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Pruebas Nacionales Adultos PREPARA - independent subject foundations study materials
Pruebas Nacionales Adultos PREPARA - independent subject foundations study resources

Pruebas Nacionales Adultos PREPARA - independent subject foundations practice questions

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Question 1Upper-secondary functions, calculus, geometry and probability

The Dominican national electrical grid recorded an energy distribution of 4.8 * 10^9 kilowatt-hours (kWh) during the first semester of the year. In the second semester, the grid distributed 3.2 * 10^9 kWh. What was the total energy distributed over the entire year, expressed in standard scientific notation?

  1. 8.0 * 10^18 kWh
  2. 1.6 * 10^9 kWh
  3. 8.0 * 10^9 kWh Correct answer.
  4. 1.536 * 10^19 kWh

Explanation

When adding numbers expressed in scientific notation with identical exponents, the coefficients are added while keeping the common power of ten: (4.8 + 3.2) * 10^9 = 8.0 * 10^9 kWh.

Question 2Upper-secondary functions, calculus, geometry and probability

Simplify the following algebraic radical expression to its simplest radical form: sqrt(75) + sqrt(48) - sqrt(27).

  1. 6 * sqrt(3) Correct answer.
  2. 12 * sqrt(3)
  3. sqrt(96)
  4. 3 * sqrt(5)

Explanation

Factoring perfect squares out of each radical: sqrt(75) = sqrt(25 * 3) = 5 * sqrt(3); sqrt(48) = sqrt(16 * 3) = 4 * sqrt(3); sqrt(27) = sqrt(9 * 3) = 3 * sqrt(3). Combining like radical terms yields (5 + 4 - 3) * sqrt(3) = 6 * sqrt(3).

Question 3Upper-secondary functions, calculus, geometry and probability

For the logical implication «If p, then q» (p → q), under which truth-value assignment is the implication false?

  1. p is true and q is false Correct answer.
  2. p is true and q is true
  3. p is false and q is true
  4. p is false and q is false

Explanation

A material implication p → q is false only when its antecedent p is true and its consequent q is false. In every case with a false antecedent, the implication is true.

Question 4Upper-secondary functions, calculus, geometry and probability

In an adult education center, 35 students study English, 28 study computing, and 12 study both subjects. How many students study at least one of the two subjects?

  1. 51 Correct answer.
  2. 63
  3. 47
  4. 75

Explanation

Use inclusion-exclusion: |E ∪ C| = |E| + |C| - |E ∩ C| = 35 + 28 - 12 = 51. The 12 students in both groups must be subtracted once because they were counted twice.

Question 5Upper-secondary functions, calculus, geometry and probability

Consider the statements: «Every student who completes all four modules receives a certificate» and «Ana completed all four modules.» Which conclusion follows deductively?

  1. Ana receives a certificate Correct answer.
  2. Ana did not attend any module
  3. Everyone who receives a certificate is Ana
  4. No student other than Ana completed the modules

Explanation

The universal conditional applies to Ana because she satisfies its antecedent. Modus ponens therefore yields the conclusion that Ana receives a certificate.

Question 6Upper-secondary functions, calculus, geometry and probability

From a point on level ground, the angle of elevation to the top of a vertical tree is 45°. If the point is 12 meters from the tree's base, what is the tree's height, ignoring eye level?

  1. 6 meters
  2. 12 meters Correct answer.
  3. 12√2 meters
  4. 24 meters

Explanation

For the right triangle, tan 45° = opposite/adjacent = h/12. Since tan 45° = 1, h = 12 meters.

Question 7Upper-secondary functions, calculus, geometry and probability

Perform the operations and simplify the following polynomial expression: (4x^2 - 7x + 5) - (2x^2 + 3x - 8) + (x^2 - 4).

  1. 3x^2 - 10x + 9 Correct answer.
  2. 3x^2 - 4x + 9
  3. x^2 - 10x - 7
  4. 3x^2 - 10x - 1

Explanation

Distributing the subtraction sign across the second polynomial: 4x^2 - 7x + 5 - 2x^2 - 3x + 8 + x^2 - 4. Grouping like terms: (4 - 2 + 1)x^2 = 3x^2; (-7 - 3)x = -10x; and constant terms (5 + 8 - 4) = 9. Combining yields 3x^2 - 10x + 9.

