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Free Practice Questions for UMSA Ingeniería PSA

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Key Facts: UMSA Ingeniería PSA Exam

PSA + CPU

2026 Admission Routes

UMSA current admission listing

3 subjects

Math, Physics, Chemistry

Official UMSA Ingeniería admission material

Not published

2026 Count and Duration

Reviewed official 2026 listing

UMSA's 2026 university listing confirms PSA and CPU routes for the Faculty of Engineering. Official engineering material identifies Mathematics, Physics, and Chemistry, but the reviewed 2026 listing does not publish weights, fee, pass mark, item count, or duration.

Sample UMSA Ingeniería PSA Practice Questions

Try these sample questions to review concepts for the UMSA Ingeniería PSA exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 98+ question experience with AI tutoring.

1Simplify the algebraic fraction by factoring: (x^3 - 8) / (x^2 - 4) for all x != ±2.
A.(x^2 + 2x + 4) / (x + 2)
B.(x^2 - 2x + 4) / (x + 2)
C.(x^2 + 4) / (x + 2)
D.(x - 2) / (x + 2)
Explanation: Factoring the numerator as a difference of cubes: x^3 - 8 = (x - 2)(x^2 + 2x + 4). Factoring the denominator as a difference of squares: x^2 - 4 = (x - 2)(x + 2). Canceling (x - 2) gives (x^2 + 2x + 4) / (x + 2).
2Rationalize the denominator of the expression: 6 / (sqrt(5) - sqrt(2)).
A.2(sqrt(5) - sqrt(2))
B.2(sqrt(5) + sqrt(2))
C.6(sqrt(5) + sqrt(2)) / 7
D.sqrt(5) + sqrt(2)
Explanation: Multiply numerator and denominator by the conjugate (sqrt(5) + sqrt(2)): 6(sqrt(5) + sqrt(2)) / [(sqrt(5))^2 - (sqrt(2))^2] = 6(sqrt(5) + sqrt(2)) / (5 - 2) = 6(sqrt(5) + sqrt(2)) / 3 = 2(sqrt(5) + sqrt(2)).
3What is the remainder when the polynomial P(x) = 2x^3 - 5x^2 + 4x - 7 is divided by (x - 2)?
A.3
B.-5
C.-3
D.1
Explanation: By the Remainder Theorem, the remainder of P(x) divided by (x - 2) is P(2). Evaluating: P(2) = 2(2)^3 - 5(2)^2 + 4(2) - 7 = 2(8) - 5(4) + 8 - 7 = 16 - 20 + 8 - 7 = -3.
4Find the discriminant and nature of the roots for the quadratic equation 3x^2 - 4x + 2 = 0.
A.Δ = 40; two distinct real roots
B.Δ = 0; one repeated real root
C.Δ = -4; two distinct real roots
D.Δ = -8; two complex conjugate roots
Explanation: The discriminant is Δ = b^2 - 4ac = (-4)^2 - 4(3)(2) = 16 - 24 = -8. Since Δ < 0, the equation has two distinct complex conjugate roots (no real solutions).
5Solve the absolute value inequality: |2x - 3| < 7.
A.-2 < x < 5
B.x < -2 or x > 5
C.-5 < x < 5
D.x < 5
Explanation: |2x - 3| < 7 is equivalent to -7 < 2x - 3 < 7. Adding 3 across the compound inequality gives -4 < 2x < 10. Dividing by 2 yields -2 < x < 5.
6What is the distance from the point P(2, 3) to the line given by the equation 4x - 3y + 11 = 0?
A.3
B.2
C.4
D.5
Explanation: Using the point-to-line distance formula d = |Ax0 + By0 + C| / sqrt(A^2 + B^2): d = |4(2) - 3(3) + 11| / sqrt(4^2 + (-3)^2) = |8 - 9 + 11| / sqrt(16 + 9) = |10| / sqrt(25) = 10 / 5 = 2.
7Find the sum of all solutions to the equation x + 6/x = 5.
A.6
B.1
C.5
D.-5
Explanation: Multiplying both sides by x (x != 0) gives x^2 + 6 = 5x -> x^2 - 5x + 6 = 0. Factoring: (x - 2)(x - 3) = 0, so solutions are x = 2 and x = 3. Their sum is 2 + 3 = 5 (or directly by Vieta's formulas, sum = -b/a = -(-5)/1 = 5).
8What is the 5th term in the binomial expansion of (x + 2y)^6?
A.160 x^2 y^4
B.60 x^4 y^2
C.240 x^3 y^3
D.240 x^2 y^4
Explanation: The (k+1)-th term in (a + b)^n is T_(k+1) = C(n, k) * a^(n-k) * b^k. For the 5th term (k = 4, n = 6): T_5 = C(6, 4) * x^(6-4) * (2y)^4 = 15 * x^2 * (16 y^4) = 240 x^2 y^4.
9Find all solutions to the trigonometric equation sin(2x) - cos(x) = 0 in the interval [0, 2π).
A.x = π/6, 5π/6
B.x = π/6, π/2, 5π/6, 3π/2
C.x = π/3, 2π/3, 4π/3, 5π/3
D.x = 0, π/2, π, 3π/2
Explanation: Use the double angle identity sin(2x) = 2 sin(x) cos(x). The equation becomes 2 sin(x) cos(x) - cos(x) = 0 -> cos(x)[2 sin(x) - 1] = 0. Case 1: cos(x) = 0 -> x = π/2, 3π/2. Case 2: sin(x) = 1/2 -> x = π/6, 5π/6. The complete set in [0, 2π) is {π/6, π/2, 5π/6, 3π/2}.
10In a triangle ABC, side a = 7, side b = 5, and side c = 8. What is the cosine of angle C (cos C)?
A.2/7
B.1/5
C.1/7
D.3/7
Explanation: By the Law of Cosines, c^2 = a^2 + b^2 - 2ab cos(C) -> 8^2 = 7^2 + 5^2 - 2(7)(5) cos(C) -> 64 = 49 + 25 - 70 cos(C) -> 64 = 74 - 70 cos(C) -> 70 cos(C) = 10 -> cos(C) = 10/70 = 1/7.

