100+ Free Yamaguchi Prefectural Public High School Entrance Examination — Mathematics Practice Questions
Prepare for the Yamaguchi Prefectural Public High School Entrance Examination — Mathematics (山口県公立高等学校入学者選抜 学力検査 数学) exam with instant access — no signup required.
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Key Facts: Yamaguchi Prefectural Public High School Entrance Examination — Mathematics Exam
Practise for the Yamaguchi Prefectural Public High School Entrance Exam in Mathematics (数学) with 100 four-option questions covering algebra, functions, geometry, data/probability, patterns and applied problems, each with a full worked solution, weighted to the official 50-minute paper sat second on 令和8年3月5日(木) (10:10-11:00). The official paper also has 短答記述 and possible 記述式 items that this MCQ bank does not reproduce, so you must still practise free-response working separately.
Sample Yamaguchi Prefectural Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Yamaguchi Prefectural Public High School Entrance Examination — Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Solve for x: 3x - 7 = 14.
2Simplify: -2(x - 4) + 3x.
3Factor: x² - 9.
4Solve the system: x + y = 10, x - y = 4.
5Solve: 2(x + 3) = 5x - 6.
6Expand: (x + 5)(x - 2).
7Simplify: √12 + √27.
8Factor: x² + 5x + 6.
9What is the value of (-3)² + (-2)³?
10Simplify the ratio 12 : 18 to lowest terms.
About the Yamaguchi Prefectural Public High School Entrance Examination — Mathematics Exam
The Yamaguchi Prefectural Public High School Entrance Examination in Mathematics (数学) tests lower-secondary graduates on numbers & expressions, equations, functions, geometry, and data & probability. From 2026 (令和8年度) a 特色選抜 replaces the old 推薦選抜 (出願 1/21-1/28, 検査 2/4(水) [or 2/5], 内定通知 2/12; every school holds a 個人面接 and may run a 学校独自検査 such as 総合問題・基礎学力検査・口頭試問・小論文・プレゼン・作文・集団討論・実技検査), alongside the 第一次募集 general selection (出願 2/13-2/24, 学力検査 3/5(木), 合格発表 3/12(木); 面接・小論文・実技検査 may be held at schools that choose them) and a 第二次募集 (3/12発表; 面接必須, 小論文・実技可). A WEB出願 system was introduced in 令和8年度. The general academic test (学力検査) is a prefecture-wide common paper covering five subjects (国語, 数学, 英語, 社会, 理科), each worth 50 points (合計 250点); for 令和8年度 the 第一次募集 学力検査 is sat on a single day, 3月5日(木). The 数学 common paper (10:10-11:00, sat second) opens with a 小問集合 (大問1,2, about 25% of points) of short basic problems, followed by larger applied problems whose text length has been increasing and which introduce new problem types; it mixes 記号選択 (multiple-choice) with 短答記述 and may include 記述式 answers, so it is not a pure multiple-choice paper. Selection combines the 学力検査 total (250) with the 調査書 (中1-3 9教科×5 = 135点) on an equal-treatment basis, with each school setting its own比重 and some applying 傾斜配点 (up to 2× via 学校指定 or 生徒指定). The 全日制 通学区域 is 山口県全域. The paper is aligned to the MEXT junior-high Course of Study (平成29年 中学校学習指導要領 数学編) and tests 知識・技能 plus 思考力・判断力・表現力.
Assessment
50-point paper aligned to the MEXT 数学 Course of Study, covering algebra — equations & expressions (28%), functions (22%), geometry (30%), data & probability (10%), patterns & sequences (5%) and applied problems (5%). The prefectural common paper opens with a 小問集合 (大問1,2, about 25% of points) of short basic problems, then larger applied problems; it mixes 記号選択 items with 短答記述 and may include 記述式 answers, so it is not a pure multiple-choice paper. The five academic-test subjects each carry 50 points (合計 250点), and 数学 is sat second on the single 学力検査 day (令和8年3月5日(木), 10:10-11:00). No official per-topic percentage weighting is published for 数学; the percentages above are this bank's own study weighting, derived from the MEXT Course of Study and the recurring 大問 structure. The paper tests 知識・技能 plus 思考力・判断力・表現力, including reading conditions and applying procedures.
