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100+ Free Nara Public High School Entrance Examination — Mathematics Practice Questions

Prepare for the Nara Prefectural High School Entrance Examination — Mathematics (奈良県公立高等学校入学者選抜学力検査 数学) exam with instant access — no signup required.

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Key Facts: Nara Public High School Entrance Examination — Mathematics Exam

Practise for the Nara Prefectural High School Entrance Exam in Mathematics with 100 four-option questions covering numbers and algebra, functions and graphs, plane and solid geometry including proof, and probability and data analysis, weighted to the official 50-minute, 50-point paper. The official paper contains constructed-response items including a written proof, so this English-language MCQ bank is a study aid, not a format simulation.

Sample Nara Public High School Entrance Examination — Mathematics Practice Questions

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

1Calculate: 12 + (−7) − (−3).
A.8
B.2
C.−2
D.22
Explanation: 12 + (−7) − (−3) = 12 − 7 + 3 = 8.
2Calculate: (−3)² − 5.
A.−14
B.4
C.−1
D.14
Explanation: (−3)² = 9, so 9 − 5 = 4.
3Simplify: −(−2)³.
A.8
B.−8
C.6
D.−6
Explanation: (−2)³ = −8, so −(−8) = 8.
4Compute: 3/4 + 1/6.
A.2/3
B.11/12
C.13/12
D.1/2
Explanation: Using LCD 12: 3/4 = 9/12 and 1/6 = 2/12, so 9/12 + 2/12 = 11/12.
5Compute: 2/3 − 5/6.
A.1/6
B.−1/6
C.−1/3
D.1/3
Explanation: Using LCD 6: 2/3 = 4/6, so 4/6 − 5/6 = −1/6.
6Multiply: (2/5) × (−3/4).
A.3/10
B.−3/10
C.−2/5
D.6/20
Explanation: Multiply numerators and denominators: (2×−3)/(5×4) = −6/20 = −3/10.
7Compute: 5/8 ÷ 1/4.
A.5/2
B.5/32
C.1/2
D.5/4
Explanation: Dividing by 1/4 equals multiplying by 4: 5/8 × 4 = 20/8 = 5/2.
8Solve the quadratic equation x² − 4x − 1 = 0 using the quadratic formula (解の公式).
A.x = 2 ± √5
B.x = −2 ± √5
C.x = 2 ± √3
D.x = 4 ± √5
Explanation: With a = 1, b = −4 and c = −1, the formula gives x = (4 ± √(16 + 4))/2 = (4 ± √20)/2 = (4 ± 2√5)/2 = 2 ± √5.
9Solve for x: 2x + 3 = 11.
A.7
B.14
C.4
D.−4
Explanation: Subtract 3 then divide by 2: 2x = 8, so x = 4.
10Solve for x: 3(x − 2) = 9.
A.3
B.15
C.1
D.5
Explanation: Divide by 3: x − 2 = 3, so x = 5.

About the Nara Public High School Entrance Examination — Mathematics Exam

The Nara Prefectural High School Entrance Examination in Mathematics tests lower-secondary graduates on calculation, algebra, functions, geometry and data analysis. From the 令和8年度 (2026) cycle the former 特色選抜 and 一般選抜 have been merged into a single 一次選抜 held in early March, and the five-subject academic test is scored out of 50 points per subject (250 points total). The paper is notable for a short-item set worth roughly forty percent of the marks and for a descriptive plane-geometry proof.

Assessment

50-minute paper worth 50 points, set as several 大問 with sub-questions. A short-item set (小問集合) covering basic problems across several fields accounts for roughly forty percent of the paper, and a descriptive plane-geometry proof (図形の証明問題) is a recurring feature. The five academic-test subjects together total 250 points.

Time Limit

50 minutes (the academic test is sat on a single day in early March, with a school-set examination on the following day where applicable)

Passing Score

No fixed pass mark. Admission is decided by each school from the 250-point five-subject academic test, the report card (調査書, 144 points in the standard pattern ①, rising to 234 in pattern ②, 198 in pattern ③ and 180 in pattern ④), and any school-set examination, with weights and 加重配点 set school by school.

