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100+ Free Hyogo Entrance Math Practice Questions

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2026 Statistics

Key Facts: Hyogo Entrance Math Exam

50 min / 100 points

Length and maximum score of the Hyogo mathematics paper (held March 12, 2026, 10:20-11:10)

Hyogo Prefectural Board of Education Reiwa 8 selection guidelines

250 + 250

Academic test 500 halved to 250 plus 250-point naishinten report card, equal 1:1 weight

Hyogo Prefectural Board of Education Reiwa 8 selection guidelines

Mar 12, 2026

Reiwa 8 academic examination date; results announced March 19, 2026 at 10:00

Hyogo Prefectural Board of Education Reiwa 8 selection schedule

JPY 2,200

Entrance examination fee for prefectural full-time high schools, paid with Hyogo revenue stamps or online settlement

Hyogo prefectural high school entrance selection guidelines

1 : 1

Academic test and junior-high report card weighted equally in Hyogo selection

Hyogo Prefectural Board of Education selection method

100

Free original practice questions in this bank

OpenExamPrep

The Hyogo public high school entrance mathematics paper is a 50-minute, 100-point written exam held on March 12, 2026, covering algebra, equations, functions, geometry, and probability, set by the Hyogo Prefectural Board of Education. This page offers 100 original practice questions with explanations as a study aid.

Sample Hyogo Entrance Math Practice Questions

Try these sample questions to test your Hyogo 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 number becomes addition, so -(-4) = +4. The expression becomes -7 + 3 + 4. Computing left to right: -7 + 3 = -4, then -4 + 4 = 0.
2Calculate the value of 4 - 2 × (-3) + (-12) ÷ 3.
A.-6
B.14
C.6
D.-2
Explanation: Multiplication and division come before addition and subtraction: -2 × (-3) = +6 and (-12) ÷ 3 = -4. The expression becomes 4 + 6 - 4 = 6.
3Calculate 2/3 + 3/4 - 1/6.
A.5/4
B.13/12
C.7/12
D.3/4
Explanation: Use the common denominator 12: 2/3 = 8/12, 3/4 = 9/12, and 1/6 = 2/12. Then 8/12 + 9/12 - 2/12 = 15/12 = 5/4.
4Evaluate the expression 3x - 2y when x = 5 and y = -3.
A.9
B.-21
C.21
D.-9
Explanation: Substitute the values: 3(5) - 2(-3) = 15 + 6 = 21. The key step is that -2y with y = -3 gives -2 × (-3) = +6.
5Expand (x + 4)(x + 7).
A.x² + 11x + 28
B.x² + 28x + 11
C.x² + 11x + 11
D.x² + 3x + 28
Explanation: Using (x + a)(x + b) = x² + (a + b)x + ab with a = 4 and b = 7: the coefficient of x is 4 + 7 = 11 and the constant term is 4 × 7 = 28. The result is x² + 11x + 28.
6Factor the expression x² - 16.
A.(x - 4)²
B.(x - 16)(x + 1)
C.(x - 4)(x + 4)
D.(x + 4)²
Explanation: This is a difference of squares: x² - 16 = x² - 4². Applying a² - b² = (a + b)(a - b) gives (x + 4)(x - 4).
7Simplify the expression 4(2a - b) - 3(a - 2b).
A.5a - 10b
B.5a + 2b
C.5a
D.5a - 2b
Explanation: Distribute each factor: 4(2a - b) = 8a - 4b and -3(a - 2b) = -3a + 6b. Combining like terms gives (8a - 3a) + (-4b + 6b) = 5a + 2b.
8Calculate √20 + √45 - √5.
A.5√5
B.4√5
C.3√5
D.√60
Explanation: Simplify each radical: √20 = 2√5, √45 = 3√5, and √5 stays as is. Then 2√5 + 3√5 - √5 = 4√5.
9Rewrite 8/√2 with a rationalized denominator.
A.4√2
B.2√2
C.8√2
D.4
Explanation: Multiply numerator and denominator by √2: (8 × √2)/(√2 × √2) = 8√2/2. Dividing 8 by 2 gives 4√2.
10Expand and simplify (x + 5)² - (x - 5)².
A.20x
B.50
C.0
D.10x
Explanation: Expand each square: (x + 5)² = x² + 10x + 25 and (x - 5)² = x² - 10x + 25. Subtracting gives (x² + 10x + 25) - (x² - 10x + 25) = 20x, since the x² and constant terms cancel.