Question 8Upper-secondary functions, calculus, geometry and probability

Factor the algebraic expression completely into linear factors: 3x^3 - 48x.

  1. 3x(x - 4)^2
  2. 3x(x^2 - 16)
  3. 3x(x - 4)(x + 4) Correct answer.
  4. (3x^2 - 12)(x + 4)

Explanation

First, factor out the greatest common monomial factor 3x: 3x(x^2 - 16). Then factor the difference of two perfect squares (x^2 - 16) into conjugate binomials: (x - 4)(x + 4). The complete factorization is 3x(x - 4)(x + 4).

Question 9Upper-secondary functions, calculus, geometry and probability

Solve the following linear equation for x: (2x - 3) / 4 - (x + 1) / 6 = 2.

  1. x = 35 / 4 Correct answer.
  2. x = 31 / 4
  3. x = 11 / 2
  4. x = 29 / 4

Explanation

Find the least common multiple of denominators 4 and 6, which is 12. Multiply the entire equation by 12: 3*(2x - 3) - 2*(x + 1) = 24. Expand: 6x - 9 - 2x - 2 = 24. Combine like terms: 4x - 11 = 24. Add 11 to both sides: 4x = 35. Therefore, x = 35 / 4 (or 8.75).

Question 10Upper-secondary functions, calculus, geometry and probability

In a school cafeteria, 3 complete daily lunches and 4 tropical juices cost a total of DOP 560. On the following day, 2 complete lunches and 5 tropical juices cost DOP 490. What is the unit cost of one lunch (x) and one tropical juice (y)?

  1. Lunch: DOP 120; Juice: DOP 50 Correct answer.
  2. Lunch: DOP 100; Juice: DOP 65
  3. Lunch: DOP 130; Juice: DOP 40
  4. Lunch: DOP 110; Juice: DOP 55

Explanation

Set up the linear system: (1) 3x + 4y = 560; (2) 2x + 5y = 490. Multiply equation (1) by 2: 6x + 8y = 1120. Multiply equation (2) by 3: 6x + 15y = 1470. Subtract: 7y = 350 -> y = DOP 50. Substitute y into (1): 3x + 4(50) = 560 -> 3x + 200 = 560 -> 3x = 360 -> x = DOP 120.

Question 11Upper-secondary functions, calculus, geometry and probability

Find the real solution roots for the quadratic equation: 2x^2 - 5x - 12 = 0.

  1. x = 4 and x = -3 / 2 Correct answer.
  2. x = -4 and x = 3 / 2
  3. x = 3 and x = -2
  4. x = 6 and x = -1

Explanation

Factoring the trinomial: find factors of a * c = 2 * (-12) = -24 that sum to -5. These are -8 and +3. Rewrite: 2x^2 - 8x + 3x - 12 = 2x(x - 4) + 3(x - 4) = (2x + 3)(x - 4) = 0. Setting each factor to zero gives x = 4 and x = -3 / 2 (or -1.5).

Question 12Upper-secondary functions, calculus, geometry and probability

Given the quadratic function f(x) = -2x^2 + 5x - 7, calculate the value of the function at the negative input x = -3, i.e., find f(-3).

  1. -40 Correct answer.
  2. -26
  3. -4
  4. 26

Explanation

Substitute x = -3 into the expression: f(-3) = -2*(-3)^2 + 5*(-3) - 7. First evaluate exponent: (-3)^2 = 9. Then multiply: -2*(9) = -18, and 5*(-3) = -15. Finally, combine terms: -18 - 15 - 7 = -40.

Question 13Upper-secondary functions, calculus, geometry and probability

Solve the linear inequality for real variable x: 5 - 3(2x - 1) <= 4x + 28.

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

Explanation

Expand the left side: 5 - 6x + 3 <= 4x + 28 -> 8 - 6x <= 4x + 28. Subtract 4x from both sides: 8 - 10x <= 28. Subtract 8: -10x <= 20. Divide by -10 (which reverses the inequality sign): x >= 20 / (-10) -> x >= -2. In interval notation: [-2, infinity).

Question 14Upper-secondary functions, calculus, geometry and probability

During building repairs in Santiago, a worker leans a straight ladder against a vertical exterior wall. The foot of the ladder is placed on level ground 9 meters away from the base of the wall, and the top of the ladder reaches a window sill 12 meters above the ground. What is the length of the ladder?

