Free Practice Questions for Politehnica București Engineering Admission

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Sample Politehnica București Engineering Admission Practice Questions

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

1For what value of parameter m in R does the linear system { x + y + z = 1, 2x - y + z = 2, 3x + my + 2z = 3 } have infinitely many solutions (compatible indeterminate)?

A.m = 0

B.m = 1

C.m = -1

D.m = 2

Explanation: The coefficient determinant is m, so infinitely many solutions require m = 0. At that value the third equation is the sum of the first two, including its right-hand side; the first two remain independent, leaving one free variable. Thus the singular system is consistent and has infinitely many solutions.

2What is the derivative of the function f(x) = ln(x + sqrt(x^2 + 1)) with respect to x?

A.1 / sqrt(x^2 + 1)

B.1 / (x + sqrt(x^2 + 1))

C.x / sqrt(x^2 + 1)

D.2x / (x^2 + 1)

Explanation: The logarithmic chain rule gives f'(x) = [1 + x/√(x²+1)]/[x + √(x²+1)]. Factoring the numerator cancels x + √(x²+1), leaving 1/√(x²+1).

3What is the value of the definite integral I = integral from 0 to pi of x * sin(x) dx?

A.pi

B.2*pi

C.0

D.pi - 2

Explanation: Using integration by parts: let u = x => du = dx, and dv = sin(x) dx => v = -cos(x). Then I = [-x * cos(x)] from 0 to pi - integral from 0 to pi of (-cos(x)) dx = (-pi*cos(pi) - 0) + [sin(x)] from 0 to pi = -pi*(-1) + (sin(pi) - sin(0)) = pi + 0 = pi.

4What is the value of the limit L = lim (x -> 0) ln(1 + 3x) / sin(4x)?

A.3/4

B.4/3

C.1

D.0

Explanation: Using fundamental limits: lim (x -> 0) ln(1 + 3x)/(3x) = 1, and lim (x -> 0) (4x)/sin(4x) = 1. Therefore ln(1 + 3x)/sin(4x) = [ln(1 + 3x)/(3x)] * [(4x)/sin(4x)] * (3/4) -> 1 * 1 * 3/4 = 3/4. Alternatively, by L'Hôpital: [3/(1+3x)] / [4*cos(4x)] evaluated at x=0 yields 3/4.

5If A is a 3x3 invertible matrix with det(A) = 3, what is the determinant of the matrix 2 * A^(-1)?

A.8/3

B.2/3

C.6

D.1/24

Explanation: For an n x n matrix M and scalar c, det(c*M) = c^n * det(M). Here n = 3 and c = 2, so det(2 * A^(-1)) = 2^3 * det(A^(-1)) = 8 * (1 / det(A)) = 8 * (1/3) = 8/3.

6What are the x-coordinates of the inflection points of f(x) = x * e^(-x^2)?

A.x = 0, x = sqrt(3/2), and x = -sqrt(3/2)

B.x = 1/sqrt(2) and x = -1/sqrt(2)

C.x = 0 only

D.x = 1 and x = -1

Explanation: First derivative: f'(x) = 1*e^(-x^2) + x*(-2x*e^(-x^2)) = (1 - 2x^2)*e^(-x^2). Second derivative: f''(x) = -4x*e^(-x^2) + (1 - 2x^2)*(-2x*e^(-x^2)) = e^(-x^2)*[-4x - 2x + 4x^3] = 2x*e^(-x^2)*(2x^2 - 3). Setting f''(x) = 0 gives x = 0 or 2x^2 - 3 = 0 => x = +-sqrt(3/2). Because f'' changes sign at each of these three points, all three are inflection points.

7What is the equation of the slant (oblique) asymptote of the rational function f(x) = (2x^2 + 1) / (x - 1) as x -> infinity?

A.y = 2x + 2

B.y = 2x - 2

C.y = 2x + 1

D.y = 2x

Explanation: Divide numerator by denominator: (2x^2 + 1) / (x - 1) = (2x(x - 1) + 2x + 1) / (x - 1) = 2x + (2x + 1)/(x - 1) = 2x + 2 + 3/(x - 1). As x -> infinity, 3/(x - 1) -> 0. Therefore, the oblique asymptote is the line y = 2x + 2.

