100+ Free Kyoto Entrance Mathematics Practice Questions
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Key Facts: Kyoto Entrance Mathematics Exam
40 min / 40 points
Length and maximum score of the Kyoto mathematics paper, one of five subjects in the 中期 selection academic test (Reiwa 8 cycle: March 6, 2026)
Kyoto Prefectural Board of Education R8 selection requirements (subject timing and marks) and official selection page
200 + 195 = 395
中期 (chūki) general selection uses the academic test (200) and report card (chōsasho, 195); both ranks must fall within the quota (step system); some schools apply weighted scoring (keisha-haitei)
Kyoto Prefectural Board of Education R8 selection requirements
Mar 6, 2026
Reiwa 8 中期 selection academic test date; results March 17, 2026; 前期 test February 16–17, 2026
Kyoto Prefectural Board of Education R8 selection schedule and Benesse Kyoto entrance info
JPY 2,200
Entrance selection fee for full-time prefectural high schools (JPY 900 part-time/teijisei), paid through the official online application site; not refunded once paid
Kyoto Prefectural Board of Education R8 (2026) selection requirements
100
Free original practice questions in this bank
OpenExamPrep
The Kyoto public high school entrance mathematics paper is a 40-minute, 40-point written exam held in the 中期 (chūki) general selection academic test (March 6, 2026), covering equations, functions, plane and solid geometry, and probability, set by the Kyoto Prefectural Board of Education. This page offers 100 original English-language practice questions with explanations as a study aid.
Sample Kyoto Entrance Mathematics Practice Questions
Try these sample questions to test your Kyoto Entrance Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Evaluate (-5) + 3 - (-4).
2Evaluate (-3) × (-4) × 2.
3Evaluate (-2)³.
4Simplify 4x - 5x + 2x.
5Expand -2(x - 5).
6Expand (x + 4)(x - 3).
7Factor x² - 25.
8Factor x² + 9x + 20.
9Factor 2x² - 8 completely.
10Evaluate √64.
About the Kyoto Entrance Mathematics Exam
The Kyoto Public High School Entrance Selection mathematics paper is created by the Kyoto Prefectural Board of Education jointly with the Kyoto City Board of Education for Kyoto City area schools. The single 40-minute, 40-point written paper, sat in the 中期 (chūki) general selection academic test (Reiwa 8 / 2026 cycle: March 6, 2026, results March 17, 2026), is a constructed-response exam in Japanese on the 2017 MEXT junior-high Course of Study, covering numbers and expressions, equations and inequalities, linear and quadratic functions, plane geometry (congruence, similarity, circles, 30-60-90 triangles, the Pythagorean theorem, compass-and-straightedge construction), solid geometry, and probability incl. quartiles (四分位数). The 中期 selection uses the academic test (200) and the report card (195); there is no fixed pass mark. This page provides 100 original English-language practice questions with detailed explanations as a study adaptation — not an official translation, not a reproduction of the official paper, and not a format simulation.
Assessment
The real Kyoto mathematics examination is a 40-minute paper scored out of 40 points (200 total across five subjects: kokugo, social studies, mathematics, science, English), sat in the 中期 (chūki) general selection academic test (Reiwa 8 / 2026 cycle: examination March 6, 2026; results March 17, 2026). It is a written, constructed-response paper in Japanese created by the Kyoto Prefectural Board of Education jointly with the Kyoto City Board of Education for Kyoto City area schools, on the 2017 (Heisei 29) MEXT junior-high Course of Study. The paper typically has six big questions (大問): basic calculation incl. 四分位数 (quartiles, new per the 2017 Course of Study), solid geometry (cylinder/cone volume & surface area), probability (tree diagrams), moving-point + function (quadratic→linear transition), plane geometry (30-60-90 triangles, similarity, circles), and regularity (nth-term formula). The 中期 selection uses the academic test (200 points) and the report card (chōsasho, 195 points); there is no fixed pass mark, and both the test rank and the report-card rank must fall within the quota (step system). Some schools apply weighted scoring (keisha-haitei, 傾斜配点) to specific subjects. This local bank is an English-language MCQ study adaptation providing 100 original practice items.
Time Limit
40 minutes for the mathematics subject paper (Reiwa 8 / 2026 中期 selection academic test on March 6, 2026; results March 17, 2026).
Passing Score
No fixed pass mark; scored out of 40 points (200 total across 5 subjects). The 中期 (chūki) general selection uses the academic test (200) and the report card (chōsasho, 195); both the test rank and the report-card rank must fall within the quota for first-stage admission (step system). Some schools apply weighted scoring (keisha-haitei, 傾斜配点) to specific subjects. Selection is by ranking within each school's quota.
Exam Fee
JPY 2,200 entrance selection fee for full-time prefectural high schools (JPY 900 part-time/teijisei), paid through the official online application site during the application period; once paid, the fee is not refunded. The fee is set out in the official Kyoto selection requirements. (Kyoto Prefectural Board of Education (京都府教育委員会), jointly with Kyoto City Board of Education (京都市教育委員会) for Kyoto City area schools)
Kyoto Entrance Mathematics Exam Content Outline
Numbers and Expressions
Positive and negative numbers, algebraic expressions, expansion and factorization, square roots, and evaluating expressions.
Equations and Inequalities
Linear equations, simultaneous equations, quadratic equations, linear inequalities, and word problems.
Functions
Proportional and inverse-proportional relationships, linear functions, and quadratic functions including rates of change and symmetry.