  1. 15 meters Correct answer.
  2. 21 meters
  3. 14.5 meters
  4. sqrt(63) meters

Explanation

Using the Pythagorean theorem (a^2 + b^2 = c^2), where base a = 9 m and height b = 12 m: c^2 = 9^2 + 12^2 = 81 + 144 = 225. Taking the square root: c = sqrt(225) = 15 meters.

Question 15Upper-secondary functions, calculus, geometry and probability

An agricultural land parcel planted with plantains in the Valverde Mao province has the shape of a trapezoid. The two parallel bases measure 140 meters and 220 meters respectively, and the perpendicular height between them is 75 meters. What is the total area of the parcel in square meters?

  1. 13,500 m^2 Correct answer.
  2. 27,000 m^2
  3. 10,500 m^2
  4. 16,200 m^2

Explanation

The area of a trapezoid is given by A = [(b_1 + b_2) / 2] * h. Substituting the given dimensions: A = [(140 + 220) / 2] * 75 = [360 / 2] * 75 = 180 * 75 = 13,500 m^2.

Question 16Upper-secondary functions, calculus, geometry and probability

A support cable 10 meters long runs from the top of a vertical pole to level ground and makes a 30° angle with the ground. How high is the pole?

  1. 5 meters Correct answer.
  2. 5√3 meters
  3. 10√3 meters
  4. 20 meters

Explanation

The cable is the hypotenuse and the pole height is opposite the 30° angle. Thus sin 30° = h/10 = 1/2, so h = 5 meters.

Question 17Upper-secondary functions, calculus, geometry and probability

A residential water storage tank (*tinaco*) installed on a rooftop has a cylindrical shape with an interior diameter of 2.0 meters (radius = 1.0 meter) and a height of 3.5 meters. Using pi = 3.14, what is the maximum volume capacity of the tank in liters, knowing that 1 cubic meter equals 1,000 liters?

  1. 10,990 liters Correct answer.
  2. 43,960 liters
  3. 21,980 liters
  4. 7,000 liters

Explanation

Volume of a cylinder is V = pi * r^2 * h. With radius r = 1.0 m and height h = 3.5 m: V = 3.14 * (1.0)^2 * 3.5 = 3.14 * 3.5 = 10.99 m^3. Converting to liters: 10.99 * 1,000 = 10,990 liters.

Question 18Upper-secondary functions, calculus, geometry and probability

Two parallel urban avenues (L1 || L2) are intersected by an oblique cross street. Two consecutive interior angles on the same side of the transversal line measure (3x + 20) degrees and (2x + 10) degrees. What is the value of x, and what are the measures of the two angles?

  1. x = 30 degrees; Angles: 110 degrees and 70 degrees Correct answer.
  2. x = 10 degrees; Angles: 50 degrees and 30 degrees
  3. x = 34 degrees; Angles: 122 degrees and 78 degrees
  4. x = 25 degrees; Angles: 95 degrees and 60 degrees

Explanation

Consecutive interior angles formed by parallel lines cut by a transversal are supplementary, summing to 180 degrees: (3x + 20) + (2x + 10) = 180 -> 5x + 30 = 180 -> 5x = 150 -> x = 30 degrees. The angles are 3(30) + 20 = 110 degrees, and 2(30) + 10 = 70 degrees.

Question 19Upper-secondary functions, calculus, geometry and probability

Two sides of a triangle measure 7 cm and 8 cm, and the included angle between them is 60°. What is the length of the third side?

  1. √57 cm Correct answer.
  2. 15 cm
  3. √113 cm
  4. 7.5 cm

Explanation

By the law of cosines, c² = 7² + 8² - 2(7)(8)cos 60° = 49 + 64 - 56 = 57. Therefore c = √57 cm.

Question 20Upper-secondary functions, calculus, geometry and probability

A cohort of 9 PREPARA adult learners recorded the following examination scores on a mathematics module: 72, 75, 78, 78, 84, 85, 88, 92, 95. What are the median and the mode of this dataset?

