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USAC PCB Guatemala practice questions

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Question 1spanish / math / biology / physics / chemistry - integrated subject foundations

In the communication process defined in the USAC Lenguaje syllabus, which element represents the physical medium or channel through which a message is transmitted from the sender to the receiver?

  1. El canal Correct answer.
  2. El código
  3. El contexto
  4. El referente

Explanation

The SUN Lenguaje guía temática lists the elements of communication as emisor, receptor, mensaje, código, canal, contexto and ruido. Of these, 'el canal' is the physical conduit, medium or sensory pathway - sound waves, paper, an electronic screen, optical fibre - through which the encoded message travels from the emisor to the receptor.

Question 2spanish / math / biology / physics / chemistry - integrated subject foundations

Identify the communicative function that predominates in the following utterance: '¡Préstame atención inmediatamente y guarda silencio durante la explicación!'

  1. Función conativa o apelativa Correct answer.
  2. Función referencial o representativa
  3. Función fática o de contacto
  4. Función metalingüística

Explanation

The utterance is formulated as an explicit imperative command aimed at influencing, directing, or modifying the behavior of the receiver. In linguistic theory, this corresponds to the función conativa or apelativa (appellative/conative function), which is centered directly on the receptor.

Question 3spanish / math / biology / physics / chemistry - integrated subject foundations

According to Ferdinand de Saussure's structural linguistics, which two inseparable components constitute the linguistic sign (el signo lingüístico)?

  1. Significante y significado Correct answer.
  2. Lengua y habla
  3. Enunciado y enunciación
  4. Sintagma y paradigma

Explanation

In Saussurean linguistics, the linguistic sign is a two-sided mental entity consisting of the 'significante' (the acoustic image or sound pattern) and the 'significado' (the mental concept or semantic representation), linked arbitrarily like two sides of a sheet of paper.

Question 4spanish / math / biology / physics / chemistry - integrated subject foundations

In Spanish lexicography, which relationship correctly describes the word pair 'tubo' (a hollow cylinder) and 'tuvo' (third-person preterite of tener)?

  1. Palabras homófonas Correct answer.
  2. Palabras homógrafas
  3. Palabras parónimas
  4. Palabras antónimas

Explanation

'Tubo' and 'tuvo' are homophones (palabras homófonas) because they share identical pronunciation in standard Spanish phonology (/ˈtubo/) due to betacism (the merger of /b/ and /v/), but possess different spelling (grafía) and distinct meanings.

Question 5spanish / math / biology / physics / chemistry - integrated subject foundations

Spanish builds new words by prefixation, by composition and by parasynthesis. Which of these four words is parasynthetic (parasintética)?

  1. Empobrecer Correct answer.
  2. Reconstruir
  3. Sacacorchos
  4. Panadería

Explanation

In parasíntesis a prefix and a suffix attach to the base at the same time, so that neither the prefixed form nor the suffixed form exists on its own. 'Empobrecer' comes from the adjective 'pobre' with en-...-ecer (en- becomes em- before p). Spanish has neither *empobre nor *pobrecer, which shows both affixes were added in a single step.

Question 6spanish / math / biology / physics / chemistry - integrated subject foundations

In the sentence 'Los investigadores entregaron el informe técnico a la decana ayer por la tarde', what syntactic function does the phrase 'a la decana' perform?

  1. Objeto indirecto (complemento indirecto) Correct answer.
  2. Objeto directo (complemento directo)
  3. Complemento circunstancial de destinatario
  4. Complemento agente

Explanation

The prepositional phrase 'a la decana' indicates the recipient or beneficiary of the verbal action 'entregaron' and can be substituted by the dative pronominal clitic 'le' ('Los investigadores le entregaron el informe técnico ayer por la tarde'), which confirms it is the objeto indirecto (indirect object).

Question 7spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following sentences exhibits the linguistic error known as 'dequeísmo'?

  1. Pienso de que la propuesta será aprobada por el consejo directivo. Correct answer.
  2. Estoy seguro de que todos los estudiantes completaron el registro.
  3. Nos enteramos de que las clases presenciales comenzarán el lunes.
  4. Tiene miedo de que los resultados de la prueba se retrasen.

Explanation

'Dequeísmo' is the inappropriate insertion of the preposition 'de' before the subordinating conjunction 'que' when introducing an object clause governed by a transitive verb that does not take a preposition. 'Pensar' takes a direct object ('Pienso eso', not *'Pienso de eso'), so the correct standard form is 'Pienso que la propuesta será aprobada'.

