Free Practice Questions for Belgrade ETF Entrance Exam

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University of Belgrade Medical School Entrance Exam — Prijemni ispit (Medicinski fakultet u Beogradu)

Practice Questions100 questions

Exam Review

Key Facts: Belgrade ETF Entrance Exam Exam

60 pts

Maximum Entrance Exam Score (Scaled by 0.6 from 100 Raw Points)

ETF Belgrade Admission Scoring Rules

40 pts

Maximum Secondary School Achievement Score

ETF Belgrade Admission Conditions

Problems Per Written Examination Paper

ETF Belgrade Entrance Examination Regulations

7,500 RSD

Application Fee for Undergraduate Admissions

ETF Belgrade Candidate Application Guidelines

Independent English-language four-option MCQ study adaptation for the University of Belgrade ETF Prijemni ispit. Each official Serbian paper has 20 weighted problems over 180 minutes. This 100-question bank covers selected mathematics and physics topics; its equal subject split is an editorial study choice, not an official topic weighting. It is not an official translation or a simulation of the exam's language environment, response count, timing, or penalty rules. Use the official papers for format practice.

Sample Belgrade ETF Entrance Exam Practice Questions

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

1Let f(x) = 3x - 2 and g(x) = x^2 + 1. What is g(f(-1))?

A.17

B.26

C.10

D.37

Explanation: Function composition applies the inner function first: f(-1) = 3*(-1) - 2 = -5. Applying g to that result gives g(-5) = (-5)^2 + 1 = 26.

2If x_1 and x_2 are the roots of the quadratic equation 3x^2 - 7x + 2 = 0, what is the value of x_1^2 + x_2^2?

A.37/9

B.49/9

C.25/9

D.41/9

Explanation: By Vieta's formulas for a quadratic equation ax^2 + bx + c = 0, the sum of the roots is x_1 + x_2 = -b/a = 7/3 and the product is x_1 * x_2 = c/a = 2/3. Using the algebraic identity x_1^2 + x_2^2 = (x_1 + x_2)^2 - 2*x_1*x_2 gives (7/3)^2 - 2*(2/3) = 49/9 - 4/3 = 49/9 - 12/9 = 37/9.

3For all real values of x where the denominators are nonzero, which of the following expressions is equivalent to (x^3 - 8) / (x^2 - 4) - (x^2 + 2x + 4) / (x + 2)?

A.0

B.1

C.2 / (x + 2)

D.(x - 2) / (x + 2)

Explanation: Factoring the difference of cubes gives x^3 - 8 = (x - 2)(x^2 + 2x + 4), and the difference of squares gives x^2 - 4 = (x - 2)(x + 2). For x != 2, canceling the common factor (x - 2) simplifies the first fraction to (x^2 + 2x + 4) / (x + 2). Subtracting the second identical fraction yields exactly 0.

4What is the modulus of the complex number w = (3 - 4i) / (1 + 2i), where i^2 = -1?

A.sqrt(5)

B.5

C.1

D.sqrt(5) / 5

Explanation: The modulus of a quotient of complex numbers is the quotient of their individual moduli: |w| = |3 - 4i| / |1 + 2i|. The numerator modulus is |3 - 4i| = sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = 5. The denominator modulus is |1 + 2i| = sqrt(1^2 + 2^2) = sqrt(5). Thus |w| = 5 / sqrt(5) = sqrt(5).

5For which real values of the parameter m does the quadratic inequality x^2 - 2(m - 1)x + (m + 5) > 0 hold for all real numbers x?

A.-1 < m < 4

B.m < -1 or m > 4

C.-4 < m < 1

D.-1 <= m <= 4

Explanation: Since the coefficient of x^2 is a = 1 > 0, the parabola opens upward and the quadratic expression is strictly positive for all real x if and only if its discriminant D is strictly negative. Here D/4 = (m - 1)^2 - 1*(m + 5) = m^2 - 2m + 1 - m - 5 = m^2 - 3m - 4 < 0. Factoring yields (m - 4)(m + 1) < 0, which holds when -1 < m < 4.

