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100+ Free Ibaraki Entrance Math Practice Questions

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2026 Statistics

Key Facts: Ibaraki Entrance Math Exam

50 min / 100 points

Length and maximum score of the Ibaraki mathematics paper (held February 26, 2026)

Ibaraki Prefectural Board of Education Reiwa 8 selection implementation rules

500 + 135

500-point academic test plus 135-point naishinten report card (grades 1–3, nine subjects), roughly equal weight

Ibaraki Prefectural Board of Education Reiwa 8 selection rules

Feb 26, 2026

Reiwa 8 academic examination date; results announced March 11, 2026 at 9:00

Ibaraki Prefectural Board of Education Reiwa 8 selection schedule

JPY 2,200

Entrance examination fee for full-time prefectural high schools (JPY 950 part-time), paid with Ibaraki revenue stamps or electronic settlement

Ibaraki prefectural high school entrance selection implementation rules

6 ōmon

Six major questions: small sets, probability, plane geometry, linear functions, solid geometry

Ibaraki Prefectural Board of Education mathematics paper structure

100

Free original practice questions in this bank

OpenExamPrep

The Ibaraki public high school entrance mathematics paper is a 50-minute, 100-point written exam held on February 26, 2026, covering numbers, equations, functions, plane and solid geometry, and probability across six major questions, set by the Ibaraki Prefectural Board of Education. This page offers 100 original practice questions with explanations as a study aid.

Sample Ibaraki Entrance Math Practice Questions

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

1Calculate the value of (-7) + (+3) - (-4).
A.-8
B.0
C.-14
D.8
Explanation: Subtracting a negative becomes addition: -(-4) = +4. So the expression is -7 + 3 + 4. Working left to right: -7 + 3 = -4, then -4 + 4 = 0.
2Evaluate (-2) × (+5) ÷ (-4).
A.5/2
B.-5/2
C.2/5
D.-10
Explanation: Multiply first: (-2)×(+5) = -10. Then divide by -4: -10 ÷ (-4) = 10/4 = 5/2. Negative divided by negative is positive.
3Compute (-3)^2 + (-2)^3.
A.1
B.15
C.-1
D.17
Explanation: (-3)^2 = 9 (even power gives positive). (-2)^3 = -8 (odd power keeps the sign). So 9 + (-8) = 1.
4Simplify 2/3 - 5/6 + 1/4 and express as a single reduced fraction.
A.1/12
B.1/4
C.-1/12
D.5/12
Explanation: Common denominator 12: 2/3 = 8/12, 5/6 = 10/12, 1/4 = 3/12. So 8/12 - 10/12 + 3/12 = (8-10+3)/12 = 1/12.
5Compute 3/4 ÷ 6/5 × 2/3.
A.5/12
B.15/24
C.5/9
D.12/15
Explanation: Division becomes multiplication by reciprocal: 3/4 × 5/6 = 15/24 = 5/8. Then × 2/3 = 10/24 = 5/12. Working left to right with division and multiplication at equal precedence.
6When x = -2 and y = 3, evaluate 3x^2 - 2xy + 1.
A.25
B.13
C.5
D.-5
Explanation: Substitute: 3(-2)^2 - 2(-2)(3) + 1 = 3(4) - 2(-6) + 1 = 12 + 12 + 1 = 25.
7Expand (x + 4)(x - 5).
A.x^2 - x - 20
B.x^2 + x - 20
C.x^2 - 9x - 20
D.x^2 - x + 20
Explanation: FOIL: x·x = x^2, x·(-5) = -5x, 4·x = 4x, 4·(-5) = -20. Combine middle: -5x + 4x = -x. So x^2 - x - 20.
8Factor x^2 - 7x + 12 completely.
A.(x-3)(x-4)
B.(x-3)(x+4)
C.(x+3)(x-4)
D.(x+3)(x+4)
Explanation: Need two numbers whose product is +12 and sum is -7. Both must be negative: -3 and -4 give product 12 and sum -7. So (x-3)(x-4).
9Factor 2x^2 - 5x - 3.
A.(2x+1)(x-3)
B.(2x-1)(x+3)
C.(2x-3)(x+1)
D.(2x-1)(x-3)
Explanation: Splitting the middle: 2x^2 - 5x - 3. Try (2x+1)(x-3) = 2x^2 - 6x + x - 3 = 2x^2 - 5x - 3. Matches.
10Simplify √72 + √50 - √32.
A.9√2
B.5√2
C.7√2
D.3√2
Explanation: Factor: √72 = √(36·2) = 6√2. √50 = √(25·2) = 5√2. √32 = √(16·2) = 4√2. So 6√2 + 5√2 - 4√2 = 7√2.

