100+ Free Okayama Public High School Entrance Examination — Mathematics Practice Questions
Prepare for the Okayama Prefectural High School Entrance Examination — Mathematics (岡山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: Okayama Public High School Entrance Examination — Mathematics Exam
Practise for the Okayama Prefectural 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 45-minute, 70-point paper. 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 Okayama Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Okayama 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.
1Calculate: 15 + (−8) − (−4).
2Calculate: (−2)³ − 5.
3Simplify: −(−3)².
4Compute: 5/6 + 1/4.
5Compute: 7/12 − 1/3.
6Multiply: (−3/5) × (10/9).
7Compute: 3/8 ÷ 6/5.
8Simplify √72 as much as possible.
9Compute: √50 + √18.
10Compute: √12 × √3.
About the Okayama Public High School Entrance Examination — Mathematics Exam
The Okayama Prefectural 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 general academic test covers five subjects (社会, 数学, 国語, 英語, 理科), each 45 minutes and 70 points (total 350), sat on 10 March 2026 in the order 社→数→国→英→理, with 合格発表 on 18 March 2026 and 5,586 candidates. 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. 岡山朝日高校 uses self-made (自校作成) problems for 国語・数学・英語; other schools use the common paper. Selection uses the 段階相関方式 with 学力 350 + 調査書 200 (中1 45 + 中2 45 + 中3 110). The 普通科学区 has 6 zones (岡山・倉敷・美作・西備・備北・東備) with 13 schools accepting prefecture-wide applicants. In the R8 (2026) results, the mathematics average (100点換算) was 57.4. The 数学 paper tendency places 小問集合 (計算・数と式, 根号・分数) at about 37%, 連立方程式 at about 15%, 資料の活用 (箱ひげ図・ヒストグラム) at about 15%, and 放物線 (二次関数) at about 15%, with 三平方の定理, 相似, 空間図形, and 確率 across the remainder.
Assessment
45-minute paper worth 70 points, 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. It is sat on 10 March 2026 within the five-subject academic test (社→数→国→英→理). The five academic-test subjects (社会, 数学, 国語, 英語, 理科) each carry 70 points for a maximum of 350 points. The paper tests 知識・技能 plus 思考力・判断力・表現力.
Time Limit
45 minutes (the 数学 paper is sat on 10 March 2026; the full academic test is held on a single day with subject order 社→数→国→英→理)
Passing Score
No fixed pass mark. Admission is decided by each school using the 段階相関方式 (correlation table method), combining the academic test (学力検査, up to 350 points) with the report card (調査書, up to 200 points). The 調査書 200 points are composed of 中1 (45) + 中2 (45) + 中3 (110 = 5 academic subjects × 5 × 2 + 4 practical subjects × 5 × 3). The first selection (第1選抜) fills about 90% of places from first-choice applicants, and the second selection (第2選抜) fills about 10% from second-choice applicants. There is no single prefecture-wide pass line; each school decides comprehensively.
Exam Fee
¥2,200 入学選抜手数料 (entrance selection fee), the figure published by Okayama Prefecture for its prefectural high schools; the same ¥2,200 applies to both the 全日制 (full-time) and 定時制 (part-time) courses. On admission a separate 入学金 of ¥5,650 is payable. The fee covers the whole 学力検査, not an individual subject paper. Source: Okayama Prefecture, 県立学校の授業料等 (https://www.pref.okayama.jp/site/16/detail-7021.html). (Okayama Prefectural Board of Education (岡山県教育委員会))
Okayama Public High School Entrance Examination — Mathematics Exam Content Outline
Numbers & Algebraic Expressions (数と式)
Signed arithmetic, fractions, square roots, algebraic manipulation, linear and quadratic equations, and simultaneous equations.
Functions (関数)
Direct and inverse proportionality, linear functions, the quadratic function y=ax², parabola vertex and intercepts, and graph reading.
Geometry (図形)
Triangle congruence and similarity, the Pythagorean theorem, circle properties, inscribed angles, chords, tangent lines, and solid-geometry surface area and volume.
