Problem 1.1 seems to be within the realm of casual curiosity for somebody who hasn't even entered undergraduate school. It's basically "I know what a matrix is, and how a matrix multiplies with a vector".
Fun random fact, back in 2009 Todai had their own "brand" of toilet paper made from recycled paper -- old archived exams that is. I think that I still have a roll stashed away in a box somewhere. Using it did give you a bit of a weird feeling knowing the anguish old students must have gone through.
That's delectably inhumane.
And this is admission to Graduate School, so the equivalent of a M.Sc. or Phd in the US, right? (i.e. Is the term graduate school the same or is this entrance to college?)
I am not sure when this would even be desirable. If a student fails a question regarding a definition (simple, memorisation) and succeeds in proving the complexity of a novel algorithm (complex, innovation). Why would I emphasise the former? Besides, there are your grades and the presentation/interview as well -- at least for the PhD.
> And this is admission to Graduate School, so the equivalent of a M.Sc. or Phd in the US, right? (i.e. Is the term graduate school the same or is this entrance to college?)
Yes, that is correct. If I remember correctly, they use the same exam for the MSc and PhD.
There really seems to be a hole in the system somewhere.
I could kinda imagine what you say happening in the US, but calling it "maths" instead of "math" implies you're elsewhere.
I'm not sure anymore as I get older that it is really a hole in a negative way. Like yes, it is a hole, but you know, you can't learn everything in your finite time.
Anyway, there are many things missing. I feel that An Introduction to Law and Legal Reasoning should be standard middle-school reading; but alas, civics has not been part of the curriculum in my life time.