100+ Free Nagano Entrance Mathematics Practice Questions
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Key Facts: Nagano Entrance Mathematics Exam
50 min / 100 points
Length and maximum score of the Nagano mathematics paper — 50 minutes, 100 points (500 across 5 subjects); sat on the 後期選抜 academic test day (国語・数学・社会・理科・英語, each 50 min).
Nagano Prefectural Board of Education selection page (令和8年度公立高等学校入学者選抜情報)
500 + 調査書 (45)
後期選抜 uses the academic test (500) and report card (調査書, 45 points, 中学3年 9教科 × 5段階); selection by 相関図; some schools apply 傾斜配点; no fixed pass mark.
Nagano Prefectural Board of Education selection requirements (実施要綱)
Two-stage selection
Nagano runs 前期選抜 (Feb, 検査Ⅰ 45 min + 検査Ⅱ 30 min plus an interview) and 後期選抜 (March, full five-subject 500-point test, all schools); this bank targets the 後期選抜 paper.
Nagano Prefectural Board of Education selection page
100
Free original practice questions in this bank
OpenExamPrep
The Nagano public high school entrance mathematics paper is a 50-minute, 100-point written exam covering algebra, equations, functions, geometry, and probability, set by the Nagano Prefectural Board of Education and sat on the 後期選抜 academic test day (five subjects, 50 minutes each). The academic test (500) combines with the 調査書 (45 points) via 相関図 (correlation diagram); no fixed pass mark. This page offers 100 original English-language practice questions with explanations as a study aid; MCQs cannot simulate the hand-written calculation, proof, and graphing sections.
Sample Nagano Entrance Mathematics Practice Questions
Try these sample questions to test your Nagano Entrance Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Compute: (-7) + 3 × (-2)
2Compute: 2/3 - 1/4
3Compute: 0.3 × 0.04
4What is the prime factorization of 84?
5Find the GCD of 36 and 48.
6Expand (x + 3)(x - 4)
7Factor x² - 8x + 15
8Simplify √72
9Compute: |-5| + |2 - 7|
10Solve the system: x + y = 7 and x - y = 1. What is (x, y)?
About the Nagano Entrance Mathematics Exam
The Nagano Public High School Entrance Selection mathematics paper is created by the Nagano Prefectural Board of Education. The single 50-minute, 100-point written paper, sat on the 後期選抜 academic test day, covers 数と式, 方程式, 関数, 図形, and 確率, on the 2017 MEXT junior-high Course of Study. Nagano runs a two-stage selection (前期選抜 and 後期選抜); this bank targets the 後期選抜 paper, which combines the academic test (500) with the 調査書 (45 points) by 相関図, and there is no fixed pass mark. This page provides 100 original English-language practice questions with detailed explanations as a study adaptation — not an official translation, not a reproduction of the official paper, and not a format simulation of the hand-written sections.
Assessment
The real Nagano mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects), sat on the 後期選抜 academic test day (five subjects, 50 minutes each: 国語・数学・社会・理科・英語). It is a written, constructed-response paper in Japanese covering 数と式, 方程式, 関数 (linear and quadratic), 図形 (plane and solid geometry, similarity, congruence, circles, Pythagoras), and 確率. Students show calculations, proofs, and graphs by hand. Nagano runs a two-stage selection — 前期選抜 (February, self-recommendation: 検査Ⅰ 45 min for 国語・社会・英語, 検査Ⅱ 30 min for 数学・理科, plus an interview) and 後期選抜 (March, general, all schools, full five-subject 500-point test) — and this bank targets the 後期選抜 paper. The 後期選抜 combines the academic test (500) with the report card (調査書, 45 points, 中学3年 9教科 × 5段階); selection is by 相関図 (correlation diagram), with no fixed pass mark. Some schools apply 傾斜配点 (weighted scoring). This local bank is an English-language MCQ study adaptation providing 100 original practice items; MCQs cannot simulate the hand-written calculation, proof, and graphing sections of the real paper.
Time Limit
50 minutes for the mathematics subject paper (後期選抜 academic test day; confirm the current cycle's exact date on the official Nagano page).
Passing Score
No fixed pass mark; the mathematics paper is scored out of 100 points (500 total across 5 subjects). The 後期選抜 combines the academic test (500) with the report card (調査書, 45 points, 中学3年 9教科 × 5段階). Selection is by 相関図 (correlation diagram) plotting 調査書 against 学力検査, with school-specific quota-based cut lines. Some schools apply 傾斜配点 (weighted scoring). There is no single prefecture-wide pass line.
Exam Fee
2,200 yen for the full-time course (全日制). The part-time (定時制) fee is lower and is not published on the prefectural selection pages — confirm it in the current 入学者選抜要綱. From the 令和8年度 (2026) cycle Nagano has used インターネット出願 (internet application), with the fee settled by electronic payment. The fee is not refunded once the application is submitted. (Nagano Prefectural Board of Education (長野県教育委員会))
Nagano Entrance Mathematics Exam Content Outline
Numbers, Expressions, and Equations
Integers, factoring, expansion, square roots, simultaneous equations, quadratic equations, and applied word problems.
