Not to talk too much on the tropes of the chapter but it always bugged me when they say "oh the exam was on the same level as elementary school in my old world" How is that possible? Why are the subjects the same? The only one that I think could have significant overlap is math and even that's not guaranteed.
Elementary school subjects through the Ages: Reading, writing, basic arythmatic, basic history, basic geography, basic "Science" ( may be magic in a magical society ), basic PE ( martial arts in "medieval" settings).
Talented kids would have started on basic math, and from there basic physics/chemistry ( mid-tier magic/alchemy), and possibly basic combat training.
The kids here are entering first year highschool, so the subjects on any entrance exam
would be more or less the same as elementary education through the ages here, even if in these settings it's more based on tutors/homeschooling than formal elementaries.
So an Isekai remembering his past life
would notice the similarities. Because the similarities are more or less inevitable given what elementary education is
for...
And the entrance exam is there to test what's stuck in the kids' noggin..