About the Hyogo Entrance Math Exam

The Hyogo Public High School Entrance Examination mathematics paper is created by the Hyogo Prefectural Board of Education. The single 50-minute, 100-point paper, sat on March 12, 2026 in the Reiwa 8 general selection, is a written exam on the 2017 MEXT junior-high Course of Study, covering numbers and expressions, equations, functions, plane and solid geometry, and probability and data analysis. Answers are entered on a printed answer sheet, mostly as a final value with some lettered-choice items, and the problems are notably text-heavy with many figures, tables, and graphs. Admission combines the five-subject scores (halved to 250 points) with the 250-point junior-high report card for a 500-point total in which the test and report card carry equal weight. 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 Hyogo 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 March 12, 2026 (Thursday) from 10:20 to 11:10, with selection results announced on March 19, 2026 (Thursday) at 10:00. The paper is created by the Hyogo Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study, running to about six major sections and roughly 30-35 sub-questions across numbers and expressions, equations, functions, plane and solid geometry, and probability and data analysis. Answers are entered on a printed answer sheet, mostly as a final numeric or algebraic value with some lettered-choice items, and Hyogo includes very few extended free-writing items. The strands are deliberately balanced, fusion problems (function with geometry, probability with geometry) are common, and the problems carry an unusually heavy load of text, figures, tables, and graphs. Each school admits applicants by combining the academic examination with the 250-point junior-high report card (naishinten, the grade-3 main-five-subject rating total multiplied by 4 for 100 points and the grade-3 practical-four-subject rating total multiplied by 7.5 for 150 points): the 500-point academic total is halved to 250 points and added to the 250-point report card for a 500-point selection score in which the academic test and the report card carry equal weight (1:1). Most full-time general and comprehensive courses use multiple-choice selection (fukusu shigan senbatsu) letting applicants list a first and second choice with a first-choice bonus of about 20-30 points by school district, while specialized courses use single selection (tandoku senbatsu), with optional special handling (tokubetsu atsukai) giving a 10% border-score reduction for notable club and special-activity records. 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 10:20-11:10 on March 12, 2026 in the Reiwa 8 general selection)

Passing Score

No fixed pass mark; scored out of 100 points (500 total across 5 subjects, halved to 250); selection adds the 250-point naishinten report card for a 500-point total with the academic test and report card weighted equally (1:1), with a first-choice bonus of about 20-30 points in multiple-choice selection

Exam Fee

JPY 2,200 entrance examination fee for prefectural full-time high schools, set out in the Hyogo selection guidelines, paid with Hyogo prefectural revenue stamps attached to the application form and from Reiwa 8 also payable through online settlement (Hyogo Prefectural Board of Education (兵庫県教育委員会))

Hyogo 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, and the Pythagorean theorem.

About 12% of this practice bank

Solid Geometry and Measurement

Surface areas and volumes of prisms, cylinders, pyramids, cones, and spheres, plus spatial relationships such as skew lines in a cube.

