Free Practice Questions for Yamanashi Entrance Mathematics

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Key Facts: Yamanashi Entrance Mathematics Exam

Yamanashi 数学 is a 100-point paper within a five-subject 学力検査 (500 points total).

Time: 45 minutes in Reiwa 8; 50 minutes from Reiwa 9 for 全日制後期募集 and 定時制.

一般選抜 treats 調査書 and 学力検査 equally; no fixed pass line is published.

入学審査料 is ¥2,200 (全日制) / ¥950 (定時制) per prefectural ordinance Article 3.

Official papers are Japanese written exams; this bank is an English-language MCQ study adaptation with calculation items.

Practise for the Yamanashi public high school entrance 数学 paper (100 points; 45 min in R8, 50 min from R9) with 100 four-option questions including real calculations. Official papers are Japanese written exams; this bank is an English MCQ study aid.

Sample Yamanashi Entrance Mathematics Practice Questions

Try these sample questions to review concepts for the Yamanashi Entrance Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Calculate: (−9) + (+5) − (−4).

A.0

B.−8

C.−18

D.8

Explanation: Removing parentheses gives −9 + 5 + 4. Working left to right: −9 + 5 = −4, then −4 + 4 = 0. Subtracting a negative number is the same as adding its opposite.

2What is the prime factorization of 90?

A.2² × 3 × 5

B.2 × 3² × 5

C.2 × 3 × 5²

D.3² × 5 × 7

Explanation: 90 ÷ 2 = 45 and 45 = 9 × 5 = 3² × 5. Therefore 90 = 2 × 3² × 5.

3Find the greatest common divisor (GCD) of 54 and 72.

A.12

B.6

C.18

D.36

Explanation: 54 = 2 × 3³ and 72 = 2³ × 3². The GCD uses the minimum powers: 2¹ × 3² = 18. By the Euclidean algorithm, 72 = 1·54 + 18 and 54 = 3·18, so the GCD is 18.

4Find the least common multiple (LCM) of 14 and 21.

A.7

B.28

C.84

D.42

Explanation: 14 = 2 × 7 and 21 = 3 × 7. The LCM takes the highest powers of all primes: 2 × 3 × 7 = 42.

5Simplify: 2⁵ × 3² ÷ (2³ × 3).

A.12

B.6

C.24

D.18

Explanation: Combine like bases: 2^{5−3} × 3^{2−1} = 2² × 3 = 4 × 3 = 12.

6Simplify √75.

A.3√5

B.5√3

C.15√3

D.25√3

Explanation: Factor out the largest perfect square: 75 = 25 × 3, so √75 = √25 × √3 = 5√3.

7Simplify (√18 − √8) ÷ √2.

A.2

B.√2

C.1

D.√5

Explanation: √18 = 3√2 and √8 = 2√2, so the numerator is 3√2 − 2√2 = √2. Then √2 ÷ √2 = 1.

8Expand (x + 4)(x − 6).

A.x² − 2x + 24

B.x² + 2x − 24

C.x² − 10x − 24

D.x² − 2x − 24

Explanation: FOIL: x·x + x(−6) + 4·x + 4(−6) = x² − 6x + 4x − 24 = x² − 2x − 24.

9Expand (3x − 2)².

A.9x² − 12x + 4

B.9x² + 12x + 4

C.9x² − 6x + 4

D.9x² − 12x − 4

Explanation: (a − b)² = a² − 2ab + b² with a = 3x and b = 2 gives 9x² − 12x + 4.

10Factor completely: x² − 9x + 20.

A.(x − 2)(x − 10)

B.(x − 4)(x − 5)

C.(x + 4)(x + 5)

D.(x − 4)(x + 5)

Explanation: Need two integers with product 20 and sum −9: −4 and −5. Hence x² − 9x + 20 = (x − 4)(x − 5).

About the Yamanashi Entrance Mathematics Exam

The Yamanashi Public High School Entrance Examination mathematics paper is set by the Yamanashi Prefectural Board of Education as part of the five-subject 学力検査. It is a 100-point written paper (45 minutes in Reiwa 8; 50 minutes from Reiwa 9) aligned to the MEXT junior-high mathematics Course of Study, covering numbers and expressions, functions, geometry, and data/probability. Official items require showing reasoning; they are not pure multiple choice. This page provides 100 original English-language MCQ practice questions with worked calculations as a study adaptation.