8What is the remainder when the polynomial P(X) = X^4 - 2X^3 + 3X - 5 is divided by X - 2?

A.1

B.-5

C.5

D.0

Explanation: By Bézout's remainder theorem, the remainder of dividing P(X) by X - 2 is P(2). Substituting X = 2: P(2) = 2^4 - 2*(2^3) + 3*(2) - 5 = 16 - 2*(8) + 6 - 5 = 16 - 16 + 6 - 5 = 1.

9In the binomial expansion of (x^2 + 1/x)^6, what is the term independent of x (constant term)?

A.15

B.20

C.6

D.1

Explanation: The general term is T_(k+1) = C(6, k) * (x^2)^(6-k) * (x^(-1))^k = C(6, k) * x^(12 - 2k - k) = C(6, k) * x^(12 - 3k). For the term to be independent of x, the exponent must be zero: 12 - 3k = 0 => 3k = 12 => k = 4. The coefficient is C(6, 4) = C(6, 2) = (6 * 5) / (2 * 1) = 15.

10What is the solution set in R of the rational inequality (x - 2) / (x + 3) >= 1?

A.(-infinity, -3)

B.(-3, infinity)

C.[-3, 2]

D.Empty set (no solution)

Explanation: Subtract 1 from both sides: (x - 2)/(x + 3) - 1 >= 0 => [(x - 2) - (x + 3)] / (x + 3) >= 0 => -5 / (x + 3) >= 0. Since the numerator -5 is strictly negative, the fraction is >= 0 if and only if the denominator is strictly negative: x + 3 < 0 => x < -3. Thus the solution set is (-infinity, -3).

About the Politehnica București Engineering Admission Exam

Independent practice for the Romanian POLITEHNICA București ETTI ordinary July Session II written admission route. The assessment combines P1 Mathematics with P2 Physics or Informatics over three hours; the Bacalaureat mean supplies P3 in the ordinary domestic-diploma calculation. This focused English-language MCQ study adaptation covers Mathematics and Physics, with worked solutions; it is not an official translation or complete admission simulation.

Exam sponsor: Universitatea Națională de Știință și Tehnologie POLITEHNICA București — Facultatea ETTI. 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

180 minutes (3 hours)

Passing Score

Minimum overall admission mean 5.00/10 (competitive ranking)

Exam / Certification Fees

125 lei (July session)

Exam sponsor website

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

Official sources

POLITEHNICA București Licență Admission Regulation 2026 · Source checked 2026-10-09Official Senate regulation specifying ETTI written admission disciplines P1 and P2, composite scoring rules, 3-hour duration, and 125 lei fee.
POLITEHNICA București Admission Syllabus (Annex XI) · Source checked 2026-10-09Official secondary-school curriculum outlines for Mathematics (Algebra/Analysis) and Physics subjects.
ETTI July Session II admission details 2026 · Source checked 2026-10-10Faculty confirmation of Mathematics and Physics or Informatics at 40% each, Bacalaureat mean at 20%, documentary eligibility and the 125 lei registration fee with reduction rules.

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.

50% of the written component; 40% of the ordinary July admission mean

P1: Mathematics (Algebra and Analysis)

Matrices, determinants, linear systems, groups, polynomials, limits, derivatives, extremum problems, and definite integrals.

50% of the written component; 40% of the ordinary July admission mean

P2: Physics (Mechanics, Thermodynamics, DC Electricity)

Forces, momentum, work and energy, heat engines, ideal gases and DC circuits. The bank does not cover the alternative Informatics paper.

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What You Need to Know

Passing score: Minimum overall admission mean 5.00/10 (competitive ranking)
Assessment: Question count not published by the exam provider
Time limit: 180 minutes (3 hours)
Exam / certification fees: 125 lei (July session) Official sources

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Frequently Asked Questions

What subjects are included in the POLITEHNICA București ETTI admission exam?

The written admission test covers two components: P1 (Mathematics) and P2 (Physics or Informatics), administered together in a single 3-hour session.

What is the registration fee for the POLITEHNICA București admission?

The official registration fee is 125 lei for the July admission session, with exemptions provided according to university regulations.