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100+ Free Ishikawa Entrance Mathematics Practice Questions

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2026 Statistics

Key Facts: Ishikawa Entrance Mathematics Exam

50 min / 100 points

Length and maximum score of the Ishikawa mathematics paper (held March 11, 2026, Day 2)

Ishikawa Prefectural Board of Education Reiwa 8 admission guidelines (bosyū yōkō)

500 + 180

500-point academic test plus 180-point naishinten report card (grades 1–3, nine subjects, grade 3 doubled: 45 + 45 + 90)

Ishikawa Prefectural Board of Education Reiwa 8 admission guidelines

Mar 10–11, 2026

Reiwa 8 academic examination dates (Day 1 kokugo/science/English, Day 2 social studies/math); results March 18, 2026 at noon

Ishikawa Prefectural Board of Education Reiwa 8 selection schedule

JPY 2,200

Entrance examination fee for full-time prefectural high schools (JPY 950 part-time/correspondence), paid with Ishikawa prefectural revenue stamps

Ishikawa prefectural public high school admission guidelines

Calculation items

About a third of this bank are genuine worked-calculation questions with numeric answers

OpenExamPrep

100

Free original practice questions in this bank

OpenExamPrep

The Ishikawa public high school entrance mathematics paper is a 50-minute, 100-point written exam held on March 11, 2026, covering equations, functions, plane and solid geometry, and probability, set by the Ishikawa Prefectural Board of Education. This page offers 100 original practice questions with explanations as a study aid.

Sample Ishikawa Entrance Mathematics Practice Questions

Try these sample questions to test your Ishikawa Entrance Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Compute (−3) × 4 − (−2).
A.−10
B.−14
C.−16
D.10
Explanation: (−3) × 4 = −12, then −12 − (−2) = −12 + 2 = −10.
2Evaluate (−2)³ − (−1)⁴.
A.−9
B.−7
C.7
D.9
Explanation: (−2)³ = −8 and (−1)⁴ = 1, so −8 − 1 = −9.
3What is the prime factorization of 84?
A.2² × 3 × 7
B.2 × 3 × 7
C.2² × 3² × 7
D.2 × 3² × 7
Explanation: 84 = 4 × 21 = 2² × 3 × 7. Check: 4 × 21 = 84.
4Find the greatest common divisor of 48 and 72.
A.24
B.12
C.8
D.6
Explanation: 48 = 2⁴ × 3 and 72 = 2³ × 3²; GCD = 2³ × 3 = 24. Check: 48 ÷ 24 = 2, 72 ÷ 24 = 3.
5Find the least common multiple of 12 and 18.
A.36
B.72
C.6
D.216
Explanation: 12 = 2² × 3, 18 = 2 × 3²; LCM = 2² × 3² = 36.
6Simplify 12a³b² ÷ 4ab.
A.3a²b
B.3a²b²
C.8a²b
D.3ab
Explanation: Divide the coefficients and subtract the repeated factors separately: 12 ÷ 4 = 3, a³ ÷ a = a², and b² ÷ b = b. The quotient is therefore 3a²b.
7A distance measured as 25,000 m is to be written to two significant figures. Which form is correct?
A.2.5 × 10⁴ m
B.2.50 × 10⁴ m
C.25 × 10³ m
D.2.5 × 10³ m
Explanation: In the significant-figure form the first factor is written as a number from 1 up to (but not including) 10, multiplied by a power of 10. Two significant figures give 2.5, and 25,000 = 2.5 × 10⁴, so the answer is 2.5 × 10⁴ m.
8Expand (x + 3)(x − 5).
A.x² − 2x − 15
B.x² + 2x − 15
C.x² − 2x + 15
D.x² − 8x − 15
Explanation: x·x = x², x·(−5) + 3·x = −2x, 3·(−5) = −15; sum = x² − 2x − 15.
9Factor x² − 7x + 12.
A.(x − 3)(x − 4)
B.(x + 3)(x + 4)
C.(x − 3)(x + 4)
D.(x − 2)(x − 6)
Explanation: Need two numbers whose product is 12 and sum −7: −3 and −4, so (x − 3)(x − 4).
10Expand (x + 2)².
A.x² + 4x + 4
B.x² + 4x + 2
C.x² + 2x + 4
D.x² + 4x
Explanation: (a+b)² = a² + 2ab + b²: x² + 4x + 4.

