100+ Free Tokyo Metropolitan Public High School Entrance Examination — Mathematics Practice Questions
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Key Facts: Tokyo Metropolitan Public High School Entrance Examination — Mathematics Exam
Practise for the Tokyo Metropolitan Public High School Entrance Exam in Mathematics (数学) with 100 four-option questions covering 数と式, 関数, 図形 and 資料の活用, including genuine worked calculations, weighted to the official 100-point, 50-minute paper sat on 令和8年2月21日(土). The official paper mixes a mark-sheet section with 記述式 answers requiring 途中の計算過程, so this English-language MCQ bank drills the underlying methods — it is not a format simulation, and you still need to practise writing solutions out.
Sample Tokyo Metropolitan Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Tokyo Metropolitan 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.
1What is the prime factorisation of 360?
2Find the greatest common divisor (GCD) of 48 and 84.
3Find the least common multiple (LCM) of 15 and 20.
4Solve for x: 3x - 5 = x + 7.
5Solve the simultaneous equations x + y = 10 and 2x - y = 5. What is x?
6Simplify the expression 3(x - 2) - 2(x + 1).
7Solve the inequality 2x + 3 ≤ 9.
8Solve x² - 7x + 12 = 0.
9Solve x² + 5x - 14 = 0.
10Simplify √98 as a surd in its simplest form.
About the Tokyo Metropolitan Public High School Entrance Examination — Mathematics Exam
The Tokyo Metropolitan Public High School Entrance Examination in Mathematics (数学) tests lower-secondary graduates on numbers and expressions, functions, geometry, and data and probability. The general academic test (学力検査) is 共通問題 (a metropolitan-wide common paper) covering five subjects (国語, 数学, 英語[リスニング含む], 社会, 理科), each worth 100 points (total 500, scaled ×1.4 to 700) and each sat for 50 minutes on one day; for 令和8年度 (2026 admission) the 第一次募集 is 2月21日(土) with 合格者発表 on 3月2日(月). The 数学 共通問題 paper combines a mark-sheet (マークシート) section with 記述式 (constructed-response) questions requiring 途中の計算過程 and proofs, so it is not a pure multiple-choice paper; ten 全日制 schools set 自校作成問題 for 数学 instead. Selection combines the scaled 学力検査 (700), the 調査書 (300, ratio 7:3) and the ESAT-J English speaking test (up to 20) for a 総合得点 of 1,020, with some schools applying 傾斜配点. 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), calculators are not permitted, and it tests 知識・技能 plus 思考力・判断力・表現力.
Assessment
100-point paper aligned to the MEXT 数学 Course of Study, covering 数と式 (25%), 関数 (25%), 図形 (30%) and 資料の活用 (20%). The 共通問題 paper mixes a mark-sheet (マークシート) section with 記述式 answers that earn partial credit for 途中の計算過程; ten 全日制 schools instead set 自校作成問題 for 数学. The five academic-test subjects each carry 100 points (max 500, scaled ×1.4 to 700), all sat on one day as 共通問題; every subject runs 50 minutes. Problems are at junior-high graduation level (中学校卒業程度); calculators are not permitted. The paper tests 知識・技能 plus 思考力・判断力・表現力.
Time Limit
Sat as part of the one-day five-subject 学力検査: each subject is a 100-point, 50-minute paper (500 points total, scaled to 700). For 令和8年度 (2026 admission) the 学力検査に基づく選抜 (第一次募集) is 2月21日(土), with 合格者発表 on 3月2日(月); the 推薦に基づく選抜 is 1月26日(月)・27日(火) and the 全日制第二次募集 / 追検査 is 3月10日(火). Calculators are not permitted. Source: 令和8年度東京都立高等学校入学者選抜実施要綱・同細目 / 日程, 東京都教育委員会.
Passing Score
No fixed prefecture-wide pass mark. The 数学 paper is scored out of 100 points. In the 学力検査に基づく選抜 the five subjects (国語・数学・英語・理科・社会) total 500 points and are scaled ×1.4 to 700; the 調査書 contributes 300 points (65-point junior-high 評定 expanded to 300, four practical subjects doubled), giving 1,000 points at the standard 7:3 ratio. The ESAT-J English speaking test adds up to 20 points for a 総合得点 of 1,020, and some schools apply 傾斜配点. Selection is competitive and relative, not against a published pass line. Source: 令和8年度東京都立高等学校入学者選抜実施要綱・同細目, 東京都教育委員会.
Exam Fee
The 入学考査料 is ¥2,200 for a 全日制 course and ¥950 for a 定時制 course, paid via the prescribed 納付書 at a Tokyo-designated financial institution (or by credit card on the internet-application site) with the receipt affixed to the 入学願書; it may be reduced or waived in cases of financial hardship. Source: 入学考査料、入学料及び授業料等の納付について (東京都教育委員会) and 令和8年度東京都立高等学校入学者選抜実施要綱・同細目. (Tokyo Metropolitan Board of Education (東京都教育委員会), 教育庁都立学校教育部高等学校教育課入学選抜担当, 〒163-8001 東京都新宿区西新宿2-8-1 都庁第二本庁舎 (TEL 03-5320-6745))
Tokyo Metropolitan Public High School Entrance Examination — Mathematics Exam Content Outline
Numbers & Expressions (数と式)
Integers, prime factorisation, linear equations, simultaneous equations (連立方程式), quadratic equations, inequalities, algebraic expressions and identities, polynomials, exponents, and square roots.
