I85PREP
⌘ K
PHUMA study materials
PHUMA study resources

PHUMA practice questions

One question at a time. Build your PHUMA understanding.

First 50 of 190 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1spanish / math / biology / formal / social - integrated subject foundations

Read the following sentence: 'A pesar de que las lluvias torrenciales inundaron las principales vías de acceso, los brigadistas de rescate lograron evacuar a todas las familias vulnerables a tiempo.' What is the primary semantic relationship established by the connector 'A pesar de que'?

  1. Concession, indicating an obstacle that does not prevent the main action Correct answer.
  2. Cause, explaining the reason why the evacuation was conducted
  3. Condition, setting a prerequisite for the rescue operation to begin
  4. Consecution, describing the direct result of the torrential rains

Explanation

The subordinating connector 'a pesar de que' is an adversative concessive conjunction in Spanish grammar. Concessive clauses introduce an impediment, obstacle, or difficulty that nevertheless fails to prevent the realization of the main clause. Therefore, the rains posed a severe obstacle, but the rescue still took place.

Question 2spanish / math / biology / formal / social - integrated subject foundations

Which of the following sentences uses the graphical accent (tilde) correctly according to Spanish diacritical accentuation rules (tilde diacrítica)?

  1. Sé muy bien que él preparó el té para su abuelo esta mañana. Correct answer.
  2. Se muy bien que el preparó el te para su abuelo esta mañana.
  3. Sé muy bien que el preparó él té para su abuelo esta mañana.
  4. Se muy bien que él preparó él te para su abuelo esta mañana.

Explanation

In Spanish diacritical accentuation, 'sé' carries a tilde when it corresponds to the verb 'saber' (or 'ser') to distinguish it from the reflexive pronoun 'se'; 'él' takes a tilde as a personal pronoun to contrast with the definite article 'el'; and 'té' takes a tilde as the noun referring to tea to differentiate it from the object pronoun 'te'. Therefore, the first sentence applies all three diacritical accents correctly.

Question 3spanish / math / biology / formal / social - integrated subject foundations

Select the option that correctly identifies the figure of speech (recurso retórico) in the line: 'El río avanzaba como una serpiente plateada entre las colinas dormidas.'

  1. Simile (Símil) and Personification (Prosopopeya) Correct answer.
  2. Hyperbole (Hipérbole) and Metonymy (Metonimia)
  3. Oxymoron (Oxímoron) and Antithesis (Antítesis)
  4. Irony (Ironía) and Alliteration (Aliteración)

Explanation

The phrase contains two distinct rhetorical devices: a simile (símil) through the explicit comparative link 'como una serpiente plateada' comparing the river to a silver snake, and personification (prosopopeya or personificación) by attributing the human state of sleeping ('dormidas') to inanimate hills. Both devices work together to create evocative imagery.

Question 4spanish / math / biology / formal / social - integrated subject foundations

Read the following short excerpt: 'La deforestación en las cuencas hidrográficas de la biosfera del Río Plátano ha alcanzado niveles críticos en el último quinquenio. Si no se implementan mecanismos punitivos estrictos contra la tala ilegal y la ganadería extensiva, la pérdida de biodiversidad endémica y el colapso de las fuentes de agua dulce serán irreversibles antes de 2035.' What is the author's primary communicative intention?

  1. To persuade authorities and the public of the urgent necessity of enacting strict conservation enforcement Correct answer.
  2. To narrate the historical settlement of cattle ranchers along the Patuca and Plátano river basins
  3. To describe the physiological traits of endangered flora species in eastern Honduras
  4. To present an entertaining fictional story regarding tropical rainforest degradation

Explanation

The text employs an argumentative discourse structure featuring an alarming factual premise followed by a conditional warning ('Si no se implementan...') projecting an irreversible outcome. Its communicative purpose is pragmatic and persuasive (conative function), intended to urge decision-makers and readers to take preventive regulatory action.

Question 5spanish / math / biology / formal / social - integrated subject foundations

Complete the verbal analogy: EFÍMERO is to PERDURABLE as BELICOSO is to:

  1. Pacífico Correct answer.
  2. Agresivo
  3. Hostil
  4. Valiente

Explanation

The relationship between 'efímero' (ephemeral/fleeting) and 'perdurable' (lasting/durable) is one of antonymy (opposites). Therefore, the analogy requires finding the antonym of 'belicoso' (warlike/aggressive/combative). The direct antonym is 'pacífico' (peaceful).

Question 6spanish / math / biology / formal / social - integrated subject foundations

Which of the following words is classified as an 'esdrújula' and therefore must always carry an orthographic accent in Spanish?