  1. Median = 84; Mode = 78 Correct answer.
  2. Median = 78; Mode = 84
  3. Median = 83; Mode = 78
  4. Median = 84; Mode = No mode

Explanation

The 9 scores are already ordered from least to greatest. For an odd number of observations (n = 9), the median is the middle observation at position (9 + 1)/2 = 5th position, which is 84. The mode is the score with the highest frequency, which is 78 (occurring twice).

Question 21Upper-secondary functions, calculus, geometry and probability

A municipal survey of 50 adult workers in an industrial free zone (*Zona Franca*) recorded their one-way commuting times: - 0 to 19 minutes: 8 workers - 20 to 39 minutes: 18 workers - 40 to 59 minutes: 14 workers - 60 to 79 minutes: 7 workers - 80 to 99 minutes: 3 workers What percentage of the surveyed workers spend 40 minutes or more on their daily commute?

  1. 48% Correct answer.
  2. 28%
  3. 52%
  4. 24%

Explanation

Workers commuting 40 minutes or more fall into the last three class intervals: 14 + 7 + 3 = 24 workers. The relative frequency percentage is (24 / 50) * 100% = 48%.

Question 22Upper-secondary functions, calculus, geometry and probability

Evaluate the limit: lim(x→2) (2x² - 8)/(x - 2).

  1. 0
  2. 2
  3. 8 Correct answer.
  4. The limit does not exist

Explanation

Factor 2x² - 8 = 2(x² - 4) = 2(x - 2)(x + 2). For x ≠ 2 the expression equals 2(x + 2), which approaches 8 as x approaches 2.

Question 23Upper-secondary functions, calculus, geometry and probability

An object's position is s(t) = 3t² + 2t meters, where t is measured in seconds. What is its instantaneous velocity at t = 2 seconds?

  1. 8 m/s
  2. 12 m/s
  3. 14 m/s Correct answer.
  4. 16 m/s

Explanation

Instantaneous velocity is the derivative of position: v(t) = s'(t) = 6t + 2. At t = 2, v(2) = 12 + 2 = 14 m/s.

Question 24Upper-secondary functions, calculus, geometry and probability

In a national energy matrix report for the Dominican Republic, the sources of electrical generation are distributed as follows: Natural Gas = 40%, Coal = 30%, Renewable Energy (Solar, Wind, Hydro) = 20%, and Fuel Oil = 10%. If this data is represented in a circular pie chart (*gráfico de sectores circulares*), what is the measure of the central angle corresponding to Renewable Energy?

  1. 72 degrees Correct answer.
  2. 54 degrees
  3. 90 degrees
  4. 36 degrees

Explanation

A complete circle comprises 360 degrees. To find the central angle for Renewable Energy (20%): Angle = 20% of 360 degrees = 0.20 * 360 = 72 degrees.

Question 25Lengua española: comprensión, gramática y expresión escrita

In the historical novel *Enriquillo* (1882) by Dominican author Manuel de Jesús Galván, what is the central thematic conflict portrayed through the rebellion of the Taíno cacique Enriquillo in the Sierra de Bahoruco?

  1. The moral and armed resistance of an indigenous leader fighting against colonial injustice and the abusive encomienda system Correct answer.
  2. A commercial rivalry between rival Spanish merchant guilds competing for royal gold export monopolies in Santo Domingo
  3. A theological dispute between Franciscan and Dominican friars over the secularization of parish churches
  4. The military defense of Hispaniola against piratical incursions by French and British privateers

Explanation

Manuel de Jesús Galván's *Enriquillo* is the foundational Dominican indigenist historical novel. It chronicles the prolonged 14-year guerrilla resistance led by the educated cacique Enriquillo in the Bahoruco mountains against Spanish colonial subjugation, concluding with Emperor Charles V granting him autonomy and dignity.

Question 26Lengua española: comprensión, gramática y expresión escrita

Read the following stanza from the patriotic poem 'Ruinas' (1876) by Dominican poet Salomé Ureña de Henríquez: 'Memorias venerandas de otros días, soberbios monumentos, del pasado esplendor las glorias mías, sus altos pensamientos al veros busco en vano; de ayer la gloria se trocó en quebranto, y hoy sobre el polvo de tu suelo santo canta el desierto y llora el patriotismo.' What symbolic meaning do the colonial ruins of Santo Domingo embody in Ureña's poetic discourse?

