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100+ Free Miyagi Entrance Mathematics Practice Questions

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2026 Statistics

Key Facts: Miyagi Entrance Mathematics Exam

50 min / 100 points

Length and maximum score of the Miyagi mathematics paper, one of five subjects in the 第一次募集 common academic test (Reiwa 8 cycle: March 4, 2026)

Miyagi Prefectural Board of Education R8 selection requirements and published academic-test problems

500 + 195 = 695

共通選抜 uses the academic test (500) and report card (調査書, 195: 9 教科 評定, 実技4教科 倍率); school-chosen 学力:調査書 ratio from 7:3 to 3:7; some schools apply weighted scoring (傾斜配点)

Miyagi Prefectural Board of Education R8 selection methods (選抜方法等一覧)

Mar 4, 2026

Reiwa 8 第一次募集 common academic test date; 追試験 March 10; results March 16, 2026 (15:00 web); 第二次募集 test March 23

Miyagi Prefectural Board of Education R8 selection schedule

JPY 2,200

Entrance selection fee for full-time prefectural high schools (JPY 950 part-time/定時制, JPY 200 correspondence/通信制), paid via the ウェブ出願システム; not refunded once paid; 入学金 JPY 5,650

Miyagi Prefectural Board of Education R8 (2026) fee schedule (入学者選抜手数料等)

100

Free original practice questions in this bank

OpenExamPrep

The Miyagi public high school entrance mathematics paper is a 50-minute, 100-point written exam held in the 第一次募集 (dai-ichi / first-stage) common academic test (March 4, 2026), with 4 大問 covering 小問集合, a rotating topic, 箱ひげ図+一次関数, and 平面図形 proofs, set by the Miyagi Prefectural Board of Education. This page offers 100 original English-language practice questions with explanations as a study aid.

Sample Miyagi Entrance Mathematics Practice Questions

Try these sample questions to test your Miyagi Entrance Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate: -3 + 5 - 8
A.-6
B.-10
C.6
D.0
Explanation: Work left to right: -3 + 5 = 2, then 2 - 8 = -6. The result is negative because the final subtraction exceeds the running total.
2Compute: (-2)^3 × (-3)
A.24
B.-24
C.48
D.-48
Explanation: First (-2)^3 = -8. Then (-8) × (-3) = 24. A negative times a negative is positive, so the product is positive 24.
3Find the value of sqrt(144) - sqrt(64).
A.4
B.20
C.8
D.80
Explanation: sqrt(144) = 12 and sqrt(64) = 8, so 12 - 8 = 4. Square roots are evaluated first, then subtracted.
4Simplify 2^3 × 2^2.
A.32
B.16
C.64
D.10
Explanation: Using the law of exponents, 2^3 × 2^2 = 2^(3+2) = 2^5 = 32. Equivalently, 8 × 4 = 32.
5Evaluate -5 × (-2 + 4).
A.-10
B.10
C.-3
D.40
Explanation: First simplify the parentheses: -2 + 4 = 2. Then -5 × 2 = -10. The single negative sign makes the product negative.
6Expand (x + 3)(x - 2).
A.x^2 + x - 6
B.x^2 + x + 6
C.x^2 - x - 6
D.x^2 + 5x - 6
Explanation: Using FOIL: x·x = x^2, x·(-2) = -2x, 3·x = 3x, 3·(-2) = -6. Combining -2x + 3x = x, so the result is x^2 + x - 6.
7Factor x^2 - 7x + 12 completely.
A.(x - 3)(x - 4)
B.(x + 3)(x - 4)
C.(x - 3)(x + 4)
D.(x + 3)(x + 4)
Explanation: We need two numbers whose product is +12 and whose sum is -7. Those numbers are -3 and -4, so x^2 - 7x + 12 = (x - 3)(x - 4).
8Evaluate a^2 - 2ab + b^2 when a = 3 and b = 1.
A.4
B.16
C.2
D.10
Explanation: Substituting: 3^2 - 2(3)(1) + 1^2 = 9 - 6 + 1 = 4. Notice this equals (a - b)^2 = (3 - 1)^2 = 4.
9Simplify 3*sqrt(2) + sqrt(8).
A.5*sqrt(2)
B.3*sqrt(2)
C.sqrt(10)
D.5
Explanation: First simplify sqrt(8) = sqrt(4·2) = 2*sqrt(2). Then 3*sqrt(2) + 2*sqrt(2) = 5*sqrt(2). Like radicals are combined just like like terms.
10Expand (2x - 3)^2.
A.4x^2 - 12x + 9
B.4x^2 + 12x + 9
C.4x^2 - 9
D.4x^2 - 12x - 9
Explanation: Using (a - b)^2 = a^2 - 2ab + b^2: (2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9. The middle term is twice the product, with a negative sign.

