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Sample FP-UNA Admission Practice Questions

Try these sample questions to review concepts for the FP-UNA Admission exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 53+ question experience with AI tutoring.

1What are the greatest common divisor (GCD) and least common multiple (LCM) of the numbers 72 and 108?
A.GCD = 18 and LCM = 432
B.GCD = 36 and LCM = 432
C.GCD = 12 and LCM = 216
D.GCD = 36 and LCM = 216
Explanation: Prime factorizing both numbers gives 72 = 2^3 * 3^2 and 108 = 2^2 * 3^3. The GCD takes the lowest powers of common prime factors: 2^2 * 3^2 = 4 * 9 = 36. The LCM takes the highest powers of all prime factors: 2^3 * 3^3 = 8 * 27 = 216.
2Which single decimal digit d makes the five-digit integer 47d38 divisible by 11?
A.7
B.8
C.9
D.5
Explanation: By the divisibility criterion for 11, the alternating sum of digits starting from the units position must be divisible by 11. Here, (8 + d + 4) - (3 + 7) = (12 + d) - 10 = d + 2. For d + 2 to be a multiple of 11 with d between 0 and 9, d must equal 9 (9 + 2 = 11), giving the number 47938.
3If 12 technicians can inspect 180 solar panels in 6 hours, how many hours will 8 technicians take to inspect 240 identical solar panels at the same working rate?
A.10 hours
B.12 hours
C.14 hours
D.16 hours
Explanation: The output rate per technician is 180 panels / (12 technicians * 6 hours) = 2.5 panels per technician-hour. With 8 technicians, the inspection rate is 8 * 2.5 = 20 panels per hour. To inspect 240 panels, they will need 240 / 20 = 12 hours.
4A laboratory server is priced at Gs. 5,000,000. It receives a seasonal commercial discount of 20%, followed by an institutional academic discount of 10% applied to the discounted price. What is the final purchase price?
A.Gs. 3,500,000
B.Gs. 3,600,000
C.Gs. 3,750,000
D.Gs. 3,800,000
Explanation: Applying successive discounts requires multiplying by the complementary percentages. After the 20% discount, the price is Gs. 5,000,000 * 0.80 = Gs. 4,000,000. Applying the subsequent 10% academic discount yields Gs. 4,000,000 * 0.90 = Gs. 3,600,000.
5What is the irreducible vulgar fraction representation of the recurring decimal 0.41666... (where only digit 6 repeats)?
A.7/18
B.25/60
C.13/30
D.5/12
Explanation: Let x = 0.41666... Multiplying by 100 gives 100x = 41.666..., and multiplying by 1000 gives 1000x = 416.666... Subtracting these gives 900x = 375, so x = 375 / 900. Dividing both numerator and denominator by 75 simplifies the fraction to 5/12.
6Simplify and rationalize the denominator of the algebraic fraction: 14 / (3 - sqrt(2)).
A.6 + 2*sqrt(2)
B.6 - 2*sqrt(2)
C.(14 + 2*sqrt(2)) / 7
D.3 + sqrt(2)
Explanation: To rationalize the denominator, multiply numerator and denominator by the conjugate (3 + sqrt(2)). The denominator becomes (3 - sqrt(2))(3 + sqrt(2)) = 3^2 - (sqrt(2))^2 = 9 - 2 = 7. The numerator becomes 14(3 + sqrt(2)). Dividing by 7 yields 2(3 + sqrt(2)) = 6 + 2*sqrt(2).
7Which of the following represents the complete algebraic factorization of 8x^3 - 27y^3?
A.(2x - 3y)(4x^2 - 6xy + 9y^2)
B.(2x - 3y)(4x^2 + 6xy + 9y^2)
C.(2x - 3y)(2x^2 + 6xy + 3y^2)
D.(2x + 3y)(4x^2 - 6xy + 9y^2)
Explanation: The formula for the difference of two cubes is a^3 - b^3 = (a - b)(a^2 + ab + b^2). Setting a = 2x and b = 3y gives (2x - 3y)((2x)^2 + (2x)(3y) + (3y)^2) = (2x - 3y)(4x^2 + 6xy + 9y^2).
8Factor the quadratic trinomial completely over the integers: 6x^2 + 11x - 10.
A.(3x + 2)(2x - 5)
B.(6x - 5)(x + 2)
C.(2x - 1)(3x + 10)
D.(3x - 2)(2x + 5)
Explanation: Using the ac method, find two factors of a*c = 6 * (-10) = -60 whose sum is b = 11. These numbers are +15 and -4. Splitting the middle term gives 6x^2 + 15x - 4x - 10 = 3x(2x + 5) - 2(2x + 5) = (3x - 2)(2x + 5).
9For what values of the real parameter k does the quadratic equation x^2 + 2(k - 1)x + (k + 5) = 0 have exactly one real root (a double root)?
A.k = 2 or k = -3
B.k = 4 or k = -1
C.k = 5 or k = -2
D.k = 1 or k = -4
Explanation: A quadratic equation has a double real root if and only if its discriminant equals zero: Delta = b^2 - 4ac = [2(k - 1)]^2 - 4(1)(k + 5) = 0. Expanding gives 4(k^2 - 2k + 1) - 4(k + 5) = 0. Dividing by 4 yields k^2 - 2k + 1 - k - 5 = 0, which simplifies to k^2 - 3k - 4 = 0. Factoring gives (k - 4)(k + 1) = 0, so k = 4 or k = -1.
10Solve the system of linear equations for x and y: 3x - 2y = 13 5x + 4y = 7
A.x = -3, y = 2
B.x = 1, y = -5
C.x = 4, y = -1/2
D.x = 3, y = -2
Explanation: Multiply the first equation by 2 to match the y-coefficients: 6x - 4y = 26. Adding this to the second equation (5x + 4y = 7) eliminates y: 11x = 33, which gives x = 3. Substituting x = 3 into 3(3) - 2y = 13 gives 9 - 2y = 13, so -2y = 4 and y = -2.

