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100+ Free Iwate Entrance Mathematics Practice Questions

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2026 Statistics

Key Facts: Iwate Entrance Mathematics Exam

50 min / 100 points

Length and maximum score of the Iwate mathematics paper (held March 4, 2027, Day 1 at 10:15)

Iwate Prefectural Board of Education Reiwa 9 selection schedule and Reiwa 8 admission guidelines (senbatsu jisshi yōkō)

1000 total

500-point academic test + 500-point report card (chōsasho) + 0–100-point school-specific test; school-chosen test-to-report ratio from 7:3, 6:4, 5:5, 4:6, or 3:7

Iwate Prefectural Board of Education Reiwa 9 selection schedule and Reiwa 8 admission guidelines

Mar 4, 2027

Reiwa 9 academic examination Day 1 — all five subject papers sat; makeup March 10–11; results March 15, 2027

Iwate Prefectural Board of Education Reiwa 9 selection schedule

JPY 2,200

Entrance selection fee for full-time prefectural high schools (JPY 950 part-time), paid with Iwate prefectural revenue stamps

Iwate 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 Iwate public high school entrance mathematics paper is a 50-minute, 100-point written exam held on March 4, 2027, covering equations, functions, plane and solid geometry, and probability, set by the Iwate Prefectural Board of Education. This page offers 100 original practice questions with explanations as a study aid.

Sample Iwate Entrance Mathematics Practice Questions

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

1Calculate: (−7) + (+4).
A.−11
B.−3
C.3
D.−28
Explanation: To add numbers with different signs, subtract the smaller absolute value from the larger and keep the sign of the larger absolute value. Here |−7| > |+4|, so the result is −(7 − 4) = −3.
2Calculate: (−5) × (−6).
A.−30
B.−11
C.11
D.30
Explanation: The product of two numbers with the same sign is positive. Multiply the absolute values: 5 × 6 = 30, and since both factors are negative, the result is +30.
3Calculate: (−3)².
A.−9
B.−6
C.6
D.9
Explanation: The exponent applies to the entire base (−3): (−3) × (−3) = 9. A negative times a negative is positive, so the square of any real number is non-negative.
4Evaluate √81.
A.8
B.9
C.40.5
D.7
Explanation: √81 is the non-negative number whose square is 81. Since 9 × 9 = 81, √81 = 9.
5Express √50 in simplest radical form.
A.2√5
B.5√2
C.25√2
D.10
Explanation: Factor 50 as 25 × 2, where 25 is a perfect square. Then √50 = √(25 × 2) = √25 × √2 = 5√2.
6Simplify √18 + √32.
A.7√4
B.7√2
C.√50
D.5√2
Explanation: Simplify each radical first: √18 = √(9×2) = 3√2 and √32 = √(16×2) = 4√2. Adding like radicals gives 3√2 + 4√2 = 7√2.
7Calculate √12 × √27.
A.18
B.9
C.36
D.√39
Explanation: Combine under one radical: √12 × √27 = √(12 × 27) = √324 = 18. Alternatively, √12 = 2√3 and √27 = 3√3, so 2√3 × 3√3 = 6 × 3 = 18.
8Expand (a + 3)².
A.a² + 9
B.a² + 6a + 9
C.a² + 6a − 9
D.a² + 3a + 9
Explanation: Use (x + y)² = x² + 2xy + y² with x = a, y = 3: (a + 3)² = a² + 2·a·3 + 3² = a² + 6a + 9.
9Expand (x + 2)(x − 2).
A.x² + 4
B.x² − 4
C.x² − 4x + 4
D.x² + 2x − 4
Explanation: This is the difference-of-squares pattern (a + b)(a − b) = a² − b². With a = x and b = 2, the product is x² − 2² = x² − 4.
10Factor x² − 16.
A.(x − 4)²
B.(x − 4)(x + 4)
C.(x + 4)²
D.(x − 2)(x + 8)
Explanation: This is a difference of squares: x² − 16 = x² − 4² = (x − 4)(x + 4).

About the Iwate Entrance Mathematics Exam

The Iwate Public High School Entrance Examination mathematics paper is created by the Iwate Prefectural Board of Education. The single 50-minute, 100-point paper, sat on March 4, 2027 (Day 1 of the Reiwa 9 general-selection academic test, at 10:15), 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 500-point report card and any school-specific test of 0–100 points (1000–1100 total). 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 Iwate mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects); in the Reiwa 9 (2027) general selection all five subject papers are sat on a single Day 1, March 4, 2027 (mathematics at 10:15), with Day 2 (March 5, 2027) reserved for school-specific tests (gakkō dokuji kensa) and the special-character selection (tokushoku senbatsu) tests, a makeup (tsuiken) on March 10–11, 2027, and full-time selection results announced on March 15, 2027 (Monday) The paper is created by the Iwate 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 (general selection, ippansha senbatsu) totals 1000–1100 points depending on the school: the 500-point academic test plus a 500-point report card (chōsasho: 660 converted to 500, weighted 1:2:3 across grades 1–3) plus a school-specific test (gakkō dokuji kensa) worth 0–100 points where a school sets one; since the Reiwa 7 (2025) cycle each school chooses one test-to-report-card ratio from 7:3, 6:4, 5:5, 4:6, or 3:7, and some schools apply weighted scoring (keisha haiten) — for example Kitakami-Shōnan weights kokugo and mathematics at ×1.5 — capped within a 500-point conversion. The recommendation selection (suisen) was replaced from 2025 by the special-character selection (tokushoku senbatsu), which runs a two-day exam with a statement of reasons (shibō riyūsho) and a school-specific 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 4, 2027, Day 1 of the Reiwa 9 general-selection academic test, at 10:15; makeup March 10–11, 2027)

