Free Practice Questions for Military Academy Belgrade Entrance Exam

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Key Facts: Military Academy Belgrade Entrance Exam Exam

45 points

Maximum mathematics contribution to admission ranking

Vojna akademija 2026/2027 civilian cadet competition

40 points

Maximum secondary-school achievement contribution

Vojna akademija 2026/2027 civilian cadet competition

15 points

Maximum physical fitness contribution

Vojna akademija 2026/2027 civilian cadet competition

2004 or later

Required birth year in the 2026/2027 civilian cadet competition

Vojna akademija and Ministry of Defence 2026 competition notices

Independent English-language four-option MCQ study adaptation for the mathematics component of the Vojna akademija entrance selection. The official assessment is in Serbian; the currently linked 2025 mathematics paper has five substantive answer choices plus N and uses negative marking. These 101 practice questions are not an official translation, a simulation of the official format or language environment, or a substitute for physical fitness and other required selection components. Current item count, duration, fee, and numeric qualifying thresholds need confirmation for the actual sitting.

Sample Military Academy Belgrade Entrance Exam Practice Questions

Try these sample questions to review concepts for the Military Academy Belgrade Entrance Exam exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 101+ question experience with AI tutoring.

1For all real numbers a and b with a != b, simplify the algebraic expression: ((a^3 - b^3) / (a - b)) - 2ab - b^2.

A.a^2 - ab

B.a^2 + ab

C.(a - b)^2

D.a^2 + b^2

Explanation: Factoring the difference of cubes gives a^3 - b^3 = (a - b)(a^2 + ab + b^2). Dividing by (a - b) yields a^2 + ab + b^2. Subtracting 2ab and then b^2 gives (a^2 + ab + b^2) - 2ab - b^2 = a^2 - ab = a(a - b).

2Rationalize the denominator of 5/(sqrt(7) + sqrt(2)) and simplify the result.

A.sqrt(7) + sqrt(2)

B.sqrt(7) - sqrt(2)

C.(sqrt(7) - sqrt(2))/5

D.5*(sqrt(7) - sqrt(2))/9

Explanation: Multiply numerator and denominator by the conjugate sqrt(7) - sqrt(2). The denominator becomes 7 - 2 = 5, giving 5*(sqrt(7) - sqrt(2))/5 = sqrt(7) - sqrt(2).

3Calculate the exact numerical value of [ (2^5 * 4^3) / 8^3 ]^2.

A.4

B.64

C.16

D.256

Explanation: Express all terms with base 2: 2^5 = 2^5, 4^3 = (2^2)^3 = 2^6, and 8^3 = (2^3)^3 = 2^9. The numerator is 2^5 * 2^6 = 2^11. Dividing by the denominator gives 2^11 / 2^9 = 2^2 = 4. Squaring the result gives 4^2 = 16.

4The remainder when P(x) = 2x^3 - 3x^2 + kx - 5 is divided by x - 2 is 9. What is the value of k?

A.4

B.10

C.-5

D.5

Explanation: By the polynomial remainder theorem, P(2) must equal 9. Substitution gives 16 - 12 + 2k - 5 = 9, or 2k - 1 = 9. Hence 2k = 10 and k = 5.

5If x < -2, simplify the expression |x + 2| - |1 - x| + 3x.

A.3x - 3

B.x - 1

C.5x + 1

D.3x + 1

Explanation: For x < -2, x + 2 < 0, so |x + 2| = -(x + 2) = -x - 2. Also, 1 - x > 0 because x < -2 implies -x > 2, so |1 - x| = 1 - x. Substituting these into the expression gives (-x - 2) - (1 - x) + 3x = -x - 2 - 1 + x + 3x = 3x - 3.

6A non-zero real number x satisfies x - 1/x = 3. What is the value of x^3 - 1/x^3?

A.27

B.36

C.18

D.30

Explanation: The identity (a - b)^3 = a^3 - b^3 - 3ab(a - b) applies with a = x, b = 1/x, and ab = 1. Thus 3^3 = x^3 - 1/x^3 - 3*3. Rearranging gives x^3 - 1/x^3 = 27 + 9 = 36.