6Find the sum of all possible real values of x satisfying the system of equations x + y = 5 and x^3 + y^3 = 35.

A.5

B.6

C.7

D.4

Explanation: Using the algebraic factorization x^3 + y^3 = (x + y)(x^2 - xy + y^2) = (x + y)((x + y)^2 - 3xy), substitute x + y = 5 to obtain 35 = 5 * (25 - 3xy), so 7 = 25 - 3xy, leading to 3xy = 18 and xy = 6. Thus x and y are the roots of the quadratic equation t^2 - 5t + 6 = 0, giving t = 2 and t = 3. The possible real values of x are 2 and 3, and their sum is 2 + 3 = 5.

7What is the product of all real solutions to the irrational equation sqrt(2x + 3) - sqrt(x - 2) = 2?

A.33

B.14

C.11

D.3

Explanation: Isolating the larger radical gives sqrt(2x + 3) = sqrt(x - 2) + 2. Squaring both sides gives 2x + 3 = (x - 2) + 4*sqrt(x - 2) + 4 = x + 2 + 4*sqrt(x - 2). Rearranging yields x + 1 = 4*sqrt(x - 2). Squaring again gives (x + 1)^2 = 16(x - 2), so x^2 + 2x + 1 = 16x - 32, which simplifies to x^2 - 14x + 33 = 0. Factoring gives (x - 3)(x - 11) = 0. Testing both in the original equation: x = 3 yields sqrt(9) - sqrt(1) = 3 - 1 = 2 (valid); x = 11 yields sqrt(25) - sqrt(9) = 5 - 3 = 2 (valid). The product of the solutions is 3 * 11 = 33.

8Let f(x) = 3^(x - 1) and g(u) = log_3(u + 2). Which real number x satisfies g(f(x)) = 2?

A.log_3(7)

B.3

C.1 + log_3(7)

D.1 + log_3(11)

Explanation: Substitution gives log_3(3^(x - 1) + 2) = 2, so 3^(x - 1) + 2 = 9. Thus 3^(x - 1) = 7 and x = 1 + log_3(7). The logarithm's argument is positive for every real x, and the exponential is strictly increasing, so this solution is unique.

9What is the set of all real solutions to the logarithmic equation log_2(x - 1) + log_2(x + 2) = 2?

A.{2}

B.{2, -3}

C.{-3}

D.{1, 2}

Explanation: The domain of real logarithms requires x - 1 > 0 and x + 2 > 0, which means x > 1. Combining the logarithms gives log_2((x - 1)(x + 2)) = 2. Converting to exponential form: (x - 1)(x + 2) = 2^2 = 4. Expanding yields x^2 + x - 2 = 4, so x^2 + x - 6 = 0, which factors as (x + 3)(x - 2) = 0. While x = -3 solves the algebraic equation, it violates the domain restriction x > 1 and is extraneous. Therefore, x = 2 is the unique valid solution.

10What is the smallest positive integer n such that (1 + i*sqrt(3))^n is a strictly positive real number?

A.6

B.3

C.12

D.4

Explanation: Convert 1 + i*sqrt(3) to trigonometric polar form: its modulus is r = sqrt(1^2 + 3) = 2, and its argument is theta = arctan(sqrt(3)/1) = pi/3. By de Moivre's formula, (1 + i*sqrt(3))^n = 2^n * (cos(n*pi/3) + i*sin(n*pi/3)). For this complex number to be a strictly positive real number, the imaginary part must vanish (sin(n*pi/3) = 0) and the real part must be positive (cos(n*pi/3) > 0). This requires n*pi/3 to be an integer multiple of 2*pi, meaning n/3 = 2k for an integer k >= 1. The smallest positive integer is n = 6 (for k = 1).

About the Belgrade ETF Entrance Exam Exam

The School of Electrical Engineering (ETF) at the University of Belgrade administers competitive written entrance examinations (Prijemni ispit) for its undergraduate programmes in Electrical Engineering and Computing (ER) and Software Engineering (SI). ER candidates can take Mathematics, Physics, or both (taking the better score), while SI candidates must take Mathematics. Each test consists of 20 weighted problems over 3 hours. Total admission score combines up to 60 points from the entrance examination with up to 40 points from secondary school academic achievement.