About the Ishikawa Entrance Mathematics Exam

The Ishikawa Public High School Entrance Examination mathematics paper is created by the Ishikawa Prefectural Board of Education. The single 50-minute, 100-point paper, sat on March 11, 2026 (Day 2 of the Reiwa 8 general-selection academic test, alongside social studies), is a written exam 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, with worked steps required on a printed answer sheet. Admission combines the 500-point academic test with the 180-point junior-high report card (grades 1–3, nine subjects, grade 3 doubled). This page provides 100 original English-language practice questions with detailed explanations as a study adaptation — not an official translation or a simulation of the official format.

Assessment

The real Ishikawa mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects); in the Reiwa 8 (2026) general selection the five-subject academic test was split over two days — Day 1, March 10, 2026 (kokugo, science, English) and Day 2, March 11, 2026 (social studies, mathematics) — with full-time selection results announced on March 18, 2026 (Wednesday) at noon. The paper is created by the Ishikawa 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, with answers shown as worked steps and short constructed responses on a printed answer sheet. Admission combines the 500-point academic test with the 180-point junior-high report card (naishinten: 45 + 45 + 90 with grade 3 doubled); no fixed weighting between the two is published — the admission guidelines direct each school to judge the report card and the test result together in the light of their relationship — and some schools apply weighted scoring (keisha haiten) to up to two subjects, within a limit of double marks. A separate recommendation admission runs an interview on February 9, 2026 with internal decisions on February 13, 2026, without an academic test. This local bank is an English-language MCQ study adaptation providing 100 original practice items.

Time Limit

50 minutes for the mathematics subject paper (held on March 11, 2026, Day 2 of the Reiwa 8 general-selection academic test, alongside social studies)

Passing Score

No fixed pass mark; scored out of 100 points (500 total across 5 subjects); selection adds the 180-point naishinten report card (grades 1–3, nine subjects on a 5-point scale, grade 3 doubled: 45 + 45 + 90 = 180), with no fixed test-to-report-card weighting published (schools judge the two together under the admission guidelines) and weighted scoring (keisha haiten) of up to two subjects, capped at double marks, allowed at some schools

Exam Fee

JPY 2,200 entrance examination fee for full-time prefectural high schools (JPY 950 for part-time and correspondence), set out in the Ishikawa admission guidelines, paid with Ishikawa prefectural revenue stamps affixed to the application form and submitted through the junior-high school principal (Ishikawa Prefectural Board of Education (石川県教育委員会))

Ishikawa Entrance Mathematics Exam Content Outline

About 18% 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 22% of this practice bank

Functions

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

About 20% of this practice bank

Plane Geometry

Angles and parallel lines, congruence and similarity, circles, the Pythagorean theorem, and compass-and-straightedge construction.

About 12% 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 10% 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 Ishikawa Entrance Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark; scored out of 100 points (500 total across 5 subjects); selection adds the 180-point naishinten report card (grades 1–3, nine subjects on a 5-point scale, grade 3 doubled: 45 + 45 + 90 = 180), with no fixed test-to-report-card weighting published (schools judge the two together under the admission guidelines) and weighted scoring (keisha haiten) of up to two subjects, capped at double marks, allowed at some schools
  • Assessment: The real Ishikawa mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects); in the Reiwa 8 (2026) general selection the five-subject academic test was split over two days — Day 1, March 10, 2026 (kokugo, science, English) and Day 2, March 11, 2026 (social studies, mathematics) — with full-time selection results announced on March 18, 2026 (Wednesday) at noon. The paper is created by the Ishikawa 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, with answers shown as worked steps and short constructed responses on a printed answer sheet. Admission combines the 500-point academic test with the 180-point junior-high report card (naishinten: 45 + 45 + 90 with grade 3 doubled); no fixed weighting between the two is published — the admission guidelines direct each school to judge the report card and the test result together in the light of their relationship — and some schools apply weighted scoring (keisha haiten) to up to two subjects, within a limit of double marks. A separate recommendation admission runs an interview on February 9, 2026 with internal decisions on February 13, 2026, without an academic test. This local bank is an English-language MCQ study adaptation providing 100 original practice items.
  • Time limit: 50 minutes for the mathematics subject paper (held on March 11, 2026, Day 2 of the Reiwa 8 general-selection academic test, alongside social studies)
  • Exam fee: JPY 2,200 entrance examination fee for full-time prefectural high schools (JPY 950 for part-time and correspondence), set out in the Ishikawa admission guidelines, paid with Ishikawa prefectural revenue stamps affixed to the application form and submitted through the junior-high school principal

