PracticeVideosBlogFlashcardsEspañol
All Practice Exams

Free Practice Questions for UEE Mathematics

Exam-style questions and explanations by OpenExamPrep.

✓ No registration✓ No credit card
100+ Questions
100% Free

Loading practice questions...

Same family resources

Explore More Mongolia General Entrance Exam (ЭЕШ) & Mongolian Language Exam (МХБШ)

Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.

Mongolian Language & Script Examination (МХБШ) (Mongolia)

Practice Questions

UEE Biology (ЭЕШ Биологи) (Mongolia)

Practice Questions

UEE Chemistry (ЭЕШ Хими) (Mongolia)

Practice Questions

UEE English (ЭЕШ Англи хэл) (Mongolia)

Practice Questions

UEE Geography (ЭЕШ Газар зүй) (Mongolia)

Practice Questions

UEE History (ЭЕШ Түүх) (Mongolia)

Practice Questions
Exam Review

Key Facts: UEE Mathematics Exam

100 minutes

Exam Duration

EEC (eec.mn/post/6813)

40 (36 + 4)

Tasks

EEC 2026 blueprint and paper

200–800

Score Scale

EEC (eec.mn/en/?p=935)

5,800 MNT

Fee

EEC fee notice (2023)

UEE Mathematics is a 100-minute EEC paper with 40 tasks (36 five-option items plus 4 open problems) and a formula sheet; results are reported on a 200–800 scale. This free 100-question bank follows the 2026 weights: algebra 30%, geometry and trigonometry 25%, analysis 20%, probability and statistics 15%, number 10%.

Sample UEE Mathematics Practice Questions

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

1Simplify the numerical expression: (2^3 * 4^(-1/2)) / 8^(2/3).
A.1
B.2
C.1/2
D.4
Explanation: Express all terms with base 2: 2^3 = 8; 4^(-1/2) = (2^2)^(-1/2) = 2^(-1) = 1/2; 8^(2/3) = (2^3)^(2/3) = 2^2 = 4. The numerator is 8 * (1/2) = 4. Dividing by the denominator gives 4 / 4 = 1.
2Evaluate the radical expression: (sqrt(12) + sqrt(27)) / sqrt(3).
A.sqrt(39)
B.3*sqrt(3)
C.6
D.5
Explanation: Simplify each radical in the numerator: sqrt(12) = sqrt(4 * 3) = 2*sqrt(3) and sqrt(27) = sqrt(9 * 3) = 3*sqrt(3). Their sum is 2*sqrt(3) + 3*sqrt(3) = 5*sqrt(3). Dividing by sqrt(3) yields (5*sqrt(3)) / sqrt(3) = 5.
3Compute the value of: log_2(32) - log_3(1/27) + log_5(1).
A.2
B.6
C.8
D.5/3
Explanation: Evaluate each logarithmic term individually: log_2(32) = log_2(2^5) = 5; log_3(1/27) = log_3(3^(-3)) = -3; log_5(1) = 0. Substituting these values gives 5 - (-3) + 0 = 5 + 3 = 8.
4In an arithmetic progression (a_n), the first term is a_1 = 7 and the common difference is d = 4. What is the 15th term a_15?
A.63
B.60
C.67
D.59
Explanation: The n-th term of an arithmetic progression is given by a_n = a_1 + (n - 1)d. For n = 15: a_15 = 7 + (15 - 1) * 4 = 7 + 14 * 4 = 7 + 56 = 63.
5Factor the quadratic polynomial 2x^2 - 5x - 3 completely over the integers.
A.(2x - 1)(x + 3)
B.(2x + 3)(x - 1)
C.(2x + 1)(x - 3)
D.(2x - 3)(x + 1)
Explanation: To factor 2x^2 - 5x - 3, find two numbers whose product is 2 * (-3) = -6 and whose sum is -5. These numbers are -6 and 1. Rewrite: 2x^2 - 6x + x - 3 = 2x(x - 3) + 1(x - 3) = (2x + 1)(x - 3).
6Simplify the rational expression: (x^2 - 9) / (2x^2 + 5x - 3) for all permissible values of x.
A.(x + 3) / (2x + 1)
B.(x - 3) / (2x - 1)
C.(x - 3) / (2x + 1)
D.(x + 3) / (2x - 1)
Explanation: Factor the numerator as a difference of squares: x^2 - 9 = (x - 3)(x + 3). Factor the denominator: 2x^2 + 5x - 3 = (2x - 1)(x + 3). Cancelling the common non-zero factor (x + 3) leaves (x - 3) / (2x - 1).
7Given that log_2(x) = 3 and log_2(y) = -2, determine the numerical value of log_2(x^2 * sqrt(y)).
A.7
B.4
C.5
D.9/2
Explanation: Apply logarithmic product and power rules: log_2(x^2 * sqrt(y)) = log_2(x^2) + log_2(y^(1/2)) = 2*log_2(x) + (1/2)*log_2(y). Substituting the given values: 2(3) + (1/2)(-2) = 6 - 1 = 5.
8In a geometric progression (b_n), the first term is b_1 = 3 and the common ratio is q = 2. What is the sum of the first 6 terms S_6?
A.186
B.381
C.192
D.189
Explanation: The sum of the first n terms of a geometric progression is S_n = b_1 * (q^n - 1) / (q - 1). For n = 6: S_6 = 3 * (2^6 - 1) / (2 - 1) = 3 * (64 - 1) / 1 = 3 * 63 = 189.
9A fair six-sided die is rolled once. What is the probability that the number rolled is greater than 4?
A.1/6
B.1/2
C.2/3
D.1/3
Explanation: There are 6 equally likely outcomes. The favorable outcomes greater than 4 are 5 and 6, so P = 2/6 = 1/3.
10Find the remainder when the polynomial P(x) = 3x^3 - 4x^2 + 2x - 5 is divided by (x - 2).
A.3
B.5
C.7
D.11
Explanation: By the Polynomial Remainder Theorem, the remainder of P(x) divided by (x - 2) is P(2). Calculate: P(2) = 3(2)^3 - 4(2)^2 + 2(2) - 5 = 3(8) - 4(4) + 4 - 5 = 24 - 16 + 4 - 5 = 7.