  1. An exclusive appreciation for architectural antiquities and Spanish monarchical authority
  2. An allegorical lament for national decay accompanied by an urgent civic call to moral and educational revival Correct answer.
  3. A romantic celebration of isolationism and rejection of modern civic institutions
  4. A historical chronicle praising the foreign military occupations that shaped the capital city

Explanation

In 'Ruinas', Salomé Ureña contrasts the glorious past of the First City of America with the political instability and moral decline of the 19th-century republic. The architectural ruins serve as an allegory urging Dominican society to rebuild the fatherland through education, peace, and civic duty.

Question 27Lengua española: comprensión, gramática y expresión escrita

Which sentence correctly matches the verb to the singular grammatical head «el grupo»?

  1. Los grupo de estudiantes universitarios presentaron una queja formal ante la decana
  2. El grupo de estudiantes universitarios presentó una queja formal ante la decana Correct answer.
  3. El grupo de estudiantes universitarios presentarán una queja formal ante la decana
  4. El grupo de estudiantes universitarios habían presentado una queja formal ante la decana

Explanation

In standard formal Spanish, when a singular collective noun ('el grupo') is modified by a plural prepositional phrase ('de estudiantes universitarios'), the nucleus of the subject is the singular noun 'grupo', which normatively governs a singular third-person verb ('presentó').

Question 28Lengua española: comprensión, gramática y expresión escrita

In the verse «¡Dios, qué buen vasallo, si hubiese buen señor!», traditionally associated with the medieval Cantar de mio Cid, what tension does the speaker express?

  1. The knight's loyalty is praised while the quality of his lord is questioned Correct answer.
  2. The knight is condemned for abandoning the Christian faith
  3. The lord is praised for rewarding every vassal fairly
  4. The speaker rejects the social bond between lord and vassal as nonexistent

Explanation

The exclamation praises the Cid as a worthy vassal but makes that praise conditional on having a worthy lord. It therefore combines admiration for the hero with criticism or doubt about royal leadership.

Question 29Lengua española: comprensión, gramática y expresión escrita

A speaker uses formal standard Spanish in a job interview but shifts to familiar Dominican expressions when speaking with close friends. Which linguistic concept best explains the change?

  1. Register variation according to audience and communicative situation Correct answer.
  2. The disappearance of the speaker's first language
  3. A spelling error caused by seseo
  4. A fixed difference in the biological capacity for language

Explanation

Speakers adjust vocabulary, pronunciation, and level of formality to suit audience, purpose, and setting. This is register or situational variation, not evidence that one variety is linguistically deficient.

Question 30Lengua española: comprensión, gramática y expresión escrita

In the sentence: 'El facilitador confirmó que las pruebas diagnósticas se realizarán el próximo sábado', what syntactic function is performed by the subordinate clause 'que las pruebas diagnósticas se realizarán el próximo sábado'?

  1. Direct Object (*Objeto Directo*) of the main transitive verb 'confirmó' Correct answer.
  2. Subject (*Sujeto*) of the main clause
  3. Circumstantial Complement of Time (*Complemento Circunstancial de Tiempo*)
  4. Agent Complement (*Complemento Agente*) in a passive structure

Explanation

The subordinate clause can be pronominalized by the neuter pronoun 'lo' ('El facilitador lo confirmó') and answers the question '¿qué confirmó el facilitador?', demonstrating that it functions as a noun subordinate clause acting as Direct Object of the verb 'confirmó'.

Question 31Lengua española: comprensión, gramática y expresión escrita

Which combination of features most clearly identifies literary Romanticism in nineteenth-century Spanish-language writing?

  1. Strict imitation of classical rules and emotional restraint
  2. Exaltation of individual feeling, freedom, nature, and conflict with social convention Correct answer.
  3. Exclusive use of scientific method and statistical evidence
  4. Rejection of the self in favor of impersonal bureaucratic language

Explanation

Romantic writing commonly foregrounds subjective emotion, individual freedom, powerful natural settings, and rebellion against restrictive social conventions.

Question 32Lengua española: comprensión, gramática y expresión escrita

A poem emphasizes musical language, sensory imagery, cosmopolitan settings, and carefully crafted symbols while reacting against ordinary utilitarian expression. Which Spanish American literary movement does it most closely reflect?