Keys to Passing

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

Ishikawa Entrance Mathematics Study Tips from Top Performers

1Show your work for every calculation item — Ishikawa's constructed-response items require worked steps, and even in MCQ form writing the intermediate step prevents sign and formula errors.
2Master linear and quadratic functions together: be 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.
3For geometry, memorize the congruence and similarity conditions (SSS, SAS, ASA; ratio of areas = square of the ratio of sides), the inscribed-angle theorem, and the Pythagorean theorem; many Ishikawa geometry items combine two of these, and one major question is usually a compass-and-straightedge construction.
4Because grade 3 is doubled in the 180-point naishinten (45 + 45 + 90), third-year ratings carry twice the weight of first- or second-year ratings — keep your ratings high from grade 1, but treat grade 3 as decisive.

Frequently Asked Questions

Is the real Ishikawa mathematics entrance paper multiple-choice?

Not entirely. Ishikawa's mathematics paper mixes lettered-choice items with short constructed-response items that require worked steps, organized into several major questions covering calculation sets, equations, functions, geometry, and probability. 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 not limited to four options, and every stem is in Japanese.

Are these questions official past exam problems?

No. Although the Ishikawa Prefectural Board of Education publishes the actual examination problems after each sitting, it does not publish them as a 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.

How long is the mathematics paper and what is the maximum score?

The mathematics paper is a single 50-minute exam scored out of 100 points, sat on March 11, 2026 (Day 2 of the Reiwa 8 general-selection academic test, alongside social studies). The five subjects total 500 points and are combined with the 180-point junior-high report card (naishinten) in selection, with the test-to-report-card ratio set by each school.

How is the naishinten (report card) score calculated in Ishikawa?

Ishikawa uses all three junior-high years: grade 1 and grade 2 each contribute 9 subjects × 5 points = 45 points, and grade 3's 9 subjects × 5 points are doubled to 90 points, giving 45 + 45 + 90 = 180 points total. Because grade 3 is doubled, third-year ratings carry the most weight; no fixed ratio between the 500-point test and this 180-point report card is published, each school judging the two together under the admission guidelines, and some schools apply weighted scoring (keisha haiten) to up to two subjects, capped at double marks — a strong mathematics candidate may benefit from a school that weights it.

Does this bank include real calculation questions?

Yes. About a third 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 counting probability outcomes — not just definitional recall.

What is the Reiwa 8 (2026) application and results schedule?

General-selection applications were accepted February 18–24, 2026, with preference-change February 27–March 3, 2026. The JPY 2,200 fee was paid with Ishikawa prefectural revenue stamps. The five-subject academic examination was held over two days, March 10–11, 2026 (kokugo, science, English on Day 1; social studies, mathematics on Day 2), with full-time results announced March 18, 2026 (Wednesday) at noon. Recommendation-admission interviews were held February 9, 2026 with internal decisions February 13, 2026.

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.

Do these details apply to the next (Reiwa 9 / 2027) entrance examination?

Most figures on this page describe the Reiwa 8 cycle, whose academic examination was sat on March 10–11, 2026. For the Reiwa 9 (2027 entrance) cycle, the Board has published the general-selection academic examination dates as March 9–10, 2027 with results March 17, 2027. The five-subject, 50-minute, 100-point structure and the report-card-plus-test selection method have been stable, but confirm the current year's application windows, fees, and selection ratios on the Ishikawa Prefectural Board of Education's own pages before relying on them.