper method but I felt like that took far too long so I just got accustomed to working it out in my head.
Listening Portion: Like many others before me have recommended, lean into the side that you're suppose to be focusing on. I also jotted if I was suppose to press a button for even/odd numbers on the joystick or throttle.
All Remaining PBM Sections: Do your best. I have no flight training whatsoever and have never played joystick/throttle video games. This portion sucked with just the individual sections before they were combined. When they were all combined I genuinely thought I was going to end up with a 3 in the PFAR section. Many recommend to write down the emergency codes when they're given to you, which is what I did, but I also had them memorized going into the exam.
My general advice would be to bring earplugs, a pen that will not run out of ink, and study as much as you can prior to the exam. If you're having to use a laptop hooked up to a monitor, be careful to not tap the mouse pad and accidentally select an answer. The office I took my exam in was loud and the specific room I was in had people occasionally walking in to get stuff. The computer I was on also was going to automatically restart, so the SSgt overseeing my exam had to restart it in between the OAR sections and remaining parts for me. Do what you can to not get distracted, ear plugs were my life saver.