Goodness me, this brings back memories having taken the entrance exam back in 2009. I am glad that they have removed the "We do not guarantee the accuracy of the English translation of the original Japanese version of the exam" clause. It should be noted that this is only one "session" of a series of exams that you take in a single day. If I remember correctly there were two computer science sessions as well, followed by a presentation of your thesis in front of the faculty once your exams had been graded. After this you had to wait for a few weeks for the final result.

It should be noted that I don't find these exams to be particularly difficult, the main difficult lies in the fact that the number of potential topics are drawn from the whole University of Tokyo undergraduate curriculum, so if you studied as an undergraduate at a different school or country -- like me -- you are at a significant disadvantage. What I did was to look at ten years or so of exams to get some statistics on what was likely to be on the exam, then locked myself in my room for the whole of January to cover portions that I had not studied before -- like network protocol specifics. In the end, it worked out for me, but I got somewhat lucky in that there were two statistics questions that I could breeze through to cover for my weaker calculus skills given my old school's focus on discrete mathematics.