100+ Free Saitama Public High School Entrance Examination — Mathematics Practice Questions
Prepare for the Saitama Prefectural Public High School Entrance Examination — Mathematics (埼玉県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: Saitama Public High School Entrance Examination — Mathematics Exam
Practise for the Saitama Prefectural Public High School Entrance Exam in Mathematics with 100 four-option questions covering 数と式, 関数, 図形, and 確率・データ, weighted to the official 100-point paper sat on 26 February 2026. The official paper contains constructed-response items (計算/証明/作図/求め方記述), so this English-language MCQ bank is a study aid, not a format simulation.
Sample Saitama Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Saitama 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.
1Evaluate (-5) + 8 - (-3).
2Simplify √72 - √50 + √18.
3Calculate (1/2 + 1/3) ÷ (1/6).
4Solve for x: 3x - 7 = 2x + 5.
5Expand (x + 3)(x - 5).
6Factor x² - 7x + 12.
7Simplify the expression 2a(a - 3) - (a² - 5a).
8Solve the simultaneous equations: x + y = 10, 2x - y = 5.
9A number when divided by 4 gives a remainder of 3, and when divided by 5 gives a remainder of 2. Which is the smallest positive number satisfying both?
10Solve 2x² - 5x - 3 = 0.
About the Saitama Public High School Entrance Examination — Mathematics Exam
The Saitama Prefectural Public 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 general academic test (学力検査) covers five subjects (国語, 社会, 数学, 理科, 英語), each worth 100 points (total 500), sat on a single day, 26 February 2026. The paper is aligned to the MEXT junior-high Course of Study (平成29年 中学校学習指導要領 数学編) and tests 知識・技能 plus 思考力・判断力・表現力, with constructed-response items including 計算, 証明, 作図, and 求め方記述. Saitama holds one 学力検査 and each school ranks candidates in a 第1次選抜 (学力検査:調査書 between 4:6 and 6:4) and a 第2次選抜 (between 3:7 and 7:3), with some schools adding a 第3次選抜. In 令和8年度, 22 designated high schools used a 学校選択問題 (school-choice paper) in mathematics and English in place of the common paper. The Board of Education writes both versions; each school decides whether to adopt the school-choice paper, which stays inside the junior-high curriculum but carries more applied problems.
Assessment
100-point paper aligned to the MEXT 数学 Course of Study with constructed-response items including 計算, 証明, 作図, and 求め方記述. The five academic-test subjects (国語, 社会, 数学, 理科, 英語) each carry 100 points for a maximum of 500 points, sat on a single day (26 February 2026). The paper tests 知識・技能 plus 思考力・判断力・表現力. In 令和8年度, 22 designated high schools used a 学校選択問題 (school-choice paper) in mathematics and English in place of the common paper. The Board of Education writes both versions; each school decides whether to adopt the school-choice paper, which stays inside the junior-high curriculum but carries more applied problems.
Time Limit
Sat on 26 February 2026 as part of the single-day five-subject 学力検査: each subject is a 100-point paper of 50 minutes, 500 points in total.
Passing Score
No fixed prefecture-wide pass mark. The mathematics paper is scored out of 100 points (500 across the five academic-test subjects, each 100 points). Saitama holds one application and one 学力検査; there is no 推薦選抜 and no 特色化選抜 in 令和8年度. Each school then ranks candidates in a 第1次選抜 and a 第2次選抜, and some schools add a 第3次選抜. The 学力検査:調査書 ratio is set by each school within 4:6 to 6:4 in the 第1次選抜 and within 3:7 to 7:3 in the 第2次選抜. The 調査書 records 中1・中2・中3, 9教科 × 5段階評定, weighted by year at 1:1:1, 1:1:2 or 1:1:3 at the school's choice, plus 特別活動等の記録 and その他の項目; attendance is not scored. There is no single prefecture-wide pass line. Source: 令和8年度入試についてのQ&A and 選抜基準, 埼玉県教育委員会.
Exam Fee
入学者選抜手数料 is ¥2,200 for the 全日制 (full-time) course and ¥950 for the 定時制 (part-time) course, paid once for the whole five-subject 学力検査 by 電子収納 (credit card or convenience store). Source: 令和8年度入試についてのQ&A and 選抜基準, 埼玉県教育委員会. (Saitama Prefectural Board of Education (埼玉県教育委員会))
Saitama Public High School Entrance Examination — Mathematics Exam Content Outline
Numbers & Algebraic Expressions (数と式)
Signed arithmetic, fractions, square roots, algebraic manipulation, linear and simultaneous equations, quadratic equations, and word-problem set-up.
