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Sample FACEN Admission Practice Questions

Try these sample questions to review concepts for the FACEN Admission exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 59+ question experience with AI tutoring.

1What is the simplified value of the arithmetic expression (2^4 * 8^2) / 4^3?
A.16
B.8
C.32
D.64
Explanation: Expressing each term with base 2 yields 8^2 = (2^3)^2 = 2^6 and 4^3 = (2^2)^3 = 2^6. The numerator becomes 2^4 * 2^6 = 2^10, and dividing by 2^6 gives 2^(10 - 6) = 2^4 = 16.
2Which polynomial represents the simplified expansion of (3x - 4)(2x + 5) - (6x^2 - 7)?
A.7x - 27
B.7x - 13
C.13x - 13
D.7x + 13
Explanation: Expanding the product produces 6x^2 + 15x - 8x - 20 = 6x^2 + 7x - 20. Subtracting (6x^2 - 7) cancels the quadratic terms and results in 7x - 20 - (-7) = 7x - 13.
3What is the complete factorization over the integers of the binomial 4x^2 - 25y^2?
A.(2x - 5y)^2
B.(4x - 25y)(x + y)
C.(2x - 5y)(2x + 5y)
D.(2x + 5y)^2
Explanation: The expression is a difference of two perfect squares, a^2 - b^2, where a = 2x and b = 5y. Applying the identity a^2 - b^2 = (a - b)(a + b) yields (2x - 5y)(2x + 5y).
4Which ordered pair (x, y) satisfies the simultaneous system of linear equations: 2x + 3y = 13 and 4x - y = 5?
A.x = 1, y = 4
B.x = 3, y = 2
C.x = 2, y = 3
D.x = 4, y = 1
Explanation: From the second equation, express y as y = 4x - 5. Substituting this into the first equation gives 2x + 3(4x - 5) = 13, which expands to 14x - 15 = 13, leading to 14x = 28 and x = 2. Then y = 4(2) - 5 = 3.
5For what real value of k does the quadratic equation x^2 - 6x + k = 0 possess exactly one real root (a double root)?
A.k = 9
B.k = 6
C.k = 36
D.k = -9
Explanation: A quadratic equation has exactly one real double root when its discriminant Delta = b^2 - 4ac equals zero. Here, Delta = (-6)^2 - 4(1)(k) = 36 - 4k = 0, which solves to k = 9.
6Given that x = 2 is a root of P(x) = x^3 - 3x^2 - 10x + 24, what is the complete factorization of P(x) into linear factors?
A.(x - 2)(x + 4)(x - 3)
B.(x - 2)(x - 4)(x + 3)
C.(x + 2)(x - 4)(x - 3)
D.(x - 2)(x - 6)(x + 2)
Explanation: Dividing x^3 - 3x^2 - 10x + 24 by (x - 2) using synthetic division gives the quotient polynomial x^2 - x - 12. Factoring this quadratic expression yields (x - 4)(x + 3), producing the complete factorization (x - 2)(x - 4)(x + 3).
7What is the simplified form of the rational expression (1 / (x - 2)) - (4 / (x^2 - 4)) for all valid x?
A.1 / (x - 2)
B.x / (x + 2)
C.1 / (x + 2)
D.(x - 6) / (x^2 - 4)
Explanation: Factoring the denominator of the second term gives x^2 - 4 = (x - 2)(x + 2). Bringing terms to the common denominator yields ((x + 2) - 4) / ((x - 2)(x + 2)) = (x - 2) / ((x - 2)(x + 2)). Canceling (x - 2) leaves 1 / (x + 2).
8What is the real solution set of the radical equation sqrt(2x + 7) = x + 2?
A.x = 1 and x = -3
B.x = 1 only
C.x = -3 only
D.No real solution
Explanation: Squaring both sides yields 2x + 7 = (x + 2)^2 = x^2 + 4x + 4, which rearranges to x^2 + 2x - 3 = 0. Factoring gives (x + 3)(x - 1) = 0. Testing x = 1 gives sqrt(9) = 3 = 1 + 2 (valid). Testing x = -3 gives sqrt(1) = 1 != -3 + 2 = -1 (extraneous). Therefore, only x = 1 is a valid solution.
9In a right triangle with right angle at vertex C, the side opposite to angle A has length 5 and the hypotenuse has length 13. What is the value of tan(A)?
A.5 / 13
B.12 / 13
C.5 / 12
D.12 / 5
Explanation: By the Pythagorean theorem, the adjacent leg b satisfies b^2 = 13^2 - 5^2 = 169 - 25 = 144, so b = 12. The tangent ratio is defined as opposite / adjacent, which gives tan(A) = 5 / 12.
10Which simplified value is identically equal to (1 - sin^2(theta)) * (1 + tan^2(theta)) for all angles theta where tan(theta) is defined?
A.sin^2(theta)
B.cos^2(theta)
C.1
D.tan^2(theta)
Explanation: Using the fundamental Pythagorean identity, 1 - sin^2(theta) = cos^2(theta). Furthermore, 1 + tan^2(theta) = sec^2(theta) = 1 / cos^2(theta). Multiplying these expressions gives cos^2(theta) * (1 / cos^2(theta)) = 1.

About the FACEN Admission Exam

Independent practice for FACEN admission topics in Matemática, Física, Química, and Comunicación. Official written assessment is in Spanish. This is an English-language, four-option MCQ study adaptation, not an official translation or format simulation. Spanish language tasks retain Spanish passages and expressions. It does not replace practical work in subsequent leveling courses.

Exam sponsor: Universidad Nacional de Asunción — Facultad de Ciencias Exactas y Naturales. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Question count not published by the exam provider

Time Limit

120 minutes

Passing Score

Ranking for career places; subject scores below 60% require post-entry leveling

Exam / Certification Fees

Current fee amount not confirmed; eligible Arancel Cero exemption

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

25% of official marks

Matemática

Arithmetic, proportions, algebra, equations, radicals, geometry, and trigonometry.

25% of official marks

Física

Units, vectors, rectilinear motion, Newton's laws, work, energy, fluids, and heat.

25% of official marks

Química

Matter, atomic structure, periodic properties, bonds, formulas, nomenclature, and organic functional groups.

25% of official marks

Comunicación

Spanish comprehension, vocabulary, word formation, spelling, grammar, and syntax.

Preparing for the FACEN Admission Exam

What You Need to Know

  • Passing score: Ranking for career places; subject scores below 60% require post-entry leveling
  • Assessment: Question count not published by the exam provider
  • Time limit: 120 minutes
  • Exam / certification fees: Current fee amount not confirmed; eligible Arancel Cero exemption Official sources

Using Our Practice Resources

  • Work through all 59 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

FACEN Admission: Suggested Study Strategy

1Check units before physical calculations.
2Reject extraneous roots after squaring equations.
3Distinguish empirical formulas from molecular formulas.
4Read Spanish passages before their English explanations.

Frequently Asked Questions

Is 60% an admission pass mark?

Places are awarded by score ranking and career vacancies. Entrants below 60% in a subject must take its leveling course, including partial assessments, practical assignments, and a final. These are subsequent requirements, not a prerequisite course for sitting the admission examination.

Are there other entrance assessment components?

The reviewed entrance regulation specifies the written evaluation and does not identify a separate oral, laboratory, or case-study entrance assessment.

Was a 2026 cycle published?

First-period registration ran from 7 January to 11 February; second-period registration ran from 8 June to 8 July, with the second examination on 11 July. Consult FACEN for the next cycle and current fee.