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100+ Free ENP Alger Access Contest Practice Questions

Prepare for the Concours d’Accès au Second Cycle de l’ENP (Polytechnique Alger) — Algeria exam with instant access — no signup required.

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2026 Statistics

Key Facts: ENP Alger Access Contest Exam

28 June 2026

Official contest date at ENP Alger campus in El Harrach

ENP Alger Official Call 2026

2 papers × 2 hours

Two compulsory 2-hour written papers, each weighted at coefficient 1

ENP Alger Contest Commission Minutes, June 2026

4 subject areas

Mathematical analysis, numerical methods, general physics, and chemistry

ENP Alger Contest Commission Minutes, June 2026

CPST / L2 ST

Eligibility based on 2 successful years in ST preparatory schools or universities

ENP Alger Access Contest Notice

English

Subjects required in English per commission minutes

ENP Alger Contest Commission Minutes, June 2026

Free 100-question English MCQ study bank for the 28 June 2026 ENP Alger second-cycle access contest. The official competition has two compulsory two-hour written papers in English; this is a study adaptation, not an official-paper simulation.

Sample ENP Alger Access Contest Practice Questions

Try these sample questions to test your ENP Alger Access Contest exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the value of the double integral ∬_D (2x + y) dA over the rectangular domain D = [0, 2] × [0, 3]?
A.21.0
B.18.0
C.24.0
D.15.0
Explanation: By Fubini's theorem, compute the iterated integral: ∫_0^2 dx ∫_0^3 (2x + y) dy = ∫_0^2 [2xy + y^2/2]_0^3 dx = ∫_0^2 (6x + 9/2) dx = [3x^2 + (9/2)x]_0^2 = 3(4) + (9/2)(2) = 12 + 9 = 21.0.
2What is the radius of convergence R of the power series ∑_{n=1}^∞ (3^n / n^2) (x - 1)^n?
A.1/3
B.3
C.1
D.Infinity
Explanation: Using d'Alembert's ratio test for the coefficients a_n = 3^n / n^2: lim_{n→∞} |a_{n+1} / a_n| = lim_{n→∞} [3^{n+1}/(n+1)^2] * [n^2/3^n] = 3 * lim_{n→∞} (n/(n+1))^2 = 3. Therefore, the radius of convergence is R = 1 / L = 1/3.
3Using Green's Theorem, what is the value of the line integral ∮_C (y^2 dx + 3xy dy) along the positively oriented circle C: x^2 + y^2 = 4?
A.0
B.4π
C.8π
D.16π
Explanation: By Green's Theorem, ∮_C (P dx + Q dy) = ∬_D (∂Q/∂x - ∂P/∂y) dA. Here P(x, y) = y^2 so ∂P/∂y = 2y, and Q(x, y) = 3xy so ∂Q/∂x = 3y. The integrand is (3y - 2y) = y. Since D is a disk centered at the origin (x^2 + y^2 <= 4) and the integrand y is odd with respect to y, the double integral ∬_D y dA vanishes by symmetry, giving 0.
4What is the outward flux of the vector field F(x, y, z) = (x, y, z) across the sphere S: x^2 + y^2 + z^2 = 9?
A.108π
B.36π
C.72π
D.144π
Explanation: By the Divergence Theorem, ∬_S F · dS = ∭_V div(F) dV. Compute the divergence: div(F) = ∂x/∂x + ∂y/∂y + ∂z/∂z = 1 + 1 + 1 = 3. The volume of the sphere of radius R = 3 is V = (4/3)π R^3 = (4/3)π (27) = 36π. Therefore, the flux is 3 * 36π = 108π.
5For the 2π-periodic function defined on [-π, π] by f(x) = |x|, what is the Fourier coefficient a_0 in the expansion f(x) = a_0/2 + ∑_{n=1}^∞ a_n cos(nx)?
A.π
B.π / 2
C.2π
D.0
Explanation: The Fourier coefficient a_0 is given by a_0 = (1/π) ∫_{-π}^π f(x) dx. Since |x| is even: a_0 = (2/π) ∫_0^π x dx = (2/π) [x^2 / 2]_0^π = (2/π) (π^2 / 2) = π. With this convention, the constant term in the series is a_0 / 2 = π / 2.
6Consider the sequence of functions f_n(x) = x / (1 + n x^2) on the interval [0, 1]. Which statement correctly characterizes its convergence as n → ∞?