Time Limit
Sat as part of the one-day five-subject 学力検査 (合計 250点, each subject 50 points) on 令和8年3月5日(木): 国語 (9:00-9:50), 数学 (10:10-11:00, sat second), 英語 (11:20-12:10), 社会 (13:00-13:50) and 理科 (14:10-15:00) in that order (each 50 minutes). The 特色選抜 検査日 is 令和8年2月4日(水) (a school that cannot finish in one day also sits 2月5日(木)). Source: 令和8年度山口県公立高等学校入学者選抜実施要領(抄), 山口県教育委員会.
Passing Score
No fixed prefecture-wide pass mark. The 数学 paper is scored out of 50 points. In the 第一次募集 the five subjects (国語・数学・英語・社会・理科) total 250 points (each subject 50 points); the 調査書 (内申点) records 中1・中2・中3 各学年 9教科×5段階評定 = 45点 (合計 135点), and 山口県教育委員会 states that 調査書の「学習の記録」と学力検査の成績は同等に取り扱う. Each school may apply 傾斜配点 — either the 学校指定方式 (the school doubles the score of one or two specified subjects, up to 2×) or the 生徒指定方式 (the applicant chooses one or two subjects to weight, up to 2×; the rate and number of subjects are set by each school). Selection is relative to other applicants, not against a published pass line. Source: 令和8年度山口県公立高等学校入学者選抜実施要領(抄), 山口県教育委員会.
Exam Fee
The 入学試験料 (入学検定料) is ¥2,200 for a full-time (全日制) course (¥700 for 定時制); it may be reduced or waived in cases of financial hardship. Source: 令和8年度山口県公立高等学校入学者選抜実施要領(抄) / 実施大綱, 山口県教育委員会. (Yamaguchi Prefectural Board of Education (山口県教育委員会), 高校教育課, 〒753-8501 山口市滝町1番1号 (TEL 083-922-3111))
Yamaguchi Prefectural Public High School Entrance Examination — Mathematics Exam Content Outline
Algebra — Equations & Expressions (数と式・方程式)
Positive and negative numbers, expanding and factoring expressions, linear and simultaneous equations, quadratic equations including the quadratic formula, ratios and proportion, square roots (平方根), and algebraic proof with letters.
Functions (関数)
Direct and inverse proportion (中1), linear functions y = ax + b with gradient and intercept (中2), and the function y = ax² (中3) — its graph, rate of change (変化の割合), and the range of y for a given range of x (変域). Follows the MEXT junior-high syllabus, so general quadratics y = ax² + bx + c, vertex form and inequalities are excluded as high-school content.
Geometry (図形)
Angles, Pythagorean theorem, area/perimeter, circles, polygons, similarity and congruence, volume/surface, special triangles and locus — including proof-style reasoning.
Data & Probability (資料の活用)
Mean, median, mode and range; quartiles and interquartile range (四分位範囲); probability with dice, coins and counters; and reading data from tables, bar charts and pie charts.
Patterns & Sequences (規則性)
Arithmetic and geometric patterns, sums and figure-pattern reasoning.
Applied Problems (文章題)
Rates, percentages, scale, tax and real-world calculation problems.
How to Pass the Yamaguchi Prefectural Public High School Entrance Examination — Mathematics Exam
What You Need to Know
- Passing score: No fixed prefecture-wide pass mark. The 数学 paper is scored out of 50 points. In the 第一次募集 the five subjects (国語・数学・英語・社会・理科) total 250 points (each subject 50 points); the 調査書 (内申点) records 中1・中2・中3 各学年 9教科×5段階評定 = 45点 (合計 135点), and 山口県教育委員会 states that 調査書の「学習の記録」と学力検査の成績は同等に取り扱う. Each school may apply 傾斜配点 — either the 学校指定方式 (the school doubles the score of one or two specified subjects, up to 2×) or the 生徒指定方式 (the applicant chooses one or two subjects to weight, up to 2×; the rate and number of subjects are set by each school). Selection is relative to other applicants, not against a published pass line. Source: 令和8年度山口県公立高等学校入学者選抜実施要領(抄), 山口県教育委員会.
