Angola Air Force Academy Entrance Exam cheat sheet

Quadratic formula: x = (−b ± √(b² − 4ac)) / (2a); discriminant Δ = b² − 4ac; Δ > 0 gives two real roots, Δ = 0 one repeated root, Δ < 0 no real roots.

Logarithm rules: log_b(xy) = log_b x + log_b y; log_b(x/y) = log_b x − log_b y; log_b(xⁿ) = n log_b x; log_b 1 = 0; log_b b = 1.

Sine rule: a/sin A = b/sin B = c/sin C = 2R; cosine rule: a² = b² + c² − 2bc cos A.

Circle: area = πr²; circumference = 2πr; sector area = ½r²θ in radians; arc length = rθ.

Line: y = mx + c; slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines have equal slopes; perpendicular slopes multiply to −1.

Mean = sum of values ÷ number of values; median = middle ordered value; mode = most frequent value; range = maximum − minimum.

Probability: P(A ∪ B) = P(A) + P(B) − P(A ∩ B); independent events: P(A ∩ B) = P(A)P(B); complement: P(not A) = 1 − P(A).

Composition: (f ∘ g)(x) = f(g(x)); inverse function swaps x and y and solves for y; domain excludes division by zero and negative even roots.

Newton's second law: F_net = ma; weight W = mg; friction f ≤ μN; near Earth's surface g ≈ 9.8 m/s².

Constant acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as.

Work W = Fd cos θ; kinetic energy = ½mv²; gravitational potential energy = mgh; power P = W/t.

Pressure p = F/A; hydrostatic pressure p = p₀ + ρgh; buoyancy F_b = ρ_fluid V_displaced g; continuity A₁v₁ = A₂v₂.

Bernoulli equation for steady ideal incompressible flow: p + ½ρv² + ρgh = constant along a streamline.

Ideal gas law PV = nRT; temperature must be absolute; first law of thermodynamics ΔU = Q − W.

Ohm's law V = IR; power P = VI = I²R = V²/R; series resistance R_total = R₁ + R₂ + …; parallel 1/R_total = 1/R₁ + 1/R₂ + ….

Magnetic force: F = qvB sin θ on a moving charge; F = BIL sin θ on a current-carrying wire; direction follows the right-hand rule.

Lift L = ½ρv²SC_L; drag D = ½ρv²SC_D; both increase with air density and with the square of airspeed.

Sujeito é o termo sobre o qual se declara algo no predicado; pode ser simples, composto, oculto, indeterminado ou inexistente.

Concordância verbal: o verbo concorda com o sujeito em número e pessoa; com sujeito composto anteposto, o verbo geralmente fica no plural.

Crase é a fusão da preposição a com o artigo a ou com pronomes demonstrativos; ocorre antes de substantivo feminino determinado.

Tipos de frase: declarativa, interrogativa, imperativa e exclamativa; cada tipo tem entoação e pontuação próprias.

Coesão textual: conectivos indicam causa, oposição, conclusão ou adição; pronomes retomam referentes e evitam repetição.

Ideia principal é a tese central do texto; detalhes e exemplos sustentam essa tese, enquanto inferências exigem evidência textual.

Texto dissertativo organiza-se em introdução, desenvolvimento e conclusão; cada parágrafo desenvolve uma ideia central.

Ortografia: usa-se mas para oposição e mais para quantidade; há indica existir ou tempo passado, e a indica tempo futuro.

1 mol = 6.022 × 10²³ partículas; a massa molar em g/mol é numericamente igual à massa atómica ou molecular.

Cálculo estequiométrico: balancear a equação, converter massa em moles, usar a razão dos coeficientes e converter para a grandeza pedida.

Concentração molar M = n/V(L); percentagem em massa = massa do soluto ÷ massa da solução × 100; diluição M₁V₁ = M₂V₂.

pH = −log[H₃O⁺]; pOH = −log[OH⁻]; a 25 °C, pH + pOH = 14; pH < 7 ácido, pH = 7 neutro, pH > 7 básico.

Nas condições padrão aproximadas de 0 °C e 1 atm, 1 mol de gás ideal ocupa cerca de 22,4 L.

