I'll also freely admit I've never taken the ASVAB. Why would I?
I think most of the contributors here would never have taken it either. As a non-US citizen, I'd never heard of it before now, but tried a sample test to get an idea of the level of knowledge and ability expected.
I admit I didn't finish it, as I got bored after about 70 questions...

Overall, the questions were fairly straightforward, and of a first to second year high school level. Maths covered basic algebra, percentages and the like, and didn't get into trigonometry or calculus (although I recall doing trig in my first couple of years at high school). General science, reading comprehension, basic mechanics (mainly relating to vehicle mechanics) and electronics were all of a similar level.
I'm not intending to disparage anyone who volunteers for military service, and I would expect the test to be a good basis for specialisation selection amongst military recruits, but it is perhaps a bit short of what's required for calculations of radiation exposures in the space environment, or understanding the complexity of the science, engineering and sheers scale of the Apollo project.