  1. Científico Correct answer.
  2. Canción
  3. Carácter
  4. Reloj

Explanation

Words in Spanish are accented based on the position of the stressed syllable. An 'esdrújula' word has the tonic stress on the antepenultimate syllable (cien - TÍ - fi - co). According to the rules of the Real Academia Española (RAE), all esdrújula words invariably carry an orthographic accent mark (tilde).

Question 7spanish / math / biology / formal / social - integrated subject foundations

Identify the option that contains an error of grammatical concord (discordancia gramatical):

  1. Hubieron muchos aspirantes en la sede de la prueba de admisión. Correct answer.
  2. La mayoría de los estudiantes aprobó el módulo introductorio de matemáticas.
  3. El grupo de manifestantes exigió pacíficamente la rendición de cuentas.
  4. Se vendieron rápidamente los boletos para el concierto benéfico del coro universitario.

Explanation

In its existential sense, 'haber' is an impersonal verb: the plural phrase that follows it ('muchos aspirantes') is a direct object, not a subject, so the verb cannot agree with it and must stay in the third-person singular - 'Hubo muchos aspirantes'. The Diccionario panhispánico de dudas expressly marks forms such as 'hubieron muchos' as incorrect, which makes this the only true concord error among the four sentences.

Question 8spanish / math / biology / formal / social - integrated subject foundations

In the sentence: 'El ministro entregó ayer los reconocimientos académicos a los investigadores más destacados de la universidad', what syntactic function does the phrase 'a los investigadores más destacados de la universidad' perform?

  1. Indirect Object (Objeto Indirecto) Correct answer.
  2. Direct Object (Objeto Directo)
  3. Prepositional Complement (Complemento de Régimen)
  4. Agent Complement (Complemento Agente)

Explanation

In this transitive clause, 'los reconocimientos académicos' is the entity transferred or delivered (Direct Object, replaceable by 'los': 'El ministro se los entregó'), while 'a los investigadores más destacados...' represents the recipients of the action (Indirect Object, replaceable by the dative clitic 'les').

Question 9spanish / math / biology / formal / social - integrated subject foundations

Determine which of the following words is formed by parasynthesis (parasíntesis):

  1. Envejecer Correct answer.
  2. Submarino
  3. Lavaplatos
  4. Desleal

Explanation

Parasynthesis is a word-formation process involving the simultaneous addition of a prefix and a suffix to a lexeme, such that neither the prefixed base without the suffix nor the suffixed base without the prefix exists as an independent word (*envejo*, *vejecer* do not exist; from root 'viejo' -> en- + viej- + -ecer).

Question 10spanish / math / biology / formal / social - integrated subject foundations

What is the meaning of the word 'INOCUO' in the following scientific passage: 'Tras extensos ensayos clínicos en roedores, los biólogos determinaron que el compuesto alcaloide resultó completamente inocuo en dosis estándar'?

  1. Harmless, incapable of causing damage or physical injury Correct answer.
  2. Ineffective, having zero medicinal or therapeutic action
  3. Poisonous, generating immediate tissue inflammation
  4. Volatile, evaporating rapidly at ambient room temperature

Explanation

The term 'inocuo' (from Latin 'innocuus') means harmless or innocuous-having no adverse, toxic, or damaging effects on an organism. It is often confused with 'inicuo' (iniquitous/unjust), but in pharmacology and toxicology, an innocuous compound produces no harm.

Question 11spanish / math / biology / formal / social - integrated subject foundations

Select the sentence where punctuation marks are used in strict compliance with normative Spanish punctuation rules:

  1. Cuando concluyó la ponencia magistral, los asistentes, entusiasmados por las revelaciones, ovacionaron al expositor. Correct answer.
  2. Cuando concluyó la ponencia magistral los asistentes entusiasmados por las revelaciones ovacionaron, al expositor.
  3. Cuando concluyó, la ponencia magistral los asistentes, entusiasmados por las revelaciones ovacionaron al expositor.
  4. Cuando concluyó la ponencia magistral, los asistentes entusiasmados, por las revelaciones, ovacionaron al expositor.

Explanation

The sentence correctly places a comma after the initial circumstantial adverbial clause ('Cuando concluyó la ponencia magistral,') and encapsulates the non-restrictive appositive/explanatory participial modifier ('entusiasmados por las revelaciones') between parenthetical commas, without inappropriately separating the verb from its direct object.

Question 12spanish / math / biology / formal / social - integrated subject foundations

Which of the following texts belongs unmistakably to the argumentative genre (texto argumentativo)?

