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Key Facts: Ehime Entrance Mathematics Exam

50 min / 50 points

Length and maximum score of the Ehime mathematics paper

Ehime Prefectural Board of Education general selection guidelines

5 subjects / 250 points

Five-subject academic examination total score

Ehime Prefectural Board of Education general selection guidelines

JPY 2,200

Entrance examination fee for full-time course

Ehime Prefectural Board of Education general selection guidelines

100

Free original calculation practice questions in this bank

OpenExamPrep

The Ehime public high school entrance mathematics paper is a 50-minute, 50-point written exam set by the Ehime Prefectural Board of Education, covering junior-high algebra, functions, geometry, statistics, and probability. This page offers 100 original calculation practice questions with full explanations.

Sample Ehime Entrance Mathematics Practice Questions

Try these sample questions to review concepts for the Ehime 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) - (-3).
A.8
B.2
C.-2
D.22
Explanation: To solve (-7) + (+12) - (-3): First, simplify subtracting a negative number: -(-3) = +3. So the expression becomes: -7 + 12 + 3. Group terms: (-7 + 12) + 3 = 5 + 3 = 8.
2Calculate the value of (-4)^2 × (-3) + 18 ÷ (-6).
A.-51
B.45
C.-55
D.51
Explanation: Evaluate operations following order of operations: 1. Exponent: (-4)^2 = 16. 2. Multiplication: 16 × (-3) = -48. 3. Division: 18 ÷ (-6) = -3. 4. Addition: -48 + (-3) = -51.
3Calculate 5/6 - 3/4 ÷ (-9/8).
A.3/2
B.1/6
C.-1/6
D.4/3
Explanation: 1. Perform the division first: 3/4 ÷ (-9/8) = 3/4 × (-8/9) = -2/3. 2. Then subtract: 5/6 - (-2/3) = 5/6 + 4/6 = 9/6 = 3/2.
4Evaluate the algebraic expression -a^2 - 3b when a = -3 and b = 4.
A.-21
B.-3
C.21
D.3
Explanation: Substitute a = -3 and b = 4 into -a^2 - 3b: 1. -a^2 = -(-3)^2 = -(9) = -9. The square is applied before the leading minus sign. 2. -3b = -3(4) = -12. 3. Sum: -9 - 12 = -21.
5Simplify the expression 4(2x - 3y) - 3(x - 5y).
A.5x + 3y
B.5x - 27y
C.11x + 3y
D.5x - 3y
Explanation: 1. Expand the parentheses: 4(2x) + 4(-3y) - 3(x) - 3(-5y) = 8x - 12y - 3x + 15y. 2. Combine like terms: (8x - 3x) + (-12y + 15y) = 5x + 3y.
6Simplify (5x - 2y)/3 - (x - 4y)/2.
A.(7x + 8y)/6
B.(7x - 16y)/6
C.(7x - 8y)/6
D.(4x + 2y)/6
Explanation: 1. Use the common denominator 6: [2(5x - 2y) - 3(x - 4y)]/6. 2. Expand the numerator: 2(5x - 2y) = 10x - 4y, and -3(x - 4y) = -3x + 12y. 3. Combine terms: (10x - 3x) + (-4y + 12y) = 7x + 8y. So the expression simplifies to (7x + 8y)/6.
7Expand and simplify 2x(x - 3) - (x + 4)(x - 1).
A.x^2 - 9x + 4
B.x^2 - 3x - 4
C.x^2 - 9x - 4
D.3x^2 - 9x + 4
Explanation: 1. Expand 2x(x - 3) = 2x^2 - 6x. 2. Expand (x + 4)(x - 1) = x^2 + 3x - 4. 3. Subtract the second expression: (2x^2 - 6x) - (x^2 + 3x - 4) = 2x^2 - 6x - x^2 - 3x + 4. 4. Combine like terms: x^2 - 9x + 4.
8If A = 2x^2 - 3x + 1 and B = x^2 + 4x - 5, find 3A - 2B.
A.4x^2 - 17x + 13
B.4x^2 - 17x + 7
C.4x^2 - 1x + 13
D.8x^2 - 17x + 13
Explanation: 1. Calculate 3A = 3(2x^2 - 3x + 1) = 6x^2 - 9x + 3. 2. Calculate 2B = 2(x^2 + 4x - 5) = 2x^2 + 8x - 10. 3. Compute 3A - 2B = (6x^2 - 9x + 3) - (2x^2 + 8x - 10) = 4x^2 - 17x + 13, since 3 - (-10) = 13.
9Solve the linear equation 4x - 7 = 2x + 9 for x.
A.x = 8
B.x = 1
C.x = -8
D.x = 16
Explanation: 1. Subtract 2x from both sides: 4x - 2x - 7 = 9, so 2x - 7 = 9. 2. Add 7 to both sides: 2x = 16. 3. Divide by 2: x = 8.
10Solve the equation (x - 3)/4 - (2x + 1)/3 = 1.
A.x = -5
B.x = -25
C.x = 5
D.x = -13
Explanation: 1. Multiply the whole equation by the LCD 12: 3(x - 3) - 4(2x + 1) = 12. 2. Expand: 3x - 9 - 8x - 4 = 12, so -5x - 13 = 12. 3. Solve: -5x = 25, so x = -5.