About the Miyagi Entrance Mathematics Exam

The Miyagi Public High School Entrance Selection mathematics paper is created by the Miyagi Prefectural Board of Education. The single 50-minute, 100-point written paper, sat in the 第一次募集 (dai-ichi / first-stage) common academic test (Reiwa 8 / 2026 cycle: March 4, 2026, 追試験 March 10, results March 16, 2026), is a constructed-response exam in Japanese on the 2017 MEXT junior-high Course of Study. It has 4 大問: 大問1 小問集合 (basic skills), 大問2 rotating topic (確率/図形/関数/数の性質), 大問3 箱ひげ図+一次関数 (box-and-whisker + linear function), and 大問4 平面図形 (plane geometry proofs). The 共通選抜 uses the academic test (500) and the report card (195), total 695, with a school-chosen 学力:調査書 ratio; there is no fixed pass mark. Miyagi is a single prefecture-wide district (全県一学区). This page provides 100 original English-language practice questions with detailed explanations as a study adaptation — not an official translation, not a reproduction of the official paper, and not a format simulation.

Assessment

The real Miyagi mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects: 国語, 数学, 社会, 英語, 理科), sat in the 第一次募集 (dai-ichi / first-stage) common academic test (Reiwa 8 / 2026 entrance cycle: examination March 4, 2026; 追試験 March 10, 2026; results March 16, 2026 at 15:00 web). It is a written, constructed-response paper in Japanese created by the Miyagi Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study. The paper has 4 大問: 大問1 is a 小問集合 (basic-skills set), 大問2 is a rotating topic (確率 / 図形 / 関数 / 数の性質), 大問3 pairs 箱ひげ図 (box-and-whisker) with 一次関数 (linear function), and 大問4 covers 平面図形 (plane geometry, including congruence/similarity proofs and circles). Miyagi operates a single prefecture-wide district (全県一学区). The 第一次募集 uses 共通選抜 (academic test 500 + 調査書 195 = 695, with school-chosen 学力:調査書 ratio from 7:3 to 3:7) and 特色選抜 (adds 面接・実技・作文). The 調査書 uses 9 教科 評定 (195 points, 実技4教科 倍率); R8 removed the 欠席状況欄. If quotas are unfilled, a 第二次募集 follows (出願 March 17–19, test March 23, results March 23/24, 2026). R8 introduced a ウェブ出願システム (cashless: credit card, PayPay, conbini, Pay-easy; 収入証紙廃止). There is no fixed pass mark. This local bank is an English-language MCQ study adaptation providing 100 original practice items.

Time Limit

50 minutes for the mathematics subject paper (Reiwa 8 / 2026 第一次募集 common academic test on March 4, 2026; 追試験 March 10, 2026; results March 16, 2026).

Passing Score

No fixed pass mark; scored out of 100 points (500 total across 5 subjects). The 共通選抜 (common selection) uses the academic test (500 points) and the report card (調査書, 195 points: 9 教科 評定, 実技4教科 倍率), total 695. Each school chooses a 学力:調査書 ratio from 7:3, 6:4, 5:5, 4:6, or 3:7. Some schools apply weighted scoring (傾斜配点) to specific subjects. The 特色選抜 adds 面接・実技・作文 (school-set; some 傾斜配点/倍率). There is no single pass line.