  1. An editorial column arguing that investing in early childhood nutrition yields superior long-term socioeconomic returns than late remedial subsidies Correct answer.
  2. A technical laboratory protocol specifying the volumetric ratios of hydrochloric acid and sodium hydroxide required for titration
  3. A news dispatch reporting the magnitude, epicenter coordinates, and recorded aftershocks of a seismic event off the coast of Roatán
  4. A chronological chronicle detailing the hour-by-hour movements of General Francisco Morazán during the Battle of La Trinidad in 1827

Explanation

An argumentative text has the primary objective of defending a thesis or viewpoint through structured reasoning, evidence, and rhetorical argumentation to convince or persuade the reader. An editorial column defending early childhood nutrition investment is a classic manifestation of argumentative prose.

Question 13spanish / math / biology / formal / social - integrated subject foundations

What is the logical conclusion that can be deduced from the following two premises? Premise 1: Every sovereign Central American nation is a signatory to the regional environmental treaty. Premise 2: Honduras is a sovereign Central American nation.

  1. Honduras is a signatory to the regional environmental treaty. Correct answer.
  2. All signatories to the regional environmental treaty are developing economies.
  3. Honduras ratified the treaty ahead of all its neighboring countries.
  4. Only Central American nations are permitted to sign the treaty.

Explanation

This represents a valid classical deductive categorical syllogism (Modus Barbara): All A (Central American nations) are B (signatories). C (Honduras) is A. Therefore, C (Honduras) must necessarily be B (a signatory to the regional environmental treaty).

Question 14spanish / math / biology / formal / social - integrated subject foundations

Identify the word that contains a hiatus (hiato) formed by a stressed closed vowel alongside an unstressed open vowel:

  1. Raíz Correct answer.
  2. Cauce
  3. Reina
  4. Ciudad

Explanation

A hiatus (hiato acentual) occurs when two contiguous vowels belong to different syllables. When an open vowel (a, e, o) is paired with a closed vowel (i, u) that carries the word's tonic stress, the closed vowel breaks the diphthong and takes an orthographic tilde, forming two separate syllables (ra - ÍZ).

Question 15spanish / math / biology / formal / social - integrated subject foundations

In the phrase 'El silencio elocuente de la asamblea', what specific literary figure of speech is demonstrated by joining two terms of contradictory nature?

  1. Oxymoron (Oxímoron) Correct answer.
  2. Hyperbaton (Hipérbaton)
  3. Anaphora (Anáfora)
  4. Pleonasmus (Pleonasmo)

Explanation

An oxymoron is a stylistic figure that combines two seemingly incompatible or contradictory words within the same syntagm, producing a new poetic or conceptual synthesis. Here, 'silencio' (absence of sound) is modified directly by 'elocuente' (speaking expressively and persuasively).

Question 16spanish / math / biology / formal / social - integrated subject foundations

Which of the following sentences correctly utilizes the relative pronoun 'cuyo'?

  1. Aquel catedrático, cuyas publicaciones recibieron premios internacionales, dictará el seminario inaugural. Correct answer.
  2. Aquel catedrático, que cuyo libro fue publicado recientemente, dictará el seminario inaugural.
  3. Aquel catedrático, a cuyo le entregaron el reconocimiento académico, dictará el seminario inaugural.
  4. Aquel catedrático, cuyos los estudiantes admiran profundamente, dictará el seminario inaugural.

Explanation

The relative possessive adjective 'cuyo' agrees in gender and number with the possessed noun that follows it ('publicaciones' -> 'cuyas publicaciones'). It must never be preceded by 'que', combined with a definite article ('cuyo el'), or used as a direct personal pronoun substitute.

Question 17spanish / math / biology / formal / social - integrated subject foundations

Read the following statement: 'El avance tecnológico no constituye en sí mismo una garantía de progreso ético; si las herramientas digitales amplifican la desinformación y socavan la empatía, el desarrollo técnico se convierte en un retroceso cívico.' What is the underlying premise of this statement?

  1. Genuine social progress requires that technological capabilities be accompanied by ethical responsibility and critical thinking Correct answer.
  2. Modern society must completely dismantle digital infrastructure to restore civic harmony
  3. Technological innovation inevitably deteriorates the moral capacity of any civilization
  4. Digital tools are strictly incapable of distributing factual scientific information

Explanation

The text posits a conditional critique: technical sophistication is neutral or even harmful if it operates detached from ethics and civic responsibility. The foundational premise is that true human progress is multidimensional and requires ethical governance to prevent regression.

Question 18spanish / math / biology / formal / social - integrated subject foundations

Select the option where all words are spelled correctly with either 'b' or 'v':

  1. Movilidad, civilidad, benevolencia, nauseabundo Correct answer.
  2. Mobilidad, civilidad, benevolencia, nauseabundo
  3. Movilidad, sivilidad, benevolencia, nauseavundo
  4. Movilidad, civilidad, venevolencia, nauseabundo

Explanation

In Spanish orthography, words ending in '-bilidad' are written with 'b' (e.g., amabilidad), with the exceptions of 'movilidad' (from móvil) and 'civilidad' (from civil), which preserve the 'v' of their primitive roots. 'Benevolencia' begins with the Latin root 'bene-' (good) and uses 'v', while adjectives ending in '-bundo' are always written with 'b'.

