COLMIL Examen Intelectual cheat sheet

Main idea = the claim the whole passage supports; details support it but do not replace it.

Tone words (critical, neutral, ironic, admiring) are signaled by adjectives and adverbs, not by topic alone.

Inference answers must be forced by the text; if a choice needs outside knowledge, it is wrong.

Scope rule: an answer broader or narrower than the passage's claim is incorrect even if true.

Passage-order strategy: answer explicit-detail questions first, then inference and main-idea questions.

Analogy relation types: part-to-whole, cause-to-effect, category-to-member, function, degree.

Negation test: insert 'not' into a conclusion; if the passage would collapse, that conclusion is central.

Hedged qualifiers (some, most, may, tends to) are safer than absolutes (all, never, must) in answer choices.

Percent change = (new − old) / old × 100; a 20% rise then 20% fall leaves 96% of the original.

Successive percentage changes multiply: (1 + a)(1 + b) − 1 gives the combined rate.

Average = sum / count; if every value rises by k, the average rises by k.

Work rates add: combined time = 1 / (1/a + 1/b) for two workers finishing in a and b.

Speed = distance / time; average speed for equal distances is the harmonic mean 2ab/(a+b).

Simple interest = P·r·t; compound interest = P(1 + r)^t − P.

Ratio scaling: if a:b = 3:5, write amounts as 3k and 5k, then solve for k.

Mixture rule: final concentration = total solute / total solution, weighted by each portion's volume.

Syllogism validity depends on form, not truth: All A are B; All B are C; therefore All A are C.

Contrapositive is always equivalent: 'If P then Q' equals 'If not Q then not P'.

Converse ('If Q then P') is not equivalent to the original conditional.

In number or letter series, test differences, then ratios, then alternating sub-series.

Matrix puzzles: check rotation (90°/180°), reflection, shading inversion, and element count per row.

Modus tollens is valid (P→Q, not Q, so not P); affirming the consequent is invalid.

Odd-one-out: classify by a single shared property (symmetry, stroke count, closed regions).

Negation of 'all A are B' is 'at least one A is not B', not 'no A is B'.

Peru's state powers: Executive (President), Legislative (Congress), Judicial (Judiciary and courts).

Peru's national holidays include 28–29 July (Independence) and 8 October (Battle of Angamos).

The United Nations was founded in 1945; its Security Council has five permanent members.

NATO is a collective-defence alliance founded in 1949; Article 5 covers an armed attack on a member.

The Antarctic Treaty (1959) reserves the continent for peaceful and scientific use.

Peru is a founding member of the Andean Community and a member of APEC and the Pacific Alliance.

Red Cross and Geneva Conventions govern humanitarian protection in armed conflict.

Verify current-office and election facts against a dated source; officeholders change and undated claims go stale.

'Porque' gives cause, 'por qué' asks a question, 'porqué' is a noun, 'por que' follows a preposition.

'Hay' (existence), 'está' (location or state), 'es' (identity or inherent trait).

'Aun' (without accent) means 'even'; 'aún' (with accent) means 'still/yet'.

'Sino' replaces a negated clause ('no A sino B'); 'si no' means 'if not'.

Impersonal 'se' and passive 'se' take a third-person verb: 'Se vende casa', 'Se habla español'.

Gerund is not used for a following action: 'Entró corriendo' is fine, but 'Salió a comprar' needs the infinitive.

'Que' vs 'de que': verbs like 'pensar' and 'creer' take 'que'; 'darse cuenta' takes 'de que'.

Accent marks distinguish meaning: 'él' (he) / 'el' (the); 'sí' (yes) / 'si' (if); 'tú' (you) / 'tu' (your).

Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a; discriminant b² − 4ac gives 2, 1, or 0 real roots.

Pythagorean theorem: a² + b² = c² for right triangles; triples include 3-4-5 and 5-12-13.

Area formulas: triangle ½bh; circle πr²; trapezoid ½(b₁ + b₂)h.

Volume: cylinder πr²h; sphere (4/3)πr³; cone (1/3)πr²h.

Slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines share m, perpendicular slopes multiply to −1.

Factorials and combinations: C(n,k) = n! / (k!(n−k)!); permutations P(n,k) = n!/(n−k)!.

Log rules: log(ab) = log a + log b; log(aⁿ) = n log a; log(a/b) = log a − log b.

Sum of interior angles of an n-gon = (n − 2) × 180°.

Cell theory: all living things are made of cells; cells arise from pre-existing cells.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; occurs in chloroplasts.

Newton's second law: F = ma; weight = mg with g ≈ 9.8 m/s² on Earth.

Water's high specific heat and polarity make it a solvent and a temperature buffer for life.

DNA base pairing: adenine–thymine, guanine–cytosine; RNA substitutes uracil for thymine.

Rock types: igneous (cooled magma), sedimentary (compacted deposits), metamorphic (heat and pressure).

Acids donate protons (lower pH); bases accept protons; pH 7 is neutral at 25 °C.

Energy flows one way through food chains; nutrients cycle through ecosystems.

Peru's Constitution of 1993 defines the state as democratic, social, independent, and unitary.

Military service in Peru is voluntary; the Armed Forces comprise Army, Navy, and Air Force.

Fundamental duties include obeying the Constitution, paying taxes, and defending the nation.

Chain of command runs from the President through the Minister of Defence to service commanders.

The Geneva Conventions protect wounded combatants, prisoners of war, and civilians in wartime.

Distinguish combatant from non-combatant; directing attacks at civilians is a war crime.

Civic virtues in the military sphere: discipline, honor, loyalty, and subordination to lawful authority.

National symbols: flag, coat of arms, and national anthem; the flag's red bands honor independence heroes.

