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100+ Free ENSH Access Contest Practice Questions

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2026 Statistics

Key Facts: ENSH Access Contest Exam

7 July 2026

Official contest date at ENSH campus in Soumâa, Blida

ENSH Official Call 2026

2 papers × 2 hours

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

ENSH Contest Commission Minutes, 14 June 2026

4 subject areas

Mathematical analysis, numerical methods, general physics, and chemistry

ENSH Contest Commission Minutes, 14 June 2026

CPST / L2 ST

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

ENSH Access Contest Notice

English + French

Subjects must be prepared in both English and French

ENSH Contest Commission Minutes, 14 June 2026

Free 100-question English MCQ study bank for the 7 July 2026 ENSH second-cycle access contest. The official competition has two compulsory two-hour bilingual English/French subject papers; this is a study adaptation, not an official-paper simulation.

Sample ENSH Access Contest Practice Questions

Try these sample questions to test your ENSH 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 directional derivative of the scalar field f(x, y) = x^2 * y + 3 * x * y^2 at the point P(1, 2) in the direction of the vector v = (3, 4)?
A.20.0
B.25.6
C.100.0
D.16.0
Explanation: The gradient of f is ∇f = (2xy + 3y^2, x^2 + 6xy). At P(1, 2), ∇f(1, 2) = (2(1)(2) + 3(4), 1^2 + 6(1)(2)) = (4 + 12, 1 + 12) = (16, 13). The unit vector in the direction of v = (3, 4) is u = (3/5, 4/5). Therefore, the directional derivative is Du f = ∇f · u = 16*(3/5) + 13*(4/5) = (48 + 52)/5 = 100/5 = 20.0.
2For f_n(x) = x^n on [0, 1], which statement correctly describes the convergence as n tends to infinity?
A.The sequence converges uniformly to zero on [0, 1]
B.The sequence converges pointwise to zero on [0, 1] but not uniformly
C.The sequence converges pointwise to a function that is 0 on [0, 1) and 1 at x = 1; convergence is not uniform on [0, 1]
D.The sequence does not converge at x = 1
Explanation: For every 0 <= x < 1, x^n tends to 0, while f_n(1) = 1 for every n. The pointwise limit is therefore discontinuous at x = 1, and the convergence cannot be uniform because a uniform limit of continuous functions on [0, 1] would be continuous. Equivalently, sup_{0 <= x < 1} x^n = 1 for every n.
3The triangular region D is described by 0 <= y <= x <= 1. Which iterated integral has the same region after reversing the order of integration?
A.Integral from y = 0 to 1, then x = 0 to y
B.Integral from y = 0 to 1, then x = y to 1
C.Integral from y = 0 to x, then x = 0 to 1
D.Integral from y = x to 1, then x = 0 to 1
Explanation: The original bounds describe the part of the unit square below the line y = x. When y is chosen first, it ranges from 0 to 1; for each fixed y, x begins at the line x = y and ends at x = 1. Thus the reversed order is 0 <= y <= 1 and y <= x <= 1.
4Let F(x, y) = P(x, y) i + Q(x, y) j be a continuously differentiable vector field defined on a simply connected open domain D in R^2. Which condition is both necessary and sufficient for F to be conservative on D?
A.∂P/∂x + ∂Q/∂y = 0 everywhere in D
B.∂P/∂x = ∂Q/∂y everywhere in D
C.∂P/∂y + ∂Q/∂x = 0 everywhere in D
D.∂P/∂y = ∂Q/∂x everywhere in D
Explanation: A C^1 vector field F = (P, Q) is conservative on a simply connected domain if and only if its curl vanishes identically: curl(F) = (∂Q/∂x - ∂P/∂y) k = 0, which means ∂P/∂y = ∂Q/∂x everywhere in D. Under this condition, F = ∇f for some scalar potential f.
