I'm intrigued by the fact that the English exam are partially English knowledge questions, partially general social science questions (geography, history), and partially interview-style questions ("Mention any English writers you have read"); it suggests that the English course is a more generalised course in those days rather than being focussed solely on language and literature.
I think I can hold my own in VIII (not familiar with Whittier, but I believe I have works by the others - that said, I'd have to look it up to confirm them, particularly Thackeray). I feel I should know more from VI; Othello is easy enough, and I feel I ought to know both In Memoriam and The Earthly Paradise, but I'm wondering if I'm confusing The Earthly Paradise with The Garden Of Earthly Delights.
We don't really learn much straight up geography or read Thackeray in US schools anymore, so section 1 is really hard.
I'm also tripped up by "prove" in the first 4 geometry questions. Like how rigorous of a proof do they want? Those are hard.
The algebra and arithmetic are extremely straightforward, though.
Yeah, that struck me; the straight questions are easy (although no calculator, of course, so I'm not sure what approximation for pi they would have used back then - 22/7?), but the proofs do require considerably more thought and detail, particularly if they're to be presented in a formal manner.
That said, when I did
my uni entrance exam and had little idea what proofs
were meant to consist of, I got by with sufficient handwaveyness to express that I had the basic concepts down just not the formal phrasing. Given this is an entrance exam, that might have been what they were looking for.