Main idea = the claim the whole passage supports; details support it but do not replace it.

Tone words (critical, neutral, ironic, admiring) are signaled by adjectives and adverbs, not by topic alone.

Inference answers must be forced by the text; if a choice needs outside knowledge, it is wrong.

Scope rule: an answer broader or narrower than the passage's claim is incorrect even if true.

Passage-order strategy: answer explicit-detail questions first, then inference and main-idea questions.

Analogy relation types: part-to-whole, cause-to-effect, category-to-member, function, degree.

Negation test: insert 'not' into a conclusion; if the passage would collapse, that conclusion is central.

Hedged qualifiers (some, most, may, tends to) are safer than absolutes (all, never, must) in answer choices.

Percent change = (new − old) / old × 100; a 20% rise then 20% fall leaves 96% of the original.

Successive percentage changes multiply: (1 + a)(1 + b) − 1 gives the combined rate.

Average = sum / count; if every value rises by k, the average rises by k.

Work rates add: combined time = 1 / (1/a + 1/b) for two workers finishing in a and b.

Speed = distance / time; average speed for equal distances is the harmonic mean 2ab/(a+b).

Simple interest = P·r·t; compound interest = P(1 + r)^t − P.

Ratio scaling: if a:b = 3:5, write amounts as 3k and 5k, then solve for k.

Mixture rule: final concentration = total solute / total solution, weighted by each portion's volume.

Syllogism validity depends on form, not truth: All A are B; All B are C; therefore All A are C.

Contrapositive is always equivalent: 'If P then Q' equals 'If not Q then not P'.

Converse ('If Q then P') is not equivalent to the original conditional.

In number or letter series, test differences, then ratios, then alternating sub-series.

Matrix puzzles: check rotation (90°/180°), reflection, shading inversion, and element count per row.

Modus tollens is valid (P→Q, not Q, so not P); affirming the consequent is invalid.

Odd-one-out: classify by a single shared property (symmetry, stroke count, closed regions).

Negation of 'all A are B' is 'at least one A is not B', not 'no A is B'.

Peru's state powers: Executive (President), Legislative (Congress), Judicial (Judiciary and courts).

Peru's national holidays include 28–29 July (Independence) and 8 October (Battle of Angamos).

The United Nations was founded in 1945; its Security Council has five permanent members.

NATO is a collective-defence alliance founded in 1949; Article 5 covers an armed attack on a member.

The Antarctic Treaty (1959) reserves the continent for peaceful and scientific use.

Peru is a founding member of the Andean Community and a member of APEC and the Pacific Alliance.

Red Cross and Geneva Conventions govern humanitarian protection in armed conflict.

Verify current-office and election facts against a dated source; officeholders change and undated claims go stale.

'Porque' gives cause, 'por qué' asks a question, 'porqué' is a noun, 'por que' follows a preposition.

'Hay' (existence), 'está' (location or state), 'es' (identity or inherent trait).

'Aun' (without accent) means 'even'; 'aún' (with accent) means 'still/yet'.

'Sino' replaces a negated clause ('no A sino B'); 'si no' means 'if not'.

Impersonal 'se' and passive 'se' take a third-person verb: 'Se vende casa', 'Se habla español'.

Gerund is not used for a following action: 'Entró corriendo' is fine, but 'Salió a comprar' needs the infinitive.

'Que' vs 'de que': verbs like 'pensar' and 'creer' take 'que'; 'darse cuenta' takes 'de que'.

Accent marks distinguish meaning: 'él' (he) / 'el' (the); 'sí' (yes) / 'si' (if); 'tú' (you) / 'tu' (your).

Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a; discriminant b² − 4ac gives 2, 1, or 0 real roots.

Pythagorean theorem: a² + b² = c² for right triangles; triples include 3-4-5 and 5-12-13.

Area formulas: triangle ½bh; circle πr²; trapezoid ½(b₁ + b₂)h.

Volume: cylinder πr²h; sphere (4/3)πr³; cone (1/3)πr²h.

Slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines share m, perpendicular slopes multiply to −1.

Factorials and combinations: C(n,k) = n! / (k!(n−k)!); permutations P(n,k) = n!/(n−k)!.

Log rules: log(ab) = log a + log b; log(aⁿ) = n log a; log(a/b) = log a − log b.

Sum of interior angles of an n-gon = (n − 2) × 180°.

Cell theory: all living things are made of cells; cells arise from pre-existing cells.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂; occurs in chloroplasts.

Newton's second law: F = ma; weight = mg with g ≈ 9.8 m/s² on Earth.

Water's high specific heat and polarity make it a solvent and a temperature buffer for life.

DNA base pairing: adenine–thymine, guanine–cytosine; RNA substitutes uracil for thymine.

Rock types: igneous (cooled magma), sedimentary (compacted deposits), metamorphic (heat and pressure).

Acids donate protons (lower pH); bases accept protons; pH 7 is neutral at 25 °C.

Energy flows one way through food chains; nutrients cycle through ecosystems.

Peru's Constitution of 1993 defines the state as democratic, social, independent, and unitary.

Military service in Peru is voluntary; the Armed Forces comprise Army, Navy, and Air Force.

Fundamental duties include obeying the Constitution, paying taxes, and defending the nation.

Chain of command runs from the President through the Minister of Defence to service commanders.

The Geneva Conventions protect wounded combatants, prisoners of war, and civilians in wartime.

Distinguish combatant from non-combatant; directing attacks at civilians is a war crime.

Civic virtues in the military sphere: discipline, honor, loyalty, and subordination to lawful authority.

National symbols: flag, coat of arms, and national anthem; the flag's red bands honor independence heroes.