A.It converges uniformly to 0 on [0, 1] with maximum error 1 / (2√n)
B.It converges pointwise to 0 but fails to converge uniformly on [0, 1]
C.It converges uniformly to f(x) = x on [0, 1]
D.It diverges at x = 0
Explanation: For any fixed x, lim_{n→∞} f_n(x) = 0, so the pointwise limit is f(x) = 0. To evaluate uniform convergence, find the maximum of f_n on [0, 1]: f'_n(x) = (1 - n x^2) / (1 + n x^2)^2 = 0 at x = 1/√n. The maximum value is f_n(1/√n) = (1/√n) / (1 + 1) = 1 / (2√n). Since sup_{x ∈ [0, 1]} |f_n(x) - 0| = 1 / (2√n) → 0 as n → ∞, the convergence is uniform.
7What is the value of the line integral ∫_C (2xy dx + x^2 dy) along any smooth path C starting at (0, 0) and ending at (2, 3)?
A.12
B.6
C.18
D.24
Explanation: Check if the vector field F = (2xy, x^2) is conservative: ∂(x^2)/∂x = 2x and ∂(2xy)/∂y = 2x. Since the partial derivatives are equal on ℝ^2, F is conservative with scalar potential φ(x, y) = x^2 y. By the fundamental theorem for line integrals, ∫_C F · dr = φ(2, 3) - φ(0, 0) = (2^2)(3) - 0 = 12.
8What is the directional derivative of f(x, y, z) = x y^2 z^3 at the point P(1, 1, 1) in the direction of the vector v = (2, -1, 2)?
A.2.0
B.6.0
C.1.5
D.3.0
Explanation: Compute the gradient: ∇f = (y^2 z^3, 2xy z^3, 3xy^2 z^2). At P(1, 1, 1), ∇f(1, 1, 1) = (1, 2, 3). The norm of v is |v| = √(2^2 + (-1)^2 + 2^2) = √(4 + 1 + 4) = 3. The unit vector is u = (2/3, -1/3, 2/3). Thus D_u f = ∇f · u = 1*(2/3) + 2*(-1/3) + 3*(2/3) = 2/3 - 2/3 + 6/3 = 2.0.
9What is the convergence status of the alternating series ∑_{n=1}^∞ (-1)^n / (n + √n)?
A.It converges conditionally
B.It converges absolutely
C.It diverges by oscillation
D.It diverges to negative infinity
Explanation: Let a_n = 1 / (n + √n). Since a_n > 0, a_n is strictly decreasing, and lim_{n→∞} a_n = 0, the alternating series converges by the Leibniz alternating series test. For absolute convergence, consider ∑ |(-1)^n / (n + √n)| = ∑ 1/(n + √n). For large n, 1/(n + √n) ~ 1/n. By the limit comparison test with the divergent harmonic series ∑ 1/n, the series of absolute values diverges. Therefore, the series converges conditionally.
10What is the volume of the solid bounded above by the paraboloid z = 4 - x^2 - y^2 and below by the xy-plane (z = 0)?
A.8π
B.4π
C.16π
D.2π
Explanation: The boundary on the xy-plane is given by 4 - x^2 - y^2 = 0, which is the circle of radius R = 2. Using cylindrical coordinates: V = ∫_0^{2π} dθ ∫_0^2 (4 - r^2) r dr = 2π ∫_0^2 (4r - r^3) dr = 2π [2r^2 - r^4/4]_0^2 = 2π [2(4) - 16/4] = 2π [8 - 4] = 8π.

About the ENP Alger Access Contest Exam

The Concours d’Accès au Second Cycle de l’ENP is the school-specific competitive entrance examination for admission to the three-year engineering cycle (ingénieur d'État) at the École Nationale Polytechnique in El Harrach, Algiers. Candidates sit two compulsory two-hour written papers: Paper 1 covers Mathematical Analysis (12/20, 1h15) and Numerical Analysis (8/20, 45m); Paper 2 covers General Physics (12/20, 1h15) and Chemistry (8/20, 45m). The official commission minutes require English subjects and the whole second-year foundational programme. This bank provides 100 English-language four-option MCQs across the published second-year CPST syllabus as a study adaptation, not an official-format simulation.

Assessment

Two compulsory two-hour written papers, each coefficient 1: Paper 1 covers Mathematical Analysis (12/20, 1h15) and Numerical Analysis (8/20, 45m); Paper 2 covers General Physics (12/20, 1h15) and Chemistry (8/20, 45m).

