100+ Free UNSA ETF Math Entrance Exam Practice Questions

Prepare for the Prijemni ispit iz matematike — Univerzitet u Sarajevu, Elektrotehnički fakultet (UNSA ETF Mathematics Entrance Exam) exam with instant access — no signup required.

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Key Facts: UNSA ETF Math Entrance Exam Exam

Tasks On The Paper

ETF UNSA, Odluka o kriterijima za rangiranje (01.06.2026)

120 min

Exam Duration

ETF UNSA, Ogledni primjer prijemnog ispita

40 pts

Max Exam Score

ETF UNSA, Odluka o kriterijima za rangiranje (01.06.2026)

Minimum Qualifying Score

ETF UNSA, Odluka o vrednovanju rezultata prijemnog ispita

40 KM

Examination Fee

Elektrotehnički fakultet UNSA

The UNSA ETF Mathematics Entrance Exam is a 120-minute paper of 20 mathematics tasks worth up to 40 points (5 tasks at 3 points, 10 at 2, 5 at 1). Candidates must show their working: a circled answer without correct working scores nothing, and there is no negative marking and no pass threshold. The fee is 40 KM. The official paper is sat in Bosnian/Croatian/Serbian; this bank is an English-language four-option MCQ study adaptation with worked solutions, not a simulation of the official answer-plus-working format.

Sample UNSA ETF Math Entrance Exam Practice Questions

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

1What is the remainder when the polynomial P(x) = 2x^4 - 3x^3 + 5x^2 - x + 7 is divided by (x - 2)?

A.33

B.25

C.41

D.15

Explanation: According to the polynomial remainder theorem (Bézout's theorem), the remainder of P(x) divided by (x - a) is P(a). For a = 2: P(2) = 2(2^4) - 3(2^3) + 5(2^2) - 2 + 7 = 2(16) - 3(8) + 5(4) - 2 + 7 = 32 - 24 + 20 - 2 + 7 = 33.

2If x_1 and x_2 are the roots of the quadratic equation 2x^2 - 6x + 1 = 0, what is the value of x_1^2 + x_2^2?

A.8

B.9

C.7

D.17/2

Explanation: By Vieta's formulas: x_1 + x_2 = -(-6)/2 = 3 and x_1 * x_2 = 1/2. We expand (x_1 + x_2)^2 = x_1^2 + x_2^2 + 2x_1 x_2. Thus: x_1^2 + x_2^2 = (x_1 + x_2)^2 - 2(x_1 x_2) = 3^2 - 2(1/2) = 9 - 1 = 8.

3Calculate the value of the complex power: (1 + i)^8.

A.16

B.-16

C.16i

D.64

Explanation: Notice that (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i. Therefore: (1 + i)^8 = [(1 + i)^2]^4 = (2i)^4 = 2^4 * i^4 = 16 * 1 = 16.

4Find the solution set for the rational inequality: (x - 1) / (x + 3) <= 0.

A.x in (-3, 1]

B.x in [-3, 1]

C.x in (-infinity, -3) U [1, infinity)

D.x in [-3, 1)

Explanation: The critical points are x = -3 (denominator zero) and x = 1 (numerator zero). The denominator cannot be zero, so x != -3 (open interval at -3). Testing intervals: for x in (-3, 1), the fraction is negative. At x = 1, it equals 0 (satisfying <= 0). Thus, x in (-3, 1].

5What is the modulus and principal argument of the complex number z = -√3 + i?

A.|z| = 2, arg(z) = 5π/6 (150°)

B.|z| = 2, arg(z) = π/6 (30°)

C.|z| = 2, arg(z) = 2π/3 (120°)

D.|z| = 4, arg(z) = 5π/6

Explanation: Modulus |z| = √((-√3)^2 + 1^2) = √(3 + 1) = √4 = 2. Since Re(z) = -√3 < 0 and Im(z) = 1 > 0, z is in the second quadrant: arg(z) = π - arctan(1/√3) = π - π/6 = 5π/6 (150°).

6Factorize the polynomial P(x) = x^3 - 7x + 6 completely into linear factors:

A.(x - 1)(x - 2)(x + 3)

B.(x + 1)(x - 2)(x - 3)

C.(x - 1)(x + 2)(x - 3)

D.(x + 1)(x + 2)(x + 3)

Explanation: Test rational roots: P(1) = 1 - 7 + 6 = 0 -> (x - 1) is a factor. Dividing: (x^3 - 7x + 6) / (x - 1) = x^2 + x - 6 = (x - 2)(x + 3). Thus, P(x) = (x - 1)(x - 2)(x + 3).

7Decompose into partial fractions: (5x - 1) / (x^2 - x - 2) = A / (x - 2) + B / (x + 1). What are the values of A and B?

A.A = 3, B = 2

B.A = 2, B = 3

C.A = 4, B = 1

D.A = 1, B = 4

Explanation: Factor denominator: x^2 - x - 2 = (x - 2)(x + 1). Set 5x - 1 = A(x + 1) + B(x - 2). For x = 2: 5(2) - 1 = A(3) -> 9 = 3A -> A = 3. For x = -1: 5(-1) - 1 = B(-3) -> -6 = -3B -> B = 2.

8Find the complex number z = (3 + 4i) / (1 - 2i):

A.-1 + 2i

B.1 + 2i

C.-1 - 2i

D.11/5 + 2i/5

Explanation: Multiply numerator and denominator by conjugate (1 + 2i): z = [(3 + 4i)(1 + 2i)] / [(1 - 2i)(1 + 2i)] = [3 + 6i + 4i + 8i^2] / [1 - 4i^2] = [3 + 10i - 8] / [1 + 4] = [-5 + 10i] / 5 = -1 + 2i.