About the FP-UNA Admission Exam

Independent practice for selected FP-UNA admission topics, including A/B mathematics and physics and Castellano relevant to C. Official written examinations are in Spanish and use five-option MCQs. This is an English-language, four-option MCQ study adaptation, not an official translation or format simulation. Spanish language material is preserved. It is partial practice: it does not cover the full Orientation C history/geography programme or replace preparation for every orientation-specific paper.

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

Assessment

Question count varies by module

Time Limit

ECB: 150 minutes. Direct-admission paper durations not confirmed.

Passing Score

ECB: ranking for CPA places. Direct admission: at least 60% aggregate and ranking for career vacancies.

Exam / Certification Fees

ECB Gs. 400,000; direct admission A/B Gs. 950,000, C Gs. 700,000; 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.

Official percentage not confirmed

Aritmética y Álgebra

Arithmetic, fractions, factoring, equations, inequalities, logarithms and exponentials; practice allocation is not an official weighting.

Official percentage not confirmed

Geometry and Calculus

Selected geometry, trigonometry, analytic geometry, limits and derivatives from A/B programmes.

Official percentage not confirmed

Física

Selected A/B mechanics, electricity, optics and heat; individual orientation programmes differ.

Official percentage not confirmed

Castellano

Selected C language and reading topics. C also requires mathematics and Paraguay history/geography, which this bank does not fully cover.

Preparing for the FP-UNA Admission Exam

What You Need to Know

  • Passing score: ECB: ranking for CPA places. Direct admission: at least 60% aggregate and ranking for career vacancies.
  • Assessment: Question count varies by module
  • Time limit: ECB: 150 minutes. Direct-admission paper durations not confirmed.
  • Exam / certification fees: ECB Gs. 400,000; direct admission A/B Gs. 950,000, C Gs. 700,000; eligible Arancel Cero exemption Official sources

Using Our Practice Resources

  • Work through all 53 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

FP-UNA Admission: Suggested Study Strategy

1Choose the official programme for your orientation.
2Study the omitted C history/geography material separately when applicable.
3Show algebraic domains and interval endpoints explicitly.
4Use ECB timing only for ECB preparation.

Frequently Asked Questions

Is ECB required for direct admission?

No. ECB selects applicants for CPA. The faculty separately permits direct-admission candidates who have not taken ECB or CPA to sit the admission examinations. No mandatory preparatory coursework, oral, practical, or case-study assessment was identified for that direct route.

Which subjects differ by orientation?

A/B admission uses Physics, Arithmetic and Algebra, Geometry and Trigonometry, and Analytic Geometry and Calculus. C uses Mathematics I and II, Paraguay History and Geography, and Castellano. ECB evaluates a smaller orientation-specific subset.

Is 60% required in every paper?

The reviewed regulation specifies 60% of the aggregate admission points, followed by ranking for vacancies. It does not state a 60% minimum in each separate paper.