Question 19spanish / math / biology / formal / social - integrated subject foundations

What is the synonym of the word 'FUGACIDAD' in the context of: 'La fugacidad de los aplausos recordó al joven actor que el prestigio escénico es perecedero'?

  1. Brevedad Correct answer.
  2. Permanencia
  3. Ostentación
  4. Opulencia

Explanation

'Fugacidad' denotes the quality of being fleeting, brief, or passing rapidly without enduring stability. In this context, its exact synonym is 'brevedad' (transience or short duration).

Question 20spanish / math / biology / formal / social - integrated subject foundations

Which of the following sentences exemplifies a passive voice construction (voz pasiva perifrástica)?

  1. El nuevo hospital regional fue inaugurado por la presidenta de la República. Correct answer.
  2. La presidenta de la República inauguró el nuevo hospital regional.
  3. Se inauguró un moderno hospital regional en la zona central.
  4. El hospital regional abrió sus puertas a la comunidad esta mañana.

Explanation

A periphrastic passive construction (voz pasiva perifrástica) in Spanish consists of the auxiliary verb 'ser' conjugated in the appropriate tense ('fue') followed by the past participle of the main transitive verb ('inaugurado'), agreeing in gender and number with the patient subject ('el hospital'), accompanied by the agent complement introduced by 'por' ('por la presidenta').

Question 21spanish / math / biology / formal / social - integrated subject foundations

In the paragraph: 'Honduras alberga una riqueza biológica excepcional; sin embargo, las presiones antropogénicas amenazan sus ecosistemas boscosos. Por ende, resulta imperativo fortalecer las áreas protegidas comunitarias.' What cohesive functions do the discourse markers 'sin embargo' and 'por ende' perform?

  1. Adversative counter-expectation (oposición/contraargumentación) and Consecutive consequence (consecución/conclusión) Correct answer.
  2. Additive inclusion (adición) and Temporal succession (secuencia temporal)
  3. Exemplification (ejemplificación) and Reformulation (recapitulación)
  4. Causal explanation (causalidad) and Disjunctive alternation (disyunción)

Explanation

'Sin embargo' is an adversative discourse connector introducing a contrast or counter-expectation against the preceding positive statement about biological richness. 'Por ende' is a consecutive/conclusive connector that introduces a direct logical deduction or consequence derived from the stated premise.

Question 22spanish / math / biology / formal / social - integrated subject foundations

Which of the following options displays correct orthography regarding words starting with or containing 'h'?

  1. Heredar, exhumar, hostil, inhóspito Correct answer.
  2. Eredar, exhumar, ostil, inhóspito
  3. Heredar, exumar, hostil, inóspito
  4. Heredar, exhumar, ostil, inóspito

Explanation

In Spanish etymological spelling: 'heredar' (from Latin hereditare) retains 'h'; 'exhumar' (ex- + humus) retains the intercalated 'h'; 'hostil' (from hostilis) begins with 'h'; and 'inhóspito' (in- + hospes) contains intercalated 'h' and takes a tilde on the antepenultimate syllable as an esdrújula.

Question 23spanish / math / biology / formal / social - integrated subject foundations

Read the following pair of sentences: I. El testigo no reveló la verdad durante el interrogatorio judicial. II. El nuevo fármaco contra la hipertensión reveló una eficacia sin precedentes. What semantic phenomenon is illustrated by the verb 'revelar' in these two contexts?

  1. Polysemy (Polisemia) Correct answer.
  2. Homophony with spelling difference (Homofonía heterográfica)
  3. Antonymy (Antonimia)
  4. Paronymy (Paronimia)

Explanation

Polysemy occurs when a single word with a common etymological origin possesses multiple related meanings depending on its semantic context. 'Revelar' (from Latin revelare) means both to disclose confidential information/secrets (Sentence I) and to manifest or demonstrate empirical results (Sentence II).

Question 24spanish / math / biology / formal / social - integrated subject foundations

Identify the option that correctly identifies the literary movement of the Honduran intellectual and national poet Juan Ramón Molina, author of 'Tierras, Mares y Cielos':

  1. Modernism (Modernismo) Correct answer.
  2. Romanticism (Romanticismo)
  3. Realism (Realismo)
  4. Neoclassicism (Neoclasicismo)

Explanation

Juan Ramón Molina (1875–1908) is Honduras's most celebrated poet and, alongside Rubén Darío, one of the central figures of the Hispanic American Modernist movement (Modernismo). His posthumously compiled masterpiece 'Tierras, Mares y Cielos' (1911) exhibits the quintessential stylistic elegance, aestheticism, and metrics of Modernism.

