Saitama Public High School Entrance Examination - Mathematics

It is the mathematics part of the entrance selection for Saitama prefectural public high schools. Your score contributes to a selection decision that also considers other subjects and, depending on the school, additional materials such as interviews or essays. Each school publishes its own selection method, so check the school you are applying to rather than assuming a uniform formula.

Those figures are set each year by the prefecture and are published in the official selection guidelines. They are not fixed for all time, so confirm the current numbers on the Saitama Prefectural Board of Education site and in the application documents for your year before you plan your pacing.

Expect a written paper combining multiple-choice items with short constructed-response questions. Calculation questions test fluency, while later items typically ask you to explain a line of reasoning, complete or write a proof of congruence or similarity, or describe a property of a graph. Answers need working, not just a final number.

The early items are straightforward curriculum-level calculation, so most prepared candidates can earn them. Difficulty rises through the geometry and function items, which require multi-step reasoning and clear written justification. The paper is designed to be completed by a well-prepared lower secondary graduate, but full marks require both speed and precise explanation.

Retake and re-application rules depend on the prefecture's selection scheme for that year and on whether vacancies remain after the main selection. Some schools conduct a supplementary selection. Read the current official guidelines carefully, and ask your school's guidance counsellor, because eligibility conditions differ between applicants.

Start with numbers and algebraic expressions and with equations, since every later topic depends on them. Then work through functions and graphs, followed by geometry, where you should practise writing congruence and similarity proofs aloud before writing them down. Finish with data and probability, and weave in timed mixed practice from the middle of your preparation onward.

Three recurring problems: arithmetic slips under time pressure, incomplete proofs that state a conclusion without naming the condition used, and misreading questions that ask for an explanation rather than a value. A fourth is spending too long on one hard geometry item and leaving easy later questions unanswered. Practise allocating time and checking working.

Yes. Proof and explanation items are a distinctive part of Japanese lower secondary mathematics and appear in this paper, typically involving congruence or similarity of triangles and the reasoning behind a property. Marks are awarded for the structure of the argument, so write each step and cite the condition that justifies it.

Sit them under timed conditions first, then mark them against the published answer key and classify each error as a knowledge gap, a calculation slip, or a reasoning gap. Redo only the missed items a week later. Past papers show the style and pacing of the real paper, but do not assume the same topics appear in the same order each year.

The Saitama Prefectural Board of Education publishes the selection guidelines, schedules, and application procedures on its official website, and individual schools publish their own selection details. Use those documents as the authority for dates, weightings, and eligibility, since they are updated for each admission year.