Question 8spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following words must carry an orthographic accent mark (tilde diacrítica) in standard Spanish when used as an interrogative or exclamative pronoun?

  1. Quién Correct answer.
  2. Fe
  3. Ti
  4. Di

Explanation

'Quién' takes an orthographic tilde diacrítica when it functions as an interrogative or exclamative word (e.g., '¿Quién llegó?', '¡Mira quién habla!'). The tilde distinguishes it from the unstressed relative pronoun 'quien', written without an accent (e.g., 'Quien avisa no es traidor'; 'el alumno, quien llegó ayer, recibió la beca').

Question 9spanish / math / biology / physics / chemistry - integrated subject foundations

In Spanish morphosyntax, what type of subordinate clause is present in the sentence: 'El estudiante que obtuvo la calificación más alta recibió una beca completa'?

  1. Proposición subordinada adjetiva (de relativo) especificativa Correct answer.
  2. Proposición subordinada adjetiva (de relativo) explicativa
  3. Proposición subordinada sustantiva de sujeto
  4. Proposición subordinada adverbial causal

Explanation

The clause 'que obtuvo la calificación más alta' modifies the nominal antecedent 'El estudiante' directly without commas, restricting or specifying its referent from a larger set. It is therefore a proposición subordinada adjetiva o de relativo especificativa (restrictive relative clause).

Question 10spanish / math / biology / physics / chemistry - integrated subject foundations

Identify the rhetorical figure of speech (figura retórica) used in the classical verse: 'Érase un hombre a una nariz pegado' by Francisco de Quevedo.

  1. Hipérbole Correct answer.
  2. Metonimia
  3. Antítesis
  4. Paradoja

Explanation

Quevedo's famous line uses extreme, deliberate exaggeration (hipérbole) to magnify the physical proportions of the nose to an impossible degree, claiming the man was attached to the nose rather than the nose to the man.

Question 11spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following sentences adheres strictly to the official Spanish rules of grammatical agreement (concordancia gramatical)?

  1. Había muchas personas esperando los resultados en el patio central. Correct answer.
  2. Habían muchas personas esperando los resultados en el patio central.
  3. Hubieron varios incidentes durante la inauguración del certamen.
  4. Hicieron días muy calurosos durante el mes de marzo en la capital.

Explanation

In impersonal constructions expressing existence or weather, the verb 'haber' (and 'hacer') functions as an impersonal verb without a grammatical subject. The following nominal phrase ('muchas personas') is the direct object (objeto directo), so the verb must remain strictly singular: 'Había muchas personas'.

Question 12spanish / math / biology / physics / chemistry - integrated subject foundations

What type of logical fallacy is committed in the argument: 'Esa teoría pedagógica no tiene validez porque su autor fue expulsado de su universidad por conducta inapropiada'?

  1. Falacia ad hominem Correct answer.
  2. Falacia ad verecundiam
  3. Falacia ad populum
  4. Falacia post hoc ergo propter hoc

Explanation

A falacia ad hominem attacks the character, personal history, or circumstances of the person making the claim rather than addressing the factual evidence, logical structure, or pedagogical validity of the theory itself.

Question 13spanish / math / biology / physics / chemistry - integrated subject foundations

In the structural typology of texts, what primary communicative intention characterizes an argumentative essay (texto argumentativo)?

  1. Defender una tesis y persuadir o convencer al lector mediante razones válidas Correct answer.
  2. Relatar una secuencia de acontecimientos cronológicos reales o ficticios
  3. Proporcionar instrucciones detalladas y secuenciales para ejecutar una tarea
  4. Exponer y describir objetivamente conceptos abstractos sin emitir juicios de valor

Explanation

The core communicative purpose of an argumentative text (ensayo o texto argumentativo) is to present a central claim or thesis and persuade or convince the reader of its validity through logical arguments, evidence, and critical reasoning.

Question 14spanish / math / biology / physics / chemistry - integrated subject foundations

Read the following short excerpt: 'El Popol Vuh, libro sagrado de los mayas k'iche's, relata que los dioses Creadores y Formadores intentaron crear al ser humano primero de lodo, luego de madera y finalmente de maíz amarillo y maíz blanco, logrando con este último dar vida a los primeros cuatro hombres dotados de inteligencia y reverencia.' Based on the text, what deduction is logically necessary?

