Tokyo Metropolitan Public High School Entrance Examination - Mathematics
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The Tokyo Metropolitan Public High School Entrance Examination in Mathematics (東京都立高等学校入学者選抜学力検査 数学) is the mathematics paper used by Tokyo's metropolitan public high schools to decide admission, usually alongside Japanese, English, social studies and science, plus an interview or essay depending on the school and selection method. It is taken by students finishing compulsory education, mainly third-year junior high students, and by some applicants with equivalent qualifications. It is a general academic-achievement test, not a specialised mathematics certification. The paper is written, answer-only in places and constructed-response elsewhere, and calculators are not permitted. It covers junior high mathematics broadly: number and algebraic expressions, linear and quadratic functions and equations, plane geometry including congruence and similarity, and data handling with probability, with an emphasis on explaining reasoning and justifying proofs rather than only computing. Because the exam rewards clear working and precise expression, preparation should combine steady coverage of all junior high topics with timed practice on past-style papers, careful checking of arithmetic, and practice writing short proofs and explanations in your own words. Candidates should confirm the current year's format, schedule and application details on the Tokyo Metropolitan Government Board of Education website, which publishes the official announcements.
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About Tokyo Metropolitan Public High School Entrance Examination - Mathematics preparation
What is the format of the mathematics paper?
It is a written test with a mix of short numerical or symbolic answers and questions requiring written explanation or proof, including graph and diagram interpretation. Calculators are not allowed. The official board publishes the current year's paper structure and answer rules, so check its site before exam day.
How difficult is the mathematics section?
Most items test standard junior high content, so a solid grasp of fundamentals earns a good share of marks. The harder part is the later constructed-response and proof questions, which reward clear reasoning. Aim to secure the routine items first, then practise explaining your thinking concisely.
Can I retake the exam if I am not admitted?
Retake and reapplication rules depend on the selection method, school and year, and some routes allow later recruitment. The metropolitan board publishes the current rules and any second-round recruitment information, so consult its official site rather than relying on past practice.
How long is the exam, and how should I manage time?
The board announces the current timetable each year. In practice, candidates should budget time so that routine calculation items are finished quickly, leaving enough minutes for the proof and explanation questions, which take longer to write. Practise with a clock so you can feel the pace.
In what order should I study the topics?
Build in this order: number and algebraic expressions, then linear equations and functions, then quadratic functions and equations, then plane geometry and similarity, then data and probability. Finish with mixed past-style papers. Weak arithmetic undermines every later topic, so fix calculation errors early.
What mistakes cost candidates the most marks?
Common losses come from sign and fraction slips, misreading what a question asks, leaving answers without units, and writing proofs that state conclusions without reasons. Also common: running out of time on the final explanation question. Show working, check arithmetic, and justify each step.
Do I need to write proofs, or just answers?
Some questions ask only for a value, but others require you to explain why a statement holds or to complete a proof. For those, state the given facts, cite the geometric or algebraic property used, and reach the conclusion in order. Clear, short reasoning scores better than long, vague prose.
Where can I find official information about the exam?
The Tokyo Metropolitan Government Board of Education publishes the official examination guidelines, schedule, application procedures and announcements on its website. Use that site for current figures and rules, and treat this page as independent study guidance rather than an official source.