100+ Free Shiga Public High School Entrance Examination — Mathematics Practice Questions
Prepare for the Shiga Prefectural Public High School Entrance Examination — Mathematics (滋賀県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: Shiga Public High School Entrance Examination — Mathematics Exam
Practise for the Shiga Prefectural Public High School Entrance Exam in Mathematics with 100 four-option questions covering 数と式, 関数, 図形, and 確率・データ, weighted to the official 100-point paper sat on 25 February 2026. The official paper contains constructed-response items (計算/証明/作図/求め方記述), so this English-language MCQ bank is a study aid, not a format simulation.
Sample Shiga Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Shiga 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.
1Evaluate (-7) + 4 - (-9).
2Calculate 2/3 - 1/4 + 5/6.
3Simplify √48 + √27 - √12.
4Solve for x: 4x - 5 = 2x + 11.
5Expand (x + 4)(x - 7).
6Factor x² + 5x - 24.
7Simplify 3x(x - 2) - (2x² - x + 5).
8Solve the simultaneous equations: x + 2y = 11, 3x - y = 12.
9Solve the simultaneous equations: 2x + 3y = 16, 3x - 2y = 11.
10Solve x² - 5x + 6 = 0.
About the Shiga Public High School Entrance Examination — Mathematics Exam
The Shiga Prefectural Public High School Entrance Examination in Mathematics tests lower-secondary graduates on calculation, algebra, functions, geometry and data analysis. In the 令和8年度 (2026) cycle the consolidated 一次募集 offers 一般型選抜 (all candidates take the 5-subject 学力検査 covering 国語, 数学, 社会, 理科, 英語, each worth 100 points for a total of 500) and 学校独自型選抜 (school-specific 作文/小論文/面接/プレゼンテーション/実技検査; 自己推薦 or 中学校長推薦; 併願 allowed). The 学力検査 is sat on 25 February 2026. 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, with constructed-response items including 計算, 証明, 作図, and 求め方記述. Each school sets its own 学力検査:個人調査報告書 ratio (個人調査報告書 135点満点) and may weight subjects per its 特色. A 二次募集 follows if places remain. The Web出願システム was introduced in 令和8年度.
Assessment
100-point paper aligned to the MEXT 数学 Course of Study with constructed-response items including 計算, 証明, 作図, and 求め方記述. The five academic-test subjects (国語, 数学, 社会, 理科, 英語) each carry 100 points for a maximum of 500 points, sat on 25 February 2026. The paper tests 知識・技能 plus 思考力・判断力・表現力. From 令和8年度, the consolidated 一次募集 offers 一般型選抜 (all candidates take the 5-subject 学力検査; selection on 学力検査 + 個人調査報告書 135点満点) and 学校独自型選抜 (school-specific 作文/小論文/面接/プレゼンテーション/実技検査; 自己推薦 or 中学校長推薦; 併願 allowed). Schools may weight subjects per their 特色. A 二次募集 follows if places remain.
Time Limit
Sat as part of the single-day five-subject 学力検査: each subject is a 100-point paper of 50 minutes, 500 points in total. For the upcoming 令和9年度 (2027) intake the 学力検査 is on 3 March 2027 (Wednesday), the 学校独自検査 on 4 March 2027 (Thursday), 追検査 on 7–8 March 2027, 入学許可予定者発表 on 11 March 2027, and 二次募集 on 17–19 March 2027. The most recent completed sitting, 令和8年度, was held on 25 February 2026.
Passing Score
No fixed prefecture-wide pass mark. The mathematics paper is scored out of 100 points (500 across the five academic-test subjects, each 100 points). From 令和8年度 (2026), Shiga consolidated selection into a single 一次募集 with two types: 一般型選抜 (selection on 学力検査 + 個人調査報告書/内申書, 135点満点) and 学校独自型選抜 (学校独自検査: 作文/小論文/面接/プレゼンテーション/実技検査). Each school sets its own 学力検査:個人調査報告書 ratio. There is no single prefecture-wide pass line. Source: 令和8年度 滋賀県立高等学校入学者選抜 実施要項, 滋賀県教育委員会.
Exam Fee
入学者選抜手数料 is ¥2,200 for the 全日制 (full-time) course for one selection and ¥4,400 for a 併願 (both selections at the same school), and ¥950 / ¥1,900 for the 定時制 (part-time) course. Applications are limited to one school (１人１校). Paid once for the whole five-subject 学力検査 via the Web出願システム (credit card, convenience store, or Pay-easy). Not refundable. Source: 令和8年度 滋賀県立高等学校入学者選抜 実施要項, 滋賀県教育委員会. (Shiga Prefectural Board of Education (滋賀県教育委員会))
Shiga Public High School Entrance Examination — Mathematics Exam Content Outline
Numbers & Algebraic Expressions (数と式)
Signed arithmetic, fractions, square roots, algebraic manipulation, linear and simultaneous equations, quadratic equations, and word-problem set-up.
Functions (関数)
Direct and inverse proportionality, linear functions y=ax+b and their graphs, the quadratic function y=ax² and the parabola, and reading information from graphs.
Geometry (図形)
Parallel-line properties, triangle congruence and similarity, the Pythagorean theorem, circle inscribed angles and tangent lines, polygons, and solid volume and surface area.
