100+ Free Kumamoto Entrance Mathematics Practice Questions
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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).
2Evaluate (-2) × 3 × (-1).
3Evaluate (-4)².
4Simplify 5x - 2x + 3x.
5Expand -3(x - 4).
6Expand (x + 3)(x - 2).
7Factor x² - 16.
8Factor x² + 7x + 12.
9Factor 3x² - 12 completely.
10Evaluate √49.
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
Numbers and Expressions
Positive and negative numbers, algebraic expressions, expansion and factorization, square roots, and evaluating expressions.
Equations and Inequalities
Linear equations, simultaneous equations, quadratic equations, linear inequalities, and word problems.
Functions
Proportional and inverse-proportional relationships, linear functions, and quadratic functions including rates of change and symmetry.
Plane Geometry
Angles and parallel lines, congruence and similarity, circles, the Pythagorean theorem, and compass-and-straightedge construction.
Solid Geometry and Measurement
Surface areas and volumes of prisms, cylinders, pyramids, cones, and spheres, and rotation of plane figures.
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
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.