Question 25spanish / math / biology / formal / social - integrated subject foundations

In the academic sentence: 'Los investigadores sustentaron su hipótesis con datos estadísticos rigurosos, lo cual permitió refutar las objeciones metodológicas', what is the grammatical category of the compound word 'lo cual'?

  1. Neuter relative pronoun referring back to the entire preceding clause Correct answer.
  2. Demonstrative adjective modifying the noun 'hipótesis'
  3. Coordinating copulative conjunction linking two independent clauses
  4. Comparative adverb expressing equivalence of degree

Explanation

'Lo cual' functions syntactically as a complex neuter relative pronoun. Unlike masculine or feminine relative pronouns that refer to specific nominal antecedents, the neuter form 'lo cual' (or 'lo que') takes an entire preceding propositional proposition ('Los investigadores sustentaron su hipótesis...') as its referential antecedent.

Question 26spanish / math / biology / formal / social - integrated subject foundations

Solve for x in the linear equation: 5(2x - 3) - 4(x + 2) = 3(x + 5) - 8.

  1. x = 10 Correct answer.
  2. x = 6
  3. x = 4
  4. x = 2

Explanation

First, expand both sides by distributing the coefficients: Left side: 10x - 15 - 4x - 8 = 6x - 23. Right side: 3x + 15 - 8 = 3x + 7. Equate both sides: 6x - 23 = 3x + 7. Subtract 3x from both sides: 3x - 23 = 7. Add 23 to both sides: 3x = 30. Divide by 3: x = 10.

Question 27spanish / math / biology / formal / social - integrated subject foundations

A merchant purchases a shipment of goods for 12,000 Honduran Lempiras (HNL). If he sells the shipment with a profit margin of 25% calculated over the cost price, and the sale is subject to a 15% sales tax (Impuesto Sobre Ventas), what is the total amount paid by the buyer including tax?

  1. 17,250 HNL Correct answer.
  2. 16,800 HNL
  3. 15,000 HNL
  4. 14,400 HNL

Explanation

Cost price = 12,000 HNL. Profit = 25% of 12,000 = 0.25 * 12,000 = 3,000 HNL. Selling price before tax = 12,000 + 3,000 = 15,000 HNL. Sales tax (ISV 15%) = 15% of 15,000 = 0.15 * 15,000 = 2,250 HNL. Total amount paid by buyer = 15,000 + 2,250 = 17,250 HNL.

Question 28spanish / math / biology / formal / social - integrated subject foundations

Factor the quadratic algebraic expression completely: 6x^2 - 7x - 20.

  1. (2x - 5)(3x + 4) Correct answer.
  2. (2x + 5)(3x - 4)
  3. (6x - 5)(x + 4)
  4. (3x - 10)(2x + 2)

Explanation

To factor 6x^2 - 7x - 20 by grouping, find two integers that multiply to (a * c) = 6 * (-20) = -120 and add to b = -7. These numbers are -15 and +8 (since -15 * 8 = -120 and -15 + 8 = -7). Rewrite the middle term: 6x^2 - 15x + 8x - 20. Group terms: 3x(2x - 5) + 4(2x - 5) = (2x - 5)(3x + 4).

Question 29spanish / math / biology / formal / social - integrated subject foundations

Find the solution set for the linear inequality: 3 - 2(x - 4) >= 5x + 18.

  1. x <= -1 Correct answer.
  2. x >= -1
  3. x <= 1
  4. x >= 1

Explanation

Expand the left side: 3 - 2x + 8 >= 5x + 18 11 - 2x >= 5x + 18 Subtract 5x from both sides: 11 - 7x >= 18 Subtract 11 from both sides: -7x >= 7 Divide both sides by -7 and reverse the inequality sign: x <= -1.

Question 30spanish / math / biology / formal / social - integrated subject foundations

In a right triangle, the hypotenuse measures 25 cm and one of the legs measures 15 cm. What is the area of the triangle in square centimeters?

  1. 150 cm^2 Correct answer.
  2. 300 cm^2
  3. 200 cm^2
  4. 187.5 cm^2

Explanation

Use the Pythagorean theorem to find the other leg (b): a^2 + b^2 = c^2. 15^2 + b^2 = 25^2 => 225 + b^2 = 625 => b^2 = 400 => b = 20 cm. The area of a right triangle is (base * height) / 2 = (15 * 20) / 2 = 300 / 2 = 150 cm^2.

Question 31spanish / math / biology / formal / social - integrated subject foundations

Solve the system of linear equations: 3x + 2y = 16 2x - y = 6 What is the value of the product xy?