  1. Las primeras dos tentativas de creación no produjeron seres con las facultades requeridas por los dioses Correct answer.
  2. El lodo y la madera eran materiales sagrados exclusivos de la nobleza maya
  3. Los primeros cuatro hombres fueron creados únicamente a partir de granos de maíz amarillo
  4. El Popol Vuh fue redactado originalmente en lengua española durante la época prehispánica

Explanation

Because the text specifies that the Creator deities made successive attempts ('primero de lodo, luego de madera y finalmente de maíz... logrando con este último dar vida a los primeros cuatro hombres dotados de inteligencia y reverencia'), it is logically deduced that the mud and wood creations failed to achieve the necessary divine attributes.

Question 15spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following words is spelled correctly with the letter 'b' according to standard orthographic rules governing suffixes in Spanish?

  1. Amabilidad Correct answer.
  2. Movilidad
  3. Civilidad
  4. Servilidad

Explanation

Words ending in the nominalizing suffix '-bilidad' are spelled with 'b' (derived from adjectives in '-ble', such as amable -> amabilidad, sociable -> sociabilidad), with only two etymological exceptions in standard Spanish: 'movilidad' (from móvil) and 'civilidad' (from civil).

Question 16spanish / math / biology / physics / chemistry - integrated subject foundations

In semantic analysis, what is the hypernym (hiperónimo) of the co-hyponyms 'quetzal', 'tucán', 'colibrí' and 'guardabarranco'?

  1. Ave Correct answer.
  2. Mamífero
  3. Reptil
  4. Anfibio

Explanation

A hypernym (hiperónimo) is a broad, overarching semantic category whose semantic field encompasses more specific member terms (hipónimos). The quetzal, toucan, hummingbird, and motmot are all specific species of birds; therefore, 'ave' is their hypernym.

Question 17spanish / math / biology / physics / chemistry - integrated subject foundations

Identify the sentence that contains an ambiguous construction (anfibología or ambigüedad sintáctica).

  1. El abogado vio al testigo cuando salía de su oficina. Correct answer.
  2. El abogado conversó con la jueza en la antesala del tribunal.
  3. El testigo declaró con serenidad ante el jurado calificado.
  4. La perito presentó el dictamen pericial antes del mediodía.

Explanation

'El abogado vio al testigo cuando salía de su oficina' contains syntactic anfibología (structural ambiguity): the possessive determiner 'su' and the clause 'cuando salía' can refer either to the lawyer (el abogado) leaving his office or to the witness (el testigo) leaving his office.

Question 18spanish / math / biology / physics / chemistry - integrated subject foundations

Which verb form represents the imperfect subjunctive (pretérito imperfecto de subjuntivo) in the second-person singular (tú) in standard Spanish?

  1. Estudiaras o estudiases Correct answer.
  2. Has estudiado
  3. Habías estudiado
  4. Estudiares

Explanation

In standard Spanish grammar, the pretérito imperfecto de subjuntivo possesses two interchangeable morphologically parallel conjugations for 'tú': the '-ra' form ('estudiaras') and the '-se' form ('estudiases').

Question 19spanish / math / biology / physics / chemistry - integrated subject foundations

What is the primary function of an adversarial discourse connector (conector discursivo adversativo) such as 'sin embargo', 'no obstante', or 'pero'?

  1. Contraponer o limitar una idea previamente expresada sin anular la proposición principal Correct answer.
  2. Añadir elementos informativos complementarios de igual jerarquía a una idea previa
  3. Indicar la causa o motivo determinante de un fenómeno expuesto con anterioridad
  4. Establecer una relación temporal de simultaneidad entre dos acciones independientes

Explanation

Adversative connectors (conectores adversativos) introduce a contrast, restriction, or objection to a preceding claim without entirely invalidating it, guiding the reader through nuanced argumentative counterpoints.

Question 20spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following sentences exhibits correct punctuation and comma usage with a vocative phrase (vocativo)?

  1. Estimados estudiantes, deben entregar el ensayo antes del viernes. Correct answer.
  2. Estimados estudiantes deben entregar, el ensayo antes del viernes.
  3. Estimados estudiantes deben, entregar el ensayo antes del viernes.
  4. Estimados, estudiantes deben entregar el ensayo antes del viernes.

Explanation

A vocativo is an appeal directed to the listener/interlocutor to call their attention. Under standard orthography, vocatives must always be isolated by commas: preceded by a comma if at the end, enclosed by commas if in the middle, or followed by a comma if at the beginning of an utterance ('Estimados estudiantes, deben...').

