Angola Naval Academy Entrance Exam cheat sheet

Quadratic formula: x = (-b ± √(b²-4ac)) / 2a solves ax² + bx + c = 0; the discriminant b²-4ac decides the number of real roots (positive: two, zero: one, negative: none).

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

Sine and cosine rules: a/sin A = b/sin B = c/sin C; and c² = a² + b² - 2ab·cos C for any triangle.

Logarithm rules: log(xy) = log x + log y; log(x/y) = log x - log y; log(xⁿ) = n·log x; log_b b = 1 and log_b 1 = 0.

Arithmetic progression: nth term aₙ = a₁ + (n-1)d; sum Sₙ = n(a₁ + aₙ)/2. Geometric progression: aₙ = a₁·rⁿ⁻¹; Sₙ = a₁(rⁿ-1)/(r-1) for r ≠ 1.

Derivative basics: d/dx(xⁿ) = n·xⁿ⁻¹; d/dx(sin x) = cos x; d/dx(eˣ) = eˣ; d/dx(ln x) = 1/x.

Probability of an event = favourable outcomes / total equally likely outcomes; P(not A) = 1 - P(A).

Trigonometric identity: sin²θ + cos²θ = 1; also tan θ = sin θ / cos θ.

Classification of words by stressed syllable: oxítona (stress on last syllable), paroxítona (penultimate), proparoxítona (antepenultimate, always accented).

Paroxítonas are accented when ending in -l, -n, -r, -x, -ps, -ã, -ãs, -ão, -ãos, -um, -uns, -i, -is, -us, or a diphthong.

Oxítonas are accented when ending in -a, -e, -o, -em, -ens (with or without s).

Crase (à) occurs before feminine nouns when the preposition a contracts with the article a; it does not occur before masculine nouns, most verbs, or repeated words.

Luís de Camões wrote Os Lusíadas (1572), an epic in ten cantos celebrating Vasco da Gama's voyage to India.

Fernando Pessoa created heteronyms including Alberto Caeiro, Ricardo Reis and Álvaro de Campos; Mensagem (1934) is his only book published in his lifetime.

José Luandino Vieira and Pepetela are major Angolan writers; Pepetela's novel Mayombe is set during the liberation struggle.

Direct object pronoun replaces the object without a preposition (o, a, os, as); indirect object pronoun replaces the object with a preposition (lhe, lhes).

Newton's second law: F = m·a; the net force equals mass times acceleration, measured in newtons.

Kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as, for constant acceleration a.

Weight is W = m·g; on Earth g ≈ 9.8 m/s², so weight is a force in newtons, distinct from mass in kilograms.

Ohm's law: V = I·R; electrical power P = V·I = I²R = V²/R.

Kinetic energy Eₖ = ½mv²; gravitational potential energy near Earth Eₚ = mgh; mechanical energy is conserved without friction.

Density ρ = m/V; pressure P = F/A; hydrostatic pressure P = ρgh.

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

Law of conservation of energy: energy is neither created nor destroyed, only transformed from one form to another.

Mole concept: 1 mole contains 6.022 × 10²³ particles (Avogadro's number) and has a mass in grams equal to the molar mass.

Molarity M = moles of solute / litres of solution; dilution obeys M₁V₁ = M₂V₂.

pH = -log[H⁺]; pH < 7 is acidic, pH = 7 neutral, pH > 7 basic at 25 °C.

Balancing equations conserves atoms of each element and charge; coefficients, not subscripts, are adjusted.

Ionic bond forms by electron transfer between a metal and a non-metal; covalent bond forms by electron sharing between non-metals.

Acid + base → salt + water (neutralisation); acid + carbonate → salt + water + carbon dioxide.

Periodic table trends: atomic radius decreases left to right across a period and increases down a group; electronegativity increases left to right and up a group.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons.

Cell theory: all living things are made of cells; the cell is the basic unit of life; new cells arise from existing cells.

Prokaryotic cells lack a membrane-bound nucleus and organelles; eukaryotic cells have a nucleus and membrane-bound organelles such as mitochondria.

Photosynthesis: 6CO₂ + 6H₂O + light energy → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts containing chlorophyll.

Cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (ATP), mainly in mitochondria.

DNA is a double helix of nucleotides with bases adenine-thymine and guanine-cytosine; RNA replaces thymine with uracil.

Blood groups follow ABO and Rh systems; group O negative is the universal red-cell donor and AB positive the universal recipient.

Human circulation is double: pulmonary circuit (heart-lung) and systemic circuit (heart-body); the left ventricle has the thickest wall.

Mendel's law of segregation: each organism carries two alleles per gene and passes one randomly to each gamete.

Angola gained independence from Portugal on 11 November 1975, proclaimed by Agostinho Neto, first President of the MPLA government.

The Berlin Conference (1884-1885) regulated European colonisation of Africa and set rules for the partition of the continent.

The Angolan Civil War (1975-2002) ended with the Luena Memorandum of Understanding after the death of Jonas Savimbi in 2002.

Angola borders the Democratic Republic of the Congo to the north and northeast, Zambia to the east, Namibia to the south, and the Atlantic Ocean to the west.

The Kwanza is Angola's currency and also the name of its main river; Luanda is the capital and largest city.

Lines of latitude: Equator 0°, Tropics at 23.5° N and S, polar circles at 66.5° N and S.

The Intertropical Convergence Zone produces heavy rainfall near the Equator; Angola's north is wetter than its arid south.

The Cold War opposed the capitalist United States bloc against the communist Soviet bloc from roughly 1947 to 1991.

The Constitution of the Republic of Angola (2010) is the supreme law; laws contrary to it have no validity.

Angola's national symbols are the flag, the national anthem (Angola Avante!) and the coat of arms.

Fundamental rights include life, liberty, equality before the law, and freedom of expression, assembly and religion.

Military hierarchy runs from soldier through corporal, sergeant, lieutenant, captain, major, lieutenant colonel, colonel to general officer ranks.

Chain of command means orders flow downward through the hierarchy and responsibility flows upward.

Military discipline requires obedience to lawful orders, punctuality, correct uniform and respect for superiors.

The armed forces (FAA) defend national sovereignty, territorial integrity and constitutional order, and support civil protection.

Conscription or voluntary military service is a civic duty; conscientious objection is regulated by law.

Verb 'to be': present am/is/are; past was/were; the past participle is been.

Present perfect: have/has + past participle, used for past actions with present relevance or unspecified time.

Reported speech shifts tense back one step: present → past, past → past perfect; 'will' becomes 'would'.

Conditionals: first (if + present, will + infinitive), second (if + past, would + infinitive), third (if + past perfect, would have + participle).

Passive voice: form of 'be' + past participle; the object becomes the subject (The report was written by the officer).

Comparative and superlative: short adjectives take -er/-est; long adjectives take more/most; irregulars include good-better-best.

Prepositions of time: in for months, years and seasons; on for days and dates; at for clock times.

Modal verbs (can, must, should, may) are followed by the bare infinitive and do not take -s in the third person.