  1. Modernismo Correct answer.
  2. Medieval epic
  3. Neoclassical didacticism
  4. Costumbrista journalism

Explanation

Spanish American Modernismo renewed poetic language through musicality, symbolism, sensory richness, and cosmopolitan imagery, reacting against prosaic or merely utilitarian expression.

Question 33Lengua española: comprensión, gramática y expresión escrita

According to the general accentuation rules in Spanish, words are categorized by the position of their tonic syllable. Which of the following groups contains exclusively *palabras esdrújulas* (stress on the antepenultimate syllable, which always carry a written accent tilde)?

  1. Canción, pared, compás, reloj
  2. Árbol, césped, carácter, difícil
  3. Brújula, química, teléfono, pájaro Correct answer.
  4. Entrégaselo, dígamelo, recuérdamelo, cómpratelo

Explanation

The words 'brú-ju-la', 'quí-mi-ca', 'te-lé-fo-no', and 'pá-ja-ro' are all stressed on the antepenultimate (*antepenúltima*) syllable and are classified as *palabras esdrújulas*, which universally require an accent mark (*tilde*) in Spanish orthography.

Question 34Lengua española: comprensión, gramática y expresión escrita

Which description best characterizes the Dominican Postumismo movement associated with Domingo Moreno Jimenes?

  1. A search for simple, direct poetic language rooted in local landscape and everyday experience Correct answer.
  2. An exclusive return to medieval chivalric vocabulary and courtly love
  3. A program requiring every poem to follow French Alexandrine meter
  4. A rejection of Dominican settings in favor of purely classical mythology

Explanation

Postumismo sought an unadorned, locally grounded poetic voice and valued Dominican landscape and everyday experience over inherited ornamental conventions.

Question 35Lengua española: comprensión, gramática y expresión escrita

Which statement best reflects a sociolinguistic understanding of Dominican Spanish?

  1. It is a legitimate regional variety with systematic patterns that vary by context and community Correct answer.
  2. It is corrupted Spanish with no grammatical regularities
  3. Every Dominican speaker uses exactly the same pronunciation in every situation
  4. Regional vocabulary makes mutual understanding with all other Spanish varieties impossible

Explanation

Dominican Spanish is a legitimate Spanish variety with systematic phonological, grammatical, and lexical patterns. As in any speech community, usage varies with region, audience, and level of formality.

Question 36Lengua española: comprensión, gramática y expresión escrita

Read the following paragraph: 'El informe meteorológico pronosticó tormentas intensas en la costa este; __________, los pescadores artesanales de Samaná decidieron asegurar sus embarcaciones y suspender las faenas en altamar.' Which discourse connector of consequence best completes the statement logically?

  1. a pesar de que
  2. por consiguiente Correct answer.
  3. sin embargo
  4. no obstante

Explanation

'Por consiguiente' is a consecutive discourse connector denoting 'as a result' or 'therefore', expressing the direct and logical outcome of the stormy weather forecast on the fishermen's decision.

Question 37Lengua española: comprensión, gramática y expresión escrita

A newspaper text presents a clear position on a public issue and supports it with reasons intended to persuade readers. Which text type and communicative purpose best describe it?

  1. Editorial; to argue for an institutional or reasoned position Correct answer.
  2. Straight news report; to avoid all interpretation and persuade no one
  3. Instruction manual; to order procedural steps
  4. Personal diary; to record private experiences for the writer alone

Explanation

An editorial advances a position on an issue and develops reasons to influence readers' judgment. Its dominant communicative purpose is argumentative.

Question 38Mechanics, fields, thermal behavior, waves and modern models

A motorcycle starts from a complete standstill (initial velocity v_0 = 0 m/s) and accelerates uniformly along a straight avenue at a = 3.0 m/s^2 for a duration of 6.0 seconds. What is the final velocity of the motorcycle, and what total distance does it cover during this interval?

  1. Final Velocity: 18 m/s; Distance: 54 meters Correct answer.
  2. Final Velocity: 18 m/s; Distance: 108 meters
  3. Final Velocity: 9 m/s; Distance: 36 meters
  4. Final Velocity: 12 m/s; Distance: 48 meters

Explanation

Final velocity in MRUA is v_f = v_0 + a*t = 0 + (3.0 * 6.0) = 18 m/s. Distance covered is d = v_0*t + 0.5*a*t^2 = 0 + 0.5 * (3.0) * (6.0)^2 = 0.5 * 3.0 * 36 = 54 meters.