Número de oxidação: elemento livre = 0; ião monoatómico = carga do ião; oxigénio geralmente −2; hidrogénio +1 com não metais.

Tendências periódicas: raio atómico aumenta ao descer no grupo e diminui ao longo do período; eletronegatividade aumenta ao subir e para a direita.

Solubilidade: semelhante dissolve semelhante; para sólidos, a temperatura geralmente aumenta a solubilidade; para gases, aumenta com pressão e diminui com temperatura.

Present simple: use the base verb, adding -s or -es for third-person singular; it expresses habits, routines, general truths, and scheduled events.

Past simple: regular verbs add -ed; irregular verbs change form; the tense describes completed actions at a definite past time.

Reading main idea: identify the topic sentence and repeated key terms; supporting details answer who, what, when, where, why, or how.

Vocabulary in context: use surrounding sentence meaning and word roots, prefixes, and suffixes to infer an unfamiliar word.

Comparative and superlative: short adjectives add -er/-est; longer adjectives use more/most; irregular examples include good–better–best.

Subject-verb agreement: singular subjects take singular verbs; compound subjects joined by and usually take plural verbs; each and every take singular verbs.

Passive voice: form with be + past participle; the object becomes the subject, and the by-agent may be omitted when unknown or unimportant.

Angola proclaimed independence from Portugal on 11 November 1975; Agostinho Neto, leader of the MPLA, became the first president.

The Angolan Civil War lasted from 1975 to 2002 and ended with the Luena Memorandum, which provided for demobilisation and reintegration.

Angola borders the Democratic Republic of the Congo to the north, Zambia to the east, Namibia to the south, and the Atlantic Ocean to the west; Cabinda is an exclave.

Capital: Luanda; official language: Portuguese; currency: kwanza; the north has a tropical climate and the south is semi-arid.

Major rivers include the Cuanza, Cunene, and Cubango; the Cuanza supports hydroelectricity, and the Benguela Current affects the coastal climate.

The 2010 Constitution guarantees fundamental rights, separation of powers, and designates the president as head of state and government.

Civic duties include obeying laws, paying taxes, respecting public property, voting, and defending national sovereignty and the environment.

National symbols include the flag with red, black, and yellow emblem, the anthem “Angola Avante,” and Independence Day on 11 November.

Deductive validity means the conclusion follows necessarily from the premises; validity is independent of whether the premises are actually true.

Contrapositive: “If P then Q” is equivalent to “If not Q then not P”; the converse and inverse are not logically equivalent.

Number sequences: test differences, ratios, alternating patterns, and square or cube patterns before predicting the next term.

Rotation: 90° clockwise maps (x, y) to (y, −x); 180° maps (x, y) to (−x, −y); reflection changes the sign of one coordinate.

Cube nets: opposite faces lie one face apart in a straight line; there are exactly 11 distinct nets that fold into a cube.

Venn syllogism: “All A are B” means A is a subset of B; “Some A are B” means the intersection of A and B is nonempty.

Mirror symmetry: a figure is symmetric if reflection across an axis maps it onto itself; test vertical, horizontal, and diagonal axes.

BMI = mass(kg) ÷ height(m)²; it is a screening measure, not a diagnosis, and may classify muscular candidates as overweight.

Aerobic fitness is commonly estimated by VO₂max using the 20 m shuttle run, a 12-minute run, or a cycle ergometer test.

Muscular endurance is assessed by repeated push-ups, sit-ups, or pull-ups within a fixed time or until exhaustion.

Flexibility is measured by the sit-and-reach test, which indicates hamstring and lower-back range of motion.

Visual acuity is tested with a Snellen chart; colour vision is tested with Ishihara plates; both are relevant to aviation roles.

Psychotechnical tests measure reaction time, spatial orientation, hand-eye coordination, attention, and tolerance to stress.

Hearing fitness is assessed by pure-tone audiometry; normal conversational hearing is around 0–25 dB hearing level.

Medical fitness screening covers cardiovascular, respiratory, neurological, and musculoskeletal systems to detect disqualifying conditions.