About the UEE Mathematics Exam

The mathematics paper of Mongolia's national university entrance examination (Элсэлтийн шалгалт, ЭШ; formerly ЭЕШ) is set by the Education Evaluation Center and written in Mongolian. OpenExamPrep offers 100 free English-language practice problems weighted like EEC's 2026 blueprint (number, algebra, analysis, geometry and trigonometry, probability and statistics), each with a worked solution. The bank is an English-language multiple-choice study adaptation, not an official translation or a simulation of the paper's five-option and open-response format.

Exam sponsor: Education Evaluation Center (Боловсролын үнэлгээний төв, БҮТ / EEC). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Part 1 (72 points): 36 five-option selection items. Part 2 (28 points): 4 multi-step problems with numerical answers filled in by the candidate. A formula sheet is provided. Scores are converted to the 200–800 scale.

Time Limit

100 minutes

Passing Score

No pass mark; results on a 200–800 scale, with university and program threshold scores (босго оноо)

Exam / Certification Fees

5,800 MNT per subject (EEC 2023 fee notice)

Exam sponsor website

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

Official sources

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.

10%

Number

Powers, roots, logarithms, percentages and real-number operations.

30%

Algebra

Expressions, equations, inequalities and systems of many types.

20%

Analysis

Functions, limits, derivatives and integrals.

25%

Geometry and trigonometry

Plane and solid geometry, triangle laws, identities, vectors and coordinates.

15%

Probability and statistics

Counting, probability rules, Bayes' formula, expected value, variance and descriptive statistics.

Preparing for the UEE Mathematics Exam

What You Need to Know

  • Passing score: No pass mark; results on a 200–800 scale, with university and program threshold scores (босго оноо)
  • Assessment: Part 1 (72 points): 36 five-option selection items. Part 2 (28 points): 4 multi-step problems with numerical answers filled in by the candidate. A formula sheet is provided. Scores are converted to the 200–800 scale.
  • Time limit: 100 minutes
  • Exam / certification fees: 5,800 MNT per subject (EEC 2023 fee notice) 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

UEE Mathematics: Suggested Study Strategy

1Algebra is the largest unit (30%); make sure you can solve every standard type of equation and inequality quickly.
2Do not skip probability and statistics: it is 15% of the 2026 points and uses the formulas printed on the formula sheet.
3Practice the Part 2 problems without options, because you must fill in the exact numerical answer.
4Check domains (logarithms, roots, denominators) before accepting a solution to an equation or inequality.
5Time yourself: 40 tasks in 100 minutes leaves about 2.5 minutes per task on average.

Frequently Asked Questions

What is the Mongolia UEE mathematics examination?

It is the mathematics subject of Mongolia's national university entrance examination (Элсэлтийн шалгалт, ЭШ; formerly ЭЕШ), set by the Education Evaluation Center (EEC) and written in Mongolian. Most science, engineering, economics and IT programs use it for admission.

How is the 2026 mathematics paper structured?

It lasts 100 minutes and has 40 tasks worth 100 points: 36 five-option selection items in Part 1 (72 points) and 4 open-response problems in Part 2 (28 points), where candidates fill in numerical answers. A formula sheet with probability formulas such as expected value, variance, total probability and Bayes' formula is printed with the paper.

What score do I need?

There is no pass mark. Scores are standardized to a 200–800 scale with a mean of 500, and each university and program sets its own minimum threshold score (босго оноо).

How much does the exam cost?

EEC's most recent published fee notice (2023) sets the fee at 5,800 MNT per subject. We did not find a separate 2026 fee notice, so check the registration portal when you register.

Why is this bank in English if the exam is in Mongolian?

OpenExamPrep publishes one English-language bank per exam. It is an independent MCQ study adaptation of the published specification, not an official translation, and it uses four options instead of the official five. Practice with EEC's Mongolian-language past papers as well.