100+ Free Armenia Mathematics Unified Exam Practice Questions

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Key Facts: Armenia Mathematics Unified Exam Exam

Armenia's Unified Entrance Exam in Mathematics (ATC / Dimord.am) is a 19-task paper across Level A and Level B, sat in 180 minutes for a 4,500 AMD fee, marked out of 80 raw points and converted to a 20-point scale on which 7.5 is the minimum positive score.

Sample Armenia Mathematics Unified Exam Practice Questions

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

1Solve the irrational equation: sqrt(2x + 7) = x + 2.

A.x = 1

B.x = 1 and x = -3

C.x = -3

D.x = 3

Explanation: Square both sides with domain restriction x + 2 >= 0 (x >= -2): 2x + 7 = (x + 2)² => 2x + 7 = x² + 4x + 4 => x² + 2x - 3 = 0. Factoring gives (x + 3)(x - 1) = 0 => x = 1 or x = -3. Since x = -3 violates x >= -2 (producing sqrt(1) = -1, false), x = 1 is the unique valid real root.

2What are all real solutions to the absolute value equation: |2x - 5| = 3x + 1?

A.x = 4/5

B.x = 4/5 and x = -6

C.x = -6

D.x = 2

Explanation: Condition 3x + 1 >= 0 => x >= -1/3. Case 1: 2x - 5 = 3x + 1 => -x = 6 => x = -6 (rejected since -6 < -1/3). Case 2: 2x - 5 = -(3x + 1) = -3x - 1 => 5x = 4 => x = 4/5 (valid since 4/5 >= -1/3).

3Solve the system of equations: { x + y = 7, x² + y² = 25 }.

A.(3, 4) and (4, 3)

B.(2, 5) and (5, 2)

C.(1, 6) and (6, 1)

D.(-3, 10) and (10, -3)

Explanation: We know (x + y)² = x² + y² + 2xy => 7² = 25 + 2xy => 49 - 25 = 2xy => 2xy = 24 => xy = 12. By Vieta's formulas, x and y are roots of t² - 7t + 12 = 0 => (t - 3)(t - 4) = 0. Thus the solutions are (3, 4) and (4, 3).

4Solve the logarithmic inequality: log3(x² - 2x) <= 1.

A.[-1, 0) U (2, 3]

B.[-1, 3]

C.(0, 2)

D.[-1, 0] U [2, 3]

Explanation: Domain: x² - 2x > 0 => x(x - 2) > 0 => x in (-infinity, 0) U (2, +infinity). Inequality: x² - 2x <= 3^1 = 3 => x² - 2x - 3 <= 0 => (x - 3)(x + 1) <= 0 => x in [-1, 3]. Intersecting with domain yields [-1, 0) U (2, 3]. Note 0 and 2 are strictly excluded.

5For what values of the parameter 'a' does the quadratic equation x² - 2(a - 1)x + (a + 5) = 0 have two distinct real roots?

A.a < -1 or a > 4

B.-1 < a < 4

C.a > 4

D.a <= -1 or a >= 4

Explanation: For two distinct real roots, discriminant D/4 > 0: D/4 = (a - 1)² - (a + 5) = a² - 2a + 1 - a - 5 = a² - 3a - 4 = (a - 4)(a + 1) > 0. The quadratic is strictly positive outside its roots: a < -1 or a > 4.

6Solve the exponential equation: 4^x - 3 * 2^x - 4 = 0.

A.x = 2

B.x = 2 and x = 0

C.x = 4

D.x = 1

Explanation: Let u = 2^x (u > 0). Then u² - 3u - 4 = 0 => (u - 4)(u + 1) = 0 => u = 4 or u = -1. Since 2^x > 0 for all real x, u = -1 has no real solutions. For u = 4: 2^x = 4 = 2² => x = 2.

7Simplify the algebraic expression: ((a^(3/2) - b^(3/2)) / (a^(1/2) - b^(1/2))) - (ab)^(1/2) for a > 0, b > 0, a != b.

A.a + b

B.a - b

C.(a + b)²

D.1

Explanation: Use difference of cubes u³ - v³ = (u - v)(u² + uv + v²) with u = sqrt(a) and v = sqrt(b): (a^(3/2) - b^(3/2)) / (a^(1/2) - b^(1/2)) = a + sqrt(ab) + b. Subtracting (ab)^(1/2) yields a + sqrt(ab) + b - sqrt(ab) = a + b.

8Solve the rational inequality: (x² - 5x + 6) / (x - 1) >= 0.

A.(1, 2] U [3, +infinity)

B.[1, 2] U [3, +infinity)

C.(-infinity, 1) U [2, 3]

D.[2, 3]

Explanation: Factor the numerator: (x - 2)(x - 3) / (x - 1) >= 0. Critical points are 1 (open), 2 (closed), 3 (closed). Sign analysis: for x < 1: (-)(-)/(-) = -; for 1 < x < 2: (-)(-)/(+) = +; for 2 < x < 3: (+)(-)/(+) = -; for x > 3: (+)(+)/(+) = +. Solution is (1, 2] U [3, +infinity).