  1. 8 Correct answer.
  2. 6
  3. 12
  4. 16

Explanation

From the second equation, express y in terms of x: y = 2x - 6. Substitute into the first equation: 3x + 2(2x - 6) = 16 => 3x + 4x - 12 = 16 => 7x = 28 => x = 4. Substitute x = 4 back into y: y = 2(4) - 6 = 2. Therefore, the product xy = 4 * 2 = 8.

Question 32spanish / math / biology / formal / social - integrated subject foundations

Simplify the rational algebraic expression to its simplest terms: (x^2 - 9) / (2x^2 + 5x - 3)

  1. (x - 3) / (2x - 1) Correct answer.
  2. (x + 3) / (2x + 1)
  3. (x - 3) / (2x + 1)
  4. (x + 3) / (2x - 1)

Explanation

Factor the numerator as a difference of squares: x^2 - 9 = (x - 3)(x + 3). Factor the denominator by grouping: 2x^2 + 5x - 3 = 2x^2 + 6x - x - 3 = 2x(x + 3) - 1(x + 3) = (2x - 1)(x + 3). Cancel the common factor (x + 3) from numerator and denominator (for x != -3): (x - 3) / (2x - 1).

Question 33spanish / math / biology / formal / social - integrated subject foundations

The arithmetic mean (average) of five numbers is 24. If a sixth number is added, the new mean becomes 27. What is the value of the sixth number?

  1. 42 Correct answer.
  2. 36
  3. 39
  4. 45

Explanation

Sum of the initial five numbers = 5 * 24 = 120. When the sixth number (x) is added, there are 6 numbers with a mean of 27: Sum of the six numbers = 6 * 27 = 162. The sixth number is the difference: 162 - 120 = 42.

Question 34spanish / math / biology / formal / social - integrated subject foundations

A cylindrical water storage tank has an internal radius of 2 meters and a height of 7 meters. Using the approximation pi = 22/7, what is the internal volume of the cylinder in cubic meters?

  1. 88 m^3 Correct answer.
  2. 176 m^3
  3. 44 m^3
  4. 616 m^3

Explanation

The volume of a cylinder is given by the formula V = pi * r^2 * h. Substituting the given values: V = (22/7) * (2)^2 * 7. The 7 in the denominator cancels with the height 7: V = 22 * 4 = 88 m^3.

Question 35spanish / math / biology / formal / social - integrated subject foundations

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If two marbles are drawn at random one after the other without replacement, what is the probability that both drawn marbles are blue?

  1. 1/11 Correct answer.
  2. 1/9
  3. 4/33
  4. 1/12

Explanation

Total number of marbles = 5 + 4 + 3 = 12. Probability of drawing the first blue marble: P(B1) = 4 / 12 = 1/3. Since the marble is not replaced, there are now 3 blue marbles left out of 11 total marbles. Probability of drawing the second blue marble: P(B2 | B1) = 3 / 11. Combined probability: P(Both blue) = (4/12) * (3/11) = (1/3) * (3/11) = 3 / 33 = 1 / 11.

Question 36spanish / math / biology / formal / social - integrated subject foundations

Find the roots of the quadratic equation: 3x^2 + 5x - 2 = 0.

  1. x = 1/3 and x = -2 Correct answer.
  2. x = -1/3 and x = 2
  3. x = 2/3 and x = -1
  4. x = 1 and x = -2/3

Explanation

Apply the quadratic formula x = (-b +- sqrt(b^2 - 4ac)) / (2a): Here a = 3, b = 5, c = -2. Discriminant: b^2 - 4ac = 5^2 - 4(3)(-2) = 25 + 24 = 49. sqrt(49) = 7. x = (-5 +- 7) / (2 * 3) = (-5 +- 7) / 6. x1 = (-5 + 7) / 6 = 2 / 6 = 1/3. x2 = (-5 - 7) / 6 = -12 / 6 = -2. The equation therefore factors as (3x - 1)(x + 2) = 0.

Question 37spanish / math / biology / formal / social - integrated subject foundations

Evaluate the following numerical expression containing integer powers and absolute values: |-18 + 6| - 3 * (-2)^3 + sqrt(144) / 4.

  1. 39 Correct answer.
  2. 27
  3. 33
  4. 15

Explanation

Evaluate term by term following the order of operations: 1. Absolute value: |-18 + 6| = |-12| = 12. 2. Power: (-2)^3 = -8, so the second term is 3 * (-8) = -24. 3. That term is subtracted, so - (-24) = +24. 4. Square root and division: sqrt(144) = 12, and 12 / 4 = 3. Combine all three terms: 12 + 24 + 3 = 39.