Functions (関数)
Linear functions, proportional and inverse proportional relationships, quadratic functions y=ax² (二次関数), parabolas, vertex and axis of symmetry, intersections of parabolas with lines, and function–geometry fusion problems.
Geometry (図形)
Congruence and similarity, triangles, quadrilaterals, circles, arcs and chords, inscribed and central angles (円周角の定理), the Pythagorean theorem (ピタゴラスの定理 / 三平方の定理), parallel-line proportionality, surface area and volume of solids, and constructions.
Data & Probability (資料の活用)
Mean, median, mode and range, histograms, frequency distributions, relative and cumulative frequency, quartiles, interquartile range and box-and-whisker plots, sampling surveys (標本調査), and probability. Variance and standard deviation are 高校 数学I content and are not tested here.
How to Pass the Tokyo Metropolitan Public High School Entrance Examination — Mathematics Exam
What You Need to Know
- Passing score: No fixed prefecture-wide pass mark. The 数学 paper is scored out of 100 points. In the 学力検査に基づく選抜 the five subjects (国語・数学・英語・理科・社会) total 500 points and are scaled ×1.4 to 700; the 調査書 contributes 300 points (65-point junior-high 評定 expanded to 300, four practical subjects doubled), giving 1,000 points at the standard 7:3 ratio. The ESAT-J English speaking test adds up to 20 points for a 総合得点 of 1,020, and some schools apply 傾斜配点. Selection is competitive and relative, not against a published pass line. Source: 令和8年度東京都立高等学校入学者選抜実施要綱・同細目, 東京都教育委員会.
- Assessment: 100-point paper aligned to the MEXT 数学 Course of Study, covering 数と式 (25%), 関数 (25%), 図形 (30%) and 資料の活用 (20%). The 共通問題 paper mixes a mark-sheet (マークシート) section with 記述式 answers that earn partial credit for 途中の計算過程; ten 全日制 schools instead set 自校作成問題 for 数学. The five academic-test subjects each carry 100 points (max 500, scaled ×1.4 to 700), all sat on one day as 共通問題; every subject runs 50 minutes. Problems are at junior-high graduation level (中学校卒業程度); calculators are not permitted. The paper tests 知識・技能 plus 思考力・判断力・表現力.
- Time limit: Sat as part of the one-day five-subject 学力検査: each subject is a 100-point, 50-minute paper (500 points total, scaled to 700). For 令和8年度 (2026 admission) the 学力検査に基づく選抜 (第一次募集) is 2月21日(土), with 合格者発表 on 3月2日(月); the 推薦に基づく選抜 is 1月26日(月)・27日(火) and the 全日制第二次募集 / 追検査 is 3月10日(火). Calculators are not permitted. Source: 令和8年度東京都立高等学校入学者選抜実施要綱・同細目 / 日程, 東京都教育委員会.
- Exam fee: The 入学考査料 is ¥2,200 for a 全日制 course and ¥950 for a 定時制 course, paid via the prescribed 納付書 at a Tokyo-designated financial institution (or by credit card on the internet-application site) with the receipt affixed to the 入学願書; it may be reduced or waived in cases of financial hardship. Source: 入学考査料、入学料及び授業料等の納付について (東京都教育委員会) and 令和8年度東京都立高等学校入学者選抜実施要綱・同細目.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Tokyo Metropolitan Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Tokyo 数学 exam?
No. The official paper is worked in Japanese and combines a mark-sheet (マークシート) section with 記述式 (constructed-response) questions that require 途中の計算過程 and proofs; its exact item count is not published. This bank is an English-language multiple-choice study adaptation of the same junior-high syllabus (数と式, 関数 including y=ax², 図形 with 相似・円周角・三平方の定理, and 資料の活用) and cannot replace writing out your own calculations in Japanese under timed conditions.
How long is the Tokyo 数学 paper and what is it worth?
It is scored out of 100 points, one of five subjects totalling 500 points (each subject 100 points), scaled ×1.4 to 700 points in the general selection. 数学 runs 50 minutes on 令和8年2月21日(土), with 合格者発表 on 3月2日(月); the 推薦 selection is 1月26日・27日 and the 第二次募集 / 追検査 is 3月10日(火).
Are calculators allowed?
No. The mathematics paper is sat without a calculator, in line with standard metropolitan academic-test rules; numerical reasoning and exact computation are expected.
How is the selection structured?
Tokyo's 学力検査に基づく選抜 combines the scaled 学力検査 (5 subjects × 100 = 500 → ×1.4 = 700) with the 調査書 (300, the 65-point junior-high 評定 expanded to 300 with the four practical subjects doubled) at a standard 7:3 ratio, then adds the ESAT-J English speaking test (up to 20 points) for a 総合得点 of 1,020. Some schools apply 傾斜配点 to emphasised subjects, and a few schools conduct 面接, 作文, 小論文 or 実技検査. Selection is relative to other applicants, not against a published pass line.
What is the 自校作成問題 system?
Ten 全日制 schools (日比谷・戸山・青山・西・八王子東・立川・国立・新宿・墨田川・国分寺) set their own 国語・数学・英語 problems instead of the 共通問題 for those three subjects; 社会・理科 remain the 共通問題. These 自校作成問題 are not mark-sheet and are harder, so targeted preparation is needed. This bank targets the 共通問題 syllabus that underlies both.
How much is the examination fee?
The 入学考査料 is ¥2,200 for a 全日制 course (¥950 for 定時制), paid via the prescribed 納付書 at a Tokyo-designated financial institution or by credit card on the internet-application site; it may be reduced or waived in cases of financial hardship.