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Key Facts: Fukushima Entrance Mathematics Exam

50 min / 50 points

Length and maximum score of the Fukushima mathematics paper

Fukushima Prefectural Board of Education Reiwa 8 admissions guidelines

5 subjects / 250 points

Five-subject academic examination total, combined with the chousasho for admission

Fukushima Prefectural Board of Education Reiwa 8 admissions guidelines

Mar 4, 2026

Academic examination date in the Reiwa 8 selection

Fukushima Prefectural Board of Education Reiwa 8 admissions guidelines

JPY 2,200

Entrance examination fee

Fukushima Prefectural Board of Education Reiwa 8 admissions guidelines

100

Free original calculation practice questions in this bank

OpenExamPrep

The Fukushima public high school entrance mathematics paper is a 50-minute, 50-point written exam set by the Fukushima Prefectural Board of Education on March 4, 2026, one of five subjects totaling 250 points and combined with the chousasho for admission. This page offers 100 original English-language MCQ calculation practice questions with full explanations as a study adaptation.

Sample Fukushima Entrance Mathematics Practice Questions

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

1Calculate the value of (-7) + (+12) - (-5).
A.10
B.0
C.-10
D.24
Explanation: Subtracting a negative number becomes addition, so -(-5) = +5. The expression is -7 + 12 + 5. Computing left to right: -7 + 12 = 5, then 5 + 5 = 10.
2Calculate the value of (-4)² × (-3) + 18 ÷ (-6).
A.-51
B.45
C.51
D.-45
Explanation: Follow the order of operations. First (-4)² = 16, then 16 × (-3) = -48, and 18 ÷ (-6) = -3. Finally, -48 + (-3) = -51.
3Calculate 5/6 - 3/4.
A.1/12
B.1/2
C.19/12
D.1/6
Explanation: Use the common denominator 12: 5/6 = 10/12 and 3/4 = 9/12. Then 10/12 - 9/12 = 1/12, which is already in lowest terms.
4Evaluate the expression 4a - 5b when a = 3 and b = -2.
A.22
B.2
C.-22
D.7
Explanation: Substitute the values: 4(3) - 5(-2) = 12 - (-10). Subtracting a negative becomes addition, so 12 + 10 = 22.
5Calculate (2/3) ÷ (-4/5) + 1/6.
A.-2/3
B.-1
C.2/3
D.-1/2
Explanation: Division comes first: (2/3) ÷ (-4/5) = (2/3) × (-5/4) = -10/12 = -5/6. Then add: -5/6 + 1/6 = -4/6 = -2/3.
6Simplify the expression 3(2x - 4) - 2(x - 5).
A.4x - 2
B.4x - 22
C.4x + 2
D.8x - 2
Explanation: Distribute each factor: 3(2x - 4) = 6x - 12 and -2(x - 5) = -2x + 10. Combine like terms: 6x - 2x = 4x and -12 + 10 = -2, giving 4x - 2.
7Simplify 18x³y² ÷ (-3xy²).
A.-6x²
B.6x²
C.-6x²y
D.-15x²
Explanation: Divide the coefficients: 18 ÷ (-3) = -6. For the variables, x³ ÷ x = x² and y² ÷ y² = 1. The result is -6x².
8Expand (x + 3)(x - 7).
A.x² - 4x - 21
B.x² + 4x - 21
C.x² - 4x + 21
D.x² - 10x - 21
Explanation: Use the pattern (x + a)(x + b) = x² + (a + b)x + ab with a = 3 and b = -7. The sum is 3 + (-7) = -4 and the product is 3 × (-7) = -21, giving x² - 4x - 21.
9Expand (2x - 3)².
A.4x² - 12x + 9
B.4x² - 6x + 9
C.4x² + 9
D.2x² - 12x + 9
Explanation: Use (a - b)² = a² - 2ab + b² with a = 2x and b = 3. Then a² = 4x², 2ab = 12x, and b² = 9, giving 4x² - 12x + 9.
10Factorize x² + 5x - 14.
A.(x + 7)(x - 2)
B.(x - 7)(x + 2)
C.(x + 14)(x - 1)
D.(x - 14)(x + 1)
Explanation: Find two numbers whose product is -14 and whose sum is +5. Those numbers are +7 and -2, since 7 × (-2) = -14 and 7 + (-2) = 5. The factorization is (x + 7)(x - 2).

About the Fukushima Entrance Mathematics Exam

The Fukushima Public High School Entrance Examination mathematics paper is one of five subject papers in the prefecture-wide academic examination set by the Fukushima Prefectural Board of Education. The 50-minute, 50-point exam covers numbers and expressions, equations, linear and quadratic functions, plane geometry, solid figures and measurement, and data handling with probability. This page provides 100 original English-language practice items with step-by-step worked solutions as a study adaptation; the official paper requires full written mathematical reasoning, which MCQ practice does not replace.

Exam sponsor: Fukushima Prefectural Board of Education. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

In the Reiwa 8 (2026) selection, the academic examination is one of five 50-minute subject papers (kokugo, shakai, suugaku, rika, and English with a broadcast listening section), each scored out of 50 points for a 250-point total, all held on March 4, 2026. Applications are submitted February 2–6, 2026 through a newly introduced WEB application system; interviews run March 4–6, 2026; results are announced via the web system on March 16, 2026 (viewable until March 24). The general selection weights the academic test and the chousasho equally in principle, and schools may apply weighted scoring to specific subjects; attendance records are not used for Reiwa 8. A late selection at under-filled schools (application March 17–18, interview March 24, results March 25, 2026) uses only the chousasho, an interview, and a short essay, with no academic test. This local bank is an English-language study adaptation offering 100 original worked calculation problems.