Question 21spanish / math / biology / physics / chemistry - integrated subject foundations

In the Maya vigesimal numbering system (Matemática Maya), what is the decimal equivalent of a numeral written with 3 bars and 2 dots in the first level (units) and 1 dot in the second level (twenties)?

  1. 37 Correct answer.
  2. 27
  3. 42
  4. 52

Explanation

In Maya vigesimal positional numeration, each bar represents 5 and each dot represents 1. Level 1 (units, multiplier 20^0 = 1): 3 bars (3 * 5 = 15) + 2 dots (2 * 1 = 2) = 17. Level 2 (twenties, multiplier 20^1 = 20): 1 dot = 1 * 20 = 20. Total decimal value = 20 + 17 = 37.

Question 22spanish / math / biology / physics / chemistry - integrated subject foundations

In the Maya positional system, what place value does the third level (from bottom to top) represent in standard vigesimal mathematics?

  1. 400 (20²) Correct answer.
  2. 20 (20¹)
  3. 1 (20⁰)
  4. 8,000 (20³)

Explanation

The standard Maya numerical system is strictly vigesimal (base 20) with vertical positional ordering. Level 1 corresponds to units (20^0 = 1), Level 2 corresponds to twenties (20^1 = 20), Level 3 corresponds to four-hundreds (20^2 = 400), and Level 4 corresponds to eight-thousands (20^3 = 8,000).

Question 23spanish / math / biology / physics / chemistry - integrated subject foundations

Convert the decimal number 845 into its Maya vigesimal positional representation.

  1. Level 3: 2 dots; Level 2: 2 dots; Level 1: 1 bar Correct answer.
  2. Level 3: 2 dots; Level 2: 1 dot; Level 1: 2 bars
  3. Level 3: 1 dot; Level 2: 4 bars; Level 1: 1 dot
  4. Level 3: 4 dots; Level 2: 0 (shell); Level 1: 1 bar

Explanation

To convert decimal 845 to base 20: 845 / 400 = 2 with a remainder of 45. Next, 45 / 20 = 2 with a remainder of 5. Finally, 5 / 1 = 5. Thus, Level 3 (400s) has value 2 (2 dots); Level 2 (20s) has value 2 (2 dots); Level 1 (units) has value 5 (1 bar). Verification: 2(400) + 2(20) + 5(1) = 800 + 40 + 5 = 845.

Question 24spanish / math / biology / physics / chemistry - integrated subject foundations

Given two propositions p and q, what are the truth values of the conditional statement p -> q when p is False and q is True?

  1. Verdadero (True) Correct answer.
  2. Falso (False)
  3. Indeterminado (Undetermined)
  4. Contradictorio (Contradictory)

Explanation

In formal propositional logic, a material conditional statement (p -> q) is False if and only if the antecedent (p) is True and the consequent (q) is False (T -> F = F). When the antecedent is False, the conditional is vacuously True regardless of the truth value of the consequent (F -> T = T).

Question 25spanish / math / biology / physics / chemistry - integrated subject foundations

In a survey of 120 high school graduates applying to USAC, 70 applied to Facultad de Ingeniería, 55 applied to Facultad de Ciencias Económicas, and 25 applied to both. How many applicants applied to neither faculty?

  1. 20 Correct answer.
  2. 45
  3. 30
  4. 25

Explanation

Using the principle of inclusion-exclusion for sets: |A U B| = |A| + |B| - |A n B|. Here, |Ingeniería U Económicas| = 70 + 55 - 25 = 100 applicants chose at least one of the two faculties. The number who applied to neither is Total - |A U B| = 120 - 100 = 20.

Question 26spanish / math / biology / physics / chemistry - integrated subject foundations

Simplify the rational algebraic fraction (x² - 25) / (x² - 2x - 15), stating the result in lowest terms.

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

Explanation

Factor both parts before cancelling. The numerator is a difference of squares: x² - 25 = (x - 5)(x + 5). The denominator is a trinomial whose factors must multiply to -15 and add to -2: x² - 2x - 15 = (x - 5)(x + 3). Dividing out the common non-zero factor (x - 5) leaves (x + 5) / (x + 3), valid for every x except 5 and -3.

