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Sample FIUNA Admission Practice Questions

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

1Factor the polynomial completely over the real numbers: P(x) = x³ - 3x² - 4x + 12.
A.(x - 3)(x² + 4)
B.(x + 3)(x - 2)(x + 2)
C.(x - 3)(x - 2)(x + 2)
D.(x - 1)(x - 3)(x + 4)
Explanation: Grouping terms gives x²(x - 3) - 4(x - 3) = (x² - 4)(x - 3). Applying the difference of two squares to (x² - 4) produces (x - 2)(x + 2)(x - 3).
2Simplify the complex rational expression for all x such that x ≠ 2 and x ≠ -2: [ (1 / (x + 2)) - (1 / (x - 2)) ] / [ 4 / (x² - 4) ].
A.1
B.-1
C.-4 / (x - 2)
D.2x / (x² - 4)
Explanation: Finding a common denominator in the numerator yields [(x - 2) - (x + 2)] / (x² - 4) = -4 / (x² - 4). Dividing this by 4 / (x² - 4) is equivalent to multiplying by (x² - 4) / 4, which simplifies directly to -4 / 4 = -1.
3Rationalize the denominator of the fraction and express it in simplest radical form: 6 / (√7 - 1).
A.√7 + 1
B.√7 - 1
C.(√7 + 1) / 6
D.6√7 + 6
Explanation: Multiplying the numerator and denominator by the conjugate (√7 + 1) gives 6(√7 + 1) / [(√7)² - 1²] = 6(√7 + 1) / (7 - 1) = 6(√7 + 1) / 6 = √7 + 1.
4Determine the sum of all valid real solutions to the equation: |2x - 5| = 3x - 10.
A.3
B.5
C.8
D.No real solution
Explanation: Solving 2x - 5 = 3x - 10 gives x = 5. Checking x = 5 yields |5| = 5, which is valid. Solving -(2x - 5) = 3x - 10 gives 5x = 15, or x = 3; however, checking x = 3 yields |1| = -1, which is extraneous because absolute values cannot equal negative numbers. Thus, x = 5 is the sole solution.
5Let r and s be the roots of the quadratic equation 2x² - 6x + 1 = 0. Find the numerical value of (1 / r) + (1 / s).
A.3
B.1/3
C.6
D.1/6
Explanation: By Vieta's formulas, the sum of roots is r + s = -(-6)/2 = 3, and the product of roots is rs = 1/2. Combining fractions gives (1 / r) + (1 / s) = (r + s) / (rs) = 3 / (1/2) = 6.
6The three roots of the cubic equation x³ - 9x² + 23x - 15 = 0 form an arithmetic progression. What is the value of the largest root?
A.5
B.3
C.7
D.1
Explanation: Let the roots in arithmetic progression be a - d, a, and a + d. By Vieta's formulas, their sum is 3a = 9, which implies a = 3. The product of roots is (3 - d)(3)(3 + d) = 15, leading to 9 - d² = 5, or d² = 4 (d = 2). Thus, the roots are 1, 3, and 5, with the largest root being 5.
7When the polynomial P(x) = 3x⁴ - 2x³ + x - 5 is divided by x - 1 using synthetic division, what is the coefficient of x² in the resulting quotient?
A.3
B.-2
C.0
D.1
Explanation: Writing the coefficients of P(x) including the missing degree-two term gives [3, -2, 0, 1, -5]. Performing synthetic division with 1: bring down 3; 3(1) + (-2) = 1; 1(1) + 0 = 1; 1(1) + 1 = 2. The quotient polynomial is 3x³ + 1x² + 1x + 2, meaning the coefficient of x² is 1.
8For f(x) = (x^2 + 1)/(x - 1), what is f'(2)?
A.4
B.-1
C.1
D.9
Explanation: The quotient rule gives f'(x) = [2x(x - 1) - (x^2 + 1)]/(x - 1)^2. At x = 2 this is (4 - 5)/1 = -1. The subtraction applies to the whole numerator x^2 + 1.
9Determine the value of z in the system of linear equations: x + y + z = 6 2x - y + z = 3 x + 2y - z = 2
A.3
B.1
C.2
D.4
Explanation: Adding the first and third equations eliminates z, giving 2x + 3y = 8. Adding the first and second equations gives 3x + 2z = 9. From the first equation, z = 6 - x - y; substituting into the second equation gives x - 2y = -3. Solving the 2x2 system {2x + 3y = 8, x - 2y = -3} yields y = 2 and x = 1. Finally, z = 6 - 1 - 2 = 3.
10Find the product xy for non-zero real numbers satisfying the reciprocal system: (2 / x) + (3 / y) = 8 and (5 / x) - (1 / y) = 3.
A.2
B.1
C.1/4
D.1/2
Explanation: Let u = 1/x and v = 1/y. The linear system is 2u + 3v = 8 and 5u - v = 3. Multiplying the second equation by 3 yields 15u - 3v = 9. Adding the equations produces 17u = 17, so u = 1, giving x = 1. Substituting u = 1 into 2(1) + 3v = 8 gives 3v = 6, so v = 2, giving y = 1/2. Thus, xy = 1 · (1/2) = 1/2.