Question 39Mechanics, fields, thermal behavior, waves and modern models

An object is placed beyond twice the focal length (beyond 2F) of a thin converging lens. Which description of the image is correct?

  1. Real, inverted, and smaller than the object Correct answer.
  2. Virtual, upright, and larger than the object
  3. Real, upright, and the same size as the object
  4. Virtual, inverted, and smaller than the object

Explanation

For a converging lens with the object beyond 2F, refracted rays meet on the opposite side between F and 2F. The image is real, inverted, and reduced.

Question 40Mechanics, fields, thermal behavior, waves and modern models

An electric crane on a construction site in Santo Domingo lifts a 200 kg load of building materials vertically to a height of 15 meters at constant speed in 30 seconds. Using gravitational acceleration g = 9.8 m/s^2, what is the mechanical work performed by the crane, and what average mechanical power does it develop?

  1. Work: 29,400 Joules; Power: 980 Watts Correct answer.
  2. Work: 3,000 Joules; Power: 100 Watts
  3. Work: 29,400 Joules; Power: 882,000 Watts
  4. Work: 14,700 Joules; Power: 490 Watts

Explanation

Work done against gravity is W = m * g * h = 200 kg * 9.8 m/s^2 * 15 m = 29,400 Joules. Power is the rate of doing work: P = W / t = 29,400 J / 30 s = 980 Watts.

Question 41Mechanics, fields, thermal behavior, waves and modern models

A 2.0 kg stone is released from rest from the top of a 20-meter cliff above a river. Neglecting air resistance and using g = 9.8 m/s^2, what is the gravitational potential energy of the stone at the top of the cliff, and what will be its kinetic energy immediately before it impacts the water surface?

  1. Potential Energy at top: 392 Joules; Kinetic Energy before impact: 392 Joules Correct answer.
  2. Potential Energy at top: 392 Joules; Kinetic Energy before impact: 0 Joules
  3. Potential Energy at top: 40 Joules; Kinetic Energy before impact: 40 Joules
  4. Potential Energy at top: 196 Joules; Kinetic Energy before impact: 392 Joules

Explanation

Gravitational potential energy is E_p = m * g * h = 2.0 kg * 9.8 m/s^2 * 20 m = 392 Joules. According to the Law of Conservation of Mechanical Energy (E_total = E_p + E_k = constant), in the absence of friction, all initial potential energy transforms into kinetic energy just before impact, so E_k = 392 Joules.

Question 42Mechanics, fields, thermal behavior, waves and modern models

A radio station antenna in Santo Domingo broadcasts an FM electromagnetic signal at a frequency of 100 Megahertz (1.0 * 10^8 Hz). Knowing that electromagnetic waves propagate through air at the speed of light c = 3.0 * 10^8 m/s, what is the wavelength of this radio broadcast wave?

  1. 3.0 meters Correct answer.
  2. 30 meters
  3. 0.33 meters
  4. 3.0 * 10^16 meters

Explanation

The fundamental wave equation relates wave speed, frequency, and wavelength: v = f * lambda -> lambda = v / f. Substituting: lambda = (3.0 * 10^8 m/s) / (1.0 * 10^8 s^-1) = 3.0 meters.

Question 43Chemical structure, reactions and organic models

Matter can be classified as pure substances (elements and compounds) or mixtures (homogeneous and heterogeneous). Which of the following examples represents a pure chemical compound?

  1. Filtered seawater collected at Boca Chica beach
  2. Pure distilled water (H2O) Correct answer.
  3. Ambient atmospheric air free of dust particles
  4. A bronze coin made of copper and tin

Explanation

Distilled water consists solely of molecules composed of hydrogen and oxygen chemically bonded in a fixed 2:1 ratio (H2O) with uniform chemical properties, classifying it as a pure chemical compound.

Question 44Chemical structure, reactions and organic models

Elements in Group 18 of the Periodic Table (such as Helium, Neon, Argon, and Krypton) are known as Noble Gases (*Gases Nobles*). What electronic property explains their extreme chemical stability and general lack of reactivity?