Question 27spanish / math / biology / physics / chemistry - integrated subject foundations

Solve the system of linear equations for x and y: 2x + 3y = 19 3x - y = 1

  1. x = 2, y = 5 Correct answer.
  2. x = 5, y = 3
  3. x = 3, y = 4
  4. x = 4, y = 3

Explanation

From the second equation, isolate y: y = 3x - 1. Substitute this into the first equation: 2x + 3(3x - 1) = 19 -> 2x + 9x - 3 = 19 -> 11x = 22 -> x = 2. Now calculate y: y = 3(2) - 1 = 6 - 1 = 5. Checking in equation 1: 2(2) + 3(5) = 4 + 15 = 19. Checking in equation 2: 3(2) - 5 = 6 - 5 = 1.

Question 28spanish / math / biology / physics / chemistry - integrated subject foundations

Solve the quadratic equation 3x² - 10x + 8 = 0 for x.

  1. x = 2 and x = 4/3 Correct answer.
  2. x = -2 and x = -4/3
  3. x = 4 and x = 2/3
  4. x = 8 and x = 3

Explanation

Apply the quadratic formula x = [-b ± √(b² - 4ac)] / (2a) with a = 3, b = -10 and c = 8. The discriminant is (-10)² - 4(3)(8) = 100 - 96 = 4, and √4 = 2, so x = (10 ± 2) / 6. Adding gives x = 12/6 = 2; subtracting gives x = 8/6 = 4/3. Factoring confirms it: (3x - 4)(x - 2) = 0.

Question 29spanish / math / biology / physics / chemistry - integrated subject foundations

In Guatemala, the value-added tax (IVA) is 12%. A university student purchases an agronomy reference textbook whose final receipt total with IVA included is Q280.00. What was the base price of the book before IVA was applied?

  1. Q250.00 Correct answer.
  2. Q246.40
  3. Q240.00
  4. Q252.00

Explanation

Let P be the base price. The final price with 12% IVA is Price = P * (1 + 0.12) = 1.12 * P. Therefore, P = Total / 1.12 = Q280.00 / 1.12 = Q250.00. Verification: 12% of Q250.00 is 0.12 * 250 = Q30.00. Base price Q250.00 + Q30.00 IVA = Q280.00.

Question 30spanish / math / biology / physics / chemistry - integrated subject foundations

Simplify the algebraic exponential expression: [ (2 a³ b⁻²)³ ] / [ 4 a⁴ b⁻⁵ ].

  1. 2 a⁵ b⁻¹ (or 2a⁵ / b) Correct answer.
  2. 2 a⁵ b¹¹
  3. 4 a⁵ / b
  4. a⁵ / (2b)

Explanation

First expand the numerator using power-of-a-product rules: (2 a³ b⁻²)³ = 2³ * (a³)³ * (b⁻²)³ = 8 a⁹ b⁻⁶. Now divide by the denominator: (8 a⁹ b⁻⁶) / (4 a⁴ b⁻⁵) = (8/4) * a^(9 - 4) * b^(-6 - (-5)) = 2 * a⁵ * b^(-6 + 5) = 2 a⁵ b⁻¹ = 2a⁵ / b.

Question 31spanish / math / biology / physics / chemistry - integrated subject foundations

A student's seven practice scores are 61, 72, 65, 90, 72, 58 and 72. What are the mean (media), median (mediana) and mode (moda) of this data set?

  1. Media = 70; mediana = 72; moda = 72 Correct answer.
  2. Media = 72; mediana = 70; moda = 72
  3. Media = 70; mediana = 90; moda = 61
  4. Media = 70; mediana = 65; moda = 72

Explanation

The mean is the sum of the data divided by how many there are: (61 + 72 + 65 + 90 + 72 + 58 + 72) / 7 = 490 / 7 = 70. To obtain the median the data must first be ordered: 58, 61, 65, 72, 72, 72, 90; with seven values the median is the fourth one, 72, because three values lie below it and three above. The mode is the value that occurs most often, and 72 appears three times.

Question 32spanish / math / biology / physics / chemistry - integrated subject foundations

A right triangle has perpendicular legs of lengths 12 cm and 16 cm. What are the length of its hypotenuse and the area of the triangle?

  1. Hypotenuse = 20 cm, Area = 96 cm² Correct answer.
  2. Hypotenuse = 20 cm, Area = 192 cm²
  3. Hypotenuse = 28 cm, Area = 96 cm²
  4. Hypotenuse = 18 cm, Area = 108 cm²

Explanation

By the Pythagorean theorem: c² = a² + b² = 12² + 16² = 144 + 256 = 400 -> c = sqrt(400) = 20 cm (this is a scaled 3-4-5 right triangle with scaling factor 4: 3*4=12, 4*4=16, 5*4=20). The area of a right triangle is Area = (1/2) * base * height = (1/2) * 12 * 16 = 96 cm².