Plane Geometry
Angles and parallel lines, congruence and similarity, circles, 30-60-90 triangles, the Pythagorean theorem, and compass-and-straightedge construction (作図).
Solid Geometry and Measurement
Surface areas and volumes of prisms, cylinders, pyramids, cones, and spheres, and rotation of plane figures.
Data Analysis and Probability
Counting outcomes, probability with and without replacement, the complement rule, tree diagrams, representative values, frequency distribution, and quartiles (四分位数).
How to Pass the Kyoto Entrance Mathematics Exam
What You Need to Know
- Passing score: No fixed pass mark; scored out of 40 points (200 total across 5 subjects). The 中期 (chūki) general selection uses the academic test (200) and the report card (chōsasho, 195); both the test rank and the report-card rank must fall within the quota for first-stage admission (step system). Some schools apply weighted scoring (keisha-haitei, 傾斜配点) to specific subjects. Selection is by ranking within each school's quota.
- Assessment: The real Kyoto mathematics examination is a 40-minute paper scored out of 40 points (200 total across five subjects: kokugo, social studies, mathematics, science, English), sat in the 中期 (chūki) general selection academic test (Reiwa 8 / 2026 cycle: examination March 6, 2026; results March 17, 2026). It is a written, constructed-response paper in Japanese created by the Kyoto Prefectural Board of Education jointly with the Kyoto City Board of Education for Kyoto City area schools, on the 2017 (Heisei 29) MEXT junior-high Course of Study. The paper typically has six big questions (大問): basic calculation incl. 四分位数 (quartiles, new per the 2017 Course of Study), solid geometry (cylinder/cone volume & surface area), probability (tree diagrams), moving-point + function (quadratic→linear transition), plane geometry (30-60-90 triangles, similarity, circles), and regularity (nth-term formula). The 中期 selection uses the academic test (200 points) and the report card (chōsasho, 195 points); there is no fixed pass mark, and both the test rank and the report-card rank must fall within the quota (step system). Some schools apply weighted scoring (keisha-haitei, 傾斜配点) to specific subjects. This local bank is an English-language MCQ study adaptation providing 100 original practice items.
- Time limit: 40 minutes for the mathematics subject paper (Reiwa 8 / 2026 中期 selection academic test on March 6, 2026; results March 17, 2026).
- Exam fee: JPY 2,200 entrance selection fee for full-time prefectural high schools (JPY 900 part-time/teijisei), paid through the official online application site during the application period; once paid, the fee is not refunded. The fee is set out in the official Kyoto selection requirements.
Keys to Passing
- Complete 500+ practice questions
- Score 80%+ consistently before scheduling
- Focus on highest-weighted sections
- Use our AI tutor for tough concepts
Kyoto Entrance Mathematics Study Tips from Top Performers
Frequently Asked Questions
Is the real Kyoto mathematics entrance paper multiple-choice?
No. The Kyoto academic test is a written, constructed-response paper in Japanese — students write their own answers and proof steps, not mark-sheet bubbles. This bank is an English-language four-option MCQ study adaptation, not official past problems or a reproduction of the official layout: real selection items are in Japanese, require written working, and the official paper's exact item count is not published.
Are these questions official past exam problems?
No. Although the Kyoto Prefectural Board of Education publishes the actual examination problems and model answers, it does not publish them as a four-option multiple-choice set. This bank is an original English-language MCQ study adaptation aligned to the 2017 MEXT junior-high Course of Study, covering equations, functions, geometry, and probability with worked-solution reasoning — not an official translation or format simulation.
How long is the mathematics paper and what is the maximum score?
The mathematics paper is a single 40-minute exam scored out of 40 points, sat in the 中期 (chūki) general selection academic test. The five academic-test subjects total 200 points and are combined with the 195-point report card in the 中期 selection. In the Reiwa 8 (2026) cycle the academic test is held on March 6, 2026, with results on March 17, 2026.
Did the Kyoto selection system change recently?
Yes. From Reiwa 9 (2027), Kyoto moves to a single 前期 (zenki) selection with 独自枠 (school-specific quota) and 共通枠 (common quota), carrying over the common academic test (5 × 40 = 200) plus report card (195 = 395 total). The test is scheduled for February 18–19, 2027, with results in early March 2027. Under Reiwa 8 (2026) the two-stage system (前期 + 中期, with 後期 only when vacancies remain) is still in use.
How are the academic test and report card combined in Kyoto's selection?
Kyoto's 中期 (chūki) general selection uses the academic test (200 points) and the report card (chōsasho, 195 points), for a total of 395. The report card comprises 5 academic subjects × 5 × 3 years = 75 and 4 practical subjects × 5 × 2 × 3 years = 120. Both the test rank and the report-card rank must fall within the quota (step system) for first-stage admission. Some schools apply weighted scoring (keisha-haitei, 傾斜配点) to specific subjects. There is no fixed pass mark.
Does this bank include real calculation questions?
Yes. A substantial share of the 100 items are genuine worked-calculation questions with numeric answers — solving simultaneous and quadratic equations, evaluating functions at a point, applying the Pythagorean theorem and similarity ratios, computing volumes and surface areas, and counting probability outcomes — not just definitional recall.
Are quartiles (四分位数) included in the curriculum?
Yes. Quartiles (四分位数) were added to the junior-high mathematics curriculum under the 2017 (Heisei 29) MEXT Course of Study and appear in the basic-calculation big question (大問1). This bank includes quartile computation questions to reflect that update.