Time Limit

50 minutes for the mathematics subject paper (March 4, 2026 in the Reiwa 8 early selection (zenki senbatsu))

Passing Score

No fixed pass mark; scored out of 50 points per subject (250 total across 5 subjects); selection combines the academic scores with the junior-high report (chousasho), weighted equally in principle in the general-selection track (ippan senbatsu), with optional per-subject weighting by school

Exam / Certification Fees

JPY 2,200 entrance examination fee per the Fukushima Prefectural Board of Education Reiwa 8 (2026) admissions guidelines

Exam sponsor website

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

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

Signed numbers, algebraic expressions, expansion and factorization, square roots and rationalization, prime factorization, and scientific notation.

About 15% of this practice bank

Equations

Linear equations, simultaneous systems, quadratic equations by factoring, square roots, and the formula, plus applied word problems.

About 20% of this practice bank

Functions and Graphs

Direct and inverse proportion, linear functions y=ax+b, quadratic functions y=ax², rates of change, domains, and intersection coordinates.

About 20% of this practice bank

Plane Geometry

Angles, parallel lines, polygons, congruence and similarity, circle theorems, tangents, and Pythagorean applications.

About 8% of this practice bank

Solid Figures and Measurement

Prisms, cylinders, cones, pyramids, and spheres: surface area, volume, and net-based problems.

About 12% of this practice bank

Data Handling and Probability

Relative frequency, mean and median, quartiles, counting outcomes for probability, complementary events, and sampling estimates.

Preparing for the Fukushima Entrance Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark; scored out of 50 points per subject (250 total across 5 subjects); selection combines the academic scores with the junior-high report (chousasho), weighted equally in principle in the general-selection track (ippan senbatsu), with optional per-subject weighting by school
  • Assessment: In the Reiwa 8 (2026) selection, the academic examination is one of five 50-minute subject papers (kokugo, shakai, suugaku, rika, and English with a broadcast listening section), each scored out of 50 points for a 250-point total, all held on March 4, 2026. Applications are submitted February 2–6, 2026 through a newly introduced WEB application system; interviews run March 4–6, 2026; results are announced via the web system on March 16, 2026 (viewable until March 24). The general selection weights the academic test and the chousasho equally in principle, and schools may apply weighted scoring to specific subjects; attendance records are not used for Reiwa 8. A late selection at under-filled schools (application March 17–18, interview March 24, results March 25, 2026) uses only the chousasho, an interview, and a short essay, with no academic test. This local bank is an English-language study adaptation offering 100 original worked calculation problems.
  • Time limit: 50 minutes for the mathematics subject paper (March 4, 2026 in the Reiwa 8 early selection (zenki senbatsu))
  • Exam / certification fees: JPY 2,200 entrance examination fee per the Fukushima Prefectural Board of Education Reiwa 8 (2026) admissions guidelines Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
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Fukushima Entrance Mathematics: Suggested Study Strategy

1Build speed and accuracy on fundamental calculation items (signed numbers, radicals, expansion, factorization) — the Fukushima paper emphasizes basic and fundamental mastery, so secure these points first.
2Practice setting up simultaneous equations and quadratic models from word-problem scenarios such as costs, speeds, and areas, a recurring pattern in prefectural applied problems.
3Because the official paper rewards written thinking, practice writing out full reasoning for similarity, circle theorem, and function problems — not just final answers.

Frequently Asked Questions

Is the official Fukushima mathematics paper multiple-choice?

No. The official paper is a constructed-response examination requiring written mathematical work, with an emphasis on basic and fundamental mastery plus questions that test written thinking. The MCQs here are an English-language study aid for testing concepts and calculation accuracy; they do not replace practicing full written solutions.

How long is the mathematics exam and what is the maximum score?

The mathematics paper lasts 50 minutes and is scored out of 50 points. Across all five subjects the academic examination totals 250 points, and admission combines these scores with the junior-high report (chousasho) — weighted equally in principle in the general-selection track (ippan senbatsu), though schools may apply weighted scoring to specific subjects.

When is the Reiwa 8 (2026) mathematics examination?

The academic examination, including mathematics, is held on March 4, 2026. Applications are submitted February 2–6, 2026 through the new WEB application system, interviews run March 4–6, 2026, and results are announced via the web system on March 16, 2026 (viewable until March 24).

What happens in the late selection (kouki senbatsu)?

The late selection is held only at schools that remain under-filled after the main selection. It uses no academic test: applicants are evaluated on the chousasho (junior-high report), an interview, and a short essay. For Reiwa 8, applications are March 17–18, 2026, the interview is March 24, and results are announced March 25, 2026.

Do these details apply to the next (Reiwa 9 / 2027) entrance examination?

The figures on this page describe the Reiwa 8 cycle, whose academic examination was sat on March 4, 2026. The Fukushima Prefectural Board of Education published its Reiwa 9 (2027 entry) school-by-school selection-method list on July 14, 2026 and has scheduled the full Reiwa 9 implementation guidelines for early October 2026. The five-subject, 50-minute, 50-point structure has been stable across recent cycles, but confirm the Reiwa 9 dates and rules on the board's own page before relying on them.