About 10% of this practice bank

Data Analysis and Probability

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

How to Pass the Hyogo Entrance Math Exam

What You Need to Know

  • Passing score: No fixed pass mark; scored out of 100 points (500 total across 5 subjects, halved to 250); selection adds the 250-point naishinten report card for a 500-point total with the academic test and report card weighted equally (1:1), with a first-choice bonus of about 20-30 points in multiple-choice selection
  • Assessment: The real Hyogo 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 March 12, 2026 (Thursday) from 10:20 to 11:10, with selection results announced on March 19, 2026 (Thursday) at 10:00. The paper is created by the Hyogo Prefectural Board of Education on the 2017 (Heisei 29) MEXT junior-high Course of Study, running to about six major sections and roughly 30-35 sub-questions across numbers and expressions, equations, functions, plane and solid geometry, and probability and data analysis. Answers are entered on a printed answer sheet, mostly as a final numeric or algebraic value with some lettered-choice items, and Hyogo includes very few extended free-writing items. The strands are deliberately balanced, fusion problems (function with geometry, probability with geometry) are common, and the problems carry an unusually heavy load of text, figures, tables, and graphs. Each school admits applicants by combining the academic examination with the 250-point junior-high report card (naishinten, the grade-3 main-five-subject rating total multiplied by 4 for 100 points and the grade-3 practical-four-subject rating total multiplied by 7.5 for 150 points): the 500-point academic total is halved to 250 points and added to the 250-point report card for a 500-point selection score in which the academic test and the report card carry equal weight (1:1). Most full-time general and comprehensive courses use multiple-choice selection (fukusu shigan senbatsu) letting applicants list a first and second choice with a first-choice bonus of about 20-30 points by school district, while specialized courses use single selection (tandoku senbatsu), with optional special handling (tokubetsu atsukai) giving a 10% border-score reduction for notable club and special-activity records. 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 10:20-11:10 on March 12, 2026 in the Reiwa 8 general selection)
  • Exam fee: JPY 2,200 entrance examination fee for prefectural full-time high schools, set out in the Hyogo selection guidelines, paid with Hyogo prefectural revenue stamps attached to the application form and from Reiwa 8 also payable through online settlement

Keys to Passing

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

Hyogo 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 function-graph reading, which anchor 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.
4Because the report card carries equal weight to the test in Hyogo, keep your grade-3 ratings high across all nine subjects — the practical four subjects are weighted 7.5× and matter as much as the main five.

Frequently Asked Questions

Is the real Hyogo mathematics entrance paper multiple-choice?

Not entirely. Hyogo's mathematics paper mixes lettered-choice items with items where you write a final numeric or algebraic answer on the answer sheet, and Hyogo is known for including very few extended free-writing items. So option-picking is part of the real paper, but you must also be able to 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 the real problems carry far more text, figures, and graphs than these stems. Work past papers under time pressure — roughly 30-35 sub-questions in 50 minutes gives you under two minutes each.

Are these questions official past exam problems?

No. Although the Hyogo 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 March 12, 2026 in the Reiwa 8 general selection (10:20-11:10). The five subjects total 500 points, which are halved to 250 and added to the 250-point junior-high report card (naishinten) for a 500-point selection score in which the academic test and the report card carry equal weight (1:1).

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

Hyogo uses grade-3 (third-year junior high) ratings only: the main five subjects (kokugo, social studies, mathematics, science, English) rating total is multiplied by 4 for 100 points, and the practical four subjects (music, art, health and physical education, technology and home economics) rating total is multiplied by 7.5 for 150 points, giving a 250-point report-card score. The academic test (500 halved to 250) and this 250-point report card are weighted equally (1:1).

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

Recommendation and special selection was held February 16, 2026 (some schools February 17) with results February 20 at 14:00. General selection applications were accepted February 25-27, 2026 with application-change through March 4 at 12:00 and the JPY 2,200 fee paid with Hyogo prefectural revenue stamps or online settlement. The academic examination was held on March 12, 2026 (Thursday), with selection results announced on March 19, 2026 (Thursday) at 10:00.

What is the multiple-choice selection (fukusu shigan senbatsu) system?

Most full-time general and comprehensive courses let applicants list a first and second choice; the first-choice school receives a bonus of about 20-30 points depending on the school district (for example about 25 points in the first district and about 30 in the fourth and fifth), while the second choice receives no bonus. Specialized courses use single selection (tandoku senbatsu) with no second choice.

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 (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 March 12, 2026. For the Reiwa 9 (2027 entrance) cycle, the Board has published the schedule: recommendation and special selection on February 16, 2027 (some schools February 17) with results February 22, 2027, and the general-selection academic examination on March 11, 2027 (Thursday) with results March 18, 2027 (Thursday). The five-subject, 50-minute, 100-point structure and the equal-weight (1:1) selection method have been stable, but confirm the current year's application windows, fees, and selection ratios on the Hyogo Prefectural Board of Education's own pages before relying on them.