100+ Free Wakayama Prefectural Public High School Entrance Examination — Mathematics Practice Questions
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Key Facts: Wakayama Prefectural Public High School Entrance Examination — Mathematics Exam
Practise for the Wakayama Prefectural Public High School Entrance Exam in Mathematics (数学) with 100 four-option questions covering 数と式, 関数, 図形, 資料の活用 and 法則性, including genuine worked calculations, weighted to the official 100-point, 50-minute common paper sat on 令和8年3月10日(火). The official paper mixes 記号選択 items with 短答, 記述 and 作図 answers requiring 途中の計算過程, so this English-language MCQ bank drills the underlying methods — it is not a format simulation, and you still need to practise writing solutions out in Japanese.
Sample Wakayama Prefectural Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Wakayama 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.
1What is the prime factorisation of 84?
2Find the greatest common divisor (GCD) of 48 and 72.
3Solve the linear equation 3x − 5 = 16 for x.
4Solve the simultaneous equations x + y = 10 and 2x + y = 14. What is the value of x?
5Find the largest integer x satisfying the inequality 2x − 3 < 7.
6Simplify (2a²b)³.
7Simplify √72 in simplest form.
8Compute √12 + √27 and express in simplest form.
9Evaluate 2³ × 2⁴.
10Expand (x + 3)(x − 5).
About the Wakayama Prefectural Public High School Entrance Examination — Mathematics Exam
The Wakayama Prefectural Public High School Entrance Examination in Mathematics (数学) tests lower-secondary graduates on numbers and expressions, functions, geometry, data and probability, and pattern reasoning. The general academic test (学力検査) is a prefecture-wide common paper covering five subjects (国語・社会・数学・理科・英語[リスニング含む]), each worth 100 points (合計 500点); for 令和8年度 (2026 admission) the 一般選抜 学力検査 is sat on a single day, 3月10日(火), with 合格発表 on 3月18日(水). The 数学 common paper (50 minutes) combines 記号選択 (multiple-choice) items with 短答, 記述 and 作図 (constructed-response and construction) questions requiring 途中の計算過程 and proofs, so it is not a pure multiple-choice paper; past papers show a 5-大問 structure (小問集合×2, 法則性/数列, 関数, 図形) at a comparatively easy level. Selection combines the 学力検査 total (500) with the 調査書 (180) on a 680-point basis, with each school setting its own比重 and some applying 傾斜配点. 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), calculators are not permitted, and it tests 知識・技能 plus 思考力・判断力・表現力.
Assessment
100-point paper aligned to the MEXT 数学 Course of Study, covering 数と式 (22%), 関数 (22%), 図形 (26%), 資料の活用 (14%) and 法則性・応用 (16%). The prefectural common paper mixes 記号選択 items with 短答, 記述 and 作図 answers that earn partial credit for 途中の計算過程; the five academic-test subjects each carry 100 points (合計 500点) and are all sat on a single day (令和8年3月10日(火)); 数学 runs 50 minutes. Problems are at junior-high graduation level (中学校卒業程度, やや易); calculators are not permitted. The paper tests 知識・技能 plus 思考力・判断力・表現力.
Time Limit
Sat as part of the one-day five-subject 学力検査 (合計 500点, each subject 100 points) on 令和8年3月10日(火): 国語, 社会, 数学, 理科 and 英語 in that order (each 50 minutes). 一般選抜 合格発表 is 3月18日(水). The 追募集 学力検査等 is 3月26日(木) with 合格発表 3月30日(月); the 特色化選抜 内定通知 is 2月6日(金). Calculators are not permitted. Source: 令和8年度和歌山県立高等学校入学者選抜実施要項, 和歌山県教育委員会.
Passing Score
No fixed prefecture-wide pass mark. The 数学 paper is scored out of 100 points. In the 一般選抜 the five subjects (国語・社会・数学・理科・英語) total 500 points (each subject 100 points); the 調査書 (内申点) adds 180 points (中1 9教科×5=45, 中2 45, 中3 9教科×5×2=90), for a 680-point basis. Each school decides the比重 between 学力検査 and 調査書 (学力検査重視 or 同等 is common) and may apply 傾斜配点 (up to 2× on a subject, most often on the subjects tied to a course's specialism). Selection is relative to other applicants, not against a published pass line. Source: 令和8年度和歌山県立高等学校入学者選抜実施要項, 和歌山県教育委員会.
Exam Fee
The 入学考査手数料 is ¥2,200; it may be reduced or waived in cases of financial hardship. Source: 令和8年度和歌山県立高等学校入学者選抜実施要項 / 令和8年度和歌山市立和歌山高等学校入学者選抜実施要項, 和歌山県教育委員会. (Wakayama Prefectural Board of Education (和歌山県教育委員会), 県立学校教育課 (和歌山県教育庁学校教育局県立学校教育課), 〒640-8585 和歌山市小松原通一丁目1番地 (TEL 073-441-3707, FAX 073-441-3652))
Wakayama Prefectural Public High School Entrance Examination — Mathematics Exam Content Outline
Numbers & Expressions (数と式)
Integers, prime factorisation, linear equations, simultaneous equations (連立方程式), inequalities, algebraic expressions, polynomials, exponents and square roots.
