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Key Facts: Nagasaki High School Entrance Exam - Mathematics Exam

Scored out of 100 points with a 50-minute time limit across 6 major question groups (大問).

Administered prefecture-wide by the Nagasaki Prefectural Board of Education (長崎県教育委員会).

The selection fee for a full-time course is 2,200 yen, and the 令和8年度 general selection was held on 17-18 February 2026.

Question bank includes exactly 100 practice items split across 4 core mathematical domains.

Prepare for the Nagasaki High School Entrance Examination Mathematics paper with 100 practice questions covering numbers and expressions, functions, geometry, and data and probability, matched to the five 大問 of the official 50-minute, 100-point paper. The official paper is answered by written working rather than multiple choice, so this English-language MCQ bank is a study aid and not a format simulation.

Sample Nagasaki High School Entrance Exam - Mathematics Practice Questions

Try these sample questions to review concepts for the Nagasaki High School Entrance Exam - Mathematics exam. 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 + 12.
A.5
B.-5
C.-19
D.19
Explanation: Adding a positive number to a negative number means moving right on the number line: -7 + 12 = 12 - 7 = 5.
2Simplify the algebraic expression: 5(2x - 3) - 3(x - 4).
A.7x - 27
B.7x - 3
C.7x + 3
D.7x - 7
Explanation: Expand each term using the distributive property: 5(2x - 3) - 3(x - 4) = 10x - 15 - 3x + 12. Grouping like terms gives (10x - 3x) + (-15 + 12) = 7x - 3.
3Calculate: (-4)^2 - 3 * (-5).
A.-31
B.1
C.31
D.-1
Explanation: First calculate the power (-4)^2 = 16. Next calculate the product -3 * (-5) = +15. Summing these values gives 16 + 15 = 31.
4Solve the linear equation: (x - 1) / 3 = (x + 3) / 5.
A.x = 4
B.x = 14
C.x = 9
D.x = 7
Explanation: Cross-multiply to clear denominators: 5(x - 1) = 3(x + 3). Expanding both sides yields 5x - 5 = 3x + 9. Subtracting 3x and adding 5 gives 2x = 14, so x = 7.
5Simplify the radical expression: √75 - √27 + √48.
A.6√3
B.5√3
C.12√3
D.2√3
Explanation: Simplify each radical into simplest radical form: √75 = 5√3, √27 = 3√3, and √48 = 4√3. Combining like terms gives (5 - 3 + 4)√3 = 6√3.
6Expand the binomial square expression: (2x - 3)^2.
A.4x² - 9
B.4x² - 12x + 9
C.4x² - 6x + 9
D.4x² + 12x + 9
Explanation: Apply the identity (a - b)^2 = a^2 - 2ab + b^2. Here a = 2x and b = 3, so (2x)^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9.
7Factor completely: 5x^2 - 45.
A.5(x - 3)^2
B.(5x - 15)(x + 3)
C.5(x - 3)(x + 3)
D.5(x² - 9x)
Explanation: First factor out the common monomial factor 5 to get 5(x^2 - 9). Then apply the difference of squares identity (x^2 - 9) = (x - 3)(x + 3), yielding 5(x - 3)(x + 3).
8Solve the system of simultaneous linear equations: 2x + y = 7 3x - y = 8
A.x = 4, y = -1
B.x = 3, y = -1
C.x = 2, y = 3
D.x = 3, y = 1
Explanation: Add the two equations to eliminate y: (2x + y) + (3x - y) = 7 + 8 => 5x = 15 => x = 3. Substitute x = 3 into 2(3) + y = 7 => 6 + y = 7 => y = 1.
9Calculate and simplify: 6 / √3 + √12.
A.4√3
B.3√3
C.5√3
D.6√3
Explanation: Rationalize the denominator of 6 / √3: (6 * √3) / 3 = 2√3. Simplify √12 = 2√3. Adding them together gives 2√3 + 2√3 = 4√3.
10Solve the quadratic equation: x^2 - 7x + 12 = 0.
A.x = -3, -4
B.x = 3, 4
C.x = 2, 6
D.x = -2, -6
Explanation: Factor the quadratic expression: x^2 - 7x + 12 = (x - 3)(x - 4) = 0. Setting each factor to zero yields x = 3 and x = 4.

About the Nagasaki High School Entrance Exam - Mathematics Exam

Comprehensive practice resource for the Nagasaki Prefectural High School Entrance Examination in Mathematics. Features 100 high-quality multiple-choice practice items covering topics from MEXT junior high curriculum standards, complete with step-by-step worked solutions and distractor breakdowns.

