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Exam Review

Key Facts: ORT Mathematics Exam

40

Official Exam Questions

CEATM (ЦООМО)

80 min

Exam Duration

CEATM (ЦООМО)

60 pts

Threshold Passing Score

Ministry of Ed & Science KR

470 KGS

Official Registration Fee

testing.kg

No

Calculators Permitted

Official Testing Rules

100

Study Adaptation Questions

Open Exam Prep

The Kyrgyzstan ORT Subject Test in Mathematics consists of 40 multiple-choice questions in 80 minutes, administered by CEATM (ЦООМО) for a fee of 470 som. A minimum score of 60 points is required for university eligibility in STEM and economics programs. This independent English-language practice bank provides 100 worked questions across algebra, equations, geometry, stereometry, and probability.

Sample ORT Mathematics Practice Questions

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

1Expand and simplify (2x − 3)(x + 5).
A.2x^2 + 13x − 15
B.2x^2 + 7x + 15
C.2x^2 + 7x − 15
D.2x^2 − 7x − 15
Explanation: Distribute term by term: (2x − 3)(x + 5) = 2x·x + 2x·5 + (−3)·x + (−3)·5 = 2x^2 + 10x − 3x − 15. Combining like terms gives 2x^2 + 7x − 15. This independent English-language practice item drills polynomial expansion used on the ORT Mathematics subject test.
2Simplify (x + 4)^2 − (x − 2)^2.
A.12x + 12
B.12x + 20
C.8x + 12
D.12x − 12
Explanation: Expand each square: (x + 4)^2 = x^2 + 8x + 16 and (x − 2)^2 = x^2 − 4x + 4. Subtract: (x^2 + 8x + 16) − (x^2 − 4x + 4) = x^2 + 8x + 16 − x^2 + 4x − 4 = 12x + 12. Equivalently, the difference of squares identity gives [(x + 4) − (x − 2)][(x + 4) + (x − 2)] = (6)(2x + 2) = 12x + 12.
3When the polynomial P(x) = x^3 − 4x^2 + 5x − 7 is divided by x − 2, what is the remainder?
A.1
B.−5
C.5
D.−13
Explanation: By the remainder theorem, the remainder on division by x − 2 equals P(2). Compute P(2) = 2^3 − 4·2^2 + 5·2 − 7 = 8 − 16 + 10 − 7. Then 8 − 16 = −8, −8 + 10 = 2, and 2 − 7 = −5. So the remainder is −5.
4If the roots of x^2 − 5x + 6 = 0 are r and s, what is r + s?
A.6
B.−5
C.1
D.5
Explanation: For x^2 + bx + c = 0 written as x^2 − (sum)x + (product) = 0, Vieta’s formulas give r + s = 5 and rs = 6. Factoring confirms (x − 2)(x − 3) = 0, so the roots are 2 and 3 and their sum is 5.
5The roots of x^2 − 3x − 4 = 0 are α and β. What is α^2 + β^2?
A.9
B.17
C.1
D.25
Explanation: Vieta gives α + β = 3 and αβ = −4. Then α^2 + β^2 = (α + β)^2 − 2αβ = 3^2 − 2(−4) = 9 + 8 = 17. Directly, the roots are 4 and −1, and 16 + 1 = 17.
6For x ≠ 3, simplify (x^2 − 9)/(x − 3).
A.x − 3
B.9
C.x^2 − 3
D.x + 3
Explanation: Factor the numerator as a difference of squares: x^2 − 9 = (x − 3)(x + 3). Cancel the common factor x − 3 (valid for x ≠ 3) to obtain x + 3.
7For x ≠ 2, simplify (x^3 − 8)/(x − 2).
A.x^2 + 2x + 4
B.x^2 − 2x + 4
C.x^2 + 4
D.x^2 + 2x − 4
Explanation: Use the difference-of-cubes formula a^3 − b^3 = (a − b)(a^2 + ab + b^2) with a = x and b = 2: x^3 − 8 = (x − 2)(x^2 + 2x + 4). Cancel x − 2 to leave x^2 + 2x + 4. Polynomial division of x^3 + 0x^2 + 0x − 8 by x − 2 yields the same quotient.
8Simplify (√12 + √27)/√3.
A.5√3
B.√13
C.5
D.2√3 + 3
Explanation: Rewrite the radicands: √12 = √(4·3) = 2√3 and √27 = √(9·3) = 3√3. Then (2√3 + 3√3)/√3 = 5√3 / √3 = 5. Splitting the fraction also gives √(12/3) + √(27/3) = √4 + √9 = 2 + 3 = 5.
9Evaluate sin 30° + cos 60°.
A.√3 / 2
B.0
C.√3
D.1
Explanation: The standard values are sin 30° = 1/2 and cos 60° = 1/2. Adding them gives 1/2 + 1/2 = 1. These are the school-table values used throughout ORT-style trigonometry.
10Evaluate 2 sin 45° cos 45°.
A.√2 / 2
B.1/2
C.1
D.2
Explanation: sin 45° = cos 45° = √2 / 2, so 2 · (√2 / 2) · (√2 / 2) = 2 · (2 / 4) = 2 · (1/2) = 1. The double-angle identity 2 sin θ cos θ = sin 2θ with θ = 45° also gives sin 90° = 1.