About the FIUNA Admission Exam

Independent practice for FIUNA A-CPI mathematics and published CPI algebra, geometry/vector, and physics topics. A-CPI is a standalone Spanish MCQ selection examination without a prior FIUNA course. The subsequent CPI is compulsory and assesses written worked solutions. This bank is an English-language, four-option MCQ study adaptation, not an official translation or format simulation, and does not substitute for writing complete solutions, compulsory attendance, or course assessment.

Exam sponsor: Universidad Nacional de Asunción — Facultad de Ingeniería. 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

Set for each examination; fixed duration not confirmed

Passing Score

A-CPI: 60% aggregate and ranking, subject to regulated vacancy exceptions. CPI: 30% minimum in each subject, 60% mean, and ranking.

Exam / Certification Fees

2026 A-CPI: Gs. 770,000; 2027 and subsequent CPI fee amounts not confirmed; eligible Arancel Cero exemption for two admission attempts

Exam sponsor website

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

Official sources

  • FIUNA admission and Convocatoria 2027 · Source checked 2026-10-09A-CPI has no prior FIUNA course. 2027 papers: 23 February and 2 March; CPI: 3 March–11 June; final examinations from 14 June.
  • Admission regulation — CD 1604/2025/005 · Source checked 2026-10-09A-CPI selection; CPI attendance, worked-response assessment, 10%/20%/70% assessment weights, and admission thresholds.
  • CPI subject programmes — CD 1604/2025/008 · Source checked 2026-10-09Álgebra y Pre-Cálculo, Geometría y Vectores, Física. Physics focuses on kinematics, statics and dynamics; Chemistry is not an examined subject.
  • A-CPI mathematics programme · Source checked 2026-10-09Faculty-linked arithmetic, algebra, plane/solid geometry and trigonometry programme.
  • 2026 A-CPI cycle · Source checked 2026-10-09The official 2026 registration notice gives an A-CPI fee of Gs. 770,000 for applicants without an approved exemption.

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.

One third of CPI subject mean

Álgebra y Pre-Cálculo

Polynomials, equations, systems, inequalities, logarithms, functions, binomial expansion, limits and derivatives; A-CPI mathematics is a separate first stage.

One third of CPI subject mean

Geometría y Vectores

Plane/solid geometry, trigonometry, vectors, lines, and conics.

One third of CPI subject mean

Física

Units, vectors, kinematics, relative motion, statics, Newton's laws, friction, and connected bodies.

Preparing for the FIUNA Admission Exam

What You Need to Know

  • Passing score: A-CPI: 60% aggregate and ranking, subject to regulated vacancy exceptions. CPI: 30% minimum in each subject, 60% mean, and ranking.
  • Assessment: Question count not published by the exam provider
  • Time limit: Set for each examination; fixed duration not confirmed
  • Exam / certification fees: 2026 A-CPI: Gs. 770,000; 2027 and subsequent CPI fee amounts not confirmed; eligible Arancel Cero exemption for two admission attempts 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

FIUNA Admission: Suggested Study Strategy

1Write a complete derivation before choosing an answer.
2Draw force and vector diagrams with a stated sign convention.
3Check excluded values and extraneous solutions.
4Use official exercise guides for worked-response practice beyond this MCQ bank.

Frequently Asked Questions

What does passing A-CPI provide?

It provides access to CPI, not final admission to an engineering degree. A-CPI evaluates arithmetic/algebra and geometry/trigonometry in two papers. The normal selection threshold is 60% aggregate with ranking; the regulation permits progressive vacancy-filling thresholds down to 50%. Its score does not carry into CPI.

What must CPI students complete?

CPI requires 80% attendance in each subject. Two partial examinations carry 10% and 20%, and the final carries 70%. Assessment is by written worked responses with credit for the solution process. Final admission requires subject minimums, the overall mean, and a place in the ranking. No separate oral or laboratory entrance examination was identified.

Is Chemistry part of this admission scope?

The published CPI subjects are Álgebra y Pre-Cálculo, Geometría y Vectores, and Física. Chemistry is not listed. Use the current applicant guide and permitted-calculator list for each paper.