ECOEMS IPN-UNAM Upper-Secondary Admission Exam (Mi Derecho, Mi Lugar)

In Spanish verbal reasoning, which word is the closest synonym for "efímero"?

• AFugaz
• BPerpetuo
• CSólido
• DAntiguo

In Spanish verbal reasoning, which word is the closest synonym for "sagaz"?

• AIngenuo
• BAstuto
• CTorpe
• DLento

In Spanish verbal reasoning, which word is the closest synonym for "prolijo" in the sense of descriptive detail?

• ASucinto
• BBreve
• CDetallado
• DSuperficial

In Spanish verbal reasoning, which word is the direct antonym of "adverso"?

• AHostil
• BFavorable
• CContrario
• DDesfavorable

In Spanish verbal reasoning, which word is the direct antonym of "altruista"?

• AGeneroso
• BSolidario
• CEgoísta
• DCaritativo

In Spanish verbal reasoning, which word is the direct antonym of "intransigente"?

• AObstinado
• BFlexible
• CInflexible
• DSevero

Complete the verbal analogy: Libro is to Biblioteca as Pintura is to:

• AEscultura
• BMuseo
• CLienzo
• DCaballete

Complete the verbal analogy: Termómetro is to Temperatura as Barómetro is to:

• AHumedad
• BPresión atmosférica
• CVelocidad del viento
• DPrecipitación

Complete the verbal analogy: Escultor is to Cincel as Pintor is to:

• ACuadro
• BPincel
• CGalería
• DRetrato

Read the following statement: "El aprovechamiento de la energía solar y eólica en México ha demostrado ser una alternativa viable para reducir la dependencia de hidrocarburos y mitigar las emisiones de gases de efecto invernadero." What is the central idea of this sentence?

• AMexico should completely halt all oil extraction immediately.
• BRenewable solar and wind energies provide a viable path to reduce fossil fuel reliance an…
• CHydrocarbon fuels are the only dependable energy source available for industrial growth.
• DWind energy is significantly more cost-effective than solar energy across Mexican regions.

Read the excerpt: "La sobreexplotación de los mantos acuíferos en la Cuenca de México no solo provoca hundimientos graduales en la infraestructura urbana, sino que compromete la disponibilidad hídrica para las futuras generaciones, haciendo urgente la captación pluvial." What can be directly inferred from this text?

• AUrban subsidence is entirely caused by geological fault lines rather than human consumpti…
• BRainwater harvesting is presented as an essential strategy to alleviate aquifer depletion…
• CThe Valley of Mexico has unlimited subterranean water resources that require no regulatio…
• DBuilding foundations in Mexico City are immune to subterranean soil compaction.

Read the argument: "Fomentar la lectura formativa desde la educación secundaria fortalece el pensamiento crítico, enriquece el léxico y permite a los jóvenes cuestionar la veracidad de la información en medios digitales." What is the primary communicative purpose of this statement?

• ATo narrate a fictional chronicle about secondary school life.
• BTo persuade the reader of the cognitive and civic benefits of promoting reading among ado…
• CTo provide an instructional technical manual on operating digital platforms.
• DTo satirize adolescent communication habits on mobile phones.

What is the next number in the sequence 4, 10, 22, 46, 94, ...?

• A142
• B188
• C190
• D192

What number completes the alternating sequence: 4, 12, 8, 24, 16, 48, ...?

• A24
• B32
• C40
• D64

Find the next number in the sequence 3, 6, 11, 18, 27, ...

• A36
• B37
• C38
• D39

What is the next fraction in the sequence: 1/2, 2/5, 3/10, 4/17, ...?

• A5/24
• B5/25
• C5/26
• D6/27

On a standard six-sided die, opposite faces always sum to 7. Which number is located directly opposite face 4?

• A2
• B3
• C5
• D6

A solid rectangular wooden block measuring 4 cm by 3 cm by 2 cm is painted blue on all outer surfaces and then cut into 1 cm unit cubes. How many of the resulting unit cubes have paint on exactly two faces?

• A8
• B12
• C16
• D20

A flat cardboard net of a cube is arranged in a standard cross: a vertical column of four squares (labeled 1 at top, 2, 3, and 4 at bottom) with two lateral wings attached to square 2 (square 5 on the left, square 6 on the right). If square 3 is placed as the bottom base of the cube, which square forms the top face?

• ASquare 1
• BSquare 2
• CSquare 4
• DSquare 5

A square sheet of paper is folded in half from left to right, and then folded in half from top to bottom, forming a smaller square with four layers. A circular punch removes a piece from the folded corner that corresponds to the exact center of the original square sheet. When the paper is completely unfolded, how many holes appear in the sheet?

• A1
• B2
• C4
• D8

A student spends 1/3 of their monthly allowance on books and 2/5 of the remainder on school transport. If they have 180 Mexican pesos remaining, what was their total initial allowance?

• A360 pesos
• B450 pesos
• C540 pesos
• D600 pesos

A stationery store offers a 20% promotional discount on a backpack, plus an additional 10% discount on the discounted price for payment in cash. What is the single equivalent overall discount percentage?

• A25%
• B28%
• C30%
• D32%

Two cyclists depart simultaneously from the same point and travel in opposite directions along a straight level road. Cyclist A travels at a constant speed of 18 km/h, and Cyclist B travels at 22 km/h. How many hours will it take for them to be 120 km apart?