About the ORT Mathematics Exam

The ORT Subject Test in Mathematics (Предметный тест ОРТ по математике / ЖРТ математика боюнча предметтик тест) is an optional standardized university entrance examination in Kyrgyzstan conducted by CEATM (ЦООМО). It is mandatory for applicants seeking admission to university degree programs in mathematics, information technology, software engineering, physics, economics, and technical disciplines. The official test contains 40 multiple-choice questions to be completed in 80 minutes. This practice test is an independent English-language MCQ study adaptation designed to help students master core high school mathematical concepts tested on the exam.

Exam sponsor: Center for Educational Assessment and Teaching Methods (ЦООМО / CEATM) under the Ministry of Education and Science of the Kyrgyz Republic. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

40 multiple-choice questions administered in a single 80-minute paper session. Each question has four choices (A, B, C, D) with exactly one correct response.

Time Limit

80 minutes

Passing Score

60 points (threshold score required to participate in state grant and contract university competitions)

Exam / Certification Fees

470 KGS (som)

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.

35%

Algebra and Analysis

Polynomials, rational functions, trigonometry, derivatives, definite integrals, and exponential-logarithmic functions

25%

Equations and Inequalities

Systems of equations, parameter-dependent problems, irrational equations, and algebraic inequalities

25%

Geometry (Planimetry & Stereometry)

Triangles, circles, 3D polyhedra (prisms, pyramids), solids of revolution (cylinders, cones, spheres), and vectors

15%

Progressions, Combinatorics & Probability

Arithmetic and geometric sequences, combinatorial counting, and classical probability

Preparing for the ORT Mathematics Exam

What You Need to Know

  • Passing score: 60 points (threshold score required to participate in state grant and contract university competitions)
  • Assessment: 40 multiple-choice questions administered in a single 80-minute paper session. Each question has four choices (A, B, C, D) with exactly one correct response.
  • Time limit: 80 minutes
  • Exam / certification fees: 470 KGS (som) 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

ORT Mathematics: Suggested Study Strategy

1Master mental and paper arithmetic to calculate quickly without a calculator under the strict 2-minute-per-question pace.
2Systematically memorize core trigonometric identities, including double-angle formulas, sum-to-product transformations, and inverse trigonometric values.
3Practice stereometry visualization by sketching 3D figures (pyramids, cones, inscribed spheres) and finding cross-sectional planes.
4Pay close attention to extraneous roots in irrational and logarithmic equations by always checking domain restrictions (ODZ / ОДЗ).
5Review standard derivative rules and geometric interpretations of the derivative, such as equations of tangent lines and points of inflection.
6Use elimination strategies on multiple-choice options by testing boundary values or substituting convenient integers.

Frequently Asked Questions

What is the ORT Subject Test in Mathematics in Kyrgyzstan?

The ORT Mathematics Subject Test (Предметный тест ОРТ по математике) is a standardized test administered by the Center for Educational Assessment and Teaching Methods (ЦООМО / CEATM). While the Main ORT Test (General Ability) is required for all university entrants, the Mathematics Subject Test is specifically required for enrollment in STEM, engineering, computer science, physics, and economics faculties.

What is the format and duration of the official ORT Mathematics test?

The official exam consists of 40 multiple-choice questions administered in a paper-and-pencil format. Candidates are allotted exactly 80 minutes (an average of 2 minutes per question). Questions evaluate deep high-school mathematics without the use of calculators or formula sheets.

What score is required to pass the ORT Mathematics subject test?

The Ministry of Education and Science of the Kyrgyz Republic sets a baseline threshold (пороговый балл), which is typically 60 points for subject tests. Achieving at least 60 points makes a candidate eligible to submit scores for state grant (scholarship) and contract-based university quotas in relevant specialties.

How much does the exam cost to take?

Registration for each ORT subject test costs 470 Kyrgyz som (KGS). Registration typically takes place in February through April at designated district educational centers across Kyrgyzstan.

In what languages is the official ORT Mathematics test offered?

Official testing by CEATM is offered in Russian and Kyrgyz. This practice platform provides an English-language study adaptation to help candidates master the mathematical methodology, problem structures, and analytical concepts required for the exam.

Are calculators or reference sheets allowed during the ORT Mathematics exam?

No. Calculators, smartwatches, formula crib sheets, and mobile devices are strictly prohibited during the official testing session. All calculations must be performed by hand in the provided scratch area of the test booklet.