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100+ Free Kochi Entrance Mathematics Practice Questions

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2026 Statistics

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 test your Kochi 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. Adding in order gives -3 + 5 = 2, then 2 + 2 = 4.
2Evaluate (-2)^3 × (-1)^2.
A.-8
B.8
C.-6
D.6
Explanation: (-2)^3 = (-2)(-2)(-2) = -8, and (-1)^2 = 1. Multiplying gives -8 × 1 = -8.
3Evaluate -(-3)^2.
A.-9
B.9
C.-6
D.6
Explanation: First square the value: (-3)^2 = 9. Then apply the leading negative sign, so -9 is the result.
4Simplify √72 to the form a√b.
A.6√2
B.8√2
C.6√3
D.4√6
Explanation: Factor 72 as 36 × 2, where 36 is the largest perfect square. Then √72 = √(36 × 2) = √36 × √2 = 6√2.
5Compute √50 × √18.
A.30
B.15√2
C.30√2
D.900
Explanation: Combine under one root: √50 × √18 = √(50 × 18) = √900 = 30. Alternatively, √50 = 5√2 and √18 = 3√2, so 5√2 × 3√2 = 15 × 2 = 30.
6Expand √2(√3 + √2).
A.√6 + 2
B.√6 + √2
C.2√2 + √3
D.√5 + 2
Explanation: Distribute √2 across the sum: √2 × √3 = √6 and √2 × √2 = √4 = 2. So the result is √6 + 2.
7Evaluate (2 + √3)(2 - √3).
A.1
B.7
C.0
D.-1
Explanation: This is a difference of squares: (2)^2 - (√3)^2 = 4 - 3 = 1. The irrational parts cancel.
8Expand (x + 3)(x - 4).
A.x^2 - x - 12
B.x^2 + x - 12
C.x^2 - 7x - 12
D.x^2 - x + 12
Explanation: Use FOIL: x·x = x^2, x·(-4) = -4x, 3·x = 3x, 3·(-4) = -12. The middle terms combine to -4x + 3x = -x, giving x^2 - x - 12.
9Factorize x^2 - 7x + 12.
A.(x - 3)(x - 4)
B.(x + 3)(x + 4)
C.(x - 3)(x + 4)
D.(x + 3)(x - 4)
Explanation: Find two numbers that multiply to 12 and add to -7: -3 and -4. So x^2 - 7x + 12 = (x - 3)(x - 4).
10Factorize 2x^2 - 5x - 3.
A.(2x + 1)(x - 3)
B.(2x - 1)(x + 3)
C.(2x - 3)(x + 1)
D.(2x + 3)(x - 1)
Explanation: Split the middle term: 2x^2 - 5x - 3 = 2x^2 - 6x + x - 3 = 2x(x - 3) + 1(x - 3) = (2x + 1)(x - 3). Checking, 2x·x = 2x^2, 2x·(-3) = -6x, 1·x = x, 1·(-3) = -3, and -6x + x = -5x.

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.

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 Fee

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. (Kochi Prefectural Board of Education (高知県教育委員会))

Kochi 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 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 fee: 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.

Keys to Passing

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

Kochi Entrance Mathematics Study Tips from Top Performers

1Show your work for every calculation item — even though the official paper is written, writing each intermediate step prevents sign and formula errors, and Kochi's selection rewards every point on the 50-point math paper.
2Master the basic calculation set first: signed numbers, square-root simplification, expansion, and factorization are your scoring foundation — drill them for speed and accuracy so you don't drop easy points on the small-question set.
3For 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 — Kochi regularly tests plane-geometry proofs.
4Be 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 — Kochi regularly tests applied functions alongside probability.
5Understand that selection weights the academic test (250) and report card (260) roughly equally, so a strong math score can complement your report card — but some schools apply weighted scoring (keisha-ka) to specific subjects, so check each school's rules.

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 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. 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.