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

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

Practise for the Shimane 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 sat on 4 March 2026. 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 Shimane Public High School Entrance Examination — Mathematics Practice Questions

Try these sample questions to test your Shimane 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: -3 + 8 - 2.

A.3

B.-3

C.5

D.13

Explanation: Work left to right with signed numbers: -3 + 8 = 5, then 5 - 2 = 3.

2Compute: (-4) × (-3) + (-6).

A.6

B.-18

C.18

D.-6

Explanation: (-4) × (-3) = 12 (product of two negatives is positive); 12 + (-6) = 6.

3Compute: (1/2) + (1/3). Express the answer as a single reduced fraction.

A.5/6

B.2/5

C.1/6

D.3/5

Explanation: Common denominator 6: 1/2 = 3/6, 1/3 = 2/6; 3/6 + 2/6 = 5/6, already reduced.

4Compute: (2/3) × (3/4) and write the answer as a reduced fraction.

A.1/2

B.1/3

C.2/3

D.8/9

Explanation: (2/3)×(3/4) = (2×3)/(3×4) = 6/12 = 1/2 after reducing by 6.

5Evaluate √144 − √25.

A.7

B.13

C.119

D.17

Explanation: √144 = 12 and √25 = 5, so 12 − 5 = 7.

6Simplify: 3√2 + 5√2 − √2.

A.7√2

B.8√2

C.15√2

D.7

Explanation: Like surds add by their coefficients: (3 + 5 − 1)√2 = 7√2.

7Rationalise and simplify: 6 / √3.

A.2√3

B.2

C.3√3

D.6√3

Explanation: Multiply numerator and denominator by √3: 6√3 / 3 = 2√3.

8Solve for x: 2x + 5 = 17.

A.x = 6

B.x = 11

C.x = 4

D.x = -6

Explanation: Subtract 5: 2x = 12; divide by 2: x = 6.

9Expand: (x + 3)(x + 4).

A.x² + 7x + 12

B.x² + 12x + 7

C.x² + x + 12

D.2x + 7

Explanation: (x+3)(x+4) = x² + 4x + 3x + 12 = x² + 7x + 12.

10Factorise: x² − 9.

A.(x − 3)(x + 3)

B.(x − 9)(x + 1)

C.(x − 3)²

D.x(x − 9)

Explanation: x² − 9 = x² − 3², a difference of two squares: (x − 3)(x + 3).

About the Shimane Public High School Entrance Examination — Mathematics Exam

The Shimane 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), each worth 50 points (total 250), sat on a single day, 4 March 2026. Selection in 一般選抜 combines the 個人調査報告書 with the 学力検査 at a school-chosen 個人調査報告書:学力検査 ratio (80:20–40:60), with up to 10 points for 面接/実技 and optional 傾斜配点. 特色選抜 runs separately, with a 特色選抜学力検査 in 国語・数学・英語 (各20点, 60 min) in late January for schools using the board-made test. 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. The 令和8年度数学 paper averaged 25.5 points out of 50 (総得点 across five subjects: 124.6/250).

Assessment

50-point paper aligned to the MEXT 数学 Course of Study covering 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), sat on a single day (4 March 2026). Problems are at junior-high graduation level; calculators are not permitted; schools 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 single-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 was on 4 March 2026 (Wed), with 面接等 on 5 March, 追検査 on 10 March, 一般選抜等合格発表 on 13 March, and 第2次募集作文・面接検査 on 19 March (合格発表 24 March). The 特色選抜学力検査 (国・数・英, 60 min) was in late January. For 令和9年度 (2027) the 特色選抜学力検査 is on 20 January 2027, with the main 実施要綱 due around October 2026.

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 the 個人調査報告書 together with the 学力検査 at a school-chosen 個人調査報告書:学力検査 ratio of 80:20, 70:30, 60:40, 50:50, or 40:60 (converted to a 100-point scale), with up to 10 points for 面接/実技 and optional 傾斜配点. There is no single prefecture-wide pass line. Source: 令和8年度島根県公立高等学校入学者選抜実施要綱 / 基本方針, 島根県教育委員会.

Exam Fee

The 入学検定料 is ¥2,200, paid through the internet出願システム (or via a 島根県収入証紙 revenue stamp for paper submission), and is not refundable. Candidates re-applying after a 特色選抜/中高一貫特別選抜 pay only an additional ¥800. Source: 令和8年度島根県公立高等学校入学者選抜実施要綱, 島根県教育委員会. (Shimane Prefectural Board of Education (島根県教育委員会), 学校教育課 (together with 松江市教育委員会 for 松江市立皆美が丘女子高等学校))

Shimane Public High School Entrance Examination — Mathematics Exam Content Outline

25%

Numbers & Expressions (数と式)

Integers, prime factorisation, equations, simultaneous equations, quadratic equations, inequalities, algebraic expressions and identities, polynomials and the Pythagorean theorem in algebra.