- Assessment: 50-point paper aligned to the MEXT 数学 Course of Study, covering algebra — equations & expressions (28%), functions (22%), geometry (30%), data & probability (10%), patterns & sequences (5%) and applied problems (5%). The prefectural common paper opens with a 小問集合 (大問1,2, about 25% of points) of short basic problems, then larger applied problems; it mixes 記号選択 items with 短答記述 and may include 記述式 answers, so it is not a pure multiple-choice paper. The five academic-test subjects each carry 50 points (合計 250点), and 数学 is sat second on the single 学力検査 day (令和8年3月5日(木), 10:10-11:00). No official per-topic percentage weighting is published for 数学; the percentages above are this bank's own study weighting, derived from the MEXT Course of Study and the recurring 大問 structure. The paper tests 知識・技能 plus 思考力・判断力・表現力, including reading conditions and applying procedures.
- Time limit: Sat as part of the one-day five-subject 学力検査 (合計 250点, each subject 50 points) on 令和8年3月5日(木): 国語 (9:00-9:50), 数学 (10:10-11:00, sat second), 英語 (11:20-12:10), 社会 (13:00-13:50) and 理科 (14:10-15:00) in that order (each 50 minutes). The 特色選抜 検査日 is 令和8年2月4日(水) (a school that cannot finish in one day also sits 2月5日(木)). Source: 令和8年度山口県公立高等学校入学者選抜実施要領(抄), 山口県教育委員会.
- Exam fee: The 入学試験料 (入学検定料) is ¥2,200 for a full-time (全日制) course (¥700 for 定時制); it may be reduced or waived in cases of financial hardship. Source: 令和8年度山口県公立高等学校入学者選抜実施要領(抄) / 実施大綱, 山口県教育委員会.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Yamaguchi Prefectural Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Yamaguchi 数学 exam?
No. The official paper opens with a 小問集合 (大問1,2, about 25% of points) of short basic problems, then larger applied problems whose text length has been increasing and which introduce new problem types; its exact item count is not published. This bank is an English-language multiple-choice study adaptation covering algebra, functions, geometry, data/probability, patterns and applied problems, each with a worked solution; it does not reproduce free-response or proof-writing tasks and cannot replace them.
How long is the Yamaguchi 数学 paper and what is it worth?
It is scored out of 50 points, one of five subjects totalling 250 points (each subject 50 points). 数学 is sat second on the single 学力検査 day (令和8年3月5日(木), 10:10-11:00). The 特色選抜 検査日 is 2月4日(水) (or 2月5日(木) for schools that need a second day).
How is the selection structured?
From 2026 (令和8年度) Yamaguchi runs a 特色選抜 (出願 1/21-1/28, 検査 2/4(水) [or 2/5], 内定通知 2/12; every school holds a 個人面接 and may run a 学校独自検査) and a 第一次募集 general selection (出願 2/13-2/24, 学力検査 3/5(木), 合格発表 3/12(木)), with a 第二次募集 for schools that did not fill. The 第一次募集 combines the 学力検査 total (5 subjects × 50 = 250 points) with the 調査書 (中1-3 9教科×5 = 135点); 山口県教育委員会 states the 調査書の「学習の記録」と学力検査の成績は同等に取り扱う. Each school may apply 傾斜配点 (up to 2× via 学校指定 or 生徒指定 on one or two subjects). Selection is relative to other applicants, not against a published pass line.
How much is the examination fee?
The 入学試験料 (入学検定料) is ¥2,200 for a full-time (全日制) course (¥700 for 定時制); it may be reduced or waived in cases of financial hardship.
Where is the exam held and who can apply?
The 全日制 通学区域 is 山口県全域 (the whole prefecture). From 令和8年度 applications are submitted through a WEB出願 system, routed through the applicant's junior high school. 周防大島高校 became 山口県立大学附属周防大島高校 and runs its own separate selection.