Toyama Prefectural Public High School Entrance Examination - Mathematics

Typically students in their final year of junior high school who are applying to Toyama prefectural public high schools, including those applying through special quotas. Applicants educated abroad or transferring in may have separate arrangements, so check the prefecture's current guidelines for your situation before assuming the standard paper applies to you.

Expect a mix: short numerical answers, multiple-choice items, and constructed-response questions where you must show working or write a proof or explanation. Small sub-questions usually build from routine calculation to a harder final part. Practise writing out reasoning in full sentences, because partial credit often depends on visible steps.

The Toyama Prefectural Board of Education publishes the current time limit, mark allocation, and question count in its official entrance-selection guidelines each year, and these can change. Do not rely on secondhand figures - check the board's website or your school's guidance materials for the year you are applying.

Most items are within normal junior high range, but the paper is longer and includes one or two reasoning-heavy parts that reward insight rather than routine drill. The difficulty comes less from advanced content than from speed, accuracy, and the ability to explain why a result is true.

Retake and second-round recruitment rules are set by the prefecture and vary by year and by school, and some schools fill remaining places through a later selection. The official announcement is the only reliable source for whether and how a second attempt is possible, so confirm there rather than with classmates.

Finish the school curriculum first, then revise in this order: algebraic expressions and equations, functions and graphs, plane geometry with proof, solid geometry, then data and probability. Geometry and proof usually take the longest to become reliable, so start them early and revisit them weekly rather than cramming at the end.

Three recur: leaving answers unsimplified or with wrong units, skipping the reasoning on proof and explanation items so the marker cannot award steps, and losing time on one hard final part while easier questions remain untouched. Practise deciding quickly when to move on, and always write the formula before substituting numbers.

Do them under the official time limit, in one sitting, with no notes. Mark them yourself against the model answer, then list every error by cause - misread, calculation, concept, or presentation. Redo only the failed items a week later; that second pass is where most of the improvement happens.

No. This is independent study material and is not affiliated with the Toyama Prefectural Board of Education. Application dates, eligibility, fees, and scoring are announced officially each year; treat the board's documents and your school's career guidance teacher as authoritative, and use this page only for practice and explanation.