100+ Free Okinawa Public High School Entrance Examination — Mathematics Practice Questions

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Key Facts: Okinawa Public High School Entrance Examination — Mathematics Exam

Practise for the Okinawa 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 50-minute, 60-point paper sat on 5 March 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 Okinawa Public High School Entrance Examination — Mathematics Practice Questions

Try these sample questions to test your Okinawa 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).

A.11

B.3

C.27

D.19

Explanation: 15 + (−8) − (−4) = 15 − 8 + 4 = 11. Subtracting a negative is adding the positive.

2Simplify the product (−3) × (−5) × (−2).

A.−30

B.30

C.−15

D.10

Explanation: An odd number of negative factors gives a negative product: (−3)(−5) = 15, then 15 × (−2) = −30.

3Compute 7/12 + 3/8 as a single reduced fraction.

A.23/24

B.5/20

C.10/20

D.21/24

Explanation: The LCD of 12 and 8 is 24. 7/12 = 14/24 and 3/8 = 9/24, so the sum is 23/24, which is already reduced.

4Simplify √72 + √50 − √32.

A.7√2

B.5√2

C.3√10

D.15√2

Explanation: √72 = 6√2, √50 = 5√2, √32 = 4√2. So 6√2 + 5√2 − 4√2 = (6 + 5 − 4)√2 = 7√2.

5Solve for x: 3(x − 2) + 4 = x + 8.

A.x = 5

B.x = 3

C.x = 7

D.x = 1

Explanation: Expand: 3x − 6 + 4 = x + 8, so 3x − 2 = x + 8. Subtract x: 2x − 2 = 8. Add 2: 2x = 10. Divide by 2: x = 5.

6Solve the simultaneous equations: y = 2x + 1 and 3x + y = 11.

A.x = 2, y = 5

B.x = 3, y = 7

C.x = 2, y = 3

D.x = 5, y = 11

Explanation: Substitute y = 2x + 1 into 3x + y = 11: 3x + 2x + 1 = 11, so 5x = 10, x = 2. Then y = 2(2) + 1 = 5.

7Factor the expression x² − 9x + 20.

A.(x − 4)(x − 5)

B.(x + 4)(x + 5)

C.(x − 4)(x + 5)

D.(x − 2)(x − 10)

Explanation: We need two numbers whose product is 20 and sum is −9: −4 and −5. So x² − 9x + 20 = (x − 4)(x − 5).

8Solve x² − 5x − 6 = 0.

A.x = 6 or x = −1

B.x = −6 or x = 1

C.x = 2 or x = 3

D.x = 6 or x = 1

Explanation: Factor: (x − 6)(x + 1) = 0, so x = 6 or x = −1. Check: product 6 × (−1) = −6 ✓ and sum 6 + (−1) = 5, so middle term −5x ✓.

9Expand and simplify (x + 3)(2x − 1).

A.2x² + 5x − 3

B.2x² − 3

C.2x² + 6x − 1

D.2x² + x − 3

Explanation: FOIL: x(2x) + x(−1) + 3(2x) + 3(−1) = 2x² − x + 6x − 3 = 2x² + 5x − 3.

10If a : b = 3 : 4 and b : c = 5 : 6, find a : c.

A.5 : 8

B.2 : 3

C.18 : 20

D.5 : 6

Explanation: Unify b: a:b = 3:4 = 15:20, b:c = 5:6 = 20:24. So a:c = 15:24 = 5:8.

About the Okinawa Public High School Entrance Examination — Mathematics Exam

The Okinawa 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 (国語, 社会, 数学, 理科, 英語), each 50 minutes and 60 points (total 300), sat over two days on 4-5 March 2026 (Day 1: 国語・理科・英語; Day 2: 社会・数学), with 合格発表 on 17 March 2026 and 追検査 on 9 March 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. All prefectural schools use the common paper; no school sets a self-made mathematics paper. Selection runs as 特色選抜 (special-character selection) and 一般選抜 (general selection) on the same schedule; the 一般選抜調査書:学力検査 ratio is 原則 5:5, adjustable 4:6–6:4 per school (Naha, Shuri-Higashi, Chinen, Miyako use 4.5:5.5; Kyuyo, Naha-Kokusai, Shuri, Kaiho, Koyo use 4:6), with 調査書 up to 165 points and 学力検査 300 points; schools may apply 傾斜配点. 普通科通学区域 has 7 zones (国頭・中頭・那覇・島尻・久米島・宮古・八重山), with up to 10% of places from outside a school's zone. There is no single prefecture-wide pass line.

Assessment

50-minute paper worth 60 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 5 March 2026 (Day 2) after the 社会 paper. The five academic-test subjects (国語, 社会, 数学, 理科, 英語) each carry 60 points for a maximum of 300 points. The paper tests 知識・技能 plus 思考力・判断力・表現力.

Time Limit

50 minutes (the 数学 paper is sat on 5 March 2026, Day 2, in the 社会→数学 morning order; the full academic test spans two days: Day 1 3/4 国・理・英, Day 2 3/5 社・数)

Passing Score

No fixed pass mark. Admission is decided by each school's 選抜委員会 using a 調査書:学力検査 ratio that is 原則 5:5, adjustable between 4:6 and 6:4 with the education superintendent's agreement. The academic test (学力検査) is up to 300 points (5 subjects × 60) and the report card (調査書) is up to 165 points. Schools may apply 傾斜配点 (weighted subject scoring). There is no single prefecture-wide pass line; each school decides comprehensively.