Question 38spanish / math / biology / formal / social - integrated subject foundations

At a Tegucigalpa bus terminal, one route departs every 18 minutes and another departs every 24 minutes. If both routes depart together at 6:00 a.m., at what time will they next depart together?

  1. 7:12 a.m. Correct answer.
  2. 6:06 a.m.
  3. 6:42 a.m.
  4. 1:12 p.m.

Explanation

The two departures coincide again after a number of minutes that is a multiple of both intervals, so the answer is the least common multiple (mínimo común múltiplo) of 18 and 24. Factor each interval: 18 = 2 * 3^2 and 24 = 2^3 * 3. Take each prime to its highest power: LCM = 2^3 * 3^2 = 8 * 9 = 72 minutes. Adding 72 minutes (1 hour 12 minutes) to 6:00 a.m. gives 7:12 a.m.

Question 39spanish / math / biology / formal / social - integrated subject foundations

A regional centre reports how its 400 new students are distributed across four faculties: Ciencias Sociales: 120 students Ingeniería: 100 students Ciencias de la Salud: 90 students Ciencias Económicas: 90 students If the same data were displayed in a pie chart, what central angle would represent the Ingeniería sector, and what percentage of the total does it hold?

  1. 90 degrees and 25% Correct answer.
  2. 100 degrees and 25%
  3. 90 degrees and 20%
  4. 72 degrees and 25%

Explanation

First find the relative frequency: 100 / 400 = 0.25, that is 25% of the intake. A pie chart distributes the full 360 degrees in proportion to that share, so the central angle is 0.25 * 360 = 90 degrees. As a check, the four sectors give 108, 90, 81 and 81 degrees, which sum to 360 degrees.

Question 40spanish / math / biology / formal / social - integrated subject foundations

Two study groups obtained these scores on the same practice test. Group A: 60, 70, 80, 90, 100 Group B: 78, 79, 80, 81, 82 Both groups have a mean of 80. Which statement correctly compares their dispersion?

  1. Group A is more dispersed: its range is 40 and Group B's is only 4 Correct answer.
  2. Both groups are equally dispersed, because they share the same mean of 80
  3. Group B is more dispersed, because its values are not evenly spaced around the mean
  4. Dispersion cannot be compared unless the two groups have different means

Explanation

Measures of central tendency such as the mean do not describe how spread out a data set is; that is the job of measures of dispersion. The range is the simplest of them: Group A has 100 - 60 = 40, while Group B has 82 - 78 = 4. Group A's scores are therefore spread ten times more widely, and any other dispersion measure would agree: the standard deviation is roughly 14.1 for Group A against roughly 1.4 for Group B.

Question 41spanish / math / biology / formal / social - integrated subject foundations

Two parallel lines are intersected by a transversal line. Two alternate interior angles are expressed algebraically as (3x + 15) degrees and (5x - 25) degrees. What is the measure of each of these angles?

  1. 75 degrees Correct answer.
  2. 105 degrees
  3. 40 degrees
  4. 20 degrees

Explanation

When two parallel lines are cut by a transversal, alternate interior angles are congruent (equal in measure): 3x + 15 = 5x - 25 Subtract 3x from both sides: 15 = 2x - 25 Add 25 to both sides: 40 = 2x => x = 20. Substitute x = 20 back into either expression: 3(20) + 15 = 60 + 15 = 75 degrees. Check with second: 5(20) - 25 = 100 - 25 = 75 degrees.

Question 42spanish / math / biology / formal / social - integrated subject foundations

What is the sum of all interior angles of a regular convex octagon (8-sided polygon)?

  1. 1,080 degrees Correct answer.
  2. 1,440 degrees
  3. 720 degrees
  4. 900 degrees

Explanation

The formula for the sum of interior angles of an n-sided convex polygon is S = (n - 2) * 180 degrees. For an octagon, n = 8: S = (8 - 2) * 180 = 6 * 180 = 1,080 degrees.

Question 43spanish / math / biology / formal / social - integrated subject foundations

If 12 agricultural workers can harvest a coffee plantation in 18 days working at a constant pace, how many days would it take 8 workers of equal productivity to harvest the same plantation?

  1. 27 days Correct answer.
  2. 12 days
  3. 24 days
  4. 30 days

Explanation

This is an inverse proportion problem: the number of workers and the days required have an inverse relationship (fewer workers require more days to complete the same amount of work). Total worker-days required = 12 workers * 18 days = 216 worker-days. With 8 workers: Days = 216 / 8 = 27 days.

Question 44spanish / math / biology / formal / social - integrated subject foundations

A student builds figures with square tiles. Figure 1 uses 4 tiles, Figure 2 uses 7 tiles, Figure 3 uses 10 tiles and Figure 4 uses 13 tiles. Which algebraic expression gives the number of tiles in Figure n, and how many tiles does Figure 20 require?

