I just took the poss test today. I passed it and was able to take the BMST and I am now waiting for the results. I took the long version of the POSS with 46 questions and 17 minutes to do the math section. the math section was broken into thirds, the first part was conversions, most you can do in your head, if I couldn't do the conversion in my head or with one division or multiplication I skipped it. There is no sense in spending 2 minutes on one problem when you can do 5 or 6 in that time. The second part of the math test was mostly single variable algebra like 4x/3 +3 =4 then solve for x, I don't remember if there were systems of equations in this part. The third part was word problems like, "if a man is 4 years older than 4 times the age of his son how old is the son if 5 years from now the sum of their ages is 41". So this part is clearly making a system of equations and solving for the son's age. I was able to solve about 41 of 46 questions but only because I skipped the longer questions.
There was an assembly test that was 20 questions and we had about 8 minutes to finish it. Some were on par with the practice test and some were a bit harder. I was able to finish this one with literally 1 second to spare.
The mechanical concepts was I think 40 questions or so and we had 20 minutes minutes to complete it. Again some of the problems were on par with the practice test and other were a bit harder. I was able to finish this with a few minutes to spare and I looked over some of the trickier problems with that time.
The reading comprehension was about 40 questions and 5 passages, we had 30 minutes to complete it. This was by far the easiest part of the test and I finished it in about 15 minutes. I took about 5 minutes to look over the questions again to double check and then just kept rereading the passages so as not to look around the room. I followed the advice of a previous poster and quickly browsed the questions before I read the passage.
The tables and graphs sections was 2 parts. In the first part you were given a table with one metric on the left column like rpm or something and then something like inches on the top row with some arbitrary values filled in on the rest of the table. There were 60 problems on the first part and you had 5 minutes to complete it. There are examples at the beginning of the test so it is very easy to start the test once they say go. I finished about 45 of 60 questions. The second part was a graph with about 5 or 6 lines on it, the lines were not differentiated in any way so when you find a value you would have to follow the line back to see which one it is. There were 30 or 40 problems on this test again with about 5 minutes to complete it, I think I finished about 75% of it.
Out of 12 or so people that I took the POSS with, only 5 passed it and were able to take the BMST. In order to prepare for the BMST I would recommend reading a chemistry 101 review on the internet, basic physics texts, with an emphasis on different types of mechanical advantages, work and energy, nuclear physics. Also study geometry, trigonometry, and using trig tables. I had never used a trig table before the test but it is easy to use. Also you might try to remember some basic trig identities, and don't forget SOHCAHTOA. When using the trig table you don't really have to do any interpolation, for an angle like 16.3 degrees just look up 16 and then pick the closest answer from the test.
That's my personal account, I hope it helps.