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100+ Free Aichi Entrance Mathematics Practice Questions

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2026 Statistics

Key Facts: Aichi Entrance Mathematics Exam

45 min / 22 points

Length and maximum score of each Aichi general-selection subject paper, including mathematics

Aichi Prefectural Board of Education selection results page

5 subjects

Japanese, social studies, mathematics, science and English (with listening) are sat by every full-time general-selection applicant

R8 Aichi selection implementation guidelines

JPY 2,200

R8 (2026) entrance examination fee for the full-time course

Aichi web application manual

100

Free original MCQ practice questions in this study bank

OpenExamPrep

The Aichi public high school entrance mathematics paper is a 45-minute, 22-point written exam set by the Aichi Prefectural Board of Education, covering algebra, functions, geometry, and data analysis from the MEXT junior-high curriculum; since 2023 it is answered on a mark sheet, and the R8 (2026) paper had 19 scored items. This page offers 100 original practice questions with worked explanations as a study aid — original items, not official past papers.

Sample Aichi Entrance Mathematics Practice Questions

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

1Calculate: (−7) + (+4) − (−3).
A.−6
B.0
C.−8
D.−14
Explanation: Removing parentheses gives −7 + 4 + 3. Working left to right: −7 + 4 = −3, then −3 + 3 = 0. Subtracting a negative number is the same as adding its opposite.
2Calculate: 12 ÷ (−3) × 2.
A.8
B.−2
C.2
D.−8
Explanation: Division and multiplication have equal priority, so work left to right: 12 ÷ (−3) = −4, then −4 × 2 = −8.
3Simplify: 3(2x − 4) − (x − 5).
A.5x − 7
B.5x − 17
C.5x + 1
D.5x + 7
Explanation: Distribute the 3: 3(2x − 4) = 6x − 12. Removing the second parentheses flips both signs: −(x − 5) = −x + 5. Combining like terms gives 6x − x − 12 + 5 = 5x − 7.
4Calculate: (1/2 + 1/3) ÷ (5/6).
A.5/6
B.25/36
C.1
D.5
Explanation: First add inside the parentheses: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Dividing by 5/6 is the same as multiplying by 6/5: (5/6) × (6/5) = 1.
5Solve the equation 3x + 7 = 22.
A.x = 29/3
B.x = 7
C.x = 5
D.x = 3
Explanation: Transpose the constant term: 3x = 22 − 7 = 15. Dividing both sides by 3 gives x = 5. Check: 3 × 5 + 7 = 22.
6Solve the simultaneous equations: 2x + 3y = 12 and x − y = 1.
A.x = 3, y = 2
B.x = 2, y = 3
C.x = 0, y = 4
D.x = 6, y = 0
Explanation: From the second equation, x = y + 1. Substituting into the first: 2(y + 1) + 3y = 12, so 5y + 2 = 12 and y = 2. Then x = 2 + 1 = 3.
7Factorize x² − 7x + 12.
A.(x + 3)(x + 4)
B.(x − 2)(x − 6)
C.(x − 1)(x − 12)
D.(x − 3)(x − 4)
Explanation: Look for two numbers whose sum is −7 and whose product is 12: −3 and −4. Therefore x² − 7x + 12 = (x − 3)(x − 4).
8Factorize x² − 9.
A.(x − 3)²
B.(x + 3)(x − 3)
C.(x + 3)²
D.(x − 9)(x + 1)
Explanation: This is a difference of squares: x² − 9 = x² − 3² = (x + 3)(x − 3).
9Calculate √12 × √3.
A.6
B.√15
C.36
D.3√2
Explanation: √12 × √3 = √36 = 6. Alternatively, √12 = 2√3, so 2√3 × √3 = 2 × 3 = 6.
10Calculate √50 − √8 + √18.
A.√60
B.10√2
C.6√2
D.4√2
Explanation: Simplify each term first: √50 = 5√2, √8 = 2√2, √18 = 3√2. Then 5√2 − 2√2 + 3√2 = 6√2.

About the Aichi Entrance Mathematics Exam

The Aichi Public High School Entrance Examination mathematics paper is one of the five subject papers in the prefecture-wide academic examination administered by the Aichi Prefectural Board of Education for admission to prefectural public high schools. In the R8 (2026) general selection, every applicant to a full-time course sits all five subjects — Japanese, social studies, mathematics, science, and English — each in 45 minutes and scored out of 22 points. The mathematics paper follows the MEXT Course of Study for junior high school and covers numbers and algebra (through quadratic equations and square roots), functions (through y = ax^2), plane and solid geometry (including congruence, similarity, the inscribed angle theorem, and the Pythagorean theorem), and data analysis with probability. Since the R5 (2023) selection every answer in the full-time general selection is recorded on a mark sheet, adopted so that all schools mark to one standard. Results are combined with the junior-high school report (chousasho) for admission; there is no single passing score. This page provides 100 original English-language practice items, including real calculation questions, as a study adaptation — original items, not official past problems.

