Angola Military Technical Institute (ISTM) Exam cheat sheet

Quadratic formula: for ax²+bx+c=0 (a≠0), x = [-b ± √(b²-4ac)] / (2a); discriminant Δ=b²-4ac gives two real roots (Δ>0), one (Δ=0), or complex roots (Δ<0).

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

Pythagorean theorem: in a right triangle, a²+b²=c², where c is the hypotenuse opposite the right angle.

Trigonometric identity: sin²θ+cos²θ=1; also sin(A+B)=sin A cos B+cos A sin B.

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

Probability of an event P(A) = favorable outcomes / total equally likely outcomes, with 0 ≤ P(A) ≤ 1; P(not A)=1−P(A).

Area formulas: triangle = ½·base·height; circle = πr²; trapezoid = ½(a+b)h; volume of cylinder = πr²h.

Newton's second law: F = m·a; force and acceleration are vectors pointing in the same direction, mass is in kilograms.

Kinematics: v = v₀+at; s = v₀t+½at²; v² = v₀²+2as (constant acceleration only).

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh; work W = F·d·cosθ.

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

Density ρ = m/V; pressure in a liquid p = ρgh; pressure p = F/A.

Wave relation: v = f·λ (speed equals frequency times wavelength); for light in vacuum c ≈ 3×10⁸ m/s.

Universal gravitation: F = G·m₁m₂/r², with G ≈ 6.67×10⁻¹¹ N·m²/kg².

SI units: force in newtons (N), energy in joules (J), power in watts (W), pressure in pascals (Pa), charge in coulombs (C).

Mole concept: 1 mol = 6.022×10²³ particles (Avogadro's number); molar mass in g/mol equals the relative formula mass numerically.

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

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

Balancing rule: atoms of each element must be equal on both sides; coefficients apply to the whole formula.

Ideal gas law: PV = nRT, with R ≈ 8.314 J/(mol·K); at STP 1 mol of gas occupies about 22.4 L.

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

Acid + base → salt + water (neutralization); acid + metal → salt + hydrogen gas.

Periodic trend: atomic radius decreases across a period and increases down a group; electronegativity increases across a period.

Classes de palavras incluem substantivo, adjetivo, verbo, advérbio, pronome, preposição, conjunção, numeral, artigo e interjeição.

Sujeito e predicado: o sujeito é o termo sobre o qual se declara algo; o predicado contém o verbo e o que se diz do sujeito.

Crase: usa-se o acento grave antes de substantivo feminino determinado (à, às); não ocorre antes de verbo, palavra masculina ou pronome pessoal.

Concordância verbal: o verbo concorda em número e pessoa com o sujeito; com sujeito composto posposto admite-se singular ou plural.

Verbos terminados em -ar pertencem à 1ª conjugação, -er à 2ª e -ir à 3ª; o pretérito perfeito indica ação concluída.

Acentuação: palavras oxítonas terminadas em a(s), e(s), o(s), em, ens são acentuadas; proparoxítonas são todas acentuadas.

Regência: 'assistir a' (ver), 'obedecer a', 'preferir A a B' - sem repetir 'mais' com 'preferir'.

Ortografia: usa-se 'ç' antes de a, o, u; 'ss' entre vogais em certos casos; 'x' após ditongo (caixa, peixe).

Present simple: add -s/-es for third person singular (he works, she goes); use for habits and general truths.

Present continuous: am/is/are + verb-ing, for actions happening now or temporary situations.

Past simple regular verbs add -ed; irregular verbs change form (go→went, see→saw, take→took).

Comparatives: short adjectives add -er (bigger); long adjectives use more (more interesting); superlatives use -est or most.

Conditionals: first conditional = if + present simple, will + infinitive; second conditional = if + past simple, would + infinitive.

Passive voice: form of 'be' + past participle (The book was written by him).

Prepositions of time: in (months, years), on (days, dates), at (hours, specific points).

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

Angola gained independence on 11 November 1975, proclaimed by the MPLA; Agostinho Neto became the first President.

The capital is Luanda, located on the Atlantic coast; Angola is in south-central Africa and is bordered by Namibia, Zambia, the DRC, and the Republic of the Congo.

The Kwanza is Angola's currency; the Kwanza River is the country's longest river entirely within Angola.

Major ethnic-linguistic groups include Ovimbundu, Ambundu (Mbundu), Bakongo, and Chokwe; Portuguese is the official language.

The civil war (1975–2002) ended with the Luena Memorandum of Understanding following the death of Jonas Savimbi in 2002.

Angola is a major oil producer; Cabinda is an important oil-producing enclave separated from the main territory.

The Battle of Cuito Cuanavale (1987–1988) was a decisive Cold War-era engagement in southern Angola.

Angola's climate ranges from tropical humid in the north to semi-arid in the south; the Benguela Current cools the coastal strip.