Exam sponsor: Yamanashi Prefectural Board of Education (山梨県教育委員会), 教育庁総務課教育企画室, 〒400-8504 甲府市丸の内1-6-1 (TEL 055-223-1750). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Five-subject 学力検査, each 100 points (500 total). 数学 time: 45 minutes (R8) / 50 minutes (R9). 一般選抜 treats 調査書 and 学力検査 equally. Official format requires written working; this bank is an English MCQ study adaptation covering 数と式, 関数, 図形, and 資料の活用.

Time Limit

45 minutes (Reiwa 8 / 2026 entrance) or 50 minutes (from Reiwa 9 / 2027 entrance) for the 数学 paper on the late-selection academic test days

Passing Score

No fixed pass mark; 数学 scored out of 100 (500 across five subjects); 一般選抜 treats 調査書 and 学力検査 equally

Exam / Certification Fees

入学審査料 ¥2,200 (全日制) / ¥950 (定時制) / free (通信制) per 山梨県立学校授業料、入学料及び入学審査料条例第三条

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Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

About 25% of this practice bank

Numbers and Expressions

Integers, fractions, prime factorisation, algebraic expressions, expansion and factorisation, square roots, and exponents.

About 15% of this practice bank

Equations and Inequalities

Linear, simultaneous and quadratic equations, linear inequalities, and word problems.

About 20% of this practice bank

Functions

Proportional and inverse proportional relationships, linear functions, and y = ax² with graphs and applications.

About 25% of this practice bank

Geometry

Congruence and similarity, circles, Pythagorean theorem, area, and solid geometry.

About 15% of this practice bank

Data Analysis and Probability

Mean, median, mode, histograms, relative frequency, and basic probability.

Preparing for the Yamanashi Entrance Mathematics Exam

What You Need to Know

Passing score: No fixed pass mark; 数学 scored out of 100 (500 across five subjects); 一般選抜 treats 調査書 and 学力検査 equally
Assessment: Five-subject 学力検査, each 100 points (500 total). 数学 time: 45 minutes (R8) / 50 minutes (R9). 一般選抜 treats 調査書 and 学力検査 equally. Official format requires written working; this bank is an English MCQ study adaptation covering 数と式, 関数, 図形, and 資料の活用.
Time limit: 45 minutes (Reiwa 8 / 2026 entrance) or 50 minutes (from Reiwa 9 / 2027 entrance) for the 数学 paper on the late-selection academic test days
Exam / certification fees: 入学審査料 ¥2,200 (全日制) / ¥950 (定時制) / free (通信制) per 山梨県立学校授業料、入学料及び入学審査料条例第三条 Official sources

Using Our Practice Resources

Work through all 100 available questions
Review every answer and explanation
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Yamanashi Entrance Mathematics: Suggested Study Strategy

1Master calculator-free arithmetic with fractions, negatives, and square roots.

2Drill simultaneous equations and quadratic equations until setup and solution are automatic.

3For geometry, practise congruence/similarity conditions and 円周角の定理 with clear reasons.

4For y = ax², connect the coefficient a to the parabola's width and direction, and practise line–parabola intersections.

5Include genuine multi-step calculation problems in every study session, not only definitions.

6Time yourself under 45–50 minute conditions and always write full working even when practising MCQs.

Frequently Asked Questions

Is the real Yamanashi 数学 entrance paper multiple-choice?

No. The official paper is a Japanese written exam requiring calculations and constructed responses with working shown. These MCQs are an English-language study adaptation of the same junior-high syllabus — not a format simulation.

How long is the Yamanashi 数学 paper?

In Reiwa 8 (2026 entrance) 数学 is 45 minutes; from Reiwa 9 (2027 entrance) 社会・数学・理科・英語 each become 50 minutes for 全日制後期募集 and 定時制, while 国語 remains 55 minutes. The paper is scored out of 100 points.

Are calculators allowed?

Standard Yamanashi junior-high entrance academic papers are sat without calculators; practise exact arithmetic, fractions, and square roots by hand.

What is the examination fee?

The 入学審査料 is ¥2,200 for full-time (全日制), ¥950 for part-time (定時制), and free for correspondence (通信制), per the prefectural ordinance.

Free Practice Questions for Yamanashi Entrance Mathematics

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