9Solve the equation: log_x(2x² - 3x - 4) = 2.

A.x = 4

B.x = 4 and x = -1

C.x = -1

D.x = 2

Explanation: By definition of logarithm: 2x² - 3x - 4 = x² => x² - 3x - 4 = 0 => (x - 4)(x + 1) = 0 => x = 4 or x = -1. Base conditions require x > 0 and x != 1. Thus x = -1 is inadmissible, leaving x = 4 as the only solution.

10Find the sum of all integer solutions to the inequality: |3x - 2| <= 7.

A.5

B.3

C.7

D.0

Explanation: |3x - 2| <= 7 <=> -7 <= 3x - 2 <= 7 => add 2: -5 <= 3x <= 9 => divide by 3: -5/3 <= x <= 3 (approx -1.67 <= x <= 3). The integer solutions are {-1, 0, 1, 2, 3}. Their sum is -1 + 0 + 1 + 2 + 3 = 5.

About the Armenia Mathematics Unified Exam Exam

The Mathematics Unified Entrance Examination (Միասնական քննություն՝ «Մաթեմատիկա») is Armenia's official centralized admissions test for university degree programs in mathematics, computer science, software engineering, physics, economics, finance, architecture, and technology. Prepared by the Assessment and Testing Center (ATC) and administered through the Dimord.am portal, the exam rigorously evaluates secondary school algebra, mathematical analysis, trigonometry, planimetry, stereometry, and probability. All candidates are evaluated on a 20-point scale. This practice bank provides an English-language MCQ study adaptation featuring worked numerical solutions.

Assessment

Centralized written examination lasting 180 minutes (3 hours). Sub-tasks come in three forms: four-option multiple choice (1 point), short numeric answer written as an integer between 0 and 999 (1 point), and clusters of six statements marked True / False / Don't know (up to 6 points, with a point deducted for each wrong statement and a floor of zero for the cluster).

Time Limit

180 minutes (3 hours)

Passing Score

7.5 out of 20 is the minimum positive score (RA Government Decision N 597-Ն, clause 67, as amended). Admission is competitive: applicants are ranked by the sum of their two unified exam scores, and ATC publishes the cut-off for every university programme each year.

Exam Fee

4,500 AMD (Assessment and Testing Center (ATC / ԳԹԿ - atc.am) / Ministry of ESCS)

Armenia Mathematics Unified Exam Exam Content Outline

30%

Algebra, Equations & Inequalities

Algebraic manipulations, radical equations, logarithmic/exponential forms, absolute values, and parametric analysis.

25%

Functions & Mathematical Analysis

Function properties, graphs, limits, derivative applications, tangent lines, optimization problems, and integral calculus.

20%

Trigonometry & Sequences

Trigonometric identities, reduction formulas, inverse functions, arithmetic and geometric progressions, permutations, and probability.

25%

Geometry (Planimetry & Stereometry)

Plane geometry theorems (triangles, quadrilaterals, circles), 3D solid geometry (prisms, pyramids, cones, spheres), and vector operations.

How to Pass the Armenia Mathematics Unified Exam Exam

What You Need to Know

Passing score: 7.5 out of 20 is the minimum positive score (RA Government Decision N 597-Ն, clause 67, as amended). Admission is competitive: applicants are ranked by the sum of their two unified exam scores, and ATC publishes the cut-off for every university programme each year.
Assessment: Centralized written examination lasting 180 minutes (3 hours). Sub-tasks come in three forms: four-option multiple choice (1 point), short numeric answer written as an integer between 0 and 999 (1 point), and clusters of six statements marked True / False / Don't know (up to 6 points, with a point deducted for each wrong statement and a floor of zero for the cluster).
Time limit: 180 minutes (3 hours)
Exam fee: 4,500 AMD

Keys to Passing

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

Armenia Mathematics Unified Exam Study Tips from Top Performers

1Master rapid factoring, algebraic simplifications, and root finding without a calculator.

2Thoroughly review trigonometric reduction formulas, sum-to-product identities, and exact values for standard angles.

3Practice 3D solid geometry visualization, particularly cross-sections of pyramids, cylinders, and cones.

4Work through official ATC sample booklets (շտեմարաններ) under strict 180-minute timed conditions.

Frequently Asked Questions

What is the Mathematics Unified Exam in Armenia?

It is the standardized national entrance examination administered by the Assessment and Testing Center (ATC) for applicants to STEM, engineering, and economics faculties in Armenia.

How many tasks are on the exam and what is the duration?

The ATC guide specifies 19 tasks with sub-tasks across Level A and Level B, sat in 180 minutes (3 hours) and marked out of 80 raw points.

What is the passing score?

A score of 7.5 or higher out of 20 counts as a positive result. Admission is decided competitively on the sum of two unified exam scores, and ATC publishes the annual cut-off for each university programme.

Are calculators allowed during the exam?

No, calculators are strictly prohibited on the official ATC Mathematics examination; all calculations must be performed by hand.

100+ Free Armenia Mathematics Unified Exam Practice Questions

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