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Exam Review

Key Facts: UTO Facultad Técnica Ingreso Exam

At least 51/100

UTO Regulatory Floor

UTO Admission Regulation

Bs 300

Semester 2/2026 Fee

UTO FT Convocatoria 2/2026

4 Technical Subjects

Álgebra/Trig/Física/Química

UTO FT Syllabus Guidelines

Admission to applied engineering and technical programmes at UTO Facultad Técnica (Oruro) includes the in-person Examen de Ingreso Directo in Álgebra, Trigonometría, Física, and Química. The Semester 2/2026 fee is Bs 300. UTO regulations set a 51/100 floor for faculty passing rules, but the current faculty cutoff is unpublished.

Sample UTO Facultad Técnica Ingreso Practice Questions

Try these sample questions to review concepts for the UTO Facultad Técnica Ingreso exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 99+ question experience with AI tutoring.

1What is the complete factorization of 8x^3 + 27?
A.(2x + 3)(4x^2 - 6x + 9)
B.(2x + 3)(4x^2 + 6x + 9)
C.(2x + 3)^3
D.(2x - 3)(4x^2 + 6x + 9)
Explanation: Applying the sum of cubes formula a^3 + b^3 = (a + b)(a^2 - ab + b^2) with a = 2x and b = 3 yields (2x + 3)((2x)^2 - (2x)(3) + 3^2) = (2x + 3)(4x^2 - 6x + 9).
2Simplify the algebraic fraction: (x^2 - 5x + 6) / (x^2 - 4) for all x != +-2.
A.(x - 3) / (x + 2)
B.(x - 3) / (x - 2)
C.(x + 3) / (x + 2)
D.(x - 2) / (x + 2)
Explanation: Factoring the numerator gives (x - 2)(x - 3). Factoring the denominator as a difference of squares gives (x - 2)(x + 2). Canceling the common factor (x - 2) leaves (x - 3) / (x + 2).
3What is the quotient and remainder when 2x^3 - 3x^2 + 4x - 5 is divided by (x - 2)?
A.Quotient: 2x^2 + x + 6; Remainder: 7
B.Quotient: 2x^2 - 7x + 18; Remainder: -41
C.Quotient: 2x^2 + x + 6; Remainder: -7
D.Quotient: 2x^2 - x + 2; Remainder: -1
Explanation: Using synthetic division with c = 2: Coefficients: [2, -3, 4, -5] Bring down 2. Multiply 2*2 = 4; add -3 + 4 = 1. Multiply 1*2 = 2; add 4 + 2 = 6. Multiply 6*2 = 12; add -5 + 12 = 7. Quotient: 2x^2 + x + 6; Remainder: 7.
4Solve the quadratic equation: 2x^2 - 7x + 3 = 0.
A.x = 3 and x = 1/2
B.x = -3 and x = -1/2
C.x = 3 and x = 2
D.x = 1 and x = 3/2
Explanation: Factoring 2x^2 - 7x + 3 = 0 gives (2x - 1)(x - 3) = 0. Setting each factor to zero yields 2x - 1 = 0 => x = 1/2, and x - 3 = 0 => x = 3.
5For what values of m does the quadratic equation x^2 + 2(m - 1)x + (m + 5) = 0 have real and equal roots (discriminant = 0)?
A.m = 4 and m = -1
B.m = -4 and m = 1
C.m = 5 and m = -1
D.m = 2 and m = -2
Explanation: Discriminant Delta = [2(m - 1)]^2 - 4(1)(m + 5) = 4(m^2 - 2m + 1) - 4(m + 5) = 4(m^2 - 2m + 1 - m - 5) = 4(m^2 - 3m - 4). Setting Delta = 0 gives m^2 - 3m - 4 = 0 => (m - 4)(m + 1) = 0 => m = 4 or m = -1.
6Solve the system of equations: 3x + 4y = 10 2x - 3y = 1
A.x = 2, y = 1
B.x = 1, y = 2
C.x = 3, y = 0
D.x = 4, y = -1
Explanation: Multiply the first equation by 3: 9x + 12y = 30. Multiply the second equation by 4: 8x - 12y = 4. Adding them gives 17x = 34 => x = 2. Substitute into the first equation: 3(2) + 4y = 10 => 6 + 4y = 10 => 4y = 4 => y = 1.
7What is the solution set of the quadratic inequality x^2 - 4x - 12 >= 0?
A.(-infinity, -2] U [6, infinity)
B.[-2, 6]
C.(-infinity, -6] U [2, infinity)
D.(-2, 6)
Explanation: Factoring gives (x - 6)(x + 2) >= 0. The roots are x = -2 and x = 6. Since the parabola opens upward, it is non-negative on the outer intervals: (-infinity, -2] U [6, infinity).
8Solve the logarithmic equation: log_3(2x - 1) = 2.
A.x = 5
B.x = 4
C.x = 9/2
D.x = 7
Explanation: Convert to exponential form: 2x - 1 = 3^2 = 9 => 2x = 10 => x = 5.
9Solve the exponential equation 2^(2x + 1) = 32.
A.x = 2
B.x = 3
C.x = 5/2
D.x = 4
Explanation: Express 32 as a power of 2: 32 = 2^5. Equating exponents: 2x + 1 = 5 => 2x = 4 => x = 2.
10What is the exact value of sin(60 deg) and cos(30 deg)?
A.Both equal sqrt(3)/2
B.Both equal 1/2
C.sin(60 deg) = 1/2, cos(30 deg) = sqrt(3)/2
D.Both equal sqrt(2)/2
Explanation: By cofunction identities, sin(60 deg) = cos(90 deg - 60 deg) = cos(30 deg). The exact geometric value for both is sqrt(3)/2.