Exam Fee

JPY 2,200 entrance selection fee (入学者選抜手数料) for full-time prefectural high schools (JPY 950 part-time/定時制, JPY 200 correspondence/通信制), paid through the official ウェブ出願システム (Web application system — credit card, PayPay, conbini, Pay-easy) during the application period; once paid, the fee is not refunded. 入学金 (entrance fee) is JPY 5,650 for 全日制. The fee is set out in the official Miyagi selection requirements. (Miyagi Prefectural Board of Education (宮城県教育委員会 / 教育庁高校教育課教育指導第二班))

Miyagi Entrance Mathematics Exam Content Outline

About 13% of this practice bank

Numbers and Expressions

Positive and negative numbers, algebraic expressions, expansion and factorization, square roots, and evaluating expressions.

About 17% of this practice bank

Equations and Inequalities

Linear equations, simultaneous equations, quadratic equations, linear inequalities, and word problems.

About 20% of this practice bank

Functions

Proportional and inverse-proportional relationships, linear functions, and quadratic functions including rates of change and symmetry.

About 20% of this practice bank

Plane Geometry

Angles and parallel lines, congruence and similarity, circles, 30-60-90 triangles, the Pythagorean theorem, tangent lines, and compass-and-straightedge construction (作図).

About 11% of this practice bank

Solid Geometry and Measurement

Surface areas and volumes of prisms, cylinders, pyramids, cones, and spheres, and rotation of plane figures.

About 19% of this practice bank

Data Analysis and Probability

Counting outcomes, probability with and without replacement, the complement rule, tree diagrams, representative values, frequency distribution, quartiles (四分位数), and box-and-whisker plots (箱ひげ図).

How to Pass the Miyagi Entrance Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark; scored out of 100 points (500 total across 5 subjects). The 共通選抜 (common selection) uses the academic test (500 points) and the report card (調査書, 195 points: 9 教科 評定, 実技4教科 倍率), total 695. Each school chooses a 学力:調査書 ratio from 7:3, 6:4, 5:5, 4:6, or 3:7. Some schools apply weighted scoring (傾斜配点) to specific subjects. The 特色選抜 adds 面接・実技・作文 (school-set; some 傾斜配点/倍率). There is no single pass line.
  • Assessment: The real Miyagi mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects: 国語, 数学, 社会, 英語, 理科), sat in the 第一次募集 (dai-ichi / first-stage) common academic test (Reiwa 8 / 2026 entrance cycle: examination March 4, 2026; 追試験 March 10, 2026; results March 16, 2026 at 15:00 web). It is a written, constructed-response paper in Japanese created by the Miyagi Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study. The paper has 4 大問: 大問1 is a 小問集合 (basic-skills set), 大問2 is a rotating topic (確率 / 図形 / 関数 / 数の性質), 大問3 pairs 箱ひげ図 (box-and-whisker) with 一次関数 (linear function), and 大問4 covers 平面図形 (plane geometry, including congruence/similarity proofs and circles). Miyagi operates a single prefecture-wide district (全県一学区). The 第一次募集 uses 共通選抜 (academic test 500 + 調査書 195 = 695, with school-chosen 学力:調査書 ratio from 7:3 to 3:7) and 特色選抜 (adds 面接・実技・作文). The 調査書 uses 9 教科 評定 (195 points, 実技4教科 倍率); R8 removed the 欠席状況欄. If quotas are unfilled, a 第二次募集 follows (出願 March 17–19, test March 23, results March 23/24, 2026). R8 introduced a ウェブ出願システム (cashless: credit card, PayPay, conbini, Pay-easy; 収入証紙廃止). There is no fixed pass mark. This local bank is an English-language MCQ study adaptation providing 100 original practice items.
  • Time limit: 50 minutes for the mathematics subject paper (Reiwa 8 / 2026 第一次募集 common academic test on March 4, 2026; 追試験 March 10, 2026; results March 16, 2026).
  • Exam fee: JPY 2,200 entrance selection fee (入学者選抜手数料) for full-time prefectural high schools (JPY 950 part-time/定時制, JPY 200 correspondence/通信制), paid through the official ウェブ出願システム (Web application system — credit card, PayPay, conbini, Pay-easy) during the application period; once paid, the fee is not refunded. 入学金 (entrance fee) is JPY 5,650 for 全日制. The fee is set out in the official Miyagi selection requirements.