Exam sponsor: University of Belgrade — School of Electrical Engineering (Elektrotehnički fakultet — ETF). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Each published 2026 paper has 20 weighted problems totaling 100 raw points, with five substantive choices A–E plus N ('Ne znam'). A correct response earns the problem's value; a wrong answer loses 16% of that value; N earns zero; blank or multiple marks lose 0.5 raw points. Raw scores are scaled by 0.6 for up to 60 admission points. The published entrance rules specify written papers and do not specify mandatory entrance assignments, oral, practical, or case-study components.

Time Limit

180 minutes (3 hours) per paper

Passing Score

Minimum 51/100 total points for budget eligibility and 30/100 total points for self-funded eligibility, alongside ranking within program admission quotas. Entrance test provides up to 60 points; secondary school GPA up to 40 points.

Exam / Certification Fees

7,500 RSD for the 2026 first-round application, covering one or both papers; the fee also applies to competition-award holders exempt from sitting a paper.

Exam sponsor website

Reported exam pass rate: not-published. Admission is competitive based on quota ranking. Reaching the 51 or 30 point threshold makes a candidate eligible for ranking, but final admission depends on quota capacity. Exam sponsor website

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

Official sources

ETF Prijemni ispit portal · Source checked 2026-10-10Central entrance examination information portal for the School of Electrical Engineering.
ETF Rules for Conducting the Entrance Examination (Pravila o održavanju prijemnog ispita) · Source checked 2026-10-10Candidate conduct, identification, 3-hour examination timing, and answer sheet submission rules.
ETF Scoring Method (Način bodovanja na prijemnom ispitu) · Source checked 2026-10-10Maximum 60 entrance points after 0.6 scaling, 40 secondary-school points, and the higher-score rule for ER candidates taking both papers. Paper-specific response penalties are documented in the published papers.
ETF Admission Conditions (Uslovi upisa) · Source checked 2026-10-10Secondary school diploma eligibility, 51-point threshold for budget and 30-point threshold for self-funded ranking.
ETF Candidate Registration and Fee (Prijavljivanje kandidata) · Source checked 2026-10-102026 first-round application fee of 7,500 RSD, including candidates exempt from sitting a paper; scanned application documents and foreign-qualification recognition requirements.
ETF Mathematics Program (Programi za prijemni ispit - Matematika) · Source checked 2026-10-10Official syllabus outlining algebra, trigonometry, geometry, stereometry, analysis, and combinatorics topics.
ETF Physics Program (Programi za prijemni ispit - Fizika) · Source checked 2026-10-10Official outline covering mechanics, fluids, thermal physics, electromagnetism, AC circuits, oscillations, optics, relativity, quantum physics, and nuclear physics. No topic percentage weights are published.
ETF 2026 entrance examination announcement · Source checked 2026-10-10Confirms the faculty's 2026 admissions and scheduled first-round mathematics and physics examinations on June 24 and 25.
Published 2026 mathematics paper · Source checked 2026-10-10Serbian assessment text, five substantive choices plus N, 16% wrong-answer deduction, zero for N, and 0.5-point deduction for blank or multiple marks.
Published 2026 physics paper · Source checked 2026-10-10Independently confirms Serbian text and the same response/penalty rules as mathematics. The PDF header says July 25, while the faculty's first-round announcement schedules physics on June 25; follow current faculty notices for dates.
ETF competition-award exemptions · Source checked 2026-10-10Qualifying awards in the final two secondary-school years can earn maximum points for the corresponding subject. Informatics awards count for SI mathematics ranking only.
ETF enrollment of foreign students · Source checked 2026-10-10Foreign-qualification recognition and enrollment documents; confirms that all ETF BSc programmes are conducted in Serbian. No additional entrance-assessment language was verified.

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.