Assessment

The real Aichi mathematics subject is one of the five academic subjects (kokugo, shakai, suugaku, rika, eigo) of the prefecture-wide general selection written examination. It follows the four MEXT junior-high strands — numbers and expressions, functions, figures, and utilization of data — with items ranging from one-line computations to multi-step reasoning. Since the R5 (2023) selection every answer is recorded on a mark sheet, so the official item type is selected-response: lettered choices for most items and digit-by-digit numeric marking for others. This local bank is an English-language study adaptation aligned to the same curriculum content, including genuine calculation items; the items are original and are not official past problems.

Time Limit

45 minutes for the mathematics subject paper (R8 / 2026 general selection)

Passing Score

No fixed pass mark; each subject paper is scored out of 22 points and admission combines academic test results with the junior-high school report (chousasho)

Exam Fee

JPY 2,200 entrance examination fee for the full-time general selection (R8 / 2026); JPY 950 for the part-time course; none for the correspondence course (Aichi Prefectural Board of Education)

Aichi Entrance Mathematics Exam Content Outline

About 25% of this practice bank; a major strand of the official paper

Numbers and Algebra

Signed numbers, algebraic manipulation, expansion and factorization, square roots, simultaneous linear equations, and quadratic equations with real calculation items.

About 20% of this practice bank

Functions

Direct and inverse proportion, linear functions, y = ax^2, rate of change, intersection of graphs, and function-based word problems.

About 25% of this practice bank

Geometry

Angle and figure properties, congruence and similarity, the inscribed angle theorem, the Pythagorean theorem, and area/volume of solids.

About 15% of this practice bank

Probability and Statistics

Counting outcomes, compound probability, mean/median/quartiles, box plots, relative frequency, and interpretation of samples.

About 15% of this practice bank

Applied and Integrated Problems

Multi-step word problems combining equations, functions, graphs, speed/distance/time, and geometric measurement in realistic settings.

How to Pass the Aichi Entrance Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark; each subject paper is scored out of 22 points and admission combines academic test results with the junior-high school report (chousasho)
  • Assessment: The real Aichi mathematics subject is one of the five academic subjects (kokugo, shakai, suugaku, rika, eigo) of the prefecture-wide general selection written examination. It follows the four MEXT junior-high strands — numbers and expressions, functions, figures, and utilization of data — with items ranging from one-line computations to multi-step reasoning. Since the R5 (2023) selection every answer is recorded on a mark sheet, so the official item type is selected-response: lettered choices for most items and digit-by-digit numeric marking for others. This local bank is an English-language study adaptation aligned to the same curriculum content, including genuine calculation items; the items are original and are not official past problems.
  • Time limit: 45 minutes for the mathematics subject paper (R8 / 2026 general selection)
  • Exam fee: JPY 2,200 entrance examination fee for the full-time general selection (R8 / 2026); JPY 950 for the part-time course; none for the correspondence course

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

Aichi Entrance Mathematics Study Tips from Top Performers

1Master the full algebra chain in order: expansion, factorization, square roots, then quadratic equations — later topics reuse earlier skills.
2For functions, always compute the rate of change and check intercepts; most Aichi-style function items reduce to these two moves.
3In geometry, mark given equal sides and angles on the figure before choosing a theorem; similarity and the inscribed angle theorem are the highest-frequency tools.
4For probability, list outcomes systematically with a table or tree diagram instead of counting in your head.
5Practice under a 45-minute cap and show working even in MCQ practice, because the official paper grades written steps.

Frequently Asked Questions

Is the real Aichi mathematics entrance paper multiple-choice?

Largely yes. Since the R5 (2023) selection the paper is answered on a mark sheet: most items are lettered choices and some, such as the geometry section, are answered by marking a numeric value digit by digit. You still have to work each problem out in full on scrap paper, so the practice items here train the same calculation, not answer-elimination.

How long is the Aichi mathematics paper and how is it scored?

The mathematics subject paper lasts 45 minutes and is scored out of 22 points under the current Aichi general selection. Admission combines all five subject results with the junior-high school report (chousasho); there is no fixed passing score.

Does this bank include real calculation questions?

Yes. A substantial share of the bank requires actual computation — equation solving, expansion, probability counting, and geometric measurement — with worked explanations for every option.

Who administers the exam and what does it cost?

The Aichi Prefectural Board of Education administers the selection. The R8 (2026) entrance examination fee is JPY 2,200 for the full-time general selection, JPY 950 for the part-time course, and free for the correspondence course.

Where can I find official past papers?

The Aichi prefecture website publishes the current year's problems, answer sheets, and answer keys (for example, the R8 entrance examination problems page on pref.aichi.jp).