Military Academy Belgrade Entrance Exam cheat sheet

Quadratic formula: for ax² + bx + c = 0 with a ≠ 0, the roots are x = (-b ± √(b² - 4ac)) / (2a); the discriminant b² - 4ac decides two real, one real, or no real roots.

Vieta's formulas: for ax² + bx + c = 0, the sum of roots equals -b/a and the product of roots equals c/a.

Arithmetic progression: nth term aₙ = a₁ + (n - 1)d; sum Sₙ = n(a₁ + aₙ)/2.

Geometric progression: nth term aₙ = a₁·q^(n-1); sum Sₙ = a₁(qⁿ - 1)/(q - 1) for q ≠ 1.

Pythagorean theorem: in a right triangle with legs a, b and hypotenuse c, a² + b² = c².

Trigonometric identity: sin²x + cos²x = 1; also sin 30° = 1/2, cos 30° = √3/2, tan 45° = 1.

Area formulas: triangle A = ½·base·height; circle A = πr²; trapezoid A = ½(a + b)h.

Logarithm rules: log(xy) = log x + log y; log(x/y) = log x - log y; log(xⁿ) = n·log x.

Probability of an event = number of favorable outcomes divided by total equally likely outcomes; P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Newton's second law: net force F = ma, where acceleration is proportional to net force and inversely proportional to mass.

Uniformly accelerated motion: v = v₀ + at and s = v₀t + ½at²; for free fall a = g ≈ 9.81 m/s².

Kinetic energy KE = ½mv²; gravitational potential energy near Earth PE = mgh; work W = F·d·cos θ.

Conservation of mechanical energy: KE + PE is constant when only conservative forces act.

Ohm's law: V = IR; electric power P = VI = I²R = V²/R.

Momentum p = mv; in an isolated system total momentum is conserved in collisions.

Wave relation: speed v = f·λ, where f is frequency and λ is wavelength.

Pressure in a fluid at depth h: p = p₀ + ρgh; buoyant force equals the weight of displaced fluid (Archimedes' principle).

Coulomb's law: force between point charges F = k·|q₁q₂|/r², with k ≈ 9×10⁹ N·m²/C².

Serbian Cyrillic has 30 letters (azbuka); the Latin alphabet (abeceda) maps one-to-one onto it.

Serbian orthography is phonetic: words are written as they are pronounced, so voicing assimilation occurs in writing (e.g., 'Srpski' spelled with s before p).

The letters ђ, ћ, џ, љ, њ, ј are single letters representing single sounds; they are never split across syllables.

Vuk Stefanović Karadžić reformed the alphabet and orthography in the 19th century; his principle was 'write as you speak'.

Nouns have three genders (masculine, feminine, neuter), two numbers, and seven cases in the singular and plural declension.

The seven cases are nominative, genitive, dative, accusative, vocative, instrumental, and locative; prepositions govern specific cases (e.g., 'u' takes accusative for motion, locative for location).

Verb aspects are perfective (completed action) and imperfective (ongoing or repeated action); tense and aspect are separate categories.

Literary periods to know include Serbian medieval literature, oral epic poetry (e.g., the Kosovo cycle), and 19th–20th century realism and modernism.

Serbia's capital is Belgrade; the country has 24 administrative districts plus the City of Belgrade.

Serbia's currency is the Serbian dinar (RSD); the country is a candidate for European Union membership.

The United Nations has 193 member states; its Security Council has five permanent members with veto power.

NATO was founded in 1949 with headquarters in Brussels; its core principle is collective defense under Article 5.

The Olympic Games are held every four years; the Summer and Winter Games alternate in a two-year cycle.

Nobel Prizes are awarded in physics, chemistry, medicine, literature, peace, and economic sciences.

Serbia observes statehood and national holidays including Statehood Day (15 February), marked by the First Serbian Uprising of 1804.

Major international organizations to recognize: EU, UN, WHO, UNESCO, OSCE, Council of Europe, and the Red Cross.

In number-series problems, check successive differences first, then ratios, then alternating or second-order patterns.

In syllogisms, a conclusion follows only if it is true in every model satisfying the premises; 'some' conclusions require overlap, not just possibility.

Negation rules: 'not all A are B' is equivalent to 'some A are not B'; 'no A is B' is equivalent to 'all A are non-B'.

A conditional 'if P then Q' is false only when P is true and Q is false; its contrapositive 'if not Q then not P' is logically equivalent.

For seating or ordering puzzles, draw a line or circle and place the most constrained item first.

In analogies, identify the relation type (part-whole, cause-effect, category, function) before choosing the matching pair.

Odd-one-out items usually differ by a single property: category membership, parity, letter position, or symmetry.

For clock and calendar problems, remember the hour hand moves 30° per hour and the minute hand 6° per minute.

Body mass index is BMI = mass(kg) / height(m)²; standard adult reference ranges are underweight <18.5, normal 18.5–24.9, overweight 25–29.9, obese ≥30.

The 12-minute run (Cooper test) estimates aerobic capacity from distance covered; the 2.4 km run is a common timed endurance measure.

The shuttle run (beep test) progressively increases pace; score is the level and shuttle reached before failure.

Push-ups, sit-ups, and pull-ups are assessed by maximum correct repetitions in a fixed time window (commonly 60 seconds for sit-ups).

Flexibility is typically measured by the sit-and-reach test, recording the furthest reach in centimeters.

Standing long jump measures explosive lower-body power; score is the horizontal distance from take-off line to nearest landing point.

Resting heart rate is commonly measured in beats per minute; lower values generally indicate better cardiovascular conditioning.

A warm-up raises muscle temperature and reduces injury risk; a cool-down aids gradual return of heart rate toward resting levels.

Informed consent must be obtained before psychological testing; candidates may withdraw without penalty unless the assessment is a legal requirement.

A medical examination for academy entry typically screens vision, hearing, cardiovascular fitness, neurological status, and orthopedic conditions.

Color vision deficiency is a common disqualifier for certain military occupational specialties, such as those involving signal or wiring work.

Psychological assessment batteries may include personality inventories, aptitude tests, and structured interviews assessing stress tolerance and teamwork.

Results of psychological testing are confidential and should be interpreted only by qualified professionals, not by untrained staff.

Body mass index and blood pressure are standard screening measurements; elevated readings usually trigger a re-test rather than immediate rejection.

A history of certain conditions (e.g., epilepsy, severe asthma, uncorrected refractive error beyond limits) may require specialist evaluation before a fitness decision.

Test anxiety can inflate or distort scores; standardized administration conditions and practice trials improve reliability.