5Evaluate the line integral I = ∫_C (2xy dx + x^2 dy), where C is any smooth path starting at the origin (0, 0) and ending at the point (2, 3).
A.12
B.18
C.6
D.24
Explanation: Notice that the differential form 2xy dx + x^2 dy is exact because ∂(2xy)/∂y = 2x and ∂(x^2)/∂x = 2x. The potential function is f(x, y) = x^2 * y. By the fundamental theorem for line integrals, I = f(2, 3) - f(0, 0) = (2^2 * 3) - 0 = 4 * 3 = 12.
6Using the Green-Riemann formula, the area of a plane region D bounded by a positively oriented simple closed curve C is given by Area(D) = (1/2) ∮_C (x dy - y dx). What is the area enclosed by the ellipse with parametric equations x(t) = a*cos(t), y(t) = b*sin(t) for t in [0, 2π]?
A.2 * π * a * b
B.π * a * b
C.(1/2) * π * a * b
D.π * (a^2 + b^2)
Explanation: With x = a*cos(t) and y = b*sin(t), we have dx = -a*sin(t) dt and dy = b*cos(t) dt. Then x*dy - y*dx = [a*cos(t)][b*cos(t)] dt - [b*sin(t)][-a*sin(t)] dt = a*b*(cos^2(t) + sin^2(t)) dt = a*b dt. Integrating from 0 to 2π yields Area = (1/2) ∫_0^{2π} a*b dt = (1/2) * a*b * 2π = π*a*b.
7Evaluate the double integral I = ∬_D (x^2 + y^2) dx dy over the circular disk D = {(x, y) in R^2 : x^2 + y^2 <= R^2}.
A.π * R^4
B.(1/4) * π * R^4
C.(1/2) * π * R^4
D.(2/3) * π * R^3
Explanation: Switching to polar coordinates (x = r*cos(θ), y = r*sin(θ), dx dy = r dr dθ), the disk is described by 0 <= r <= R and 0 <= θ <= 2π. The integrand is x^2 + y^2 = r^2. The integral becomes I = ∫_0^{2π} dθ * ∫_0^R r^3 dr = 2π * [r^4 / 4]_0^R = 2π * (R^4 / 4) = (π * R^4) / 2.
8Compute the triple integral I = ∭_V z dx dy dz over the upper solid hemisphere V = {(x, y, z) in R^3 : x^2 + y^2 + z^2 <= R^2, z >= 0}.
A.(1/3) * π * R^4
B.(3/8) * π * R^4
C.(1/2) * π * R^4
D.(1/4) * π * R^4
Explanation: Using spherical coordinates (x = ρ*sin(φ)*cos(θ), y = ρ*sin(φ)*sin(θ), z = ρ*cos(φ), dV = ρ^2*sin(φ) dρ dφ dθ), the upper hemisphere corresponds to 0 <= ρ <= R, 0 <= φ <= π/2, and 0 <= θ <= 2π. The integral is I = ∫_0^{2π} dθ * ∫_0^{π/2} cos(φ)*sin(φ) dφ * ∫_0^R ρ^3 dρ = 2π * [sin^2(φ)/2]_0^{π/2} * [ρ^4/4]_0^R = 2π * (1/2) * (R^4/4) = (π * R^4) / 4.
9Using the Gauss-Ostrogradsky divergence theorem, find the outward flux of the vector field F(x, y, z) = 2x i - y j + 3z k across the closed spherical surface S defined by x^2 + y^2 + z^2 = R^2.
A.(16/3) * π * R^3
B.4 * π * R^3
C.(8/3) * π * R^3
D.16 * π * R^2
Explanation: By the divergence theorem, the outward flux is ∬_S F · n dS = ∭_V div(F) dV. The divergence of F is div(F) = ∂(2x)/∂x + ∂(-y)/∂y + ∂(3z)/∂z = 2 - 1 + 3 = 4. Since the divergence is constant, the flux is 4 * Volume(V) = 4 * (4/3 * π * R^3) = (16/3) * π * R^3.
10Let C be the boundary of the plane triangle with vertices A(1, 0, 0), B(0, 1, 0), and C(0, 0, 1), oriented in the direction A -> B -> C -> A. Use Stokes' theorem to evaluate the line integral ∮_C F · dr, where F(x, y, z) = y i + z j + x k.
A.-3
B.-3/2
C.3/2
D.0
Explanation: By Stokes' theorem, ∮_C F · dr = ∬_S (curl F) · n dS. We compute curl(F) = (∂(x)/∂y - ∂(z)/∂z) i + (∂(y)/∂z - ∂(x)/∂x) j + (∂(z)/∂x - ∂(y)/∂y) k = (0 - 1) i + (0 - 1) j + (0 - 1) k = -i - j - k = (-1, -1, -1). The plane containing the triangle has equation x + y + z = 1 with upward unit normal n = (1/√3)(i + j + k). Thus (curl F) · n = (-1 - 1 - 1)/√3 = -3/√3 = -√3. The area of the equilateral triangle with side length s = √2 is Area(S) = (√3/4) * s^2 = (√3/4) * 2 = √3/2. Therefore, the integral is (-√3) * (√3/2) = -3/2.