About the UTO Facultad Técnica Ingreso Exam

The Examen de Ingreso Directo for the Facultad Técnica at the Universidad Técnica de Oruro (UTO) provides admission to higher technical and technology engineering careers in Oruro. This is an independent English-language MCQ study adaptation based on the faculty's official syllabus in Álgebra, Trigonometría, Física, and Química. It is not an official translation or format simulation.

Exam sponsor: Facultad Técnica, Universidad Técnica de Oruro (Oruro). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

In-person faculty knowledge assessment in Álgebra, Trigonometría, Física, and Química. UTO regulations require the faculty-set passing mark to be no lower than 51/100; the current Facultad Técnica call does not state the exact cutoff.

Time Limit

Not published in the reviewed Semester 2/2026 call

Passing Score

Faculty-set cutoff of at least 51/100 under UTO regulations; exact current Facultad Técnica cutoff not published

Exam / Certification Fees

Bs 300 for the Semester 2/2026 call

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.

24 of 99 practice questions; official weight not published

Álgebra

Factoring, algebraic fractions, synthetic division, linear and quadratic equations, systems of equations, inequalities, logarithms, and exponential equations

22 of 99 practice questions; official weight not published

Trigonometría

Trigonometric ratios, unit circle, fundamental Pythagorean identities, sum/difference formulas, double-angle identities, law of sines, and law of cosines

27 of 99 practice questions; official weight not published

Física

Vectors, scalar products, dimensional analysis, rectilinear motion (MRU/MRUV), projectile motion, Newton's laws, friction, and mechanical work/energy/power

26 of 99 practice questions; official weight not published

Química

Atomic structure, electron configuration, periodic trends, chemical bonding, inorganic nomenclature, stoichiometry, gas laws, and solution concentrations

Preparing for the UTO Facultad Técnica Ingreso Exam

What You Need to Know

  • Passing score: Faculty-set cutoff of at least 51/100 under UTO regulations; exact current Facultad Técnica cutoff not published
  • Assessment: In-person faculty knowledge assessment in Álgebra, Trigonometría, Física, and Química. UTO regulations require the faculty-set passing mark to be no lower than 51/100; the current Facultad Técnica call does not state the exact cutoff.
  • Time limit: Not published in the reviewed Semester 2/2026 call
  • Exam / certification fees: Bs 300 for the Semester 2/2026 call Official sources

Using Our Practice Resources

  • Work through all 99 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

UTO Facultad Técnica Ingreso: Suggested Study Strategy

1Master algebraic factoring techniques (difference of squares, sum/difference of cubes, and trinomials) and synthetic division.
2Memorize exact trigonometric values (30°, 45°, 60°) and fundamental identities.
3Practice solving kinematics (MRU/MRUV/free fall) and dynamics problems (inclined planes with friction) step-by-step.
4Reinforce chemical stoichiometry, molar mass calculations, and inorganic nomenclature rules.

Frequently Asked Questions

What degree programmes are offered by the UTO Facultad Técnica?

The faculty offers technical and engineering technology degrees in areas including Electricidad Industrial, Electromecánica, Mecánica Automotriz, Mecánica Industrial, Química Industrial, and Construcciones Civiles.

What subjects are evaluated on the entrance exam?

The examination tests four core scientific and technical subjects: Álgebra, Trigonometría, Física, and Química.

What is the passing score for admission?

UTO regulations require a faculty's passing mark to be at least 51/100, but the reviewed Semester 2/2026 Facultad Técnica call does not publish its exact cutoff.