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100+ Free Kumamoto Entrance Mathematics Practice Questions

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2026 Statistics

Key Facts: Kumamoto Entrance Mathematics Exam

50 min / 50 points

Length and maximum score of the Kumamoto mathematics paper, one of five subjects in the later-selection academic test (Reiwa 9 cycle: March 4–5, 2027)

Kumamoto Prefectural Board of Education R8 selection requirements (subject timing and marks) and R9 basic policy (schedule)

250 + 180

Later (ippan) general selection uses the academic test (250) and report card (chōsasho, 180), with the five academic subjects' ratings corrected (hosei) by the test scores; some schools apply weighted scoring (keisha-ka)

Kumamoto Prefectural Board of Education R8 selection requirements (subject timing and marks) and R9 basic policy (schedule)

Mar 4–5, 2027

Reiwa 9 later-selection academic test dates; results March 12, 2027; application window February 12–17, 2027

Kumamoto Prefectural Board of Education R9 basic policy (published 9 June 2026) and Benesse Kumamoto R9 entrance schedule

JPY 2,200

Entrance selection fee for full-time prefectural high schools (JPY 950 part-time/teijisei), paid through the official online application site; not refunded once paid

Kumamoto Prefectural Board of Education R8 (2026) selection requirements

100

Free original practice questions in this bank

OpenExamPrep

The Kumamoto public high school entrance mathematics paper is a 50-minute, 50-point written exam held on Day 2 of the later (ippan) general selection academic test (March 4–5, 2027), covering equations, functions, plane and solid geometry, and probability, set by the Kumamoto Prefectural Board of Education. This page offers 100 original English-language practice questions with explanations as a study aid.

Sample Kumamoto Entrance Mathematics Practice Questions

Try these sample questions to test your Kumamoto 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 - (-2).
A.4
B.0
C.6
D.-6
Explanation: Rewrite -(-2) as +2, so the expression becomes -3 + 5 + 2 = 4. Working left to right, -3 + 5 = 2, then 2 + 2 = 4.
2Evaluate (-2) × 3 × (-1).
A.6
B.-6
C.8
D.-8
Explanation: There are two negative factors, so the product is positive: (-2) × 3 = -6, then -6 × (-1) = 6.
3Evaluate (-4)².
A.16
B.-16
C.8
D.-8
Explanation: The exponent applies to -4 as a whole: (-4) × (-4) = 16. A square is always non-negative.
4Simplify 5x - 2x + 3x.
A.6x
B.4x
C.6
D.10x
Explanation: Combine the coefficients of like terms: 5 - 2 + 3 = 6, so the expression is 6x.
5Expand -3(x - 4).
A.-3x + 12
B.-3x - 12
C.3x + 12
D.-3x - 4
Explanation: Distribute -3 to both terms: -3 × x = -3x and -3 × (-4) = +12, giving -3x + 12.
6Expand (x + 3)(x - 2).
A.x² + x - 6
B.x² - x - 6
C.x² + 5x - 6
D.x² + x + 6
Explanation: Using FOIL: x·x = x², x·(-2) = -2x, 3·x = 3x, 3·(-2) = -6. Combine -2x + 3x = x, giving x² + x - 6.
7Factor x² - 16.
A.(x + 4)(x - 4)
B.(x - 4)²
C.(x + 4)²
D.(x + 2)(x - 8)
Explanation: This is a difference of squares: a² - b² = (a + b)(a - b) with a = x and b = 4, so x² - 16 = (x + 4)(x - 4).
8Factor x² + 7x + 12.
A.(x + 3)(x + 4)
B.(x + 2)(x + 6)
C.(x + 1)(x + 12)
D.(x - 3)(x - 4)
Explanation: Find two numbers that multiply to 12 and add to 7: those are 3 and 4, so x² + 7x + 12 = (x + 3)(x + 4).
9Factor 3x² - 12 completely.
A.3(x + 2)(x - 2)
B.3(x - 2)²
C.3(x + 2)²
D.(3x - 6)(3x + 6)
Explanation: First factor out 3: 3(x² - 4). Then x² - 4 is a difference of squares: 3(x + 2)(x - 2).
10Evaluate √49.
A.7
B.14
C.24
D.√7
Explanation: The principal square root of 49 is the non-negative number whose square is 49, which is 7.