9For what value of parameter m is the polynomial P(x) = x^3 - 4x^2 + mx - 6 divisible by (x - 3)?

A.m = 5

B.m = -5

C.m = 3

D.m = 7

Explanation: By the factor theorem, P(3) must equal 0: P(3) = 3^3 - 4(3^2) + m(3) - 6 = 27 - 36 + 3m - 6 = 0 -> 3m - 15 = 0 -> 3m = 15 -> m = 5.

10Find the sum of the cubes of the roots (x_1^3 + x_2^3) of the equation x^2 - 4x + 2 = 0:

A.40

B.64

C.56

D.32

Explanation: From Vieta's formulas: s = x_1 + x_2 = 4 and p = x_1 x_2 = 2. Using identity: x_1^3 + x_2^3 = (x_1 + x_2)^3 - 3 x_1 x_2 (x_1 + x_2) = 4^3 - 3(2)(4) = 64 - 24 = 40.

About the UNSA ETF Math Entrance Exam Exam

The Prijemni ispit iz matematike at the Elektrotehnički fakultet (ETF) of the Univerzitet u Sarajevu (UNSA) is the faculty entrance examination required for every first-cycle programme except the distance-learning form of Data Science and Artificial Intelligence. It is governed by ETF's own Odluka o vrednovanju rezultata prijemnog ispita and Odluka o kriterijima za rangiranje, both adopted on 1 June 2026 for the 2026/2027 cycle. The scope is elementary mathematics: the faculty publishes an Ogledni primjer prijemnog ispita and sells a Zbirka zadataka used in its instruktivna nastava.

Assessment

Twenty mathematics tasks: 5 tasks worth 3 points, 10 worth 2 points and 5 worth 1 point, giving a 40-point maximum. Candidates circle an answer and must show the working; full correct working scores the full mark, clearly incomplete working scores half, and clearly incorrect working scores zero regardless of the circled answer. There is no negative marking and no minimum score.

Time Limit

120 minutes (2 hours)

Passing Score

No threshold — ETF's Odluka o vrednovanju rezultata states the entrance exam 'nema praga'. The 40 exam points are added to points for general secondary achievement (max 20), grades in mother tongue/English, mathematics and physics (max 40), competition results and a 5-point straight-5 bonus, producing one ranking list.

Exam Fee

40 KM (Univerzitet u Sarajevu — Elektrotehnički fakultet)

UNSA ETF Math Entrance Exam Exam Content Outline

not published

Algebra, Polynomials & Complex Numbers

Algebraic and radical manipulation, Vieta's formulas, polynomial divisibility, binomial expansions, number systems, and complex numbers.

not published

Equations, Inequalities & Systems

Quadratic, higher-order, irrational, exponential, logarithmic and modulus equations and inequalities, including parameter problems.

not published

Trigonometry

Trigonometric identities, transformation formulas, trigonometric equations and inequalities, and applications in geometric figures.

not published

Functions, Sequences & Analytic Geometry

Domain, parity, periodicity and inverse functions, arithmetic and geometric progressions, and lines and conics in the Cartesian plane.

not published

Planimetry, Stereometry & Combinatorics

Plane geometry theorems, 3D geometry of prisms, pyramids and round solids, and elementary combinatorics.

How to Pass the UNSA ETF Math Entrance Exam Exam

What You Need to Know

Passing score: No threshold — ETF's Odluka o vrednovanju rezultata states the entrance exam 'nema praga'. The 40 exam points are added to points for general secondary achievement (max 20), grades in mother tongue/English, mathematics and physics (max 40), competition results and a 5-point straight-5 bonus, producing one ranking list.
Assessment: Twenty mathematics tasks: 5 tasks worth 3 points, 10 worth 2 points and 5 worth 1 point, giving a 40-point maximum. Candidates circle an answer and must show the working; full correct working scores the full mark, clearly incomplete working scores half, and clearly incorrect working scores zero regardless of the circled answer. There is no negative marking and no minimum score.
Time limit: 120 minutes (2 hours)
Exam fee: 40 KM

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

UNSA ETF Math Entrance Exam Study Tips from Top Performers

1Work through ETF's published Ogledni primjer prijemnog ispita and the faculty Zbirka zadataka, as they define the problem styles and difficulty level.

2Always write out the full solution: on the real paper a circled answer earns nothing unless the working supports it.

3Practice solving algebra, trigonometry, and geometry problems without a calculator to build speed and accuracy.

4Pay close attention to domain restrictions when solving logarithmic, irrational, and rational equations.

Frequently Asked Questions

How is the UNSA ETF mathematics entrance exam scored?

The paper has 20 tasks: 5 are worth 3 points, 10 are worth 2 points and 5 are worth 1 point, giving a 40-point maximum. A task counts only if the circled answer is supported by the working — full correct working earns the full mark, clearly incomplete working earns half, and clearly incorrect working earns zero. There is no negative marking and no minimum qualifying score.

Are calculators allowed during the ETF entrance exam?

No. Candidates are not permitted to use calculators, mobile phones, or formula sheets during the examination. All calculations must be performed by hand.

In what language is the official examination delivered?

The official exam is administered in Bosnian, Croatian, or Serbian. This practice bank provides an English-language MCQ study adaptation with fully worked calculations.