Functions (関数)
Direct and inverse proportionality, linear functions y=ax+b and their graphs, the quadratic function y=ax² and the parabola, and reading information from graphs.
Geometry (図形)
Parallel-line properties, triangle congruence and similarity, the Pythagorean theorem, circle inscribed angles and tangent lines, polygons, and solid volume and surface area.
Data Analysis & Probability (資料の活用と確率)
Histograms and box plots, mean/median/mode/range, sample surveys, and probability with dice, coins, marbles and cards including tree diagrams and two-trial events.
How to Pass the Saitama Public High School Entrance Examination — Mathematics Exam
What You Need to Know
- Passing score: No fixed prefecture-wide pass mark. The mathematics paper is scored out of 100 points (500 across the five academic-test subjects, each 100 points). Saitama holds one application and one 学力検査; there is no 推薦選抜 and no 特色化選抜 in 令和8年度. Each school then ranks candidates in a 第1次選抜 and a 第2次選抜, and some schools add a 第3次選抜. The 学力検査:調査書 ratio is set by each school within 4:6 to 6:4 in the 第1次選抜 and within 3:7 to 7:3 in the 第2次選抜. The 調査書 records 中1・中2・中3, 9教科 × 5段階評定, weighted by year at 1:1:1, 1:1:2 or 1:1:3 at the school's choice, plus 特別活動等の記録 and その他の項目; attendance is not scored. There is no single prefecture-wide pass line. Source: 令和8年度入試についてのQ&A and 選抜基準, 埼玉県教育委員会.
- Assessment: 100-point paper aligned to the MEXT 数学 Course of Study with constructed-response items including 計算, 証明, 作図, and 求め方記述. The five academic-test subjects (国語, 社会, 数学, 理科, 英語) each carry 100 points for a maximum of 500 points, sat on a single day (26 February 2026). The paper tests 知識・技能 plus 思考力・判断力・表現力. In 令和8年度, 22 designated high schools used a 学校選択問題 (school-choice paper) in mathematics and English in place of the common paper. The Board of Education writes both versions; each school decides whether to adopt the school-choice paper, which stays inside the junior-high curriculum but carries more applied problems.
- Time limit: Sat on 26 February 2026 as part of the single-day five-subject 学力検査: each subject is a 100-point paper of 50 minutes, 500 points in total.
- Exam fee: 入学者選抜手数料 is ¥2,200 for the 全日制 (full-time) course and ¥950 for the 定時制 (part-time) course, paid once for the whole five-subject 学力検査 by 電子収納 (credit card or convenience store). Source: 令和8年度入試についてのQ&A and 選抜基準, 埼玉県教育委員会.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Saitama Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Saitama mathematics exam?
No. The official paper is written in Japanese with constructed-response items including 計算, 証明, 作図, and 求め方記述. This bank is an English-language multiple-choice study adaptation of the same syllabus content and cannot replace writing out your own proofs and working under timed conditions.
How long is the Saitama mathematics paper and what is it worth?
It is scored out of 100 points, one of five subjects that together total 500 points (each subject 100 points). The five-subject 学力検査 is sat on a single day, 26 February 2026, each paper 50 minutes in the order 国語, 数学, 社会, 理科, 英語. 実技検査・面接 follow on 27 February at schools that set them, the 追検査 is on 3 March and results are announced on 6 March 2026.
How is the selection structured in 2026?
Saitama holds one application and one 学力検査; there is no 推薦選抜 and no 特色化選抜 in 令和8年度. Each school then ranks candidates in a 第1次選抜 and a 第2次選抜, and some schools add a 第3次選抜. The 学力検査:調査書 ratio is set by each school within 4:6 to 6:4 in the 第1次選抜 and within 3:7 to 7:3 in the 第2次選抜. The 調査書 records 中1・中2・中3, 9教科 × 5段階評定, weighted by year at 1:1:1, 1:1:2 or 1:1:3 at the school's choice, plus 特別活動等の記録 and その他の項目; attendance is not scored. There is no prefecture-wide pass line.
What is the 学校選択問題?
In 令和8年度, 22 designated high schools used a 学校選択問題 (school-choice paper) in mathematics and English in place of the common paper. The Board of Education writes both versions; each school decides whether to adopt the school-choice paper, which stays inside the junior-high curriculum but carries more applied problems.
How much is the examination fee?
The 入学者選抜手数料 (entrance examination fee) for a Saitama prefectural public high school is ¥2,200 for the 全日制 course. It is paid once for the whole five-subject 学力検査, not per subject paper.
When was the 2026 paper sat?
The 令和8年度 学力検査 was held on a single day, 26 February 2026, covering 国語, 社会, 数学, 理科 and 英語 (each 100 points, 500 total).