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The national college entrance examination in Japan is conducted twice a year: the first is the national unified examination, and the second is a self-directed examination by each university. Generally speaking, Japanese candidates first need to pass the unified national university entrance examination in January, and only after passing it can they be eligible to participate in the second entrance examination organized by major universities in February or March. Japanese universities mainly select outstanding talents through independent proposition, and the mathematical content of the questions mainly involves the following aspects: elementary number theory, elementary algebra, elementary geometry, calculus, and probability. This book selects some questions from the 2020 entrance mathematics exam for famous Japanese universities, which can help us better understand Japan's basic education to a certain extent.