Exam Fee

入学考査料 (entrance examination fee) for an Okinawa prefectural high school is ¥2,200 for the 全日制 (full-time) course and ¥950 for the 定時制 (part-time) course. For the 第2次募集 (second recruitment) the fee is ¥1,100 (full-time) and ¥475 (part-time). It is paid once for the whole five-subject 学力検査, not per subject paper. Source: 令和8年度沖縄県立高等学校全日制・定時制課程入学者選抜実施要項. (Okinawa Prefectural Board of Education (沖縄県教育委員会))

Okinawa Public High School Entrance Examination — Mathematics Exam Content Outline

25%

Numbers & Algebraic Expressions (数と式)

Signed arithmetic, fractions, square roots, algebraic manipulation, linear and quadratic equations, and simultaneous equations.

22%

Functions (関数)

Direct and inverse proportionality, linear functions, the quadratic function y=ax², parabola vertex and intercepts, and graph reading.

33%

Geometry (図形)

Triangle congruence and similarity, the Pythagorean theorem, circle properties, inscribed angles, chords, tangent lines, and solid-geometry surface area and volume.

20%

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 Okinawa Public High School Entrance Examination — Mathematics Exam

What You Need to Know

Passing score: No fixed pass mark. Admission is decided by each school's 選抜委員会 using a 調査書:学力検査 ratio that is 原則 5:5, adjustable between 4:6 and 6:4 with the education superintendent's agreement. The academic test (学力検査) is up to 300 points (5 subjects × 60) and the report card (調査書) is up to 165 points. Schools may apply 傾斜配点 (weighted subject scoring). There is no single prefecture-wide pass line; each school decides comprehensively.
Assessment: 50-minute paper worth 60 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 5 March 2026 (Day 2) after the 社会 paper. The five academic-test subjects (国語, 社会, 数学, 理科, 英語) each carry 60 points for a maximum of 300 points. The paper tests 知識・技能 plus 思考力・判断力・表現力.
Time limit: 50 minutes (the 数学 paper is sat on 5 March 2026, Day 2, in the 社会→数学 morning order; the full academic test spans two days: Day 1 3/4 国・理・英, Day 2 3/5 社・数)
Exam fee: 入学考査料 (entrance examination fee) for an Okinawa prefectural high school is ¥2,200 for the 全日制 (full-time) course and ¥950 for the 定時制 (part-time) course. For the 第2次募集 (second recruitment) the fee is ¥1,100 (full-time) and ¥475 (part-time). It is paid once for the whole five-subject 学力検査, not per subject paper. Source: 令和8年度沖縄県立高等学校全日制・定時制課程入学者選抜実施要項.

Keys to Passing

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Okinawa Public High School Entrance Examination — Mathematics Study Tips from Top Performers

1Drill signed arithmetic, fraction operations and square-root simplification to fluency, since the Okinawa paper's short-answer calculation set rewards fast, accurate computation with 根号 and 分数 under a 50-minute limit.

2Practise simultaneous-equation (連立方程式) word problems, including setting up equations from a written condition and checking both equations.

3Learn to read 箱ひげ図 (box plots) and ヒストグラム (histograms) quickly for the 資料の活用 area: identify the median, quartiles and IQR from a box plot, and estimate frequencies from histogram bar areas.

4Master the parabola y=ax²: find the vertex, axis of symmetry and x-intercepts, and combine with 根号 calculations — the 放物線 area commonly mixes these two skills.

5Drill the Pythagorean theorem (三平方の定理) on right triangles, rectangles, squares and solid figures, and practise 相似 and 空間図形 problems, since 図形 is the largest content area at 33% of the paper.

6Use tree diagrams (樹形図) for two-trial probability (two dice, draws without replacement) and be able to list favourable outcomes systematically rather than guessing.

7Manage the 50 minutes across the short calculation items and the longer constructed-response 大問: attempt the calculation items first to bank marks, then allocate remaining time to 連立方程式, 資料, and 放物線 in proportion to their weight.

Frequently Asked Questions

Is this question bank the same as the real Okinawa 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 Okinawa mathematics paper and what is it worth?

It lasts 50 minutes and is scored out of 60 points, one of five subjects that together total 300 points (each subject 60 points). Mathematics is sat on 5 March 2026 (Day 2), after the 社会 paper.

How is the selection structured in 2026?

Okinawa runs 特色選抜 and 一般選抜 on the same schedule. In 一般選抜 each school's 選抜委員会 combines the academic test (学力検査, up to 300 points) with the report card (調査書, up to 165 points) using a 調査書:学力検査 ratio that is 原則 5:5, adjustable 4:6–6:4 per school (e.g. Naha, Shuri-Higashi, Chinen, Miyako use 4.5:5.5; Kyuyo, Naha-Kokusai, Shuri, Kaiho, Koyo use 4:6). There is no prefecture-wide pass line.

How much is the examination fee?

The 入学考査料 (entrance examination fee) for an Okinawa prefectural high school is ¥2,200 for the 全日制 (full-time) course and ¥950 for the 定時制 (part-time) course. For the 第2次募集 it is ¥1,100 (full-time) and ¥475 (part-time). It is paid once for the whole five-subject 学力検査, not per subject paper.

When was the 2026 paper sat and when were results announced?

The 令和8年度学力検査 was held over two days on 4-5 March 2026 (Day 1: 国語・理科・英語; Day 2: 社会・数学), with 追検査 (makeup) on 9 March 2026 and 合格発表 on 17 March 2026 on each school's website.

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).

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