Exam sponsor: Nagasaki Prefectural Board of Education (長崎県教育委員会). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

50-minute paper worth 100 points, set as five 大問: a mixed set of short items (30 points, including a compass-and-straightedge construction), data analysis, probability and algebraic proof (17 points), functions from a parabola and line (15 points), plane and solid geometry (16 points), and an integrated problem applying geometry to an everyday context (22 points). Parts of the paper are issued at two difficulty levels (A問題 / B問題), and each high school decides which version its applicants sit.

Time Limit

50 minutes

Passing Score

No fixed pass mark. Admission is decided by each school from the 500-point five-subject academic test, the junior high school report card (調査書, 135 points across three years), and an interview (面接) held after the day-2 papers, with weights and any 傾斜配点 set school by school.

Exam / Certification Fees

2,200 yen for a full-time (全日制) course; the part-time (定時制) fee follows the national standard of 950 yen. Confirm both in the current 実施要領.

Exam sponsor website

Reported exam pass rate: Not published (varies by high school and course). Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25%

Domain 1: Numbers & Algebraic Expressions (数と式)

Positive and negative integer operations, radical simplifications, algebraic expansion, factoring, linear systems, and quadratic equation solution strategies.

25%

Domain 2: Functions & Graphs (関数)

Proportional/inverse proportional relationships, linear graphs y=ax+b, quadratic parabolas y=ax², rates of change, coordinate geometry intersections, and motion modeling.

30%

Domain 3: Plane & Solid Geometry (図形)

Angle bisectors, triangle similarity, Pythagorean theorem applications, inscribed circle theorems, 3D surface areas, and spatial solid volumes.

20%

Domain 4: Data Analysis & Probability (データの活用と確率)

Probability with dice, cards, and marbles, relative frequency tables, box-and-whisker plots, interquartile ranges, and sample size estimation.

0%

Domain 5: Comprehensive Problem Solving (総合問題)

Synthesized multi-domain problems combining functional graphing, geometric deduction, and algebraic problem-solving.

Preparing for the Nagasaki High School Entrance Exam - Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark. Admission is decided by each school from the 500-point five-subject academic test, the junior high school report card (調査書, 135 points across three years), and an interview (面接) held after the day-2 papers, with weights and any 傾斜配点 set school by school.
  • Assessment: 50-minute paper worth 100 points, set as five 大問: a mixed set of short items (30 points, including a compass-and-straightedge construction), data analysis, probability and algebraic proof (17 points), functions from a parabola and line (15 points), plane and solid geometry (16 points), and an integrated problem applying geometry to an everyday context (22 points). Parts of the paper are issued at two difficulty levels (A問題 / B問題), and each high school decides which version its applicants sit.
  • Time limit: 50 minutes
  • Exam / certification fees: 2,200 yen for a full-time (全日制) course; the part-time (定時制) fee follows the national standard of 950 yen. Confirm both in the current 実施要領. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Nagasaki High School Entrance Exam - Mathematics: Suggested Study Strategy

1Master fundamental computation techniques in Daimon 1 (大問1) to secure quick, high-yield points without losing time.
2Practice finding linear equations and quadratic function coefficients quickly using given coordinate pairs.
3Review key geometric theorems including the Pythagorean theorem, similar triangle ratios, and circle inscribed angle properties.
4Understand box plots and interquartile range (IQR) concepts, which are frequently tested under the updated MEXT curriculum.
5Build calculation confidence with square roots, factoring, and quadratic formulas to avoid numerical mistakes under timed conditions.
6Simulate full 50-minute exam sessions to manage time effectively across all 6 major question groups.

Frequently Asked Questions

What is the examination fee for the Nagasaki Prefectural High School Entrance Exam?

The selection fee for a full-time (全日制) course is 2,200 yen, paid electronically during the period announced by the prefectural 高校教育課. The part-time (定時制) fee follows the national standard of 950 yen; confirm both in the current 実施要領.

How long is the Mathematics subject test and how is it scored?

The Mathematics test is 50 minutes long and scored out of 100 points as part of a 5-subject total of 500 points.

Who administers the Nagasaki Public High School Entrance Exam?

The test is prepared and administered by the Nagasaki Prefectural Board of Education (長崎県教育委員会).

What topics are tested on the Nagasaki Mathematics exam?

The exam covers the complete MEXT junior high curriculum: numbers and algebraic expressions, linear and quadratic functions, plane and solid geometry, and data analysis with probability.

Are calculators permitted in the Nagasaki Mathematics exam?

No, electronic calculators are strictly prohibited during the Nagasaki Prefectural High School Entrance Examination.

What is a competitive score on the Mathematics paper?

While there is no fixed passing mark, top-tier public high schools in Nagasaki Prefecture generally require candidates to score 75 to 85+ out of 100 points in Mathematics.

How can I best prepare using this question bank?

Work through all 100 questions, review the detailed step-by-step calculations in the explanations, and practice timed 50-minute mock sessions to build speed and accuracy.