Passing Score

No fixed pass mark; scored out of 100 points (500 total across 5 subjects); general selection totals 1000–1100 points — the 500-point academic test plus a 500-point report card (chōsasho: 660 converted to 500, weighted 1:2:3 across grades 1–3) plus a school-specific test (gakkō dokuji kensa) worth 0–100 points where a school sets one — with the test-to-report-card ratio chosen by each school from 7:3, 6:4, 5:5, 4:6, or 3:7 since the Reiwa 7 cycle, and weighted scoring (keisha haiten) of specific subjects allowed at some schools within a 500-point conversion

Exam Fee

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

Iwate 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 Iwate Entrance Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark; scored out of 100 points (500 total across 5 subjects); general selection totals 1000–1100 points — the 500-point academic test plus a 500-point report card (chōsasho: 660 converted to 500, weighted 1:2:3 across grades 1–3) plus a school-specific test (gakkō dokuji kensa) worth 0–100 points where a school sets one — with the test-to-report-card ratio chosen by each school from 7:3, 6:4, 5:5, 4:6, or 3:7 since the Reiwa 7 cycle, and weighted scoring (keisha haiten) of specific subjects allowed at some schools within a 500-point conversion
  • Assessment: The real Iwate mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects); in the Reiwa 9 (2027) general selection all five subject papers are sat on a single Day 1, March 4, 2027 (mathematics at 10:15), with Day 2 (March 5, 2027) reserved for school-specific tests (gakkō dokuji kensa) and the special-character selection (tokushoku senbatsu) tests, a makeup (tsuiken) on March 10–11, 2027, and full-time selection results announced on March 15, 2027 (Monday) The paper is created by the Iwate 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 (general selection, ippansha senbatsu) totals 1000–1100 points depending on the school: the 500-point academic test plus a 500-point report card (chōsasho: 660 converted to 500, weighted 1:2:3 across grades 1–3) plus a school-specific test (gakkō dokuji kensa) worth 0–100 points where a school sets one; since the Reiwa 7 (2025) cycle each school chooses one test-to-report-card ratio from 7:3, 6:4, 5:5, 4:6, or 3:7, and some schools apply weighted scoring (keisha haiten) — for example Kitakami-Shōnan weights kokugo and mathematics at ×1.5 — capped within a 500-point conversion. The recommendation selection (suisen) was replaced from 2025 by the special-character selection (tokushoku senbatsu), which runs a two-day exam with a statement of reasons (shibō riyūsho) and a school-specific 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 4, 2027, Day 1 of the Reiwa 9 general-selection academic test, at 10:15; makeup March 10–11, 2027)
  • Exam fee: JPY 2,200 entrance selection fee for full-time prefectural high schools (JPY 950 for part-time), set out in the Iwate admission guidelines, paid with Iwate prefectural revenue stamps affixed to the A-sheet of 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

Iwate Entrance Mathematics Study Tips from Top Performers

1Show your work for every calculation item — Iwate'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 Iwate geometry items combine two of these, and one major question is usually a compass-and-straightedge construction.
4Because grade 3 carries the heaviest weight in the 500-point report card (1:2:3 across grades 1–3), third-year ratings matter most — keep your ratings high from grade 1, but treat grade 3 as decisive.

Frequently Asked Questions

Is the real Iwate mathematics entrance paper multiple-choice?

Not entirely. Iwate'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 Iwate 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 4, 2027 (Day 1 of the Reiwa 9 general-selection academic test, at 10:15, alongside the other four subjects). The five subjects total 500 points and are combined with the 500-point report card and any school-specific test of 0–100 points (1000–1100 total) in selection, with the test-to-report-card ratio chosen by each school.

How is the report card (chōsasho) score calculated in Iwate?

Iwate uses all three junior-high years and all nine subjects. The five academic subjects are weighted ×2 in grade 1, ×4 in grade 2, ×6 in grade 3, and the four practical subjects (music, art, health-and-physical-education, technology-and-home-economics) are weighted ×3, ×6, ×9 — a 1:2:3 grade ratio — totaling 660 points, which is converted by 2/3 to 440 points. Because grade 3 carries the most weight, third-year ratings matter most; since the Reiwa 7 (2025) cycle each school chooses one test-to-report-card ratio from 7:3, 6:4, 5:5, 4:6, or 3:7, and some schools weight specific subjects — 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 9 (2027) examination and results schedule?

The Reiwa 9 application and preference-change windows are set out in the implementation guidelines (senbatsu jisshi yōkō), which the prefecture publishes later in the cycle; in the preceding Reiwa 8 cycle applications ran February 4–10 with preference change February 13–19. The JPY 2,200 fee was paid with Iwate prefectural revenue stamps. The five-subject academic examination was held on March 4–5, 2027 (all five academic subjects on Day 1, March 4; school-specific and special-character tests on Day 2, March 5), with a makeup March 10–11, 2027, and full-time results announced March 15, 2027 (Monday)

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 9 (2027 entrance) cycle, whose academic examination is scheduled for March 4–5, 2027. For the Reiwa 9 (2027 entrance) cycle, the Board has published the general-selection academic examination dates as March 4–5, 2027 with a makeup March 10–11, 2027 and results March 15, 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 Iwate Prefectural Board of Education's own pages before relying on them.