Data Analysis & Probability (資料の活用と確率)
Histograms and box plots, median, mean and range, sample surveys, relative frequency, and probability with dice, coins and marbles.
How to Pass the Okayama Public High School Entrance Examination — Mathematics Exam
What You Need to Know
- Passing score: No fixed pass mark. Admission is decided by each school using the 段階相関方式 (correlation table method), combining the academic test (学力検査, up to 350 points) with the report card (調査書, up to 200 points). The 調査書 200 points are composed of 中1 (45) + 中2 (45) + 中3 (110 = 5 academic subjects × 5 × 2 + 4 practical subjects × 5 × 3). The first selection (第1選抜) fills about 90% of places from first-choice applicants, and the second selection (第2選抜) fills about 10% from second-choice applicants. There is no single prefecture-wide pass line; each school decides comprehensively.
- Assessment: 45-minute paper worth 70 points, 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. It is sat on 10 March 2026 within the five-subject academic test (社→数→国→英→理). The five academic-test subjects (社会, 数学, 国語, 英語, 理科) each carry 70 points for a maximum of 350 points. The paper tests 知識・技能 plus 思考力・判断力・表現力.
- Time limit: 45 minutes (the 数学 paper is sat on 10 March 2026; the full academic test is held on a single day with subject order 社→数→国→英→理)
- Exam fee: ¥2,200 入学選抜手数料 (entrance selection fee), the figure published by Okayama Prefecture for its prefectural high schools; the same ¥2,200 applies to both the 全日制 (full-time) and 定時制 (part-time) courses. On admission a separate 入学金 of ¥5,650 is payable. The fee covers the whole 学力検査, not an individual subject paper. Source: Okayama Prefecture, 県立学校の授業料等 (https://www.pref.okayama.jp/site/16/detail-7021.html).
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Okayama Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Okayama mathematics exam?
No. The official paper is written in Japanese with constructed-response items including 計算, 証明, 作図, and items where the 求め方 (working) must be written out. This bank is an English-language multiple-choice study adaptation of the same syllabus content and cannot replace showing your own mathematical reasoning.
How long is the Okayama mathematics paper and what is it worth?
It lasts 45 minutes and is scored out of 70 points, one of five subjects that together total 350 points (each subject 70 points). The five subjects are sat on 10 March 2026 in the order 社→数→国→英→理.
How is the selection structured in 2026?
Okayama uses the 段階相関方式 (correlation table method), combining the academic test (学力検査, up to 350 points) with the report card (調査書, up to 200 points = 中1 45 + 中2 45 + 中3 110). The first selection (第1選抜) fills about 90% of places from first-choice applicants, and the second selection (第2選抜) fills about 10% from second-choice applicants. Each school decides comprehensively; there is no prefecture-wide pass line.
How much is the examination fee?
The 入学選抜手数料 (entrance selection fee) for an Okayama prefectural high school is ¥2,200, the same for the 全日制 and 定時制 courses. It is paid once for the whole five-subject 学力検査, not per subject paper. Students who are admitted then pay a separate 入学金 of ¥5,650. Okayama Prefecture publishes both figures on its 県立学校の授業料等 page.
When was the 2026 paper sat and when were results announced?
The 令和8年度 学力検査 was held on 10 March 2026 (数学 sat within the 社→数→国→英→理 order), with 合格発表 on 18 March 2026. A 特別入学者選抜 was also held on 4 February 2026 (国・数・英 three subjects, 45 min/70 points each, 英語聞き取り included).
What content areas does the mathematics paper cover?
The paper follows the MEXT junior-high Course of Study (平成29年 中学校学習指導要領 数学編) and covers 数と式 (signed arithmetic, fractions, square roots, equations), 関数 (proportion, linear and quadratic functions, parabolas), 図形 (similarity, Pythagorean theorem, circles, solid geometry), and 資料の活用と確率 (histograms, box plots, sample surveys, probability). In R8 the 数学 average (100点換算) was 57.4.