7Factor the polynomial x^4 + 4 into the product of two real quadratic polynomials.

A.(x^2 + 2)^2

B.(x^2 - 2)(x^2 + 2)

C.(x^2 - 2x + 2)(x^2 + 2x + 2)

D.(x^2 - 4x + 4)(x^2 + 4x + 4)

Explanation: Use Sophie Germain's identity by completing the square: x^4 + 4 = (x^2)^2 + 2*(x^2)*2 + 2^2 - 4x^2 = (x^2 + 2)^2 - (2x)^2. As a difference of squares, this factors into ((x^2 + 2) - 2x)((x^2 + 2) + 2x) = (x^2 - 2x + 2)(x^2 + 2x + 2).

8Simplify the radical expression sqrt(7 + 4*sqrt(3)) - sqrt(7 - 4*sqrt(3)).

A.4*sqrt(3)

B.4

C.2

D.2*sqrt(3)

Explanation: Notice that 7 + 4*sqrt(3) = 4 + 4*sqrt(3) + 3 = 2^2 + 2*(2)*sqrt(3) + (sqrt(3))^2 = (2 + sqrt(3))^2. Thus, sqrt(7 + 4*sqrt(3)) = 2 + sqrt(3). Similarly, 7 - 4*sqrt(3) = (2 - sqrt(3))^2, and since 2 > sqrt(3), sqrt(7 - 4*sqrt(3)) = 2 - sqrt(3). The difference is (2 + sqrt(3)) - (2 - sqrt(3)) = 2*sqrt(3).

9The polynomial P(x) = x^3 + ax^2 + bx - 6 is divisible by (x - 1)(x + 2). What is the value of a + b?

A.5

B.3

C.-1

D.7

Explanation: If P(x) is divisible by (x - 1)(x + 2), then 1 and -2 are roots of P(x). Setting P(1) = 0 gives 1 + a + b - 6 = 0, which immediately yields a + b = 5. (To verify individual coefficients: P(-2) = -8 + 4a - 2b - 6 = 0 => 4a - 2b = 14 => 2a - b = 7. Adding a + b = 5 and 2a - b = 7 gives 3a = 12 => a = 4, so b = 1, confirming a + b = 5).

10Simplify the rational expression: [ x/(x - 1) - (x + 1)/x ] / [ (x^2 + x) / (x^2 - 1) ] for all allowed values of x.

A.1 / x

B.1 / x^2

C.(x - 1) / x^2

D.x / (x + 1)

Explanation: The original expression requires x != -1, 0, 1. Its numerator simplifies to [x^2 - (x - 1)(x + 1)]/[x(x - 1)] = 1/[x(x - 1)], while the divisor simplifies to x/(x - 1). Multiplying by the reciprocal gives [1/[x(x - 1)]]*[(x - 1)/x] = 1/x^2, with all original restrictions retained.

About the Military Academy Belgrade Entrance Exam Exam

Vojna akademija runs a competitive cadet entrance selection that includes written mathematics and physical fitness testing after psychological and military medical assessment. The 2026/2027 civilian competition also requires security clearance and ranks eligible candidates using school achievement, mathematics, and fitness results. This bank provides independent mathematics practice; it does not assess medical or psychological suitability or physical performance.

Exam sponsor: Vojna akademija, Univerzitet odbrane u Beogradu, Ministry of Defence of the Republic of Serbia. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The 2026 cadet selection has psychological and military medical assessment, followed by written mathematics and physical fitness testing; only candidates with the required mathematics result proceed to fitness testing. Security clearance is also required. Ranking combines up to 40 school-achievement points, 45 mathematics points, and 15 fitness points. The published 2025 paper uses negative marking, but its precise rules should not be assumed for a different sitting. No oral, essay, coursework, or case-study component is specified in the reviewed 2026 notice; Vojno vazduhoplovstvo additionally requires parachute and flight selection training.