About the Kumamoto Entrance Mathematics Exam

The Kumamoto Public High School Entrance Selection mathematics paper is created by the Kumamoto Prefectural Board of Education. The single 50-minute, 50-point written paper, sat on Day 2 of the later (ippan) general selection academic test (Reiwa 9 / 2027 cycle: March 4–5, 2027), 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, the Pythagorean theorem, compass-and-straightedge construction), solid geometry, and probability. From the 2026 (Reiwa 8) cycle the former A/B school-choice problems were abolished and all prefectural schools (except Kumamoto City schools) use a common paper. The later selection uses the academic test (250) and the report card (180); 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 Kumamoto mathematics examination is a 50-minute paper scored out of 50 points (250 total across five subjects: kokugo, social studies, mathematics, science, English), sat on Day 2 (11:10–12:00) of the later (ippan) general selection academic test (Reiwa 9 / 2027 entrance cycle: examination March 4–5, 2027; results March 12, 2027). It is a written, constructed-response paper in Japanese created by the Kumamoto Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study. From the 2026 (Reiwa 8) cycle the former A/B school-choice problems for mathematics were abolished and all prefectural schools (except Kumamoto City schools) use a common paper. The paper typically has six big questions: a small-question set (basic calculation, about 26 of 50 points), data utilization, solid geometry, functions and geometry, and plane geometry with compass-and-straightedge construction (sakuzu) and congruence/similarity proofs appearing every year. The later (ippan) general selection uses the academic test (250 points) and the report card (chōsasho, 180 points); the five academic subjects' report-card ratings are corrected (hosei) using the academic-test scores and ranked within each school's quota, and some schools apply weighted scoring (keisha-ka) to specific subjects. 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 9 / 2027 later-selection academic test on March 4–5, 2027; results March 12, 2027). In the published Reiwa 8 timetable mathematics ran 11:10–12:00 on Day 2.

Passing Score

No fixed pass mark; scored out of 50 points (250 total across 5 subjects). The later (ippan) general selection uses the academic test (250) and the report card (chōsasho, 180); the five academic subjects' report-card ratings are corrected (hosei) using the academic-test scores, and both rankings must fall within the quota for first-stage admission. Under the prefecture's special-scoring rule the mathematics score is doubled for risū-ka science-and-mathematics departments and the futsū-ka risū course (for example, Kumamoto Second HS risū-ka doubles mathematics and science; Tōryō HS risū-ka doubles mathematics). Selection is by ranking within each school's quota.

Exam Fee

JPY 2,200 entrance selection fee (nyūgaku sentaku tesūryō) for full-time prefectural high schools (JPY 950 part-time/teijisei), paid through the official online application site (shutsugan sait) during the application period; once paid, the fee is not refunded. The fee is set out in the official Kumamoto selection requirements (nyūgakusha sentaku yōkō). (Kumamoto Prefectural Board of Education (熊本県教育委員会))

Kumamoto 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, the Pythagorean theorem, and compass-and-straightedge construction.

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, and representative values.

How to Pass the Kumamoto 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 later (ippan) general selection uses the academic test (250) and the report card (chōsasho, 180); the five academic subjects' report-card ratings are corrected (hosei) using the academic-test scores, and both rankings must fall within the quota for first-stage admission. Under the prefecture's special-scoring rule the mathematics score is doubled for risū-ka science-and-mathematics departments and the futsū-ka risū course (for example, Kumamoto Second HS risū-ka doubles mathematics and science; Tōryō HS risū-ka doubles mathematics). Selection is by ranking within each school's quota.
  • Assessment: The real Kumamoto mathematics examination is a 50-minute paper scored out of 50 points (250 total across five subjects: kokugo, social studies, mathematics, science, English), sat on Day 2 (11:10–12:00) of the later (ippan) general selection academic test (Reiwa 9 / 2027 entrance cycle: examination March 4–5, 2027; results March 12, 2027). It is a written, constructed-response paper in Japanese created by the Kumamoto Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study. From the 2026 (Reiwa 8) cycle the former A/B school-choice problems for mathematics were abolished and all prefectural schools (except Kumamoto City schools) use a common paper. The paper typically has six big questions: a small-question set (basic calculation, about 26 of 50 points), data utilization, solid geometry, functions and geometry, and plane geometry with compass-and-straightedge construction (sakuzu) and congruence/similarity proofs appearing every year. The later (ippan) general selection uses the academic test (250 points) and the report card (chōsasho, 180 points); the five academic subjects' report-card ratings are corrected (hosei) using the academic-test scores and ranked within each school's quota, and some schools apply weighted scoring (keisha-ka) to specific subjects. 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 9 / 2027 later-selection academic test on March 4–5, 2027; results March 12, 2027). In the published Reiwa 8 timetable mathematics ran 11:10–12:00 on Day 2.
  • Exam fee: JPY 2,200 entrance selection fee (nyūgaku sentaku tesūryō) for full-time prefectural high schools (JPY 950 part-time/teijisei), paid through the official online application site (shutsugan sait) during the application period; once paid, the fee is not refunded. The fee is set out in the official Kumamoto selection requirements (nyūgakusha sentaku yōkō).

