Go through the 1001 ASTB questions and you'll find plenty of info there. but yeah....I say the only good thing of buying a study book is for the practice tests, so you get a hang of how the language, mechanical and aeronautical information work. But here are my takeaways
MaTHeMatics:
you're not going to get anything past precalculus, however, it is an adaptive test, so it gets harder the more right questions you get....I'm an engineer so questions got very tricky after the 10th one or so, and ended up running out of time without answering them all....I'd say...make sure you know to Factor, know basics of Probability, know the properties of exponentials and logarithms, lots of averages, unit conversion, calculating the price kinda thing..... know how to solve the problems of the "if Jeffrey Epstein is running at a 6 mph pace north and he's being chased by pursuers who are a mile away but running at 6.5 mph, how long before he kills himself?" type......if you know how to convert numbers on the decimal scale into binary, learn how to do that too, I got two questions like that.....the problems themselves were not too complicated granted you can do them quickly enough....so make sure to practice lots of them.
Reading:
just make sure you read the whole fucking thing, is annoying, boring as hell, but just push through and READ the whole thing before answering.
Mechanical:
There's a deck of like 300 flashcards going around with questions for this section which I found real helpful, but again, I am an engineer so I already knew a lot of these. Something I got asked which I wasn't expecting was a bit of auto shop stuff....like names of parts involved in braking or steering processes.....so if you want to study that too...however, the Mechanical portion doesn't seem to have any bearing on the ASTB, so it'd be overkill in my opinion
ANIT:
there's also a deck going around with like 300 flashcards....learn ALL OF THEM....add to that....know all the possible ways any part of the ship can be named...I got some weird ones here that I wasn't expecting. Know who everyone relevant to Naval History and Aviation is and study ALL THE AIRCRAFT PLATFORMS, all their missions, nomenclature....all that shit.....this last part is what got me, since I didn't study that part as much and I got questions such as ......" For X mission, which of the following aircraft is best...." and then just a bunch of nomenclatures.
PBM
Expect to get better with the joystick part as you go. It'd be helpful to use that simulator they got going around here so you get used to the inverted thingy. whenever you're in the last few trials with the joystick when they be throwing everything at once...LISTEN FIRST....then take care of your 2D target, then your up and down target....As far as the UAV portion, compass trick all day
hope this helps