100+ Free Tokushima Public High School Entrance Examination — Mathematics Practice Questions
Prepare for the Tokushima Prefectural Public High School Entrance Examination — Mathematics (徳島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: Tokushima Public High School Entrance Examination — Mathematics Exam
Practise for the Tokushima Prefectural 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 as the 第2時限 on 3月4日 in 令和9年度. The official paper is handwritten and requires 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 Tokushima Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Tokushima 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.
1Compute: -9 + 4 - (-3).
2Compute: (-2)^3 - (-3)^2.
3Compute 5/6 - 1/4 and write the answer as a reduced fraction.
4Find the prime factorisation of 84.
5Solve for x: 3x - 7 = 2x + 5.
6Solve the simultaneous equations: x + y = 10, x - y = 4.
7Solve: 2(x - 3) ≤ 4x + 2. Which set describes x?
8Simplify: 3a(2a - 5) - 2(a^2 + 3).
9Factorise: x^2 - 7x + 12.
10Solve x^2 - 5x + 6 = 0.
About the Tokushima Public High School Entrance Examination — Mathematics Exam
The Tokushima Prefectural 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 県内同一問題 (a prefecture-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); 国語 runs 55 minutes (作文含む) and the other four subjects 50 minutes each, all sat on one day. For 令和9年度 (2027) the 一般選抜 学力検査 is 3月3日(水), with 数学 as the 第2時限 paper at 10:20-11:10; 面接等 is 3月4日(木), 追検査 is 3月10日(水) and 合格者発表 is 3月13日(土). The 数学 paper is worked by hand in Japanese and requires 途中の計算過程 with partial credit, so it is not a multiple-choice paper. Selection is competitive and relative and runs in two stages — a 第1次選考 limited to applicants in the top 80% of the 募集人員 on both 調査書 評定 (195点満点) and 学力検査 得点 (500点), then a 第2次選考 that weighs the two equally on a 相関表 — with up to 100点 of 傾斜配点 per school and a required 面接. 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%). Answers are handwritten, including 途中の計算過程 that earns partial credit. The five academic-test subjects each carry 100 points (max 500), all sat on a single day as 県内同一問題; 国語 runs 55 minutes (作文含む) and the other four subjects 50 minutes each. 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 paper, 500 points in total. For 令和9年度 (2027) the 一般選抜 学力検査 is 3月3日(水), with 数学 as the 第2時限 paper at 10:20-11:10 (50 minutes); 面接等 follows on 3月4日(木), 追検査 is 3月10日(水) and 合格者発表 is 3月13日(土). 育成型・連携型選抜 run earlier (検査 2月2日(火), 結果通知 2月6日(土)) and 第2次募集選抜 runs later (検査 3月25日(木), 結果通知 3月26日(金)). Calculators are not permitted. Source: 令和9年度 徳島県公立高等学校入学者選抜日程 / 生徒募集選抜要項, 徳島県教育委員会教育創生課.
Passing Score
No fixed prefecture-wide pass mark. The 数学 paper is scored out of 100 points (500 across the five 学力検査 subjects, each 100 points). Selection is competitive and relative, and runs in two stages. In the 第1次選考 a school selects from applicants who rank within the top 80% of its 募集人員 on both the 調査書 評定 and the 学力検査 score, with 面接 results also taken into account. All remaining applicants go to the 第2次選考, where the 評定 and the 学力検査 得点 are weighed equally using a 相関表 (correlation table) of the two. The 調査書 評定値合計 is out of 195点 and the 学力検査 out of 500点; a school may add up to a combined 100点 of 傾斜配点 to the subjects it emphasises. 面接 is also required for 一般選抜. Admission is relative to other applicants, not against a published pass line. Source: 徳島県公立高等学校生徒募集選抜要項, 徳島県教育委員会.
