100+ Free Shizuoka Public High School Entrance Examination — Mathematics Practice Questions
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Key Facts: Shizuoka Public High School Entrance Examination — Mathematics Exam
Practise for the Shizuoka Prefectural Public High School Entrance Exam in Mathematics (数学) with 100 four-option questions covering 数と式, 関数, 図形 and 資料の活用, with many calculation problems, weighted to the official 50-point paper structured in seven 大問 and sat on 3月4日 alongside the other four subjects. The official paper contains 記述式/論述式 proof and calculation items, so this English-language MCQ bank is a study aid, not a format simulation.
Sample Shizuoka Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Shizuoka 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.
1Compute: -5 + 9 - 3.
2Compute: (-6) × (-2) + (-4).
3Compute (1/2) + (1/3) and write the answer as a single reduced fraction.
4Compute (3/5) × (10/9) and write the answer as a reduced fraction.
5What is the prime factorisation of 84?
6Find the greatest common divisor of 48 and 36.
7Find the least common multiple of 12 and 18.
8Solve for x: 2x + 3 = 11.
9Simplify: 3(x - 2) - 2(x + 1).
10Solve for x: 5x - 2 = 3x + 10.
About the Shizuoka Public High School Entrance Examination — Mathematics Exam
The Shizuoka Prefectural Public High School Entrance Examination in Mathematics (数学) tests lower-secondary graduates on numbers and expressions, functions, geometry, and data and probability. In the 令和8年度 (2026) cycle the general academic test (学力検査) covers five subjects (国語, 数学, 社会, 理科, 英語[放送含む]), each worth 50 points (total 250), all sat on one day (3月4日), with 面接など on 3月5日. The 数学 paper is structured in seven 大問: 大問1 小問集合, 大問2 作図と確率, 大問3 連立方程式, 大問4 空間図形, 大問5 資料の活用, 大問6 二次関数, 大問7 平面図形. Selection in 一般選抜 combines 学力検査 250点 with 調査書(内申) 45点, with schools offering a 裁量枠 (school-discretion quota) and a 共通枠 (common quota); some schools add 面接/実技/作文/小論文, and 専門学科共通枠 may use 傾斜配点. 再募集 (second round) uses 面接 + 作文 or 小論文 with no 学力検査. 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, with 記述式/論述式 calculation and proof items. Function and geometry items (大問6 二次関数 and 大問7 平面図形) are the hardest.
Assessment
50-point paper aligned to the MEXT 数学 Course of Study, structured in seven 大問: 大問1 小問集合, 大問2 作図と確率, 大問3 連立方程式, 大問4 空間図形, 大問5 資料の活用, 大問6 二次関数, 大問7 平面図形. It covers 数と式, 関数, 図形 and 資料の活用, with 記述式/論述式 calculation and proof items. The five academic-test subjects (国語, 数学, 社会, 理科, 英語) each carry 50 points (max 250), all sat on a single day (3月4日 for 令和8年度). Problems are at junior-high graduation level; calculators are not permitted; 専門学科共通枠 may apply 傾斜配点. 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: each subject is a 50-point paper of 50 minutes, 250 points in total. For 令和8年度 the 学力検査 is on 3月4日(水) and 面接など on 3月5日(木). 願書提出: 2月17日〜2月19日; 志願先変更: 2月25日〜2月26日; 追検査: 3月10日(火); 選抜結果発表: 3月13日(金)正午以降. 再募集 (second round) uses 面接 + 作文 or 小論文 with no 学力検査.
Passing Score
No fixed prefecture-wide pass mark. The 数学 paper is scored out of 50 points (250 across the five 学力検査 subjects, each 50 points). 一般選抜 selects on 学力検査 250点 + 調査書(内申) 45点, with schools offering a 裁量枠 (school-discretion quota) and a 共通枠 (common quota); some schools add 面接/実技/作文/小論文, and 専門学科共通枠 may use 傾斜配点. There is no single prefecture-wide pass line. Source: 令和8年度 静岡県公立高等学校入学者選抜 実施要綱, 静岡県教育委員会.
Exam Fee
The 入学検定料 is ¥2,200 for a 全日制 course, the standard prefectural rate for full-time public high schools. The payment instrument is specified in each year's 実施要綱 and changed when 静岡県収入証紙 were withdrawn at the end of 令和7年 — check the current method on the 静岡県教育委員会 高校教育課 selection page. (Shizuoka Prefectural Board of Education (静岡県教育委員会), 高校教育課, 〒420-8601 静岡市葵区追手町9-6)
Shizuoka 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), quadratic equations, inequalities, algebraic expressions and identities, polynomials, exponents, and square roots.