50% of practice bank (20 problems on the official paper)

Matematika (Mathematics)

Algebra, polynomials, equations and inequalities, logarithms, trigonometry, complex numbers, planimetry, stereometry, analytic geometry, combinatorics, sequences, limits, and differential calculus.

50% of practice bank (20 problems on the official paper)

Fizika (Physics)

Classical mechanics, fluid mechanics, molecular physics, thermodynamics, electrostatics, DC electric circuits, electromagnetism, oscillations and waves, optics, and special relativity.

Preparing for the Belgrade ETF Entrance Exam Exam

What You Need to Know

Passing score: Minimum 51/100 total points for budget eligibility and 30/100 total points for self-funded eligibility, alongside ranking within program admission quotas. Entrance test provides up to 60 points; secondary school GPA up to 40 points.
Assessment: Each published 2026 paper has 20 weighted problems totaling 100 raw points, with five substantive choices A–E plus N ('Ne znam'). A correct response earns the problem's value; a wrong answer loses 16% of that value; N earns zero; blank or multiple marks lose 0.5 raw points. Raw scores are scaled by 0.6 for up to 60 admission points. The published entrance rules specify written papers and do not specify mandatory entrance assignments, oral, practical, or case-study components.
Time limit: 180 minutes (3 hours) per paper
Exam / certification fees: 7,500 RSD for the 2026 first-round application, covering one or both papers; the fee also applies to competition-award holders exempt from sitting a paper. Official sources

Using Our Practice Resources

Work through all 100 available questions
Review every answer and explanation
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Belgrade ETF Entrance Exam: Suggested Study Strategy

1Review the official syllabus outlines for Mathematics and Physics on the ETF prijemni portal and practice with collections of past entrance exam problems.

2Read your paper's scoring instructions. The published 2026 papers deduct 16% of the problem value for a wrong answer, award zero for Ne znam, and deduct 0.5 raw points for blank or multiple marks.

3Work thoroughly through analytical geometry, trigonometry, and stereometry problems, drawing accurate geometric sketches for each step.

4Master dimensional analysis and SI unit conversions in physics problems involving mechanics, thermodynamics, and circuit analysis.

Frequently Asked Questions

What is the official exam format and scoring at ETF?

Each written paper has 20 weighted problems over 180 minutes. The published 2026 mathematics and physics papers both offer five substantive options A–E plus N (Ne znam / I don't know). A correct response earns the full problem value; a wrong response loses 16% of that value; N earns zero. Blank or multiple marks lose 0.5 raw points. The maximum raw score is 100, scaled by 0.6 to a maximum of 60 admission points. Follow the instructions for your own paper and sitting.

Can candidates take both mathematics and physics?

Yes. Electrical Engineering and Computing (ER) candidates can take Mathematics, Physics, or both, using the higher score. Software Engineering (SI) ranking requires Mathematics. Qualifying competition-award holders can receive maximum points and exemption from sitting the corresponding paper; informatics awards count only toward SI mathematics ranking. The application fee still applies to these exempt candidates.

What are the eligibility and threshold requirements for admission?

Applicants must have completed a four-year secondary school. Admission scoring combines secondary school GPA (up to 40 points) and entrance examination results (up to 60 points) for a maximum of 100 points. To be eligible for state-budget financing, a candidate must achieve at least 51 points and place within the program's budget quota. To be eligible for self-funded study, a candidate must achieve at least 30 points and place within the self-funded quota.

In what language is the official examination administered?

The published 2026 mathematics and physics papers are in Serbian (sr), and ETF confirms that all its BSc programmes are conducted in Serbian. No additional entrance-assessment language has been verified. This is an independent English-language MCQ study adaptation, not an official translation or a simulation of the Serbian assessment environment.

What does this practice question bank provide?

It provides 100 independent English-language four-option study questions, with worked solutions and feedback for each distractor. The 50 mathematics and 50 physics questions cover selected topics from the faculty's published outlines. ETF publishes no fixed topic percentage distribution in those outlines. This selection does not exhaust either outline, and SI applicants should prioritize mathematics.