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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?
A.2² × 3³ × 5
B.2² × 3² × 5²
C.2³ × 3³ × 5
D.2² × 3³ × 5²
Explanation: 540 = 4 × 135 = 2² × 27 × 5 = 2² × 3³ × 5. Dividing successively by primes confirms 540 = 4 × 135 = 4 × 27 × 5.
2Find the greatest common divisor (GCD) of 72 and 108.
A.36
B.24
C.18
D.12
Explanation: 72 = 2³ × 3² and 108 = 2² × 3³. The GCD takes the minimum power of each common prime: 2² × 3² = 4 × 9 = 36.
3Find the least common multiple (LCM) of 18 and 30.
A.90
B.60
C.180
D.30
Explanation: 18 = 2 × 3² and 30 = 2 × 3 × 5. The LCM takes the highest power of each prime: 2 × 3² × 5 = 90.
4Evaluate (-2)³.
A.-8
B.8
C.-6
D.6
Explanation: (-2)³ = (-2) × (-2) × (-2) = 4 × (-2) = -8. An odd power of a negative number is negative.
5Evaluate 7 - (-3) + (-4).
A.6
B.-6
C.10
D.-10
Explanation: Subtracting a negative is addition: 7 - (-3) = 7 + 3 = 10, then 10 + (-4) = 6.
6Simplify √72.
A.6√2
B.8√2
C.3√8
D.6√3
Explanation: 72 = 36 × 2, and √36 = 6, so √72 = √(36 × 2) = 6√2. Extract the largest square factor.
7Simplify √50.
A.5√2
B.25
C.2√5
D.5√5
Explanation: 50 = 25 × 2, and √25 = 5, so √50 = 5√2.
8Simplify √12 + √27.
A.5√3
B.√39
C.6√3
D.5√9
Explanation: √12 = 2√3 and √27 = 3√3, so √12 + √27 = 2√3 + 3√3 = 5√3. Only like surds can be combined.
9Which of these numbers is irrational (無理数)?
A.√5
B.√16
C.0.25
D.22/7
Explanation: An irrational number cannot be written as a fraction of two integers, and its decimal neither terminates nor repeats. 5 is not a perfect square, so √5 = 2.2360... never terminates or repeats. A square root is rational only when the number under it is a perfect square.
10Simplify (-2a²b)³.
A.-8a⁶b³
B.-6a⁵b³
C.8a⁶b³
D.-8a⁵b²
Explanation: Each factor is cubed: (-2)³ = -8, (a²)³ = a⁶, and (b)³ = b³, giving -8a⁶b³. Powers are multiplied when raised to a power.

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

25%

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.

25%

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.

30%

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).

20%

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

1Master exact arithmetic without a calculator — common fractions, square roots and simplification — because the paper is sat calculator-free.
2For 連立方程式 (simultaneous equations), drill both the mechanical solution and the applied word-problem set-up, since applied items test translation from text to equations.
3For geometry, write proofs in the standard assertion-reason format, citing the congruence/similarity condition explicitly, because 記述 proof problems and 作図 (construction) items reward structure.
4For 二次関数 y=ax², memorise how a changes the parabola's width and direction, and practise finding the vertex, axis of symmetry and intersections with a line — function–geometry fusion items are among the hardest.
5For 資料の活用, compute mean, median, relative frequency, interquartile range and probability fluently, practise reading histograms and 箱ひげ図 (box-and-whisker plots) quickly, and be ready to estimate a population from a 標本調査.
6Practise both 記号選択 (multiple-choice) and 短答 / 記述 working — Tottori's common paper uses both — and time yourself on full 50-minute papers, leaving the longest proof, 作図 or applied item for last.

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.