Data Analysis & Probability (資料の活用と確率)
Histograms and box plots, mean/median/mode/range, sample surveys, and probability with dice, coins, marbles and cards including tree diagrams and two-trial events.
How to Pass the Shiga Public High School Entrance Examination — Mathematics Exam
What You Need to Know
- Passing score: No fixed prefecture-wide pass mark. The mathematics paper is scored out of 100 points (500 across the five academic-test subjects, each 100 points). From 令和8年度 (2026), Shiga consolidated selection into a single 一次募集 with two types: 一般型選抜 (selection on 学力検査 + 個人調査報告書/内申書, 135点満点) and 学校独自型選抜 (学校独自検査: 作文/小論文/面接/プレゼンテーション/実技検査). Each school sets its own 学力検査:個人調査報告書 ratio. There is no single prefecture-wide pass line. Source: 令和8年度 滋賀県立高等学校入学者選抜 実施要項, 滋賀県教育委員会.
- Assessment: 100-point paper aligned to the MEXT 数学 Course of Study with constructed-response items including 計算, 証明, 作図, and 求め方記述. The five academic-test subjects (国語, 数学, 社会, 理科, 英語) each carry 100 points for a maximum of 500 points, sat on 25 February 2026. The paper tests 知識・技能 plus 思考力・判断力・表現力. From 令和8年度, the consolidated 一次募集 offers 一般型選抜 (all candidates take the 5-subject 学力検査; selection on 学力検査 + 個人調査報告書 135点満点) and 学校独自型選抜 (school-specific 作文/小論文/面接/プレゼンテーション/実技検査; 自己推薦 or 中学校長推薦; 併願 allowed). Schools may weight subjects per their 特色. A 二次募集 follows if places remain.
- Time limit: Sat as part of the single-day five-subject 学力検査: each subject is a 100-point paper of 50 minutes, 500 points in total. For the upcoming 令和9年度 (2027) intake the 学力検査 is on 3 March 2027 (Wednesday), the 学校独自検査 on 4 March 2027 (Thursday), 追検査 on 7–8 March 2027, 入学許可予定者発表 on 11 March 2027, and 二次募集 on 17–19 March 2027. The most recent completed sitting, 令和8年度, was held on 25 February 2026.
- Exam fee: 入学者選抜手数料 is ¥2,200 for the 全日制 (full-time) course for one selection and ¥4,400 for a 併願 (both selections at the same school), and ¥950 / ¥1,900 for the 定時制 (part-time) course. Applications are limited to one school (１人１校). Paid once for the whole five-subject 学力検査 via the Web出願システム (credit card, convenience store, or Pay-easy). Not refundable. Source: 令和8年度 滋賀県立高等学校入学者選抜 実施要項, 滋賀県教育委員会.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Shiga Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Shiga mathematics exam?
No. The official paper is written in Japanese with constructed-response items including 計算, 証明, 作図, and 求め方記述. This bank is an English-language multiple-choice study adaptation of the same syllabus content and cannot replace writing out your own proofs and working under timed conditions.
How long is the Shiga mathematics paper and what is it worth?
It is scored out of 100 points, one of five subjects that together total 500 points (each subject 100 points), and each paper runs 50 minutes. For the 令和9年度 (2027) intake the five-subject 学力検査 is on 3 March 2027, the 学校独自検査 on 4 March, 追検査 on 7–8 March, 入学許可予定者発表 on 11 March, and 二次募集 on 17–19 March 2027.
How is the selection structured in 2026?
From 令和8年度, Shiga consolidated selection into a single 一次募集 with two types: 一般型選抜 (all take the 5-subject 学力検査; selection on 学力検査 + 個人調査報告書 135点満点) and 学校独自型選抜 (school-specific 作文/小論文/面接/プレゼンテーション/実技検査; 自己推薦 or 中学校長推薦; 併願 allowed). Each school sets its own 学力検査:個人調査報告書 ratio and may weight subjects per its 特色. A 二次募集 follows if places remain. There is no prefecture-wide pass line.
What is the 学校独自型選抜?
学校独自型選抜 is a selection type within the 一次募集 where hopefuls take a 学校独自検査 set by each school — which may include 作文, 小論文, 面接, プレゼンテーション, or 実技検査. Candidates apply via 自己推薦 or 中学校長推薦, and 併願 with 一般型選抜 is allowed.
How much is the examination fee?
The 入学者選抜手数料 (entrance examination fee) for a Shiga prefectural public high school is ¥2,200 for the 全日制 course when you apply to one selection, and ¥4,400 when you apply to two. Because applications are limited to one school (１人１校), the doubled fee means a 併願 — entering both the 学校独自型選抜 and the 一般型選抜 at the same school — not applying to two different schools. The 定時制 course is ¥950 for one selection and ¥1,900 for two. It is paid once for the whole five-subject 学力検査 via the Web出願システム and is not refundable.
When is the next Shiga entrance examination?
The next sitting is the 令和9年度 (2027) intake: the five-subject 学力検査 is on 3 March 2027 (Wednesday) and the 学校独自検査 on 4 March 2027 (Thursday), with applications from 28 January to 9 February 2027 and results on 11 March 2027. The most recent completed sitting was 令和8年度, held on 25 February 2026. Always confirm dates against the 滋賀県教育委員会 selection page.