Time Limit

Not confirmed for 2026; archived 2023 instructions specify 120 minutes, while the published 2019 Academy regulation states 150 minutes. Confirm the instructions for your sitting.

Passing Score

Ranking within the approved quota on a 100-point scale (40 school achievement + 45 mathematics + 15 fitness), subject to qualifying assessments. The 2026 notice requires a mathematics threshold before fitness testing but does not state its numeric value.

Exam / Certification Fees

Not published in the reviewed 2026 competition; confirm with admissions. Ministry-funded cadet education does not establish a zero application fee, and candidates pay selection travel costs.

Exam sponsor website

Reported exam pass rate: not-published. No overall pass rate was found in the reviewed official materials; admission depends on selection results and the approved quota. Exam sponsor website

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

Official sources

Vojna akademija — 2026/2027 civilian cadet competition · Source checked 2026-10-10Current identity, provider, eligibility, selection stages, ranking points, travel costs, and Ministry-funded cadet education. Does not establish a zero application fee or publish a mathematics item count, time limit, or numeric qualifying threshold.
Ministry of Defence — additional 2026/2027 cadet competition · Source checked 2026-10-10Official 1 June 2026 notice independently confirms continued admissions, birth in 2004 or later, and the mathematics and fitness selection components.
Vojna akademija — entrance preparation and official past papers · Source checked 2026-10-10The preparation page currently links a mathematics collection, papers through 2025, and physical fitness instructions.
University of Defence — mathematics preparation collection (2016) · Source checked 2026-10-10Still linked by the Academy: chapters 1–9 cover algebra, functions, equations, exponentials and logarithms; chapters 10–13 cover trigonometry and geometry; chapters 14–17 cover progressions, binomial coefficients, complex numbers, proportions and percentages. These are study topics, not published topic weights.
Vojna akademija — official mathematics paper, 23 July 2025 · Source checked 2026-10-10Serbian paper with 15 tasks: +3 for a correct answer, -0.5 for an incorrect answer, 0 for N, and -1 for multiple or absent responses. These are the archived paper's rules, not independently confirmed rules for every 2026 sitting.
Vojna akademija — archived instructions, 22 April 2023 · Source checked 2026-10-10Explicitly dated instructions allow 120 minutes and describe 15 tasks and six response positions including N; not evidence of a confirmed 2026 duration.
University of Defence — Academy admission regulation, SVL 12/2019 · Source checked 2026-10-10Still listed on the University's regulations page. Specifies Serbian delivery and a 150-minute mathematics test; its timing differs from the archived 2023 sitting instructions, so current timing requires confirmation.
Vojna akademija — physical fitness instructions · Source checked 2026-10-10Currently linked instructions dated 25 November 2022 describe four fitness disciplines; physical performance cannot be replaced by these mathematics MCQs.

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.

14 practice questions

Algebra, Real Numbers, and Polynomials

Algebraic identities, factors, remainders, rational expressions, powers, and radicals. These counts describe our practice inventory; no official mathematics topic percentages were found.

1 practice question

Real Functions

Determine a rational function's range using a non-negative square and endpoint analysis.

15 practice questions

Equations and Inequalities

Linear and quadratic equations, systems, Vieta's formulas, absolute values, radicals, parameters, and rational inequalities.

15 practice questions

Exponential and Logarithmic Functions

Logarithm properties, exponential substitution, equations, inequalities, and domain restrictions.

15 practice questions

Trigonometry

Reference angles, addition and double-angle formulas, identities, equations, and triangle trigonometry.

15 practice questions

Planimetry and Stereometry

Triangles, quadrilaterals, circles, similar figures, pyramids, cylinders, cones, and spheres.

13 practice questions

Analytic Geometry

Coordinates, lines, distances, circles, tangents, ellipses, hyperbolas, and centroids.

12 practice questions

Progressions, Combinatorics, and Complex Numbers

Arithmetic and geometric progressions, binomial coefficients, elementary counting, and complex-number algebra.

