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Key Facts: Georgia Unified Math Exam

51

Maximum Total Points

NAEC Georgia

10 GEL

Examination Fee

NAEC Official

180 min

Time Limit (3 Hours)

NAEC Regulations

> 10.2

Competence Threshold (> 20%)

NAEC Passing Rule

4

Official Test Languages (GE, RU, HY, AZ)

NAEC Administration

Georgia's Unified National Examination in Mathematics (ერთიანი ეროვნული გამოცდა მათემატიკაში), run by NAEC, is the essential entrance examination for STEM, computer science, and economics programs with a 51-point maximum and a 3-hour duration for 10 GEL. The official test contains open-ended mathematical proofs; this bank is an English-language MCQ study adaptation featuring step-by-step worked solutions.

Sample Georgia Unified Math Practice Questions

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

1An item's price is increased by 20%, and subsequently discounted by 15% during a seasonal sale. What is the net percentage change from the original price?
A.+5.0%
B.+2.0%
C.-5.0%
D.+3.5%
Explanation: Let the original price be P. After a 20% increase, the price becomes 1.20P. A 15% discount then gives 1.20P * (1 - 0.15) = 1.20P * 0.85 = 1.02P, representing a net increase of +2.0%.
2Evaluate the arithmetic expression: (3/4 - 2/5) / (7/20 + 1/2).
A.7/17
B.1/2
C.5/17
D.7/10
Explanation: Compute the numerator: 3/4 - 2/5 = 15/20 - 8/20 = 7/20. Compute the denominator: 7/20 + 1/2 = 7/20 + 10/20 = 17/20. Dividing the two fractions gives (7/20) / (17/20) = 7/17.
3Simplify the expression: (27^(2/3) * 16^(3/4)) / 36^(1/2).
A.6
B.12
C.18
D.24
Explanation: Evaluating each component: 27^(2/3) = (3^3)^(2/3) = 3^2 = 9; 16^(3/4) = (2^4)^(3/4) = 2^3 = 8; and 36^(1/2) = 6. Substituting these values yields (9 * 8) / 6 = 72 / 6 = 12.
4Simplify the radical expression: sqrt(75) - sqrt(27) + sqrt(48) - sqrt(12).
A.3*sqrt(3)
B.4*sqrt(3)
C.5*sqrt(3)
D.6*sqrt(3)
Explanation: Extract square factors from each radicand: sqrt(75) = 5*sqrt(3), sqrt(27) = 3*sqrt(3), sqrt(48) = 4*sqrt(3), and sqrt(12) = 2*sqrt(3). Combining like radical terms yields (5 - 3 + 4 - 2)*sqrt(3) = 4*sqrt(3).
5Compute the exact numerical value of: log_2(48) - log_2(3) + log_3(81).
A.6
B.7
C.8
D.9
Explanation: Apply the quotient rule of logarithms: log_2(48) - log_2(3) = log_2(48/3) = log_2(16) = 4. Since 81 = 3^4, log_3(81) = 4. Adding these results gives 4 + 4 = 8.
6Solve the logarithmic equation for real x: log_3(x - 2) + log_3(x + 4) = 3.
A.5
B.7
C.5 and -7
D.9
Explanation: The domain requires x - 2 > 0 and x + 4 > 0, so x > 2. Combining logarithms gives log_3((x - 2)(x + 4)) = 3, which translates to x^2 + 2x - 8 = 3^3 = 27. Solving x^2 + 2x - 35 = 0 gives (x - 5)(x + 7) = 0. Since x = -7 violates the domain restriction, the unique valid real solution is x = 5.
7Evaluate the expression: (log_5(8) * log_2(25)) + log_4(64).
A.8
B.9
C.10
D.12
Explanation: Using logarithm power rules, log_5(8) = log_5(2^3) = 3*log_5(2), and log_2(25) = log_2(5^2) = 2*log_2(5). Their product is 3 * 2 * (log_5(2) * log_2(5)) = 6 * 1 = 6. Since 64 = 4^3, log_4(64) = 3. Summing these terms gives 6 + 3 = 9.
8If r1 and r2 are the roots of the quadratic equation 2x^2 - 7x + 4 = 0, what is the value of (1/r1 + 1/r2)?
A.7/8
B.7/4
C.7/2
D.4/7
Explanation: By Vieta's formulas, the sum of the roots is r1 + r2 = -(-7)/2 = 7/2, and the product of the roots is r1 * r2 = 4/2 = 2. The sum of the reciprocals is (1/r1 + 1/r2) = (r1 + r2) / (r1 * r2) = (7/2) / 2 = 7/4.
9For what value of the constant k is the polynomial P(x) = 2x^3 - 5x^2 + kx - 6 divisible by (x - 2)?
A.3
B.4
C.5
D.6
Explanation: By the Remainder Theorem, P(x) is divisible by (x - 2) if and only if P(2) = 0. Substituting x = 2: P(2) = 2(2^3) - 5(2^2) + k(2) - 6 = 2(8) - 5(4) + 2k - 6 = 16 - 20 + 2k - 6 = 2k - 10 = 0. Solving gives 2k = 10, so k = 5.
10How many distinct real roots does the polynomial equation x^4 - 13x^2 + 36 = 0 have?
A.2
B.3
C.4
D.0
Explanation: Let u = x^2. The equation becomes u^2 - 13u + 36 = 0, which factors as (u - 4)(u - 9) = 0, yielding u = 4 and u = 9. Substituting back: x^2 = 4 gives x = +-2, and x^2 = 9 gives x = +-3. This yields 4 distinct real roots: -3, -2, 2, 3.

