Free Practice Questions for Kochi Entrance Mathematics
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Key Facts: Kochi Entrance Mathematics Exam
50 min / 50 points
Length and maximum score of the Kochi mathematics paper (A-schedule academic test; Reiwa 9 cycle March 3-4, 2027)
Kochi Prefectural Board of Education R8 selection guidelines and Benesse
250 + 260 (roughly equal)
Academic test (250) and report card (260) treated roughly equally (hobo dōtō) in A-schedule selection, with statement of intent, interview, and, for some schools, a practical test
Kochi Prefectural Board of Education selection guidelines and Benesse
Mar 3-4, 2027
Reiwa 9 A-schedule academic test dates; results March 12, 2027; application window February 1-3, 2027
Benesse Kochi R9 entrance schedule (czemi.benesse.ne.jp) and Kochi selection guidelines
JPY 2,200
Entrance examination fee for full-time prefectural high schools (JPY 950 part-time/teijisei), paid with a Kochi prefectural revenue stamp; hardship exemptions available by prefectural ordinance
Kochi Prefectural Board of Education entrance selection guidelines
100
Free original practice questions in this bank
OpenExamPrep
The Kochi public high school entrance mathematics paper is a 50-minute, 50-point written exam held in the A-schedule academic test (March 3-4, 2027), covering equations, functions, plane and solid geometry, and probability, set by the Kochi Prefectural Board of Education. This page offers 100 original English-language practice questions with explanations as a study aid.
Sample Kochi Entrance Mathematics Practice Questions
Try these sample questions to review concepts for the Kochi Entrance Mathematics exam. 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)^2.
3Evaluate -(-3)^2.
4Simplify √72 to the form a√b.
5Compute √50 × √18.
6Expand √2(√3 + √2).
7Evaluate (2 + √3)(2 - √3).
8Expand (x + 3)(x - 4).
9Factorize x^2 - 7x + 12.
10Factorize 2x^2 - 5x - 3.
About the Kochi Entrance Mathematics Exam
The Kochi Public High School Entrance Selection mathematics paper is created by the Kochi Prefectural Board of Education. The single 50-minute, 50-point written paper, sat in the A-schedule academic test (Reiwa 9 / 2027 cycle: March 3-4, 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 and solid geometry, and probability. Admission treats the academic test (250) and the report card (260) roughly equally, together with the statement of intent, interview, and, for some schools, a practical test; 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.
Exam sponsor: Kochi Prefectural Board of Education (高知県教育委員会). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.
Assessment
The real Kochi mathematics examination is a 50-minute paper scored out of 50 points (250 total across five subjects: kokugo, social studies, mathematics, science, English), sat in the A-schedule academic test (Reiwa 9 / 2027 entrance cycle: examination March 3-4, 2027; results March 12, 2027). It is a written, constructed-response paper in Japanese created by the Kochi Prefectural Board of Education on the 2017 (Heisei 29) 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. Admission (A-schedule main selection) treats the academic test (250 points) and the report card (chōsasho, 260 points) roughly equally (hobo dōtō), together with the statement of intent (shigan riyūsho), an individual interview, and — for some schools — a practical test (jitsugi kensa); some schools apply weighted scoring (keisha-ka) to specific subjects. There is no fixed pass mark; selection is by ranking within each school's quota. 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 A-schedule academic test on March 3-4, 2027; results March 12, 2027)
Passing Score
No fixed pass mark; scored out of 50 points (250 total across 5 subjects). The A-schedule main selection treats the academic test (250) and the report card (260) roughly equally, combined with the statement of intent, interview, and, for some schools, a practical test; some schools apply weighted scoring (keisha-ka) to specific subjects. Selection is by ranking within each school's quota.
Exam / Certification Fees
JPY 2,200 entrance examination fee (nyūgaku tesuryō) for full-time prefectural high schools (JPY 950 part-time/teijisei), paid with a Kochi prefectural revenue stamp; Kochi Commercial High School (administered by the Kochi City Board of Education) is paid in cash or postal money order. A prefectural ordinance provides non-collection and exemption for welfare-recipient and economic-hardship applicants.