Functions (関数)
Linear functions, direct and inverse proportion, quadratic functions y=ax² (二次関数), parabola vertex and axis of symmetry, intersections of parabolas with lines, and function–geometry fusion problems.
Geometry (図形)
Congruence and similarity, triangles, quadrilaterals, circles, arcs and chords, inscribed and central angles (円周角の定理), the Pythagorean theorem (三平方の定理), parallel-line proportionality, surface area and volume of solids, and constructions (作図).
Data & Probability (資料の活用)
Mean, median, mode and range, histograms, frequency distributions, quartiles, interquartile range and box-and-whisker plots (箱ひげ図), sampling surveys (標本調査), and probability.
Patterns & Applied Problems (法則性・応用)
Pattern and sequence (法則性) reasoning, inductive rule-finding, and multi-step applied/word problems that fuse algebra, functions and geometry.
How to Pass the Wakayama 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 100 points. In the 一般選抜 the five subjects (国語・社会・数学・理科・英語) total 500 points (each subject 100 points); the 調査書 (内申点) adds 180 points (中1 9教科×5=45, 中2 45, 中3 9教科×5×2=90), for a 680-point basis. Each school decides the比重 between 学力検査 and 調査書 (学力検査重視 or 同等 is common) and may apply 傾斜配点 (up to 2× on a subject, most often on the subjects tied to a course's specialism). Selection is relative to other applicants, not against a published pass line. Source: 令和8年度和歌山県立高等学校入学者選抜実施要項, 和歌山県教育委員会.
- Assessment: 100-point paper aligned to the MEXT 数学 Course of Study, covering 数と式 (22%), 関数 (22%), 図形 (26%), 資料の活用 (14%) and 法則性・応用 (16%). The prefectural common paper mixes 記号選択 items with 短答, 記述 and 作図 answers that earn partial credit for 途中の計算過程; the five academic-test subjects each carry 100 points (合計 500点) and are all sat on a single day (令和8年3月10日(火)); 数学 runs 50 minutes. Problems are at junior-high graduation level (中学校卒業程度, やや易); calculators are not permitted. The paper tests 知識・技能 plus 思考力・判断力・表現力.
- Time limit: Sat as part of the one-day five-subject 学力検査 (合計 500点, each subject 100 points) on 令和8年3月10日(火): 国語, 社会, 数学, 理科 and 英語 in that order (each 50 minutes). 一般選抜 合格発表 is 3月18日(水). The 追募集 学力検査等 is 3月26日(木) with 合格発表 3月30日(月); the 特色化選抜 内定通知 is 2月6日(金). Calculators are not permitted. Source: 令和8年度和歌山県立高等学校入学者選抜実施要項, 和歌山県教育委員会.
- Exam fee: The 入学考査手数料 is ¥2,200; it may be reduced or waived in cases of financial hardship. Source: 令和8年度和歌山県立高等学校入学者選抜実施要項 / 令和8年度和歌山市立和歌山高等学校入学者選抜実施要項, 和歌山県教育委員会.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Wakayama Prefectural Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Wakayama 数学 exam?
No. The official paper is worked in Japanese and combines 記号選択 (multiple-choice) items with 短答 (short-answer), 記述 (constructed-response) and 作図 (construction) questions that require 途中の計算過程 and proofs; its exact item count is not published. This bank is an English-language multiple-choice study adaptation of the same junior-high syllabus (数と式, 関数 including y=ax², 図形 with 相似・円周角・三平方の定理・作図, 資料の活用 and 法則性) and cannot replace writing out your own calculations in Japanese under timed conditions.
How long is the Wakayama 数学 paper and what is it worth?
It is scored out of 100 points, one of five subjects totalling 500 points (each subject 100 points). 数学 runs 50 minutes on 令和8年3月10日(火), with 一般選抜 合格発表 on 3月18日(水); the 特色化選抜 内定通知 is 2月6日(金), and the 追募集 学力検査等 is 3月26日(木) with 合格発表 3月30日(月).
Are calculators allowed?
No. The mathematics paper is sat without a calculator, in line with standard prefectural academic-test rules; numerical reasoning and exact computation are expected.
How is the selection structured?
Wakayama's 一般選抜 combines the 学力検査 total (5 subjects × 100 = 500 points) with the 調査書 (内申点, 180 points: 中1 45 + 中2 45 + 中3 90) on a 680-point basis. Each school decides the比重 between 学力検査 and 調査書 (学力検査重視 or 同等 is common) and may apply 傾斜配点 (up to 2× on a subject, most often on the subjects tied to a course's specialism). Some schools add 面接 (interview) or 実技検査. Selection is relative to other applicants, not against a published pass line.
How much is the examination fee?
The 入学考査手数料 is ¥2,200; it may be reduced or waived in cases of financial hardship.