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100+ Free Mie Entrance Mathematics Practice Questions

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2026 Statistics

Key Facts: Mie Entrance Mathematics Exam

45 min / 50 points

Length and maximum score of the Mie mathematics paper, one of five subjects in the 後期選抜 common academic test (Reiwa 8 cycle: March 10, 2026)

Mie Prefectural Board of Education R8 selection requirements (実施要項) and published academic-test problems

250 + 45 = 295

後期選抜 uses the academic test (250) and report card (調査書, 45: 中3, 9 教科 × 5 段階評定); 3-stage selection; some schools apply weighted scoring (傾斜配点)

Mie Prefectural Board of Education R8 selection requirements (実施方針)

Mar 10, 2026

Reiwa 8 後期選抜 common academic test date; results March 17, 2026; 前期 test February 3–4, 2026, results February 13, 2026

Mie Prefectural Board of Education R8 selection schedule and Benesse Mie entrance schedule

JPY 2,200

Entrance selection fee for full-time prefectural high schools (JPY 950 part-time/定時制), paid via the official Web application system; not refunded once paid

Mie Prefectural Board of Education R8 (2026) selection requirements (実施要項)

100

Free original practice questions in this bank

OpenExamPrep

The Mie public high school entrance mathematics paper is a 45-minute, 50-point written exam held in the 後期選抜 (kōki / second-stage) common academic test (March 10, 2026), covering equations, functions, plane and solid geometry, and probability, set by the Mie Prefectural Board of Education. This page offers 100 original English-language practice questions with explanations as a study aid.

Sample Mie Entrance Mathematics Practice Questions

Try these sample questions to test your Mie 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 removes more than 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.
10Compute 1/2 + 1/3 - 1/6.
A.2/3
B.1
C.5/6
D.1/6
Explanation: The common denominator is 6: 3/6 + 2/6 - 1/6 = 4/6 = 2/3. Reduce the fraction to lowest terms.

About the Mie Entrance Mathematics Exam

The Mie Public High School Entrance Selection mathematics paper is created by the Mie Prefectural Board of Education. The single 45-minute, 50-point written paper, sat in the 後期選抜 (kōki / second-stage) common academic test (Reiwa 8 / 2026 cycle: March 10, 2026, results March 17, 2026), is a constructed-response exam in Japanese on the 2017 MEXT junior-high Course of Study, covering numbers and expressions, equations and inequalities, linear and quadratic functions, plane geometry (congruence, similarity, circles, 30-60-90 triangles, the Pythagorean theorem, compass-and-straightedge construction, and a written proof), solid geometry, and probability incl. quartiles (四分位数). The 後期選抜 uses the academic test (250) and the report card (45), total 295, with 3-stage selection; there is no fixed pass mark. 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 Mie mathematics examination is a 45-minute paper scored out of 50 points (250 total across five subjects: 国語, 数学, 社会, 英語, 理科), sat in the 後期選抜 (kōki / second-stage) common academic test (Reiwa 8 / 2026 entrance cycle: examination March 10, 2026; results March 17, 2026). It is a written, constructed-response paper in Japanese created by the Mie Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study. The 後期選抜 common paper is uniform across the prefecture; a basic-skills 小問集合 accounts for roughly 40% of the score, and a written plane-geometry proof (図形の証明) appears regularly, alongside functions, probability (tree diagrams), and solid geometry. The 後期選抜 uses the academic test (250 points) and the report card (調査書, 45 points: 中3, 9 教科 × 5 段階評定), total 295, with 3-stage selection. Some schools apply weighted scoring (傾斜配点). There is no fixed pass mark. This local bank is an English-language MCQ study adaptation providing 100 original practice items.

Time Limit

45 minutes for the mathematics subject paper (Reiwa 8 / 2026 後期選抜 common academic test on March 10, 2026; results March 17, 2026).

Passing Score

No fixed pass mark; scored out of 50 points (250 total across 5 subjects). The 後期選抜 (kōki / second-stage) selection uses the academic test (250) and the report card (調査書, 45 points: 中3, 9 教科 × 5 段階評定), total 295. Selection proceeds in 3 stages: first, from those selected by the report card, about 80% of the quota is taken in descending academic-test score; then half of the remaining quota from the report-card-selected pool by test score; then the rest using each school's 'especially-weighted selection materials' (特に重視する選抜資料等). Some schools apply weighted scoring (傾斜配点) to specific subjects. There is no single pass line.

Exam Fee

JPY 2,200 entrance selection fee (入学選抜手数料) for full-time prefectural high schools (JPY 950 part-time/定時制), paid through the official Web application system (電子納付 or 三重県収入証紙) during the application period; once paid, the fee is not refunded. The fee is set out in the official Mie selection requirements (実施要項). (Mie Prefectural Board of Education (三重県教育委員会))

Mie 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 18% of this practice bank

Equations and Inequalities

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

About 21% of this practice bank

Functions

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

About 19% of this practice bank

Plane Geometry

Angles and parallel lines, congruence and similarity, circles, 30-60-90 triangles, the Pythagorean theorem, 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 18% of this practice bank

Data Analysis and Probability

Counting outcomes, probability with and without replacement, the complement rule, tree diagrams, representative values, frequency distribution, and quartiles (四分位数).