About the Ibaraki Entrance Math Exam

The Ibaraki Public High School Entrance Examination mathematics paper is created by the Ibaraki Prefectural Board of Education. The single 50-minute, 100-point paper, sat on February 26, 2026 in the Reiwa 8 general selection, is a written exam on the 2017 MEXT junior-high Course of Study, organized into six major questions covering small-problem calculation sets, probability, plane geometry with proofs, linear functions, and solid geometry. Answers are entered on a printed answer sheet, mostly as a final value with some lettered-choice items, and geometry proofs are a noted Ibaraki feature. Admission combines the 500-point academic test with the 135-point junior-high report card (grades 1–3, nine subjects) with the two weighted roughly equally. 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 Ibaraki mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects: kokugo, social studies, mathematics, science, and English including a listening test); in the Reiwa 8 (2026) general selection it was sat on February 26, 2026 (Thursday), with selection results announced on March 11, 2026 (Wednesday) at 9:00. The paper is created by the Ibaraki Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study, organized into six major questions: small-problem calculation sets (ōmon 1–2), probability (ōmon 3), plane geometry with proofs (ōmon 4, a noted Ibaraki feature), linear functions (ōmon 5), and solid geometry (ōmon 6). Answers are entered on a printed answer sheet, mostly as a final numeric or algebraic value with some lettered-choice items. Admission combines the 500-point academic test with the 135-point junior-high report card (naishinten: grade-1, grade-2, and grade-3 nine-subject 5-point ratings, 9 × 5 × 3 years = 135 points); in the common selection (kyōtsū senbatsu) the test and the report card are weighted roughly equally, with the specific conversion ratio set by each school, and most schools admit through a two-stage A-group (ryō jun'i chōfuku hōshiki, both-rank duplication) and B-group process with a second-choice school option (dai-ni kibō kō). 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 February 26, 2026 in the Reiwa 8 general selection)

Passing Score

No fixed pass mark; scored out of 100 points (500 total across 5 subjects); selection adds the 135-point naishinten report card (grades 1–3, nine subjects on a 5-point scale) with the academic test and report card weighted roughly equally in common selection, through a two-stage A-group/B-group process

Exam Fee

JPY 2,200 entrance examination fee for full-time prefectural high schools (JPY 950 for part-time), set out in the Ibaraki selection rules, paid with Ibaraki prefectural revenue stamps attached to the application form and from Reiwa 8 also payable through electronic settlement via the Ibaraki Electronic Application service (Ibaraki Prefectural Board of Education (茨城県教育委員会))

Ibaraki Entrance Math Exam Content Outline

About 20% 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 equation-based word problems.

About 22% of this practice bank

Functions

Proportional and inverse proportional relationships, linear functions, and quadratic functions y = ax² including rates of change and coordinate geometry.

About 18% of this practice bank

Plane Geometry

Angles and parallel lines, congruence and similarity, triangles and quadrilaterals, circles, the Pythagorean theorem, and trigonometric ratios.

About 12% of this practice bank

Solid Geometry and Measurement

Surface areas and volumes of prisms, cylinders, pyramids, cones, and spheres, plus spatial relationships and rotation of plane figures.

About 10% of this practice bank

Data Analysis and Probability

Counting outcomes, probability with and without replacement, complement rule, representative values, quartiles, and frequency tables.

How to Pass the Ibaraki Entrance Math 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 135-point naishinten report card (grades 1–3, nine subjects on a 5-point scale) with the academic test and report card weighted roughly equally in common selection, through a two-stage A-group/B-group process
  • Assessment: The real Ibaraki mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects: kokugo, social studies, mathematics, science, and English including a listening test); in the Reiwa 8 (2026) general selection it was sat on February 26, 2026 (Thursday), with selection results announced on March 11, 2026 (Wednesday) at 9:00. The paper is created by the Ibaraki Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study, organized into six major questions: small-problem calculation sets (ōmon 1–2), probability (ōmon 3), plane geometry with proofs (ōmon 4, a noted Ibaraki feature), linear functions (ōmon 5), and solid geometry (ōmon 6). Answers are entered on a printed answer sheet, mostly as a final numeric or algebraic value with some lettered-choice items. Admission combines the 500-point academic test with the 135-point junior-high report card (naishinten: grade-1, grade-2, and grade-3 nine-subject 5-point ratings, 9 × 5 × 3 years = 135 points); in the common selection (kyōtsū senbatsu) the test and the report card are weighted roughly equally, with the specific conversion ratio set by each school, and most schools admit through a two-stage A-group (ryō jun'i chōfuku hōshiki, both-rank duplication) and B-group process with a second-choice school option (dai-ni kibō kō). 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 February 26, 2026 in the Reiwa 8 general selection)
  • Exam fee: JPY 2,200 entrance examination fee for full-time prefectural high schools (JPY 950 for part-time), set out in the Ibaraki selection rules, paid with Ibaraki prefectural revenue stamps attached to the application form and from Reiwa 8 also payable through electronic settlement via the Ibaraki Electronic Application service