Time Limit

4 hours total (two 2-hour written papers held on 28 June 2026)

Passing Score

Competitive ranking for the remaining 20% of pedagogical places; no fixed minimum pass mark is published in the 2026 ENP Alger materials.

Exam Fee

No separate candidate exam fee is published in the 2026 ENP Alger event notice or commission minutes. (École Nationale Polytechnique (ENP Alger))

ENP Alger Access Contest Exam Content Outline

Paper 1 (12/20 pts; 30 questions)

Mathematical Analysis

Double and triple integrals, vector analysis, numerical and function series, power series, Fourier series and transforms, and partial differential equations.

Paper 1 (8/20 pts; 20 questions)

Numerical Analysis

Numerical linear algebra (Gaussian elimination, LU, iterative solvers), root-finding algorithms, polynomial interpolation, numerical quadrature, and initial value ODE solvers.

Paper 2 (12/20 pts; 30 questions)

General Physics & Mechanics

Free, damped, forced, coupled, and anharmonic oscillations; vibrating strings; acoustic and elastic waves in fluids and solids; and electromagnetic waves.

Paper 2 (8/20 pts; 20 questions)

Chemistry & Solutions

Solutions and kinetics; acid-base, solubility, redox, and complexation equilibria; organic nomenclature, stereochemistry, electronic effects, and reaction mechanisms.

How to Pass the ENP Alger Access Contest Exam

What You Need to Know

  • Passing score: Competitive ranking for the remaining 20% of pedagogical places; no fixed minimum pass mark is published in the 2026 ENP Alger materials.
  • Assessment: Two compulsory two-hour written papers, each coefficient 1: Paper 1 covers Mathematical Analysis (12/20, 1h15) and Numerical Analysis (8/20, 45m); Paper 2 covers General Physics (12/20, 1h15) and Chemistry (8/20, 45m).
  • Time limit: 4 hours total (two 2-hour written papers held on 28 June 2026)
  • Exam fee: No separate candidate exam fee is published in the 2026 ENP Alger event notice or commission minutes.

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

ENP Alger Access Contest Study Tips from Top Performers

1Master multivariable calculus and series from Analyse 3 and Analyse 4: double/triple integrals, Green/Stokes theorems, uniform convergence, and Fourier series.
2Practise numerical linear algebra and root-finding: LU factorization, condition numbers, Jacobi/Gauss-Seidel iterations, and Newton-Raphson order of convergence.
3Review Physique 3 oscillatory systems: compute natural frequencies, damping ratios, quality factors, and resonance amplitudes for mechanical and electrical oscillators.
4Strengthen wave mechanics in Physique 4: standing waves on strings, acoustic impedance, reflection/transmission at boundaries, and Maxwell's equations.
5Balance chemistry between Chimie 3 solution equilibria (buffers, solubility product, Nernst cell potentials) and Chimie 4 organic reaction mechanisms (SN1/SN2, E1/E2, aromatic electrophilic substitution).

Frequently Asked Questions

What is the format and date of the 2026 ENP Alger Access Contest?

The contest was held on Sunday 28 June 2026 at the École Nationale Polytechnique campus in El Harrach, Algiers. It comprised two compulsory two-hour written papers, each with coefficient 1: Paper 1 combined Mathematical Analysis (12/20, 1h15) and Numerical Analysis (8/20, 45m); Paper 2 combined General Physics (12/20, 1h15) and Chemistry (8/20, 45m).

Who is eligible to participate in the ENP Alger Access Contest?

Eligibility covers students who have successfully completed two preparatory years in Sciences and Technology (CPST / formation de base ST) higher schools, qualifying rerouted preparatory candidates, and university ST students with at least two completed undergraduate years and no repeat year, competing for the remaining 20% quota of pedagogical places.

What language is used for the examination papers?

The official 2026 commission minutes specify English as the language of the examination subjects for the ENP Alger concours.

Is there an oral or practical examination?

No oral, practical, assignment, or case-study component is published in the official 2026 ENP Alger notices. Admission is determined solely by candidate eligibility validation and ranking on the written papers.

Is this bank an official-format simulation?

No. The official examination consists of two written papers, but the official materials do not publish their item types. This bank is an English-language MCQ study adaptation designed to reinforce theoretical comprehension and problem-solving skills across the published CPST syllabus.

Is there an examination fee for candidates?

No separate candidate examination fee is published in the official 2026 ENP Alger event notice or commission minutes.