Functions
Linear functions, proportion and inverse proportion, the junior-high quadratic y=ax² (a parabola through the origin), rate of change, line-and-parabola intersections, and applied graphs.
Geometry (図形)
Plane figures, triangles and quadrilaterals, similarity and congruence, circles (inscribed angles, tangents), Pythagoras, and solid figures (volume, surface area).
Probability and Data
Probability, counting, sample surveys, histograms, and central-tendency measures.
How to Pass the Nagano Entrance Mathematics Exam
What You Need to Know
- Passing score: No fixed pass mark; the mathematics paper is scored out of 100 points (500 total across 5 subjects). The 後期選抜 combines the academic test (500) with the report card (調査書, 45 points, 中学3年 9教科 × 5段階). Selection is by 相関図 (correlation diagram) plotting 調査書 against 学力検査, with school-specific quota-based cut lines. Some schools apply 傾斜配点 (weighted scoring). There is no single prefecture-wide pass line.
- Assessment: The real Nagano mathematics examination is a 50-minute paper scored out of 100 points (500 total across five subjects), sat on the 後期選抜 academic test day (five subjects, 50 minutes each: 国語・数学・社会・理科・英語). It is a written, constructed-response paper in Japanese covering 数と式, 方程式, 関数 (linear and quadratic), 図形 (plane and solid geometry, similarity, congruence, circles, Pythagoras), and 確率. Students show calculations, proofs, and graphs by hand. Nagano runs a two-stage selection — 前期選抜 (February, self-recommendation: 検査Ⅰ 45 min for 国語・社会・英語, 検査Ⅱ 30 min for 数学・理科, plus an interview) and 後期選抜 (March, general, all schools, full five-subject 500-point test) — and this bank targets the 後期選抜 paper. The 後期選抜 combines the academic test (500) with the report card (調査書, 45 points, 中学3年 9教科 × 5段階); selection is by 相関図 (correlation diagram), with no fixed pass mark. Some schools apply 傾斜配点 (weighted scoring). This local bank is an English-language MCQ study adaptation providing 100 original practice items; MCQs cannot simulate the hand-written calculation, proof, and graphing sections of the real paper.
- Time limit: 50 minutes for the mathematics subject paper (後期選抜 academic test day; confirm the current cycle's exact date on the official Nagano page).
- Exam fee: 2,200 yen for the full-time course (全日制). The part-time (定時制) fee is lower and is not published on the prefectural selection pages — confirm it in the current 入学者選抜要綱. From the 令和8年度 (2026) cycle Nagano has used インターネット出願 (internet application), with the fee settled by electronic payment. The fee is not refunded once the application is submitted.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Nagano Entrance Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is the real Nagano mathematics paper a multiple-choice test?
No — the real paper is a written, constructed-response exam in Japanese that requires hand-written calculations, proofs, and graphs. This 100-question bank is an original English-language MCQ study adaptation aligned to the 2017 MEXT junior-high Course of Study, not a reproduction or format simulation of the official paper.
Are these questions official past exam problems?
No. This bank is an original English-language MCQ study adaptation aligned to the 2017 MEXT junior-high Course of Study, covering algebra, equations, functions, geometry, and probability — not an official translation or format simulation.
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 as one of five academic-test subjects totaling 500 points on the 後期選抜 academic test day (国語・数学・社会・理科・英語, each 50 minutes).
How are the academic test and report card combined in Nagano's 後期選抜?
Nagano's 後期選抜 uses the academic test (500 points) and the report card (調査書, 45 points from 中学3年, 9教科 × 5段階). Selection is by 相関図 (correlation diagram) plotting 調査書 against 学力検査, with school-specific quota-based cut lines. Some schools apply 傾斜配点 (weighted scoring). There is no single prefecture-wide pass line.
What is Nagano's two-stage selection system?
Nagano runs 前期選抜 (February, self-recommendation, with 検査Ⅰ 45 min covering 国語・社会・英語 and 検査Ⅱ 30 min covering 数学・理科, plus an interview and any 作文・小論文・実技検査 the school sets) and 後期選抜 (March, general selection at all schools, with the full five-subject 500-point 学力検査). This bank targets the 後期選抜 paper. Confirm the current cycle's details on the official Nagano page.
How much is the Nagano entrance selection fee?
The entrance selection fee (入学考査料) is 2,200 yen for a full-time (全日制) course. The part-time (定時制) fee is lower, but neither amount is published on the prefectural selection pages, so confirm both in the current 入学者選抜要綱. From the 令和8年度 (2026) cycle Nagano has used インターネット出願 (internet application), with the fee settled by electronic payment. It is not refunded once the application is submitted, and it is a selection fee only, separate from tuition.
Can MCQs simulate the hand-written sections of the real paper?
No. The real paper requires hand-written calculations, proofs, and graphs. Four-option MCQs cannot reproduce those tasks. This bank instead offers algebra, function, geometry, and probability items to help prepare for those sections.