About the Ehime Entrance Mathematics Exam

The Ehime Public High School Entrance Examination mathematics paper is one of five subject papers in the prefecture-wide academic examination set by the Ehime Prefectural Board of Education. The 50-minute, 50-point exam covers numbers and algebra, linear and quadratic functions, plane and spatial geometry, data analysis, and probability. This page provides 100 original English-language practice items with step-by-step worked solutions as a study adaptation.

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

Assessment

The real Ehime mathematics subject is one of five academic subjects of the prefecture-wide entrance examination administered over two days in early March. The mathematics paper lasts 50 minutes and is scored out of 50 points, following the MEXT junior-high mathematics curriculum from fundamental calculation to applied geometry and functions. This local bank is an English-language study adaptation offering 100 original worked calculation problems.

Time Limit

50 minutes for the mathematics subject paper

Passing Score

No fixed pass mark; scored out of 50 points (250 total across 5 subjects); selection combines academic test results with junior-high report cards (chousasho) and interview

Exam / Certification Fees

JPY 2,200 entrance examination fee for the full-time course per the Ehime Prefectural Board of Education general selection 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 30% of this practice bank

Numbers and Algebra

Positive/negative numbers, linear and quadratic equations, simultaneous systems, square roots, and polynomial factorization.

About 25% of this practice bank

Functions and Graphs

Direct/inverse proportion, linear functions y=ax+b, quadratic functions y=ax^2, rates of change, and intersection coordinates.

About 25% of this practice bank

Plane Geometry

Angles, parallel lines, triangle congruence and similarity, circle properties, and Pythagorean applications.

About 10% of this practice bank

Spatial Geometry

Prisms, pyramids, cylinders, cones, spheres, surface area, volume, and solid nets.

About 10% of this practice bank

Data Analysis and Probability

Histograms, measures of central tendency, relative frequency, and counting outcomes for probability.

Preparing for the Ehime Entrance Mathematics Exam

What You Need to Know

  • Passing score: No fixed pass mark; scored out of 50 points (250 total across 5 subjects); selection combines academic test results with junior-high report cards (chousasho) and interview
  • Assessment: The real Ehime mathematics subject is one of five academic subjects of the prefecture-wide entrance examination administered over two days in early March. The mathematics paper lasts 50 minutes and is scored out of 50 points, following the MEXT junior-high mathematics curriculum from fundamental calculation to applied geometry and functions. This local bank is an English-language study adaptation offering 100 original worked calculation problems.
  • Time limit: 50 minutes for the mathematics subject paper
  • Exam / certification fees: JPY 2,200 entrance examination fee for the full-time course per the Ehime Prefectural Board of Education general selection guidelines Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Ehime Entrance Mathematics: Suggested Study Strategy

1Ensure fast, accurate calculation on fundamental algebra items (first section of the paper) to secure baseline points.
2Practice setting up simultaneous equations and quadratic models from word problem scenarios.
3Review similarity ratios and circle theorems for geometry proof and length calculations.

Frequently Asked Questions

Is the official Ehime mathematics paper multiple-choice?

No. The official paper requires showing written mathematical work and numerical answers. The MCQs here are a study aid for testing concepts and calculation accuracy.

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.