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

Miyagi Entrance Mathematics Study Tips from Top Performers

1Secure the 小問集合 first — signed numbers, square-root simplification, expansion, factorization, and 四分位数 (quartile computation) are speed-critical and account for roughly 40% of the paper; fast accuracy here builds the base for the harder later questions.
2Practice the written plane-geometry proof (図形の証明) — it appears regularly in 大問4; write out congruence/similarity statements with the correct three-pair conditions (SSS/SAS/ASA and the similarity ratios), and rehearse stating the conclusion explicitly.
3For probability, draw tree diagrams (樹形図) for both with-replacement and without-replacement scenarios, and use the complement rule P(not A) = 1 − P(A) when the complement is easier to count.
4Master cylinder and cone volume and surface area, especially the cone lateral area πrl (with slant height from l² = r² + h²); the solid-geometry question regularly combines both.
5Know the 30-60-90 triangle side ratios (1 : √3 : 2) cold and combine them with similarity proofs and the inscribed-angle theorem (円周角の定理).
6For 箱ひげ図 (box-and-whisker) and 一次関数 (linear function) in 大問3, practice computing Q1, Q3, and IQR from both odd and even sample sizes, reading box plots, and combining the data with a linear function to find intersection points.

Frequently Asked Questions

Is the real Miyagi mathematics entrance paper multiple-choice?

No. The Miyagi 第一次募集 academic test is a written, constructed-response paper in Japanese — students write their own answers and proof steps, not mark-sheet bubbles. The paper has 4 大問 including a 小問集合, a rotating topic, 箱ひげ図+一次関数, and 平面図形 proofs. This bank is an English-language four-option MCQ study adaptation, not official past problems or a reproduction of the official layout: real selection items are in Japanese, require written working, and the official paper's exact item count is not published.

Are these questions official past exam problems?

No. Although the Miyagi Prefectural Board of Education publishes the actual examination problems and model answers (学力検査問題及び正答表), it does not publish them as a four-option multiple-choice set. This bank is an original English-language MCQ study adaptation aligned to the 2017 MEXT junior-high Course of Study, covering equations, functions, geometry, and probability with worked-solution reasoning — not an official translation or format simulation.

How long is the mathematics paper and what is the maximum score?

The mathematics paper is a single 50-minute exam scored out of 100 points, sat in the 第一次募集 (dai-ichi / first-stage) common academic test. The five academic-test subjects (国語, 数学, 社会, 英語, 理科) total 500 points and are combined with the 195-point report card (調査書) for a total of 695 in the 共通選抜. In the Reiwa 8 (2026) cycle the academic test is held on March 4, 2026, with 追試験 March 10 and results on March 16, 2026.

How are the academic test and report card combined in Miyagi's selection?

Miyagi's 共通選抜 (common selection) uses the academic test (500 points) and the report card (調査書, 195 points: 9 教科 評定, 実技4教科 倍率), total 695. Each school chooses a 学力:調査書 ratio from 7:3, 6:4, 5:5, 4:6, or 3:7. Some schools apply weighted scoring (傾斜配点) to specific subjects. The 特色選抜 adds 面接・実技・作文 (school-set; some 傾斜配点/倍率). There is no fixed pass mark. If quotas are unfilled, a 第二次募集 follows.

Does Miyagi use a single prefecture-wide school district?

Yes. Miyagi operates as 全県一学区 — a single prefecture-wide district. Students may apply to any prefectural high school in Miyagi, regardless of where they live. This differs from prefectures that restrict students to their local school district.

Is the Miyagi selection system changing for 2027?

The framework carries over to Reiwa 9 (2027): the 第一次募集 academic test is scheduled for March 3, 2027, 追試験 March 9, 2027, and results March 15, 2027. The 5-subject academic test (5 × 100 = 500) and report-card framework remain the same, with the 共通選抜/特色選抜 and first/second 募集 structure continuing.

Are quartiles (四分位数) and box-and-whisker plots (箱ひげ図) included in the curriculum?

Yes. Quartiles (四分位数) and box-and-whisker plots (箱ひげ図) were added to the junior-high mathematics curriculum under the 2017 (Heisei 29) MEXT Course of Study. Miyagi's 大問3 regularly pairs 箱ひげ図 with 一次関数 (linear function). This bank includes quartile computation, IQR, and outlier-detection questions to reflect that update.