Question 33spanish / math / biology / physics / chemistry - integrated subject foundations

A circular irrigation zone on a farm has a radius of 7 meters. Using pi = 22/7, what are its exact circumference and area?

  1. Circumference = 44 m, Area = 154 m² Correct answer.
  2. Circumference = 44 m, Area = 308 m²
  3. Circumference = 22 m, Area = 154 m²
  4. Circumference = 88 m, Area = 616 m²

Explanation

Circumference C = 2 * pi * r = 2 * (22/7) * 7 = 2 * 22 = 44 m. Area A = pi * r² = (22/7) * 7² = (22/7) * 49 = 22 * 7 = 154 m².

Question 34spanish / math / biology / physics / chemistry - integrated subject foundations

In a right triangle with acute angle theta, if sin(theta) = 3/5, what is the exact value of tan(theta)?

  1. 3/4 Correct answer.
  2. 4/3
  3. 4/5
  4. 5/4

Explanation

In a right triangle, sin(theta) = opposite / hypotenuse = 3/5. By the Pythagorean identity, adjacent = sqrt(5² - 3²) = sqrt(25 - 9) = sqrt(16) = 4. Therefore, tan(theta) = opposite / adjacent = 3/4.

Question 35spanish / math / biology / physics / chemistry - integrated subject foundations

Evaluate the exact value of the trigonometric numerical expression: sin(30°) + cos(60°) + tan(45°).

  1. 2 Correct answer.
  2. 1.5
  3. 1
  4. 2.5

Explanation

From the standard exact values of trigonometric functions for special acute angles: sin(30°) = 1/2, cos(60°) = 1/2, and tan(45°) = 1. Summing these values gives: 1/2 + 1/2 + 1 = 1 + 1 = 2.

Question 36spanish / math / biology / physics / chemistry - integrated subject foundations

In an arithmetic progression, the first term is a₁ = 4 and the common difference is d = 3. What is the value of the 20th term (a₂₀)?

  1. 61 Correct answer.
  2. 64
  3. 58
  4. 60

Explanation

The formula for the n-th term of an arithmetic progression is a_n = a_1 + (n - 1)d. For n = 20, a_1 = 4, and d = 3: a_20 = 4 + (20 - 1) * 3 = 4 + 19 * 3 = 4 + 57 = 61.

Question 37spanish / math / biology / physics / chemistry - integrated subject foundations

What is the sum of the first 6 terms of a geometric progression whose first term is a₁ = 3 and common ratio is r = 2?

  1. 189 Correct answer.
  2. 192
  3. 96
  4. 381

Explanation

The formula for the sum of the first n terms of a geometric sequence is S_n = a_1 * (r^n - 1) / (r - 1). Here a_1 = 3, r = 2, and n = 6. r^6 = 2^6 = 64. S_6 = 3 * (64 - 1) / (2 - 1) = 3 * 63 / 1 = 189. Alternatively, sum the individual terms: 3 + 6 + 12 + 24 + 48 + 96 = 189.

Question 38spanish / math / biology / physics / chemistry - integrated subject foundations

Factor the difference of cubes completely into real polynomials: 8x³ - 27.

  1. (2x - 3)(4x² + 6x + 9) Correct answer.
  2. (2x - 3)(4x² - 6x + 9)
  3. (2x + 3)(4x² - 6x + 9)
  4. (2x - 3)³

Explanation

The algebraic factorization formula for the difference of two cubes is a³ - b³ = (a - b)(a² + ab + b²). For 8x³ - 27, a = 2x and b = 3. a² = (2x)² = 4x², ab = (2x)(3) = 6x, and b² = 3² = 9. Substituting gives: (2x - 3)(4x² + 6x + 9).

Question 39spanish / math / biology / physics / chemistry - integrated subject foundations

What is the natural domain in the real numbers (R) for the function f(x) = sqrt(x - 4) / (x - 7)?

  1. [4, 7) U (7, infinity) Correct answer.
  2. [4, infinity)
  3. (4, 7) U (7, infinity)
  4. (-infinity, 7) U (7, infinity)

Explanation

Two conditions must be met for f(x) to be real-valued: 1) The radicand of the even root must be non-negative: x - 4 >= 0 -> x >= 4. 2) The denominator cannot be zero: x - 7 != 0 -> x != 7. Combining both restrictions yields the interval [4, 7) U (7, infinity).

Question 40spanish / math / biology / physics / chemistry - integrated subject foundations

Given the functions f(x) = 2x + 3 and g(x) = x² - 1, calculate the composite function value (g o f)(2).

