Looking at my father's War Manual textbooks (published ~39, versions of older texts), it seems like the sequence was much like it is now:
*Geometry (very similar content to what I had in the 80s)
*College Algebra (almost exactly matches Algebra 2, even has a "refresher chapter" at the beginning to cover contents of "high school algebra")
*Planar trigonometry AND spherical trigonometry
*Analytic geometry (conic sections, rotations and translations)
*Calculus (very similar to the AP course I took in the 1980s, even to including almost identical chapters on sequences/series and on ODEs)
Note the placement of geometry is same as the current US stereotypical pattern, not mixed like Saxon or (some) Common Core.
Probably only the first two courses were expected to occur in high school, but smarter students might be accelerated and encounter some of the other materials.
The presence of spherical trig makes that a lot harder topic. The curriculum does seem to lack vectors, which seems unfortunate to me. Also there is no "pre-calc" in the sense of a course where you learn a little bit of differentiating and antiderivatives prior to the AP calculus to make that transition softer. (But then school systems seem to vary a lot now on how the treat the path after algebra 2 and before AP calc, even now. There is little clear definition of what should be in a "precalculus" course.)