About the ENSH Access Contest Exam

The Concours d’Accès au Second Cycle de l’ENSH is the school-specific competitive examination for admission to first year of the second cycle at the École Nationale Supérieure d'Hydraulique in Blida. Candidates sit two compulsory two-hour written papers: Paper 1 covers Mathematical Analysis and Numerical Analysis, and Paper 2 covers Physics and Chemistry; each paper has coefficient 1. The 2026 commission minutes require the subjects to be prepared in both English and French. This bank provides 100 English-language four-option MCQs across the published second-year syllabus as a study adaptation, not a simulation of the official paper or item types.

Assessment

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

Time Limit

4 hours total (two 2-hour written papers held on 7 July 2026)

Passing Score

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

Exam Fee

No separate candidate exam fee is published in the 2026 ENSH event notice or commission minutes. (École Nationale Supérieure d'Hydraulique (ENSH))

ENSH 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; 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 ENSH 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 ENSH materials.
  • Assessment: Two compulsory two-hour written papers, each coefficient 1: Paper 1 covers Mathematical Analysis (12/20) and Numerical Analysis (8/20); Paper 2 covers General Physics (12/20) and Chemistry (8/20).
  • Time limit: 4 hours total (two 2-hour written papers held on 7 July 2026)
  • Exam fee: No separate candidate exam fee is published in the 2026 ENSH 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

ENSH Access Contest Study Tips from Top Performers

1Connect each question to the published Analyse 3 and Analyse 4 outline: multiple integrals and vector analysis, series, Fourier analysis, and partial differential equations.
2Review numerical linear algebra: ensure you can compute matrix condition numbers, set up LU factorization, and state precise convergence conditions for Jacobi and Gauss-Seidel iterations via diagonal dominance.
3For Physique 3, compare free, damped, forced, coupled, and anharmonic oscillations; for Physique 4, practise wave propagation in strings, fluids, solids, and electromagnetic fields.
4Divide chemistry revision between Chimie 3 solution equilibria and kinetics and Chimie 4 organic nomenclature, stereochemistry, electronic effects, and reaction mechanisms.
5Solve full written problems alongside these MCQs because the official materials specify written subject papers but do not publish an official four-option MCQ format.

Frequently Asked Questions

What is the format and date of the 2026 ENSH Access Contest?

The contest is held on Tuesday 7 July 2026 at the ENSH campus in Soumâa, Blida. It comprises two compulsory two-hour written papers, each with coefficient 1. Paper 1 combines Mathematical Analysis (12/20) and Numerical Analysis (8/20); Paper 2 combines General Physics (12/20) and Chemistry (8/20).

Who is eligible to participate in the ENSH Access Contest?

Eligibility covers students who have successfully completed two preparatory years in Sciences and Technology (CPST / formation de base ST) higher schools without being retained through the 80% quota sur titre, specified rerouted preparatory students, and university ST students with at least two completed years without repeating, subject to the official notice's second-degree restriction.

Is there an oral or practical examination?

No oral, practical, assignment, or case-study component is published in the 2026 ENSH materials. The candidate dossier establishes eligibility, and the assessed competition consists of the two written subject papers.

Is this bank an official-format simulation?

No. The 2026 commission minutes require the official subjects in both English and French, but they do not publish an item count or identify a four-option MCQ format. This English-language MCQ bank adapts the published syllabus for study and does not reproduce the official paper format.

What is the passing score or quota for admission?

Admission is strictly competitive based on the weighted ranking of candidates (composite score across the two papers, each coefficient 1) within the pedagogical quota of available places for the second cycle. No universal minimum pass mark is published in advance.

Is there a registration fee for the contest?

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