Well I just took the ASTB yesterday. I'm currently in college as a Pilot major, hold Commercial Multi, CFI, CFII, AGI with 415 hours and counting. Decided in January to give my life-long dream a shot. After scheduling my ASTB for July, I received an email about flight instructing Naval Academy Midshipmen for their Powered Flight Program (Naval Academy version of IFS, basically). After immediately dropping everything to head out there in search of Letters at the end of the summer (ended up getting two, one from a VERY well known officer), I returned in time to have a grand total of two days to study so I can make sure I am up for the next board and not miss school. I hammered out math one day, then mechanical / reading the next, ignoring the Aviation section due to my background (same questions I've already had before).
Math:
This really wasn't so bad. I think I had one or two word problems, and the rest were algebra for the most part. If you get them correct, as mentioned, they get tougher. Near the end of the test was finding X when it was underneath two cube roots set equal to each-other. It took me a few seconds to think about it, but even that wasn't too bad. I did not have any matrices or logarithms, however I did study them because I know they could come up. The entire math section took be about 15-20 minutes.
Reading:
When studying, I used the Accepted book. After doing about 10 problems and getting the correct answer in the book, I thought it would be just like that on the test... it wasn't. As mentioned hundreds of times by now, you get one right they get harder... and this was no different. It's pretty confusing when it gets to some of the higher-level Navy stuff, and I missed one, knew it when I saw an easier question, then clicked the wrong answer when trying to answer quickly, and a downward spiral started from there. BE PATIENT, I had to just sit back and take a breather, then resumed. Sometimes, that's the best way. I finished with about 5 minutes left.
Mechanical:
I was expecting this section to be really tough, but surprisingly it was the opposite for me at least. I think I had one mechanical advantage question involving which horse did more work in relation to the slope of an incline. There were a few questions regarding aerodynamics, but I think this section took me about 7 minutes in total. There are GREAT study guides on this site to review for it.
Aviation / Navy section:
Aviation questions were just as everyone has said. A couple about aerodynamics and then a bunch of questions about the Navy such as the first attack aircraft used on the carrier, and what torpedo bomber was introduced just before the Battle of Midway and had a 20 year career I think? What do the guys in the green hats do on the flight deck. Again, the study guides to a great job of covering most of it.
Aptitude Test:
This was... interesting. I heard about it and thought it would be different than what it was. Just try to do your best. You will be following one aircraft up and down with the throttle, and another aircraft up/down left/right with the stick. Later, a stream of letters and numbers will run through both ears, and you'll be told to listen to the left or right ear, and press the trigger for even numbers, or the clutch button on the throttle for odd. After that, you'll be tracking the aircraft and they will give you the following emergency procedures:
Engine Failure- Fuel Full, Prop Full, Clutch Button
Engine Fire- Fuel off, Prop Out, Clutch Button
Prop failure or something of that nature- Fuel Full, prop half, clutch button
I had them all memorized, but when it came to the actual application of moving the switches I went off of what was 100% and 0% when I calibrated the controls in the beginning. The actual gauges are very gauge as well, because the top of each is red, the bottom orange, middle green. I think my score was lowered on this section because of this, as I got the message saying I failed the procedure when I know I did it right according to the mechanical 100% settings... Oh well.
Final score was 7/8/8 60, which I am very happy with for only 2 days of studying. The goal you should be shooting for (according to my recruiter) is 7/7/7 58 for SNA, and 7/7/7 55 for NFO to be competitive in the selections.
Good luck!