Functions (関数)
Linear functions, proportional and inverse proportional relationships, quadratic functions y=ax² (二次関数), parabolas, vertex and axis of symmetry, intersections of parabolas with lines, and applied 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 (ピタゴラスの定理), parallel-line proportionality, surface area and volume of solids, constructions and proof.
Data & Probability (資料の活用)
Mean, median, mode and range, histograms, frequency distributions, relative frequency, quartiles and box-and-whisker plots, variance, sampling surveys, and probability.
How to Pass the Shizuoka 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 (250 across the five 学力検査 subjects, each 50 points). 一般選抜 selects on 学力検査 250点 + 調査書(内申) 45点, with schools offering a 裁量枠 (school-discretion quota) and a 共通枠 (common quota); some schools add 面接/実技/作文/小論文, and 専門学科共通枠 may use 傾斜配点. There is no single prefecture-wide pass line. Source: 令和8年度 静岡県公立高等学校入学者選抜 実施要綱, 静岡県教育委員会.
- Assessment: 50-point paper aligned to the MEXT 数学 Course of Study, structured in seven 大問: 大問1 小問集合, 大問2 作図と確率, 大問3 連立方程式, 大問4 空間図形, 大問5 資料の活用, 大問6 二次関数, 大問7 平面図形. It covers 数と式, 関数, 図形 and 資料の活用, with 記述式/論述式 calculation and proof items. The five academic-test subjects (国語, 数学, 社会, 理科, 英語) each carry 50 points (max 250), all sat on a single day (3月4日 for 令和8年度). Problems are at junior-high graduation level; calculators are not permitted; 専門学科共通枠 may apply 傾斜配点. 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: each subject is a 50-point paper of 50 minutes, 250 points in total. For 令和8年度 the 学力検査 is on 3月4日(水) and 面接など on 3月5日(木). 願書提出: 2月17日〜2月19日; 志願先変更: 2月25日〜2月26日; 追検査: 3月10日(火); 選抜結果発表: 3月13日(金)正午以降. 再募集 (second round) uses 面接 + 作文 or 小論文 with no 学力検査.
- Exam fee: The 入学検定料 is ¥2,200 for a 全日制 course, the standard prefectural rate for full-time public high schools. The payment instrument is specified in each year's 実施要綱 and changed when 静岡県収入証紙 were withdrawn at the end of 令和7年 — check the current method on the 静岡県教育委員会 高校教育課 selection page.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Shizuoka Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Shizuoka 数学 exam?
No. The official paper is written in Japanese with 記述式/論述式 calculation and proof items, and its exact item count is not published. This bank is an English-language multiple-choice study adaptation of the same syllabus content (including 二次関数 and 三角比) and cannot replace writing out your own proofs and calculations in Japanese under timed conditions.
How long is the Shizuoka 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), and each paper runs 50 minutes. All five subjects are sat on one day — 3月4日(水) for 令和8年度 — with 面接など on 3月5日(木).
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?
Shizuoka 一般選抜 selects on 学力検査 250点 + 調査書(内申) 45点, with schools offering a 裁量枠 (school-discretion quota) and a 共通枠 (common quota); some schools add 面接/実技/作文/小論文, and 専門学科共通枠 may use 傾斜配点. 再募集 (second round) uses 面接 + 作文 or 小論文 with no 学力検査. 願書提出 is 2月17日〜2月19日, 志願先変更 2月25日〜2月26日, 選抜結果発表 3月13日正午以降.
What is the structure of the 数学 paper?
The paper has seven 大問: 大問1 小問集合, 大問2 作図と確率, 大問3 連立方程式, 大問4 空間図形, 大問5 資料の活用, 大問6 二次関数, 大問7 平面図形. Function and geometry items (大問6 and 大問7) are the hardest. The paper tests 知識・技能 plus 思考力・判断力・表現力, with 記述式/論述式 proof and calculation items.
How much is the examination fee?
The 入学検定料 for a 全日制 course is ¥2,200, the standard prefectural rate for full-time public high schools; 定時制 courses pay less. Because 静岡県収入証紙 were withdrawn at the end of 令和7年, confirm the current payment instrument in the year's 実施要綱 on the 静岡県教育委員会 高校教育課 page.