25%

Functions (関数)

Linear functions, proportional/inverse proportional relationships, quadratic functions y=ax², parabolas, domain and range, function graphs, and applied problems.

30%

Geometry (図形)

Congruence and similarity, triangles, quadrilaterals, circles, arcs and chords, inscribed and central angles, the Pythagorean theorem, parallel-line proportionality, surface area and volume of solids, constructions and proof.

20%

Data & Probability (資料の活用)

Mean, median, mode and range, histograms, frequency and cumulative frequency distributions, relative frequency, quartiles and box-and-whisker plots, sampling surveys, and probability.

How to Pass the Shimane 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 the 個人調査報告書 together with the 学力検査 at a school-chosen 個人調査報告書:学力検査 ratio of 80:20, 70:30, 60:40, 50:50, or 40:60 (converted to a 100-point scale), with up to 10 points for 面接/実技 and optional 傾斜配点. There is no single prefecture-wide pass line. Source: 令和8年度島根県公立高等学校入学者選抜実施要綱 / 基本方針, 島根県教育委員会.
Assessment: 50-point paper aligned to the MEXT 数学 Course of Study covering 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), sat on a single day (4 March 2026). Problems are at junior-high graduation level; calculators are not permitted; schools 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 single-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 was on 4 March 2026 (Wed), with 面接等 on 5 March, 追検査 on 10 March, 一般選抜等合格発表 on 13 March, and 第2次募集作文・面接検査 on 19 March (合格発表 24 March). The 特色選抜学力検査 (国・数・英, 60 min) was in late January. For 令和9年度 (2027) the 特色選抜学力検査 is on 20 January 2027, with the main 実施要綱 due around October 2026.
Exam fee: The 入学検定料 is ¥2,200, paid through the internet出願システム (or via a 島根県収入証紙 revenue stamp for paper submission), and is not refundable. Candidates re-applying after a 特色選抜/中高一貫特別選抜 pay only an additional ¥800. Source: 令和8年度島根県公立高等学校入学者選抜実施要綱, 島根県教育委員会.

Keys to Passing

Complete 500+ practice questions
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Shimane Public High School Entrance Examination — Mathematics Study Tips from Top Performers

1Master exact arithmetic without a calculator — common fractions, square roots and simplification — because the paper is sat calculator-free.

2For simultaneous and quadratic equations, drill both the mechanical solution and the applied word-problem set-up, since application items test translation from text to equations.

3For geometry, write proofs in the standard assertion-reason (理由と结论) format, citing the congruence/similarity condition explicitly, because 記述式 proof items reward structure.

4For quadratic functions y=ax², memorise how a changes the parabola's width and direction, and practise finding the vertex, axis of symmetry and intersections with a line.

5For 資料の活用, compute mean, median, variance and probability fluently, and practise reading histograms and box-and-whisker plots quickly.

6Time yourself on full 50-minute papers, leaving the longest proof or applied item for last, since pacing is the most common reason for unfinished papers.

Frequently Asked Questions

Is this question bank the same as the real Shimane 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 quadratic functions and trigonometric ratios) and cannot replace writing out your own proofs and calculations in Japanese under timed conditions.

How long is the Shimane 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 are sat on a single day: for 令和8年度 that day was 4 March 2026. The 令和8年度数学 paper averaged 25.5 points out of 50 across all 一般選抜 examinees.

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?

Shimane runs 特色選抜 (総合選抜, 中高一貫特別選抜, スポーツ特別選抜; a 特色選抜学力検査 in 国・数・英, 各20点, 60 min, is held in late January for schools using the board-made test) and 一般選抜 (five-subject 学力検査 on 4 March, 面接等 on 5 March, 追検査 on 10 March, 合格発表 on 13 March). 一般選抜 selects on 個人調査報告書 + 学力検査 at a school-chosen 個人調査報告書:学力検査 ratio (80:20, 70:30, 60:40, 50:50 or 40:60), with up to 10 points for 面接/実技 and optional 傾斜配点. Under-capacity schools hold a 第2次募集 (作文・面接 on 19 March, 合格発表 on 24 March).

Does the 数学 paper include proofs and quadratic functions?

Yes. The MEXT 平成29年中学校学習指導要領数学編 includes proof (証明), quadratic functions (二次関数 y=ax²) and trigonometric ratios (三角比), and Shimane's prefectural paper tests all of these, often in 記述式 form.

How much is the examination fee?

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

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