Keys to Passing

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

Ibaraki Entrance Math Study Tips from Top Performers

1Practice every calculation by writing out the steps and producing the answer yourself — on the real paper you write the value on the answer sheet rather than picking from options, so MCQ practice alone lets you work backwards from the choices.
2Master the quadratic equation toolkit (factorization and the quadratic formula) and linear-function graph reading, which anchor ōmon 5 and the multi-step problems at the end of the official paper.
3For geometry, rehearse congruence and similarity proof structure (claim, reason, conclusion) and Pythagorean theorem applications in both plane and solid figures — proof problems are a noted Ibaraki feature (ōmon 4).
4Because the 135-point report card (all three junior-high years, nine subjects) is weighted roughly equally to the 500-point test in Ibaraki, keep your ratings high across all nine subjects from grade 1 onward — the practical four subjects matter as much as the academic five.

Frequently Asked Questions

Is the real Ibaraki mathematics entrance paper multiple-choice?

Not entirely. Ibaraki's mathematics paper mixes lettered-choice items with items where you write a final numeric or algebraic answer on the answer sheet, and the paper is organized into six major questions (small-problem sets, probability, plane geometry, linear functions, and solid geometry). So option-picking is part of the real paper, but you must also produce the answer yourself. 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. Work past papers under time pressure — six major questions with many sub-questions in 50 minutes leaves well under two minutes each.

Are these questions official past exam problems?

No. Although the Ibaraki 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, with genuine worked-calculation items across numbers and expressions, equations, functions, geometry, and probability.

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 February 26, 2026 in the Reiwa 8 general selection. The five subjects total 500 points and are combined with the 135-point junior-high report card (naishinten) in selection, with the academic test and the report card weighted roughly equally.

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

Ibaraki uses all three junior-high years (grade 1, grade 2, and grade 3): the nine subjects (kokugo, social studies, mathematics, science, English, music, art, health and physical education, and technology and home economics) are each rated on a 5-point scale, giving 9 × 5 = 45 points per year and 45 × 3 years = 135 points total. In the common selection the 500-point academic test and this 135-point report card are weighted roughly equally, with the specific conversion ratio set by each school.

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

Web application (shigansha jōhō nyūryoku) ran January 7–28, 2026, with paper application acceptance February 5–9, 2026 and application-change (shigan-saki henkō) on February 10 and 12, 2026. The JPY 2,200 fee was paid with Ibaraki prefectural revenue stamps or electronic settlement. The academic examination was held on February 26, 2026 (Thursday), with selection results announced on March 11, 2026 (Wednesday) at 9:00; the makeup examination (tsuiken) was March 4–5, 2026 and second recruitment (dai-ni boshū) application March 12–13, 2026.

What is the common selection (kyōtsū senbatsu) two-stage process?

In the common selection, applicants who did not pass the special selection (tokushoku senbatsu) and those who applied only to the common selection are judged in a two-stage process: the A-group selection (A-gun senbatsu) uses a both-rank duplication method (ryō jun'i chōfuku hōshiki) that lets applicants list a first and a second-choice school, and the B-group selection (B-gun senbatsu) follows for remaining places. The specific conversion ratio of the test and report card is set by each school.

What parts of the junior-high mathematics curriculum does the exam cover?

The paper covers the 2017 MEXT junior-high mathematics curriculum in six major questions: numbers and expressions (including square roots), linear/simultaneous/quadratic equations and inequalities, proportional/linear/quadratic functions, plane geometry with proofs and the Pythagorean theorem, solid geometry and measurement, and data analysis with probability. This bank distributes its 100 items across those six strands.

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 February 26, 2026. For the Reiwa 9 (2027 entrance) cycle, the Board has published the schedule: academic examination on February 25, 2027 (Thursday) with results March 11, 2027 (Thursday). 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 Ibaraki Prefectural Board of Education's own pages before relying on them.