  1. 48 Correct answer.
  2. 13
  3. 9
  4. 47

Explanation

By definition of composite functions, (g o f)(2) = g(f(2)). First evaluate the inside function at x = 2: f(2) = 2(2) + 3 = 4 + 3 = 7. Next, evaluate g at 7: g(7) = 7² - 1 = 49 - 1 = 48.

Question 41spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following propositions represents a fundamental postulate of classical Cell Theory (Teoría Celular)?

  1. Toda célula proviene de otra célula preexistente (Omnis cellula e cellula) Correct answer.
  2. Los virus son las unidades anatómicas y funcionales más pequeñas de la vida
  3. Las células animales poseen pared celular de celulosa para soporte mecánico
  4. La generación espontánea origina microorganismos en medios estériles

Explanation

Rudolf Virchow in 1855 added the third classical tenet of cell theory: 'Omnis cellula e cellula' (all cells arise from pre-existing cells through cellular division), alongside the postulates of Schleiden and Schwann establishing that all organisms are composed of one or more cells and that the cell is the basic structural and functional unit of life.

Question 42spanish / math / biology / physics / chemistry - integrated subject foundations

What type of covalent bond connects the alpha-carboxyl group of one amino acid to the alpha-amino group of an adjacent amino acid in a protein chain?

  1. Enlace peptídico Correct answer.
  2. Enlace fosfodiéster
  3. Enlace glucosídico
  4. Enlace éster

Explanation

A peptide bond (enlace peptídico) is a covalent amide linkage formed by a condensation/dehydration reaction between the carboxyl group (-COOH) of one amino acid and the amino group (-NH2) of another, releasing a water molecule (H2O).

Question 43spanish / math / biology / physics / chemistry - integrated subject foundations

Which complex carbohydrate serves as the primary glucose storage polysaccharide in animal tissues, primarily synthesized and stored in the liver and skeletal muscle?

  1. Glucógeno Correct answer.
  2. Almidón
  3. Celulosa
  4. Quitina

Explanation

Glycogen (glucógeno) is a heavily branched polymer of alpha-D-glucose (with alpha-1,4 and alpha-1,6 glycosidic bonds) that serves as the major energy reserve polysaccharide in animals, stored in hepatic cells and skeletal muscle fibers.

Question 44spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following cellular structures is present in eukaryotic cells but completely absent in prokaryotic organisms (such as bacteria)?

  1. Envoltura nuclear (carioteca) delimitando el material genético Correct answer.
  2. Ribosomas para la síntesis de proteínas
  3. Membrana plasmática compuesta por fosfolípidos
  4. Material genético constituido por ácido desoxirribonucleico (ADN)

Explanation

The defining diagnostic distinction of eukaryotic cells ('eu' = true, 'karyon' = nucleus) is the presence of a membrane-bound nucleus (envoltura nuclear o carioteca) that encapsulates the chromosomes, separating transcription from translation. Prokaryotes lack membrane-enclosed nuclei, maintaining their circular DNA in an unenclosed nucleoid region.

Question 45spanish / math / biology / physics / chemistry - integrated subject foundations

Which of the following is evidence for biological evolution drawn specifically from comparative anatomy (anatomía comparada)?

  1. Las extremidades anteriores del ser humano, la ballena y el murciélago comparten el mismo plan óseo básico (estructuras homólogas) Correct answer.
  2. Las alas de una mariposa y las alas de un ave cumplen la misma función de vuelo (estructuras análogas)
  3. La secuencia de aminoácidos del citocromo c es casi idéntica entre primates cercanos
  4. La presencia exclusiva de marsupiales en Australia se explica por la separación de los continentes

Explanation

Comparative anatomy compares body plans across species. The forelimbs of a human, a whale and a bat are homologous: beneath a hand, a flipper and a wing lies the same arrangement of humerus, radius, ulna, carpals and digits. The same structure serving grasping, swimming and flight is explained by descent with modification from a common ancestor.

Question 46spanish / math / biology / physics / chemistry - integrated subject foundations

In the human urinary system, what is the nephron (nefrona) and where does the filtration of blood plasma begin?