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, affixed as 徳島県収入証紙 on the 入学願書 and submitted via the junior-high principal; applicants to 徳島市立高等学校 pay in cash. The fee is not refunded once paid. Source: 令和9年度 徳島県公立高等学校生徒募集選抜要項 (2026年7月31日修正版), 徳島県教育委員会. (Tokushima Prefectural Board of Education (徳島県教育委員会), 教育創生課 学区制・入試担当, 〒770-8570 徳島市万代町１丁目１番地 (TEL 088-621-3120))
Tokushima 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), 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 Tokushima 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 (500 across the five 学力検査 subjects, each 100 points). Selection is competitive and relative, and runs in two stages. In the 第1次選考 a school selects from applicants who rank within the top 80% of its 募集人員 on both the 調査書 評定 and the 学力検査 score, with 面接 results also taken into account. All remaining applicants go to the 第2次選考, where the 評定 and the 学力検査 得点 are weighed equally using a 相関表 (correlation table) of the two. The 調査書 評定値合計 is out of 195点 and the 学力検査 out of 500点; a school may add up to a combined 100点 of 傾斜配点 to the subjects it emphasises. 面接 is also required for 一般選抜. Admission is relative to other applicants, not against a published pass line. Source: 徳島県公立高等学校生徒募集選抜要項, 徳島県教育委員会.
- 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%). Answers are handwritten, including 途中の計算過程 that earns partial credit. The five academic-test subjects each carry 100 points (max 500), all sat on a single day as 県内同一問題; 国語 runs 55 minutes (作文含む) and the other four subjects 50 minutes each. 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 paper, 500 points in total. For 令和9年度 (2027) the 一般選抜 学力検査 is 3月3日(水), with 数学 as the 第2時限 paper at 10:20-11:10 (50 minutes); 面接等 follows on 3月4日(木), 追検査 is 3月10日(水) and 合格者発表 is 3月13日(土). 育成型・連携型選抜 run earlier (検査 2月2日(火), 結果通知 2月6日(土)) and 第2次募集選抜 runs later (検査 3月25日(木), 結果通知 3月26日(金)). Calculators are not permitted. Source: 令和9年度 徳島県公立高等学校入学者選抜日程 / 生徒募集選抜要項, 徳島県教育委員会教育創生課.
- 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, affixed as 徳島県収入証紙 on the 入学願書 and submitted via the junior-high principal; applicants to 徳島市立高等学校 pay in cash. The fee is not refunded once paid. Source: 令和9年度 徳島県公立高等学校生徒募集選抜要項 (2026年7月31日修正版), 徳島県教育委員会.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Tokushima Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Tokushima 数学 exam?
No. The official paper is worked by hand in Japanese and requires 途中の計算過程; its exact item count is not published and the prefecture does not publish past papers online. 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 Tokushima 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). 数学 is the 第2時限 paper and runs 50 minutes (10:20-11:10) on 3月3日(水) for 令和9年度; 面接等 is 3月4日(木), 追検査 is 3月10日(水) and 合格者発表 is 3月13日(土).
Are calculators allowed?
No. The mathematics paper is sat without a calculator, in line with standard prefectural academic-test rules; numerical reasoning and exact computation are expected.
How is the selection structured?
Tokushima combines 調査書(評定値合計 195点満点, with 音楽・美術・保健体育・技術家庭 doubled) with 学力検査 (500点). The 第1次選考 selects from applicants who are within the top 80% of the 募集人員 on both the 調査書 評定 and the 学力検査 score; everyone else is considered in the 第2次選考, where the two are weighed equally using a 相関表 (correlation table). A school may add up to a combined 100点 of 傾斜配点, and 面接 is required. 全日制普通科 is subject to a 学区制 except at 城東・富岡東・川島高校, and each applicant may apply to only one school per selection type.
What kinds of problems appear on the 数学 paper?
The paper covers 数と式, 関数, 図形 and 資料の活用, aligned to the MEXT 平成29年 中学校学習指導要領 数学編 at 中学校卒業程度. Everything is handwritten, with 途中の計算過程 that earns partial credit. The paper tests 知識・技能 plus 思考力・判断力・表現力.
How much is the examination fee?
The 入学考査料 for a 全日制 course is ¥2,200 (¥950 for 定時制), affixed as 徳島県収入証紙 on the 入学願書 and submitted via the junior-high principal; applicants to 徳島市立高等学校 pay in cash. The fee is not refunded once paid.