How to Pass the Mie Entrance Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark; scored out of 50 points (250 total across 5 subjects). The 後期選抜 (kōki / second-stage) selection uses the academic test (250) and the report card (調査書, 45 points: 中3, 9 教科 × 5 段階評定), total 295. Selection proceeds in 3 stages: first, from those selected by the report card, about 80% of the quota is taken in descending academic-test score; then half of the remaining quota from the report-card-selected pool by test score; then the rest using each school's 'especially-weighted selection materials' (特に重視する選抜資料等). Some schools apply weighted scoring (傾斜配点) to specific subjects. There is no single pass line.
  • Assessment: The real Mie mathematics examination is a 45-minute paper scored out of 50 points (250 total across five subjects: 国語, 数学, 社会, 英語, 理科), sat in the 後期選抜 (kōki / second-stage) common academic test (Reiwa 8 / 2026 entrance cycle: examination March 10, 2026; results March 17, 2026). It is a written, constructed-response paper in Japanese created by the Mie Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study. The 後期選抜 common paper is uniform across the prefecture; a basic-skills 小問集合 accounts for roughly 40% of the score, and a written plane-geometry proof (図形の証明) appears regularly, alongside functions, probability (tree diagrams), and solid geometry. The 後期選抜 uses the academic test (250 points) and the report card (調査書, 45 points: 中3, 9 教科 × 5 段階評定), total 295, with 3-stage selection. Some schools apply weighted scoring (傾斜配点). There is no fixed pass mark. This local bank is an English-language MCQ study adaptation providing 100 original practice items.
  • Time limit: 45 minutes for the mathematics subject paper (Reiwa 8 / 2026 後期選抜 common academic test on March 10, 2026; results March 17, 2026).
  • Exam fee: JPY 2,200 entrance selection fee (入学選抜手数料) for full-time prefectural high schools (JPY 950 part-time/定時制), paid through the official Web application system (電子納付 or 三重県収入証紙) during the application period; once paid, the fee is not refunded. The fee is set out in the official Mie selection requirements (実施要項).

Keys to Passing

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

Mie 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 Mie; 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 quadratic functions y = ax², practice finding the axis of symmetry, the vertex, and the rate of change between two x-values; Mie's function question often pairs a moving point with a region change.

Frequently Asked Questions

Is the real Mie mathematics entrance paper multiple-choice?

No. The Mie 後期選抜 academic test is a written, constructed-response paper in Japanese — students write their own answers and proof steps, not mark-sheet bubbles, and a written plane-geometry proof (図形の証明) appears regularly. 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 Mie Prefectural Board of Education publishes the actual examination problems and model answers (学力検査問題等), 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 45-minute exam scored out of 50 points, sat in the 後期選抜 (kōki / second-stage) common academic test. The five academic-test subjects (国語, 数学, 社会, 英語, 理科) total 250 points and are combined with the 45-point report card (調査書) for a total of 295. In the Reiwa 8 (2026) cycle the academic test is held on March 10, 2026, with results on March 17, 2026.

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

Mie's 後期選抜 uses the academic test (250 points) and the report card (調査書, 45 points: 中3, 9 教科 × 5 段階評定), total 295. Selection proceeds in 3 stages: roughly 80% of the quota is filled from the report-card-selected pool by descending academic-test score; then half of the remaining quota from that pool by test score; then the remainder using each school's 'especially-weighted selection materials' (特に重視する選抜資料等). Some schools apply weighted scoring (傾斜配点) to specific subjects. There is no fixed pass mark.

Is the Mie selection system changing for 2027?

Mie keeps the two-stage 前期選抜 + 後期選抜 structure for Reiwa 9 (2027). New for 2027 is a フレキシブル特別枠 (flexible special quota) tied to the みえ版フレキシブル高校 initiative, which allows 併修 (concurrent enrollment) with 定時制・通信制 at some 全日制 schools. The Reiwa 9 後期 academic test is scheduled for March 9, 2027, with results March 16, 2027, and 前期 on February 2–3, 2027. The common 5-subject academic test (5 × 50 = 250) and report-card framework carry over.

Does this bank include real calculation questions?

Yes. A substantial share of the 100 items are genuine worked-calculation questions with numeric answers — solving simultaneous and quadratic equations, evaluating functions at a point, applying the Pythagorean theorem and similarity ratios, computing volumes and surface areas, and counting probability outcomes — not just definitional recall.

Are quartiles (四分位数) included in the curriculum?

Yes. Quartiles (四分位数) were added to the junior-high mathematics curriculum under the 2017 (Heisei 29) MEXT Course of Study and appear in the basic-skills 小問集合. This bank includes quartile computation questions to reflect that update.