100+ Free Niigata Public High School Entrance Examination — Mathematics Practice Questions
Prepare for the Niigata Prefectural High School Entrance Examination — Mathematics (新潟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: Niigata Public High School Entrance Examination — Mathematics Exam
Practise for the Niigata Prefectural High School Entrance Exam in Mathematics with 100 four-option questions covering numbers and algebra, functions and graphs, plane and solid geometry, and probability and data analysis, weighted to the official 50-minute, 100-point paper. The official paper contains constructed-response items, so this English-language MCQ bank is a study aid, not a format simulation.
Sample Niigata Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Niigata 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: 15 + (−9) − (−4).
2Calculate: (−2)² − 6.
3Simplify: −(−3)³.
4Compute: 5/6 + 1/4.
5Compute: 7/8 − 1/3.
6Multiply: (3/7) × (−2/9).
7Compute: 3/5 ÷ 1/10.
8Solve the quadratic equation x² − 6x + 2 = 0 using the quadratic formula (解の公式).
9Solve for x: 4x − 5 = 11.
10Solve for x: 2(x + 3) = 14.
About the Niigata Public High School Entrance Examination — Mathematics Exam
The Niigata Prefectural High School Entrance Examination in Mathematics tests lower-secondary graduates on calculation, algebra, functions, geometry and data analysis. In the 令和8年度 (2026) cycle the full-time academic test covers five subjects (国語, 社会, 数学, 理科, 英語), each 50 minutes and 100 points, with mathematics sat from 11:10 to 12:00 on 4 March 2026. The 令和8年度 official commentary reports high correct rates on basic calculation and basic geometry and low correct rates on cross-domain application and integrated developmental reasoning. Mathematics was the lowest-scoring of the five subjects in 令和8年度, averaging 42.8 out of 100 against a five-subject average of 49.5.
Assessment
50-minute paper worth 100 points, built from 5 大問 and about 22 小問: a 小問集合, a second 小問集合 requiring the working to be shown, 一次関数の利用, 文字式の利用, and a combined circle-and-plane-geometry problem in 令和8年度. It carries one written 図形の証明 proof, one 作図 construction, and roughly seven items where the 求め方 must be written out — an unusually high proportion of working-out marks. The five academic-test subjects (国語, 社会, 数学, 理科, 英語) together total 500 points, and the mathematics paper is sat from 11:10 to 12:00. The 令和8年度 official commentary reports high correct rates on basic calculation and basic geometry and low correct rates on cross-domain application and integrated developmental reasoning.
Time Limit
50 minutes (the academic test is sat on a single day in early March; the 令和8年度 本検査 was on 4 March 2026, with the 追検査 on 9 March 2026)
Passing Score
No fixed pass mark. Admission is decided by each school from the 500-point five-subject academic test, the report card (調査書, 135 points maximum = 9 subjects × 5 × 3 years), and any school-set examination, with the selection ratio set per school from the five 調査書:学力検査 weightings allowed by the 令和8年度 実施要項 — 7:3, 6:4, 5:5, 4:6 or 3:7. Some schools and departments also apply 傾斜配点, doubling the weighting of one or more designated subjects so the five-subject maximum rises above 500 points.
Exam Fee
2,200 yen for a full-time (全日制) course and 950 yen for a part-time (定時制) course (入学考査料). A separate 入学料 of 5,650 yen (full-time) or 2,100 yen (part-time) is due at enrolment. Confirm all figures in the current 実施要項. (Niigata Prefectural Board of Education (新潟県教育委員会), 高等学校教育課)
Niigata Public High School Entrance Examination — Mathematics Exam Content Outline
Numbers & Algebraic Expressions (数と式)
Positive and negative arithmetic, algebraic manipulation, linear and quadratic equations, and simultaneous equations.
Functions & Graphs (関数)
Direct and inverse proportionality, linear functions, the quadratic function y=ax², and rates of change.
Plane & Solid Geometry (図形)
Triangle congruence and similarity, the Pythagorean theorem, circle properties, inscribed angles, and solid-geometry surface area and volume.
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 Niigata 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 500-point five-subject academic test, the report card (調査書, 135 points maximum = 9 subjects × 5 × 3 years), and any school-set examination, with the selection ratio set per school from the five 調査書:学力検査 weightings allowed by the 令和8年度 実施要項 — 7:3, 6:4, 5:5, 4:6 or 3:7. Some schools and departments also apply 傾斜配点, doubling the weighting of one or more designated subjects so the five-subject maximum rises above 500 points.
- Assessment: 50-minute paper worth 100 points, built from 5 大問 and about 22 小問: a 小問集合, a second 小問集合 requiring the working to be shown, 一次関数の利用, 文字式の利用, and a combined circle-and-plane-geometry problem in 令和8年度. It carries one written 図形の証明 proof, one 作図 construction, and roughly seven items where the 求め方 must be written out — an unusually high proportion of working-out marks. The five academic-test subjects (国語, 社会, 数学, 理科, 英語) together total 500 points, and the mathematics paper is sat from 11:10 to 12:00. The 令和8年度 official commentary reports high correct rates on basic calculation and basic geometry and low correct rates on cross-domain application and integrated developmental reasoning.
- Time limit: 50 minutes (the academic test is sat on a single day in early March; the 令和8年度 本検査 was on 4 March 2026, with the 追検査 on 9 March 2026)
- Exam fee: 2,200 yen for a full-time (全日制) course and 950 yen for a part-time (定時制) course (入学考査料). A separate 入学料 of 5,650 yen (full-time) or 2,100 yen (part-time) 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
Niigata Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
How long is the Niigata mathematics paper and what is it worth?
It lasts 50 minutes and is scored out of 100 points, one of five subjects that together total 500 points. Some schools and departments then apply 傾斜配点, doubling the weighting of one or more designated subjects so their five-subject maximum rises above 500 points.
What is distinctive about the Niigata mathematics paper?
The 令和8年度 official commentary reports high correct rates on basic calculation and basic geometry, and low correct rates on cross-domain application and integrated developmental reasoning, so the paper rewards flexible multi-step problem solving.
How is the selection structured in 2026?
Niigata runs 特色化選抜 (interview-based, abolished after 2026 and replaced by 学校設定枠 from 2027) and 一般選抜 (学力検査 plus an optional 学校独自検査; in 2026 新潟中央高校音楽科 uses 実技), with 欠員補充のための2次募集 and 海外帰国生徒等特別選抜 also available.
When were the 2026 papers sat?
The 令和8年度 学力検査 本検査 was held on 4 March 2026, with the 追検査 on 9 March and 合格発表 on 12 March 2026. The mathematics paper was sat from 11:10 to 12:00.
How much is the examination fee?
The 入学考査料 is 2,200 yen for a full-time (全日制) course and 950 yen for a part-time (定時制) course. A separate 入学料 of 5,650 yen (full-time) or 2,100 yen (part-time) is due at enrolment after passing.
How are the academic test and the report card combined?
The 実施要項 sets out five permitted 調査書:学力検査 weightings — 7:3, 6:4, 5:5, 4:6 and 3:7 — and each school picks one for its own selection. The 調査書 (135 points maximum = 9 subjects × 5 × 3 years) and the 学力検査 (500 points) are each converted to a 1000-point scale, then compressed by that weighting.
Is this question bank the same as the real exam?
No. The official paper is written in Japanese with constructed-response items. This bank is an English-language multiple-choice study adaptation of the same syllabus content and cannot replace showing your own mathematical reasoning.