  1. They have a single valence electron that is easily donated to nonmetals
  2. They have a completely filled outer valence shell with a stable octet (8 valence electrons, or 2 for helium) Correct answer.
  3. They have an odd number of protons that prevents any ionic bonding
  4. They exist exclusively as diatomic liquid molecules at standard temperature

Explanation

Noble gases have completely filled outermost electron shells (a stable octet of ns^2 np^6, or 1s^2 for helium). This stable electron configuration gives them low chemical potential energy, making them virtually inert under standard conditions.

Question 45Chemical structure, reactions and organic models

Which of the following chemical substances is formed through ionic bonding (*enlace iónico*) via the complete transfer of valence electrons between a metal and a nonmetal?

  1. Sodium chloride (NaCl) Correct answer.
  2. Methane gas (CH4)
  3. Water vapor (H2O)
  4. Molecular oxygen (O2)

Explanation

Sodium chloride (NaCl) is formed between sodium (an alkali metal with low electronegativity) and chlorine (a halogen with high electronegativity). Sodium transfers its single valence electron to chlorine, forming Na+ and Cl- ions held together by strong electrostatic attraction.

Question 46Chemical structure, reactions and organic models

What is the oxidation state (*número de oxidación*) of sulfur (S) in sulfuric acid (H2SO4), given that hydrogen has an oxidation number of +1 and oxygen has an oxidation number of -2?

  1. +6 Correct answer.
  2. +4
  3. -2
  4. +2

Explanation

In a neutral compound, the sum of oxidation numbers must equal zero: 2*(H) + 1*(S) + 4*(O) = 0. Substituting: 2*(+1) + S + 4*(-2) = 0 -> +2 + S - 8 = 0 -> S - 6 = 0 -> S = +6.

Question 47Chemical structure, reactions and organic models

According to the Law of Conservation of Mass (Lavoisier's Law), atoms are neither created nor destroyed during a chemical reaction. Balance the chemical equation for the complete combustion of propane: C3H8 + ? O2 -> 3 CO2 + 4 H2O. What stoichiometric coefficient must be placed before oxygen (O2)?

  1. 5 Correct answer.
  2. 10
  3. 3
  4. 7

Explanation

Count the oxygen atoms in the products: 3 CO2 has 3 * 2 = 6 oxygen atoms; 4 H2O has 4 * 1 = 4 oxygen atoms. Total oxygen atoms in products = 6 + 4 = 10 atoms. To provide 10 oxygen atoms from diatomic O2 molecules on the reactant side, the required coefficient is 10 / 2 = 5.

Question 48Chemical structure, reactions and organic models

Examine the following chemical reaction: Zn (s) + 2 HCl (aq) -> ZnCl2 (aq) + H2 (g). What type of chemical reaction does this represent?

  1. Single displacement reaction (*reacción de desplazamiento simple o sustitución*) Correct answer.
  2. Synthesis or direct combination reaction (*reacción de síntesis*)
  3. Decomposition reaction (*reacción de descomposición*)
  4. Double displacement or precipitation reaction (*reacción de doble desplazamiento*)

Explanation

In this reaction, elemental zinc displaces hydrogen from hydrochloric acid to form zinc chloride and release hydrogen gas. Because a single free element replaces another element in a compound (A + BC -> AC + B), it is classified as a single displacement (single replacement) reaction.

Question 49Chemical structure, reactions and organic models

The pH scale measures the acidity or alkalinity of an aqueous solution. If a sample of citrus fruit juice has a hydrogen ion concentration [H+] = 1.0 * 10^-4 M, what is its pH value, and how is the solution classified?

  1. pH = 4.0; classified as an acidic solution Correct answer.
  2. pH = 10.0; classified as a basic (alkaline) solution
  3. pH = 7.0; classified as a neutral solution
  4. pH = 1.0; classified as a strongly basic solution

Explanation

pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration: pH = -log[H+] = -log(1.0 * 10^-4) = 4.0. Because a pH less than 7 indicates acidity, the juice is classified as an acidic solution.

Question 50Chemical structure, reactions and organic models

Methane has the molecular formula CH4 and contains only single carbon-hydrogen bonds. To which class of organic compounds does it belong?

  1. Alkane Correct answer.
  2. Alkene
  3. Alcohol
  4. Carboxylic acid

Explanation

Methane is the simplest alkane. Alkanes are saturated hydrocarbons whose carbon atoms are joined through single bonds.