100+ Free Tottori Prefectural Public High School Entrance Examination — Mathematics Practice Questions
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Key Facts: Tottori Prefectural Public High School Entrance Examination — Mathematics Exam
Practise for the Tottori 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 50-point, 50-minute common paper sat on 令和8年3月5日(木). The official paper mixes 記号選択 items with 短答, 記述 and 作図 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 in Japanese.
Sample Tottori Prefectural Public High School Entrance Examination — Mathematics Practice Questions
Try these sample questions to test your Tottori Prefectural 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 540?
2Find the greatest common divisor (GCD) of 72 and 108.
3Find the least common multiple (LCM) of 18 and 30.
4Evaluate (-2)³.
5Evaluate 7 - (-3) + (-4).
6Simplify √72.
7Simplify √50.
8Simplify √12 + √27.
9Which of these numbers is irrational (無理数)?
10Simplify (-2a²b)³.
About the Tottori Prefectural Public High School Entrance Examination — Mathematics Exam
The Tottori 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 a prefecture-wide common paper (県内同一問題) covering five subjects (国語, 数学, 社会, 理科, 英語[リスニング含む]), each worth 50 points (合計 250点); for 令和8年度 (2026 admission) the 一般入学者選抜 学力検査 is 3月5日(木) with 合格発表 on 3月16日(月). The 数学 common paper combines 記号選択 (multiple-choice) items with 短答, 記述 and 作図 (constructed-response and construction) questions requiring 途中の計算過程 and proofs, so it is not a pure multiple-choice paper; all schools use the same common papers (no 自校作成問題). Selection combines the 学力検査 total with the 調査書 at a ratio between 8:2 and 2:8, with schools free to apply 傾斜配点 (1-2 subjects multiplied by 1×-2×). 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
50-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 prefectural common paper mixes 記号選択 items with 短答, 記述 and 作図 answers that earn partial credit for 途中の計算過程; all schools use the same common papers (no 自校作成問題). The five academic-test subjects each carry 50 points (合計 250点), sat over two days as prefectural common papers; 数学 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 two-day five-subject 学力検査: 国語, 数学, 社会 and 理科 are each 50-minute, 50-point papers and 英語 is a 60-minute, 50-point paper with listening (合計 250点). For 令和8年度 (2026 admission) the 学力検査 is 3月5日(木) (with a 3月6日(金) second-day schedule and a 追検査 on 3月11日(水) for influenza-absence cases), and 一般入学者選抜 合格発表 is 3月16日(月). Calculators are not permitted. Source: 令和8年度鳥取県立高等学校入学者選抜方針, 鳥取県教育委員会.
Passing Score
No fixed prefecture-wide pass mark. The 数学 paper is scored out of 50 points. In the 一般入学者選抜 the five subjects (国語・数学・社会・理科・英語) total 250 points (each subject 50 points); schools may apply 傾斜配点 by multiplying 1 or 2 emphasised subjects' scores by more than 1× and up to 2×. The 学力検査 total and the 調査書 (school record) are combined at a ratio between 8:2 and 2:8, set by each school. Selection is competitive and relative, not against a published pass line. Source: 令和8年度鳥取県立高等学校入学者選抜方針, 鳥取県教育委員会.
Exam Fee
The 入学選抜手数料 is ¥2,200 for a 全日制 course and ¥1,000 for a 定時制 course; it may be reduced or waived in cases of financial hardship. Source: 県立高等学校の授業料について (鳥取県教育委員会, https://www.pref.tottori.lg.jp/87663.htm) and 令和8年度鳥取県立高等学校入学者選抜方針. (Tottori Prefectural Board of Education (鳥取県教育委員会), 事務局高等学校課, 〒680-8570 鳥取市東町一丁目271番地 (TEL 0857-26-7916 [指導担当] / 0857-26-7929 / 0857-26-7917 / 0857-26-7517, FAX 0857-26-0408))
Tottori Prefectural 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 (作図).
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 (箱ひげ図), 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 Tottori Prefectural 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 50 points. In the 一般入学者選抜 the five subjects (国語・数学・社会・理科・英語) total 250 points (each subject 50 points); schools may apply 傾斜配点 by multiplying 1 or 2 emphasised subjects' scores by more than 1× and up to 2×. The 学力検査 total and the 調査書 (school record) are combined at a ratio between 8:2 and 2:8, set by each school. Selection is competitive and relative, not against a published pass line. Source: 令和8年度鳥取県立高等学校入学者選抜方針, 鳥取県教育委員会.
- Assessment: 50-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 prefectural common paper mixes 記号選択 items with 短答, 記述 and 作図 answers that earn partial credit for 途中の計算過程; all schools use the same common papers (no 自校作成問題). The five academic-test subjects each carry 50 points (合計 250点), sat over two days as prefectural common papers; 数学 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 two-day five-subject 学力検査: 国語, 数学, 社会 and 理科 are each 50-minute, 50-point papers and 英語 is a 60-minute, 50-point paper with listening (合計 250点). For 令和8年度 (2026 admission) the 学力検査 is 3月5日(木) (with a 3月6日(金) second-day schedule and a 追検査 on 3月11日(水) for influenza-absence cases), and 一般入学者選抜 合格発表 is 3月16日(月). Calculators are not permitted. Source: 令和8年度鳥取県立高等学校入学者選抜方針, 鳥取県教育委員会.
- Exam fee: The 入学選抜手数料 is ¥2,200 for a 全日制 course and ¥1,000 for a 定時制 course; it may be reduced or waived in cases of financial hardship. Source: 県立高等学校の授業料について (鳥取県教育委員会, https://www.pref.tottori.lg.jp/87663.htm) and 令和8年度鳥取県立高等学校入学者選抜方針.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Tottori Prefectural Public High School Entrance Examination — Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is this question bank the same as the real Tottori 数学 exam?
No. The official paper is worked in Japanese and combines 記号選択 (multiple-choice) items with 短答 (short-answer), 記述 (constructed-response) and 作図 (construction) 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・作図, and 資料の活用) and cannot replace writing out your own calculations in Japanese under timed conditions.
How long is the Tottori 数学 paper and what is it worth?
It is scored out of 50 points, one of five subjects totalling 250 points (each subject 50 points). 数学 runs 50 minutes on 令和8年3月5日(木), with 一般入学者選抜 合格発表 on 3月16日(月); the 特色入学者選抜 is 2月3日(火) with 合格発表 on 2月10日(火), and a 追検査 (for influenza-absence cases) is 3月11日(水).
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?
Tottori's 一般入学者選抜 combines the 学力検査 total (5 subjects × 50 = 250 points, with schools free to apply 傾斜配点 multiplying 1-2 subjects by 1×-2×) with the 調査書 (school record) at a ratio between 8:2 and 2:8 set by each school. All applicants also sit a 面接 (interview), and some schools add 作文 or 実技検査. Selection is relative to other applicants, not against a published pass line. Unlike Tokyo, Tottori uses common prefectural papers at all schools and has no 自校作成問題.
How much is the examination fee?
The 入学選抜手数料 is ¥2,200 for a 全日制 course (¥1,000 for 定時制); it may be reduced or waived in cases of financial hardship.