About the Georgia Unified Math Exam

The Unified National Examination in Mathematics (ერთიანი ეროვნული გამოცდა მათემატიკაში) is the mandatory or elective university entrance examination administered across Georgia by NAEC. It tests graduating secondary students on arithmetic, algebra, trigonometry, geometry (planimetry and stereometry), coordinate geometry, vectors, and probability and statistics. The official 2026 NAEC mathematics syllabus is organised as algebra, geometry (planimetry and stereometry), data analysis with probability and statistics, and units of measurement; it does not include limits, derivatives or integrals.

Exam sponsor: National Assessment and Examinations Center (NAEC). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Standardized national written examination administered by NAEC in Georgia covering arithmetic, algebra, functions, trigonometry, planimetry, stereometry, vectors, probability and statistics. Local practice bank is an English-language MCQ study adaptation.

Time Limit

180 minutes (3 hours)

Passing Score

Candidates must exceed 20% of the 51 maximum points (greater than 10.2 points) to meet the minimum competence threshold. Admission to STEM, economics, computer science, engineering, and architecture faculties is competitive based on scaled scores.

Exam / Certification Fees

10 GEL

Exam sponsor website

Reported exam pass rate: Competence threshold requires > 10.2 points; admission to competitive STEM faculties is ranked competitively by scaled score. State grants covering 50%, 70%, or 100% of university tuition fees are awarded to the highest-scoring applicants nationally based on scaled scores. This describes exam candidates, not OpenExamPrep users or results from using our resources. 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.

25%

Arithmetic, Algebra & Number Theory

Real numbers, radicals, rational exponents, logarithms, polynomials, quadratic/higher equations, linear/non-linear systems, inequalities, and progressions.

25%

Functions, Trigonometry & Equations

Domain and range, parity, monotonicity, periodicity, greatest and least values, function composition, graph transformations, and exponential, logarithmic, irrational and trigonometric equations and inequalities.

30%

Planimetry & Stereometry

Triangle theorems, quadrilaterals, circle geometry, lines/planes in space, dihedral angles, prisms, cylinders, pyramids, cones, and spheres.

20%

Vectors, Coordinate Geometry, Probability & Statistics

2D vectors, dot products, lines, circles in Cartesian coordinates, combinatorics, classical/independent probability, and statistical measures.

Preparing for the Georgia Unified Math Exam

What You Need to Know

  • Passing score: Candidates must exceed 20% of the 51 maximum points (greater than 10.2 points) to meet the minimum competence threshold. Admission to STEM, economics, computer science, engineering, and architecture faculties is competitive based on scaled scores.
  • Assessment: Standardized national written examination administered by NAEC in Georgia covering arithmetic, algebra, functions, trigonometry, planimetry, stereometry, vectors, probability and statistics. Local practice bank is an English-language MCQ study adaptation.
  • Time limit: 180 minutes (3 hours)
  • Exam / certification fees: 10 GEL 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

Georgia Unified Math: Suggested Study Strategy

1Thoroughly review logarithmic properties, change of base formulas, and domain restrictions for equations involving radicals and logs.
2Memorize key trigonometric identities including double-angle formulas and the Law of Cosines to solve geometric triangles rapidly.
3Practise locating the vertex of a parabola with x = -b/(2a) to read off greatest and least values and increasing/decreasing intervals without calculus.
4Master spatial visualization for stereometry: practice calculating lateral areas, heights, and volumes of pyramids, truncated cones, and spheres.
5Use vector dot products (u · v = 0) to efficiently prove perpendicularity in coordinate and 2D geometric problems.
6Carefully analyze conditional wording in combinatorics and probability: distinguish between permutations (order matters) and combinations (subsets).

Frequently Asked Questions

What is the Unified National Examination in Mathematics in Georgia?

It is the standardized national entrance exam administered by NAEC (National Assessment and Examinations Center) required for admission to STEM, computer science, engineering, architecture, and economics programs in Georgian universities.

What is the passing threshold for the NAEC Mathematics exam?

To pass the minimum competence threshold, candidates must score strictly greater than 20% of the total 51 points (i.e., more than 10.2 points). Mathematics uses a 20% barrier, unlike most NAEC subjects, which use 25%. High-demand STEM faculties establish much higher practical admission cut-offs based on candidate ranking.

How long is the exam and how much is the registration fee?

The examination lasts 180 minutes (3 hours). The official registration fee is 10 GEL per subject for Georgian school graduates.

What languages is the official examination administered in?

NAEC sets this paper in Georgian. Eligible candidates, principally those whose general education was obtained in an occupied territory, may apply to NAEC in advance to sit history, mathematics, chemistry, geography, physics, biology, fine and applied arts, and civic education in Russian. Armenian and Azerbaijani versions exist for the General Skills test only, not for this subject. This practice bank is an English-language MCQ study adaptation and is not an official NAEC translation.