Syllogism validity: if All A are B and All B are C, then All A are C; a valid conclusion must follow necessarily from the premises.

Contrapositive: 'If P then Q' is logically equivalent to 'If not Q then not P'; the converse ('If Q then P') is not equivalent.

Number series: check differences, ratios, alternating patterns, and squares/cubes before assuming a single rule.

Odd-one-out: identify the shared property (category, parity, prime/composite, part of speech) that all but one item satisfy.

Analogy A:B :: C:? requires the same relation (function, part-whole, cause-effect, antonym) between both pairs.

Percent change = (new − old)/old × 100; successive percentage changes do not simply add.

General knowledge: the United Nations was founded in 1945; its headquarters is in New York City.

Direction sense: track turns cumulatively (a left then a right returns to the original heading) and draw a simple diagram.

Sum of interior angles of a polygon with n sides = (n−2)·180°; a triangle's angles sum to 180°.

Slope of a line through two points: m = (y₂−y₁)/(x₂−x₁); parallel lines have equal slopes, perpendicular slopes multiply to −1.

Binomial expansion: (a+b)² = a²+2ab+b²; (a+b)(a−b) = a²−b².

Simple interest I = P·r·t; compound amount A = P(1+r)ⁿ.

Mean = sum of values / count; median is the middle value of ordered data; mode is the most frequent value.

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

Average speed = total distance / total time; velocity is speed with direction; acceleration = change in velocity / time.

Momentum p = m·v; in an isolated system total momentum is conserved in collisions.

Frequency and period: f = 1/T; period is measured in seconds and frequency in hertz.

Heat energy Q = m·c·ΔT, where c is specific heat capacity; latent heat Q = m·L during a phase change.

Refraction: light bends toward the normal when entering a denser medium (n₁ sin θ₁ = n₂ sin θ₂).

Electrical resistance in series adds (R = R₁+R₂); in parallel 1/R = 1/R₁+1/R₂.

Atomic number Z = number of protons; mass number A = protons + neutrons; isotopes differ in neutrons only.

Ionic bond forms by electron transfer between metal and nonmetal; covalent bond forms by electron sharing between nonmetals.

Avogadro's law: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Percentage yield = (actual yield / theoretical yield) × 100.

Empirical formula gives the simplest whole-number ratio of atoms; molecular formula is a whole-number multiple of it.

A catalyst increases reaction rate by lowering activation energy without being consumed.

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

Adjunto adnominal acompanha o substantivo (artigo, adjetivo, pronome adjetivo); o complemento nominal completa o sentido de nomes.

Voz passiva analítica: ser + particípio (A casa foi construída); voz ativa: sujeito pratica a ação.

Uso de 'porque' (causa), 'por que' (pergunta ou por qual razão), 'porquê' (substantivo) e 'por quê' (fim de frase).

Discurso direto usa travessão ou aspas; discurso indireto transforma tempos verbais e pronomes.

Figuras de linguagem: metáfora (comparação implícita), metonímia (troca por proximidade), hipérbole (exagero).

Articles: 'a/an' for indefinite singular countable nouns; 'the' for specific or previously mentioned nouns.

Present perfect: have/has + past participle, for past actions with present relevance; used with since and for.

Relative pronouns: who (people), which (things), where (places), whose (possession).

Countable vs uncountable: 'much' with uncountable, 'many' with countable; 'a few' countable, 'a little' uncountable.

Reported speech shifts tense back one step (present→past, will→would) and adjusts pronouns and time words.

Question form: auxiliary before subject (Do you work? / Where does she live?).

Angola's official language is Portuguese; national languages include Umbundu, Kimbundu, Kikongo, and Chokwe.

The Portuguese arrived in the late 15th century; Paulo Dias de Novais founded Luanda in 1576.

Angola's Constitution of 2010 defines the country as a democratic state; the President is head of state and government.

The Namib Desert lies along the southern coast; the central plateau (planalto) has a milder climate than the coast.

Angola borders the Atlantic Ocean to the west; the enclave of Cabinda lies north of the Congo River mouth.

Major exports include crude oil, diamonds, and coffee; the port of Lobito serves as a regional trade corridor.

Set operations: union (A∪B) contains all elements in either; intersection (A∩B) contains elements in both.

Negation rules: not (P and Q) = (not P) or (not Q); not (P or Q) = (not P) and (not Q).

Coding-decoding: map letters to numbers by alphabet position (A=1, B=2, … Z=26) to test shift patterns.

Blood-relation puzzles: draw a family tree and mark gender and generation explicitly before answering.

Ratio and proportion: if a:b = c:d then ad = bc; use cross-multiplication to solve for an unknown.

General knowledge: the African Union was established in 2002, replacing the Organisation of African Unity (founded 1963).