1 practice question

Proportions and Percentages

Use inverse proportion to distinguish a percentage decrease from the corresponding percentage increase.

Preparing for the Military Academy Belgrade Entrance Exam Exam

What You Need to Know

Passing score: Ranking within the approved quota on a 100-point scale (40 school achievement + 45 mathematics + 15 fitness), subject to qualifying assessments. The 2026 notice requires a mathematics threshold before fitness testing but does not state its numeric value.
Assessment: The 2026 cadet selection has psychological and military medical assessment, followed by written mathematics and physical fitness testing; only candidates with the required mathematics result proceed to fitness testing. Security clearance is also required. Ranking combines up to 40 school-achievement points, 45 mathematics points, and 15 fitness points. The published 2025 paper uses negative marking, but its precise rules should not be assumed for a different sitting. No oral, essay, coursework, or case-study component is specified in the reviewed 2026 notice; Vojno vazduhoplovstvo additionally requires parachute and flight selection training.
Time limit: Not confirmed for 2026; archived 2023 instructions specify 120 minutes, while the published 2019 Academy regulation states 150 minutes. Confirm the instructions for your sitting.
Exam / certification fees: Not published in the reviewed 2026 competition; confirm with admissions. Ministry-funded cadet education does not establish a zero application fee, and candidates pay selection travel costs. Official sources

Using Our Practice Resources

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Military Academy Belgrade Entrance Exam: Suggested Study Strategy

1Practice algebraic transformations and retain the original domain restrictions after simplifying expressions or squaring equations.

2Use the Academy's official past papers alongside this English-language study adaptation to practice reading Serbian mathematical instructions.

3Review the actual sitting's time limit and response penalties; archived papers and instructions can differ.

4Study geometry, functions, progressions, complex numbers, proportions, and percentages from the Academy's preparation collection.

5Prepare separately for the official physical fitness and other selection requirements using the Academy's instructions.

Frequently Asked Questions

What are the official assessment format and scoring?

The 2026 notice specifies written mathematics and physical fitness after psychological and medical assessment, with security checks also required. Ranking awards up to 40 points for school achievement, 45 for mathematics, and 15 for fitness. The currently linked 23 July 2025 paper contains 15 mathematics tasks, each with five substantive choices plus N: correct answers earn 3 points, wrong answers lose 0.5, N earns 0, and multiple or absent responses lose 1. Confirm the actual sitting's count, timing, and response rules.

Who can apply in the 2026/2027 civilian cadet competition?

Applicants must have Serbian citizenship and residence, be born in 2004 or later, and have completed or be in the final year of a four-year secondary school. Required achievement and conduct grades, criminal-record conditions, and psychological, medical, and security criteria also apply. Specified engineering programs require technical secondary education or gimnazija. Vojno vazduhoplovstvo adds medical criteria and parachute and flight selection training; consult the full competition for program-specific conditions.

Is the application fee the same as the cost of cadet education?

The reviewed 2026 notice states that the Ministry of Defence pays cadet education costs under a contract and that candidates pay travel costs during selection. It does not state an application or entrance-test fee, so a zero fee cannot be confirmed. Confirm application costs with admissions; graduates enter professional military service, and failure to meet contractual obligations may require repayment of education costs.

What language is used, and what does this practice bank adapt?

The Academy admission regulation specifies Serbian, and the published 2025 paper is in Serbian. This is an independent English-language MCQ study adaptation of mathematics topics, with four answer options. It is not an official translation or a simulation of the exam's format, language environment, timing, or penalty rules, and it cannot replace physical or other required selection components. No official English sitting was identified in the reviewed sources.

How are mathematics topics distributed in this bank?

The Academy's currently linked preparation collection provides the study scope, including algebra, functions, equations, logarithms, trigonometry, geometry, progressions, complex numbers, and percentages. No official percentage weighting among mathematics topics was found. The section counts shown here describe OpenExamPrep's 101-question practice bank, not an official blueprint or the number of tasks in the entrance examination.