Exam sponsor websiteFees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.
Official sources
- Kochi Prefectural Board of Education — Reiwa 8 Public High School Entrance Selection (令和8年度高知県公立高等学校入学者選抜)
- Kochi R8 Academic Test Problems and Model Answers (令和8年度学力検査問題)
- Benesse — Kochi Public High School Entrance Exam System and Tendencies (高知県公立高校受験 入試制度・出題傾向)
- MEXT Course of Study for Junior High School (2017 notification)
Our practice resources: topics covered
We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.
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.
Preparing for the Kochi 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 A-schedule main selection treats the academic test (250) and the report card (260) roughly equally, combined with the statement of intent, interview, and, for some schools, a practical test; some schools apply weighted scoring (keisha-ka) to specific subjects. Selection is by ranking within each school's quota.
- Assessment: The real Kochi mathematics examination is a 50-minute paper scored out of 50 points (250 total across five subjects: kokugo, social studies, mathematics, science, English), sat in the A-schedule academic test (Reiwa 9 / 2027 entrance cycle: examination March 3-4, 2027; results March 12, 2027). It is a written, constructed-response paper in Japanese created by the Kochi Prefectural Board of Education on the 2017 (Heisei 29) 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. Admission (A-schedule main selection) treats the academic test (250 points) and the report card (chōsasho, 260 points) roughly equally (hobo dōtō), together with the statement of intent (shigan riyūsho), an individual interview, and — for some schools — a practical test (jitsugi kensa); some schools apply weighted scoring (keisha-ka) to specific subjects. There is no fixed pass mark; selection is by ranking within each school's quota. 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 A-schedule academic test on March 3-4, 2027; results March 12, 2027)
- Exam / certification fees: JPY 2,200 entrance examination fee (nyūgaku tesuryō) for full-time prefectural high schools (JPY 950 part-time/teijisei), paid with a Kochi prefectural revenue stamp; Kochi Commercial High School (administered by the Kochi City Board of Education) is paid in cash or postal money order. A prefectural ordinance provides non-collection and exemption for welfare-recipient and economic-hardship applicants. Official sources
Using Our Practice Resources
- Work through all 100 available questions
- Review every answer and explanation
- Track weak areas and revisit them
- Use our AI tutor for tough concepts
Kochi Entrance Mathematics: Suggested Study Strategy
Frequently Asked Questions
Is the real Kochi mathematics entrance paper multiple-choice?
No. The Kochi 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 Kochi 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 covering topics from 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. The five academic-test subjects total 250 points and are combined with the 260-point report card in selection. In the Reiwa 9 (2027) cycle the A-schedule academic test is held on March 3-4, 2027, with results on March 12, 2027.
How are the academic test and report card combined in Kochi's selection?
Kochi's A-schedule main selection treats the academic test (250 points) and the report card (chōsasho, 260 points) roughly equally (hobo dōtō), together with the statement of intent (shigan riyūsho), an individual interview, and — for some schools — a practical test. Some schools apply weighted scoring (keisha-ka) to specific subjects. There is no fixed pass mark; selection is by ranking within each school's quota.
How is the report card (chōsasho) score calculated in Kochi?
Kochi's report card totals 260 points across the three junior-high years: year-1 65 points (five academic subjects × 5-point scale plus four practical subjects × 5-point scale × 2), year-2 65 points the same way, and year-3 130 points (five academic subjects × 10-point scale plus four practical subjects × 10-point scale × 2). The four practical subjects (music, art, physical education, technology/home economics) are doubled.
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 parts of the junior-high mathematics curriculum does the exam cover?
The paper covers the 2017 MEXT junior-high mathematics curriculum: 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. This bank distributes its 100 items across those areas.
What is the Reiwa 9 (2027) examination and results schedule?
For the Reiwa 9 (2027 entrance) cycle, the A-schedule application window is February 1-3, 2027, with a preference-change period February 8-10, 2027. The academic test is held March 3-4, 2027, and results are announced March 12, 2027. The JPY 2,200 entrance examination fee (JPY 950 part-time) is set out in the official Kochi selection guidelines, with exemptions for hardship cases.