• A2.5 hours
• B3.0 hours
• C3.5 hours
• D4.0 hours

In a secondary school classroom, the ratio of boys to girls is 3 to 4. If 6 new girls join the class and the number of boys remains unchanged, the new ratio of boys to girls becomes 1 to 2. How many boys are in the class?

• A6
• B9
• C12
• D15

A water cistern can be filled by an inlet pipe in 4 hours, while an outlet drain can completely empty it in 6 hours. If both the inlet pipe and the drain are left open simultaneously starting with an empty cistern, how many hours will it take to fill the cistern completely?

• A8 hours
• B10 hours
• C12 hours
• D24 hours

In Spanish linguistic studies, what function of language (función del lenguaje) predominates in the sentence: "¡Cierra la puerta inmediatamente y toma asiento!"?

• AFunción referencial
• BFunción poética
• CFunción apelativa o conativa
• DFunción metalingüística

Which communicative function of language predominates in the following textbook statement: "El agua hierve a 100 °C a nivel del mar debido a la presión atmosférica normal"?

• AFunción emotiva
• BFunción referencial
• CFunción fática
• DFunción apelativa

Identify the direct object (objeto directo) in the Spanish sentence: "La profesora entregó los reconocimientos a los alumnos más destacados."

• ALa profesora
• Bentregó
• Clos reconocimientos
• Da los alumnos más destacados

In Spanish syntax, which of the following sentences features a compound predicate (predicado compuesto)?

• ALos estudiantes leyeron atentamente el examen.
• BCarlos y Sofía prepararon la maqueta de geografía.
• CEl atleta entrenó en la pista y descansó en las bancas.
• DLas campanas de la iglesia sonaron al amanecer.

In the Spanish complex sentence: "Aunque llovió intensamente durante la tarde, los brigadistas completaron la jornada de reforestación", what type of subordinate clause is introduced by the conjunction "Aunque"?

• AOración subordinada sustantiva
• BOración subordinada adverbial concesiva
• COración subordinada adverbial causal
• DOración subordinada adjetiva explicativa

Which of the following Spanish sentences correctly maintains grammatical agreement (concordancia gramatical) between subject and verb?

• ALos integrantes del equipo llegó tarde al entrenamiento.
• BHabían muchas personas esperando la apertura de la biblioteca.
• CLa mayoría de los votantes eligió la propuesta educativa.
• DHubieron varios accidentes viales en la autopista.

According to the general accentuation rules of Spanish orthography, which of the following words is correctly written with an orthographic accent (tilde)?

• AArbol
• BCántaro
• CExámen
• DImágen

Which Spanish sentence uses the diacritic accent (acento diacrítico) correctly?

• AYo se que tú estudias con dedicación.
• BEl libro es para mí hermano mayor.
• CSé paciente y escucha los consejos de tus maestros.
• DTe invito a tomar una taza de te verde mañana, si tu quieres.

Identify the Spanish sentence that correctly applies the semicolon (punto y coma) according to standard punctuation rules:

• ALos participantes llegaron temprano; sin embargo la reunión comenzó con retraso.
• BEl equipo de robótica investigó durante meses; no obstante, el certamen fue pospuesto por…
• CCompramos manzanas; peras, plátanos; y uvas en el mercado.
• DAyer fuimos al museo; porque teníamos boletos de cortesía.

Simplify the numerical expression following standard order of operations: 15 - 3 * (4 - 2) + 18 / 3.

• A12
• B15
• C18
• D24

What is the value of the fraction expression: (2/3 + 1/4) / (5/6 - 1/2)?

• A7/4
• B11/4
• C3/2
• D13/6

The Earth completes one rotation (360° of longitude) in about 24 hours, and standard time zones (husos horarios) are based on that rate. How many degrees of longitude correspond to a one-hour difference in standard time?

• A1°
• B15°
• C24°
• D30°

Expand the binomial square (special algebraic product): (3x - 4)².

• A9x² - 16
• B9x² - 12x + 16
• C9x² - 24x + 16
• D9x² + 24x + 16

Factor the algebraic difference of two squares: 25x² - 49y².

• A(5x - 7y)²
• B(5x - 7y)(5x + 7y)
• C(25x - 49y)(x + y)
• D(5x + 7y)²

A Mexican state has an absolute population of 1,800,000 inhabitants and a territory of 36,000 km². What is its relative population (population density)?

• A0.02 inhabitants/km²
• B5 inhabitants/km²
• C50 inhabitants/km²
• D500 inhabitants/km²

Solve for x in the linear equation: 3(x - 2) + 4 = 19.

• Ax = 5
• Bx = 7
• Cx = 8
• Dx = 9

Solve the linear equation with fractional terms: (2x + 5)/3 - (x - 1)/2 = 2.

• Ax = -2
• Bx = -1
• Cx = 1
• Dx = 3

What is the solution pair (x, y) to the system of linear equations: 2x + y = 11 3x - 2y = 6?

• Ax = 3, y = 5
• Bx = 4, y = 3
• Cx = 5, y = 1
• Dx = 2, y = 7

In a right triangle, the two perpendicular legs measure 6 cm and 8 cm. What is the length of the hypotenuse?

• A9 cm
• B10 cm
• C12 cm
• D14 cm

What is the area of a trapezoid whose major base is 14 cm, minor base is 8 cm, and height is 6 cm?

• A44 cm²
• B66 cm²
• C84 cm²
• D132 cm²

Two parallel lines are intersected by a transversal secant line. If one alternate interior angle measures 65°, what is the measure of the consecutive interior angle located on the same side of the transversal?

• A65°
• B115°
• C125°
• D135°