About the UMSA Ingeniería PSA Exam

The UMSA Facultad de Ingeniería continues to offer PSA and Curso Prefacultativo admission in 2026. This independent bank is an English-language MCQ study adaptation of the officially identified Mathematics, Physics, and Chemistry foundation. It is not an official translation, does not simulate an unpublished 2026 item format, and does not replace Spanish source material or calculation practice.

Exam sponsor: Facultad de Ingeniería — Universidad Mayor de San Andrés. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Faculty knowledge examination. Official engineering admission material identifies Matemática, Física, and Química as separate tested subjects; the reviewed 2026 listing does not state item types or any oral, practical, assignment, or case-study component.

Time Limit

Not published in the reviewed official 2026 listing

Passing Score

Not published in the reviewed official 2026 listing

Exam / Certification Fees

Not published in the reviewed official 2026 listing

Exam sponsor website

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

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 subject; weight not published

Matemática

Algebra, functions, trigonometry, and analytic geometry

Official subject; weight not published

Física

Mechanics, energy, momentum, equilibrium, and fluids

Official subject; weight not published

Química

Atomic structure, bonding, nomenclature, stoichiometry, gases, and solutions

Preparing for the UMSA Ingeniería PSA Exam

What You Need to Know

  • Passing score: Not published in the reviewed official 2026 listing
  • Assessment: Faculty knowledge examination. Official engineering admission material identifies Matemática, Física, and Química as separate tested subjects; the reviewed 2026 listing does not state item types or any oral, practical, assignment, or case-study component.
  • Time limit: Not published in the reviewed official 2026 listing
  • Exam / certification fees: Not published in the reviewed official 2026 listing Official sources

Using Our Practice Resources

  • Work through all 98 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

UMSA Ingeniería PSA: Suggested Study Strategy

1Build algebra and trigonometry fluency before timed multi-step problems.
2Draw free-body diagrams and track units in every physics calculation.
3Balance equations before completing chemistry quantity calculations.
4Check the current faculty notice for logistics that are not published on the central listing.

Frequently Asked Questions

Is the UMSA Faculty of Engineering PSA current in 2026?

Yes. UMSA's current admission listing identifies the Faculty of Engineering as offering PSA and CPU admission.

Which subjects should applicants review?

Official Faculty of Engineering admission material identifies Mathematics, Physics, and Chemistry. No official percentage weights were found in the reviewed 2026 listing.

Does this practice bank reproduce the official exam?

No. The bank is an English-language MCQ study adaptation. The current official listing does not publish the 2026 item type, count, duration, or formal language policy.