Exam Fee

2,200 yen for a full-time (全日制) course (入学検定料); the part-time (定時制) fee follows the national standard of 950 yen. A separate 入学料 of 5,650 yen is due at enrolment. Confirm all figures in the current 実施要項. (Nara Prefectural Board of Education (奈良県教育委員会))

Nara Public High School Entrance Examination — Mathematics Exam Content Outline

25%

Numbers & Algebraic Expressions (数と式)

Positive and negative arithmetic, algebraic manipulation, linear and quadratic equations, and simultaneous equations.

25%

Functions & Graphs (関数)

Direct and inverse proportionality, linear functions, the quadratic function y=ax², and rates of change.

30%

Plane & Solid Geometry (図形)

Triangle congruence and similarity, the Pythagorean theorem, circle properties, and the descriptive proof that recurs on the Nara paper.

20%

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

Probability with dice, cards and coins, relative frequencies, histograms and box plots.

How to Pass the Nara Public High School Entrance Examination — Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark. Admission is decided by each school from the 250-point five-subject academic test, the report card (調査書, 144 points in the standard pattern ①, rising to 234 in pattern ②, 198 in pattern ③ and 180 in pattern ④), and any school-set examination, with weights and 加重配点 set school by school.
  • Assessment: 50-minute paper worth 50 points, set as several 大問 with sub-questions. A short-item set (小問集合) covering basic problems across several fields accounts for roughly forty percent of the paper, and a descriptive plane-geometry proof (図形の証明問題) is a recurring feature. The five academic-test subjects together total 250 points.
  • Time limit: 50 minutes (the academic test is sat on a single day in early March, with a school-set examination on the following day where applicable)
  • Exam fee: 2,200 yen for a full-time (全日制) course (入学検定料); the part-time (定時制) fee follows the national standard of 950 yen. A separate 入学料 of 5,650 yen is due at enrolment. Confirm all figures in the current 実施要項.

Keys to Passing

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

Nara Public High School Entrance Examination — Mathematics Study Tips from Top Performers

1Master the short-item set first: at roughly forty percent of the paper it is the largest single source of marks, so drill basic problems across every field for speed and accuracy.
2Practise writing out a plane-geometry proof in full sentences, naming each reason (for example the congruence condition or the inscribed-angle theorem) — this descriptive proof recurs on the Nara paper.
3Learn the quadratic function y=ax² together with its parabola, axis of symmetry and vertex, since it combines with geometry in higher-mark items.
4Drill probability with two trials (two dice, two draws) using a tree diagram, and be able to read a histogram and box plot quickly.
5Check whether your target school applies 加重配点 to the five-subject total, since this changes how much each extra mathematics mark is worth.
6Time yourself on past Nara papers released by the prefecture, since the 50 minutes must cover both the short-item set and the longer proof and function items.

Frequently Asked Questions

How long is the Nara mathematics paper and what is it worth?

It lasts 50 minutes and is scored out of 50 points, one of five subjects that together total 250 points. Some schools then multiply the five-subject total by 1.2 to 1.6 under 加重配点.

What is distinctive about the Nara mathematics paper?

A short-item set (小問集合) worth roughly forty percent of the paper draws basic problems from several fields, and a descriptive plane-geometry proof (図形の証明問題) appears most years.

How is the 令和8年度 selection different from before?

From the 令和8年度 (2026) cycle the former 特色選抜 and 一般選抜 have been merged into a single 一次選抜 held in early March, and candidates may apply to a first- and a second-choice school.

When were the 2026 papers sat?

The 令和8年度 一次選抜 academic test (学力検査) was held on 4 March 2026, with the school-set examination on 5 March and results announced on 13 March 2026.

How much is the examination fee?

The 入学検定料 is 2,200 yen for a full-time (全日制) course, paid through the Nara Web 出願 system. A separate 入学料 of 5,650 yen is due at enrolment after passing.

Is this question bank the same as the real exam?

No. The official paper is written in Japanese with constructed-response items including a written geometry proof. This bank is an English-language multiple-choice study adaptation of the same syllabus content and cannot replace showing your own mathematical reasoning.