Keys to Passing

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

Kumamoto Entrance Mathematics Study Tips from Top Performers

1Secure the small-question set first — about 26 of the 50 points come from the first two big questions, so drill signed numbers, square-root simplification, expansion, and factorization for speed and accuracy before tackling the harder later questions.
2For geometry, learn the congruence and similarity conditions (SSS, SAS, ASA; ratio of areas = square of the ratio of sides), the inscribed-angle theorem, tangent-radius perpendicularity, and the Pythagorean theorem, and write the proof flow out fully — Kumamoto tests compass-and-straightedge construction (sakuzu) and plane-geometry proofs every year.
3Be fluent converting between a linear function's slope-intercept form and its graph, and know how to find the axis of symmetry and vertex of y = ax² — Kumamoto regularly tests applied functions alongside geometry in the functions-and-geometry big question.
4If a proof in the final plane-geometry question is hard, use the stated result to attempt the follow-up part — Kumamoto's big-question (2) can often be solved from the result of (1) even when the proof itself is difficult, so do not abandon the whole question.
5Understand that the later selection uses the academic test (250) and report card (180) with the five academic subjects' ratings corrected by the test scores — some schools weight mathematics (keisha-ka), so a strong math score can complement your report card; check each school's rules.

Frequently Asked Questions

Is the real Kumamoto mathematics entrance paper multiple-choice?

No. The Kumamoto academic test is a written, constructed-response paper in Japanese — students write their own answers and proof steps, not mark-sheet bubbles. 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 Kumamoto Prefectural Board of Education publishes the actual R8 examination problems and model answers, 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 50 points, sat on Day 2 of the two-day academic test; under the published Reiwa 8 timetable it ran 11:10–12:00. The five academic-test subjects total 250 points and are combined with the 180-point report card in the later (ippan) general selection. In the Reiwa 9 (2027) cycle the academic test is held on March 4–5, 2027, with results on March 12, 2027.

Did the Kumamoto mathematics paper change recently?

Yes. From the 2026 (Reiwa 8) cycle the former A/B school-choice problems for mathematics (and English) were abolished, so all prefectural schools — except Kumamoto City schools — now sit a common paper. The paper still typically has six big questions: a small-question set (about 26 of 50 points), data utilization, solid geometry, functions and geometry, and plane geometry, with compass-and-straightedge construction (sakuzu) and congruence/similarity proofs appearing every year.

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

Kumamoto's later (ippan) general selection uses the academic test (250 points) and the report card (chōsasho, 180 points). The five academic subjects' report-card ratings are corrected (hosei) using the academic-test scores; candidates whose academic-test rank and report-card rank both fall within the quota are admitted in the first stage. Some schools apply weighted scoring (keisha-ka) to specific subjects. There is no fixed pass mark.

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.

What is the Reiwa 9 (2027) examination and results schedule?

For the Reiwa 9 (2027 entrance) cycle, the earlier (tokushoku) selection application window is January 20–25, 2027 with the test on February 2, 2027. The later (ippan) general selection application window is February 12–17, 2027, the academic test is held March 4–5, 2027, and results are announced March 12, 2027. The JPY 2,200 entrance selection fee (JPY 950 part-time) is set out in the official Kumamoto selection requirements.