  1. Es la unidad funcional del riñón, y la filtración comienza en el glomérulo, dentro de la cápsula de Bowman Correct answer.
  2. Es la unidad funcional del riñón, pero la filtración comienza en la vejiga urinaria
  3. Es el conducto que transporta la orina desde el riñón hasta la vejiga
  4. Es la capa muscular del riñón que impulsa la orina hacia la uretra

Explanation

The nephron is the functional unit of the kidney, and each human kidney holds on the order of a million of them. Filtration begins in the renal corpuscle, where blood pressure in the glomerular capillaries forces water and small solutes out of the plasma and into Bowman's capsule. The filtrate then travels through the proximal tubule, the loop of Henle, the distal tubule and the collecting duct, where reabsorption and secretion adjust its composition to form urine.

Question 47spanish / math / biology / physics / chemistry - integrated subject foundations

How does the lysogenic cycle (ciclo lisogénico) of a bacteriophage differ from the lytic cycle (ciclo lítico)?

  1. En el ciclo lisogénico el ADN viral se integra al cromosoma bacteriano como profago y se replica junto con la célula, sin destruirla de inmediato Correct answer.
  2. En el ciclo lisogénico el virus destruye la célula hospedera inmediatamente después de inyectar su material genético
  3. En el ciclo lisogénico el virus se replica fuera de la célula, sin necesidad de un hospedero
  4. En el ciclo lisogénico el virus fabrica sus propios ribosomas y enzimas para sintetizar sus proteínas

Explanation

In the lytic cycle the phage immediately commandeers the host machinery, assembles new virions and bursts the bacterium. In the lysogenic cycle the viral DNA instead inserts itself into the bacterial chromosome as a prophage and is copied passively each time the bacterium divides, so the host survives and hands the viral genome on to its descendants. Stress such as ultraviolet radiation can later induce the prophage to excise itself and switch to the lytic cycle.

Question 48spanish / math / biology / physics / chemistry - integrated subject foundations

What happens to human erythrocytes (glóbulos rojos) when placed in an environment with a solute concentration significantly lower than their internal cytoplasm (solución hipotónica)?

  1. Experimentan entrada masiva de agua por ósmosis y sufren lisis celular (hemólisis) Correct answer.
  2. Pierden agua hacia el medio externo y sufren crenación (arrugamiento)
  3. Mantienen su volumen inalterado gracias a su pared celular rígida
  4. Expulsan solutos por transporte activo hasta igualar la presión hidrostática

Explanation

In a hypotonic solution (solución hipotónica), the solute concentration outside the cell is lower than inside, creating an osmotic gradient where water rushes into the erythrocyte. Lacking a rigid cell wall to generate opposing turgor pressure, the animal cell swells and eventually bursts-a process known as hemólisis (hemolysis).

Question 49spanish / math / biology / physics / chemistry - integrated subject foundations

How does active transport (transporte activo) across the cell membrane fundamentally differ from facilitated diffusion (difusión facilitada)?

  1. El transporte activo moviliza solutos contra su gradiente electroquímico y consume energía metabólica (ATP) Correct answer.
  2. El transporte activo no requiere proteínas transportadoras de membrana
  3. La difusión facilitada requiere hidrólisis directa de nucleótidos trifosfato
  4. El transporte activo moviliza exclusivamente moléculas de agua mediante acuaporinas

Explanation

Active transport moves substances 'uphill' against their concentration or electrochemical gradient, requiring direct or indirect expenditure of cellular metabolic energy (such as ATP hydrolysis in the Na+/K+ ATPase pump). In contrast, facilitated diffusion is a passive mechanism that moves solutes 'downhill' along their gradient through carrier proteins or channel proteins without consuming metabolic energy.

Question 50spanish / math / biology / physics / chemistry - integrated subject foundations

During aerobic cellular respiration, where in the eukaryotic cell does glycolysis (glucólisis) occur, and what is its net yield per molecule of glucose?

  1. Ocurre en el citosol (citoplasma) y genera una ganancia neta de 2 ATP, 2 NADH y 2 moléculas de piruvato Correct answer.
  2. Ocurre en la matriz mitocondrial y genera 4 ATP netos y 2 FADH₂
  3. Ocurre en las crestas mitocondriales y produce 32 ATP y dióxido de carbono
  4. Ocurre en el estroma del cloroplasto y consume 2 moléculas de ATP

Explanation

Glycolysis is an anaerobic cytoplasmic pathway that takes place in the cytosol outside the mitochondria. It breaks down one 6-carbon glucose molecule into two 3-carbon pyruvate molecules, consuming 2 ATP in the energy investment phase and generating 4 ATP and 2 NADH in the payoff phase, resulting in a net yield of 2 ATP, 2 NADH, and 2 pyruvate.