  1. 3n + 1, requiring 61 tiles Correct answer.
  2. 3n, requiring 60 tiles
  3. 4n - 1, requiring 79 tiles
  4. n + 3, requiring 23 tiles

Explanation

The tile counts increase by a constant 3 at each step (4, 7, 10, 13), so the pattern is linear and the coefficient of n is 3. Writing the rule as 3n + b and testing Figure 1: 3(1) + b = 4, so b = 1. The rule is therefore 3n + 1, and it reproduces the whole sequence: 3(2) + 1 = 7, 3(3) + 1 = 10, 3(4) + 1 = 13. For Figure 20: 3(20) + 1 = 61 tiles.

Question 45spanish / math / biology / formal / social - integrated subject foundations

What is the median of the following set of data values? 14, 22, 9, 31, 18, 14, 27, 35

  1. 20 Correct answer.
  2. 18
  3. 22
  4. 21

Explanation

First, arrange the n = 8 data values in ascending order: 9, 14, 14, 18, 22, 27, 31, 35. Because n is even, the median is the arithmetic mean of the two central numbers (the 4th and 5th terms): 4th term = 18; 5th term = 22. Median = (18 + 22) / 2 = 40 / 2 = 20.

Question 46spanish / math / biology / formal / social - integrated subject foundations

Determine the vertex coordinates of the parabola represented by the quadratic function: f(x) = 2x^2 - 12x + 11.

  1. (3, -7) Correct answer.
  2. (-3, 65)
  3. (3, 7)
  4. (6, 11)

Explanation

The x-coordinate of the vertex of a parabola f(x) = ax^2 + bx + c is given by h = -b / (2a): Here a = 2, b = -12, c = 11. h = -(-12) / (2 * 2) = 12 / 4 = 3. Find the y-coordinate k by evaluating f(3): k = f(3) = 2(3)^2 - 12(3) + 11 = 2(9) - 36 + 11 = 18 - 36 + 11 = -7. Thus, the vertex is (3, -7).

Question 47spanish / math / biology / formal / social - integrated subject foundations

In a survey of 100 first-year university students, 60 study English, 45 study French, and 20 study both languages. How many students study neither English nor French?

  1. 15 Correct answer.
  2. 25
  3. 20
  4. 10

Explanation

By the Principle of Inclusion-Exclusion for sets: |E U F| = |E| + |F| - |E ∩ F| = 60 + 45 - 20 = 85 students study at least one of the two languages. The number of students studying neither language is the complement: Total - |E U F| = 100 - 85 = 15.

Question 48spanish / math / biology / formal / social - integrated subject foundations

A circle is inscribed in a square with an area of 64 cm^2. What is the area of the inscribed circle in square centimeters (in terms of pi)?

  1. 16 pi cm^2 Correct answer.
  2. 64 pi cm^2
  3. 32 pi cm^2
  4. 8 pi cm^2

Explanation

The side length of the square is s = sqrt(Area) = sqrt(64) = 8 cm. A circle inscribed in a square has a diameter equal to the side length of the square: d = s = 8 cm. Therefore, the radius of the circle is r = d / 2 = 8 / 2 = 4 cm. The area of the circle is A = pi * r^2 = pi * (4)^2 = 16 pi cm^2.

Question 49spanish / math / biology / formal / social - integrated subject foundations

Simplify the radical expression: sqrt(72) - 3*sqrt(8) + sqrt(50).

  1. 5*sqrt(2) Correct answer.
  2. 7*sqrt(2)
  3. 4*sqrt(2)
  4. 3*sqrt(2)

Explanation

Simplify each radical by extracting perfect square factors: 1. sqrt(72) = sqrt(36 * 2) = 6*sqrt(2). 2. 3*sqrt(8) = 3*sqrt(4 * 2) = 3 * 2*sqrt(2) = 6*sqrt(2). 3. sqrt(50) = sqrt(25 * 2) = 5*sqrt(2). Combine the terms: 6*sqrt(2) - 6*sqrt(2) + 5*sqrt(2) = 0 + 5*sqrt(2) = 5*sqrt(2).

Question 50spanish / math / biology / formal / social - integrated subject foundations

The sum of three consecutive integers is 114. What is the value of the largest of the three integers?

  1. 39 Correct answer.
  2. 38
  3. 37
  4. 40

Explanation

Let the three consecutive integers be n, n + 1, and n + 2. Their sum is: n + (n + 1) + (n + 2) = 114 3n + 3 = 114 3n = 111 => n = 37. The integers are 37, 38, and 39. The question asks for the largest integer, which is n + 2 = 39.