100+ Free ENSTP Access Contest Practice Questions

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2026 Statistics

Key Facts: ENSTP Access Contest Exam

27 June 2026

Official contest date at ENSTP campus in Kouba, Algiers

ENSTP Official Call 2026

2 papers × 2 hours

Two compulsory 2-hour written papers: 09:00-11:00 and 11:30-13:30

ENSTP Second Cycle Examination Flyer, June 2026

4 subject areas

Mathematical analysis, numerical methods, general physics, and chemistry

ENSTP Second Cycle Examination Flyer, June 2026

50 admitted

Official results list 50 candidates admitted after the 2026 written examination

ENSTP Concours Results Notice, July 2026

CPST / L2 ST

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

ENSTP Access Contest Notice

Free 100-question English MCQ study bank for the 27 June 2026 ENSTP Kouba second-cycle access contest. The official competition has two compulsory two-hour written papers; this is a study adaptation, not an official-paper simulation.

Sample ENSTP Access Contest Practice Questions

Try these sample questions to test your ENSTP 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 (x^2 + y^2) dA over the circular disk D: x^2 + y^2 <= 4?

A.8π

B.4π

C.16π

D.2π

Explanation: Convert to polar coordinates: x^2 + y^2 = r^2 and dA = r dr dθ. The region is 0 <= r <= 2 and 0 <= θ <= 2π. Compute ∬_D (x^2 + y^2) dA = ∫_0^{2π} dθ ∫_0^2 r^2 * r dr = 2π ∫_0^2 r^3 dr = 2π [r^4 / 4]_0^2 = 2π (16 / 4) = 8π.

2Using Green's Theorem, what is the value of the line integral ∮_C (x dy - y dx) along the positively oriented boundary C of an ellipse x^2/a^2 + y^2/b^2 = 1?

A.2πab

B.πab

C.0

D.4πab

Explanation: Here P(x, y) = -y and Q(x, y) = x. By Green's Theorem, ∮_C (P dx + Q dy) = ∬_D (∂Q/∂x - ∂P/∂y) dA. Compute ∂Q/∂x = 1 and ∂P/∂y = -1, so the integrand is 1 - (-1) = 2. Thus ∮_C (x dy - y dx) = 2 ∬_D dA = 2 * Area(D). Since the area of the ellipse is π a b, the integral evaluates to 2π a b.

3What does the ratio test determine regarding the convergence of the series ∑_{n=1}^∞ (n^2 + 1) / 2^n?

A.It converges absolutely because lim |a_{n+1} / a_n| = 1/2 < 1

B.It diverges because lim |a_{n+1} / a_n| = 2 > 1

C.The ratio test is inconclusive because the limit is 1

D.It converges conditionally by the alternating series test

Explanation: Compute the ratio of consecutive terms: a_{n+1} / a_n = [((n+1)^2 + 1) / 2^{n+1}] * [2^n / (n^2 + 1)] = (1/2) * [(n^2 + 2n + 2) / (n^2 + 1)]. Taking the limit as n → ∞: lim_{n→∞} |a_{n+1} / a_n| = (1/2) * 1 = 1/2. Since L = 1/2 < 1, the series converges absolutely by d'Alembert's ratio test.

4What is the radius of convergence R of the power series ∑_{n=1}^∞ (x - 2)^n / (n * 4^n)?

A.4

B.2

C.1/4

D.1

Explanation: Let c_n = 1 / (n * 4^n). Compute the ratio limit: lim_{n→∞} |c_n / c_{n+1}| = lim_{n→∞} [(n+1) * 4^{n+1}] / [n * 4^n] = 4 * lim_{n→∞} (n+1)/n = 4. Therefore, the radius of convergence is R = 4. The series converges for |x - 2| < 4.

5What is the divergence of the vector field F(x, y, z) = (x y, y z, z x) evaluated at the point P(2, 3, 4)?

A.9

B.24

C.14

D.0

Explanation: Compute the divergence: div(F) = ∂(xy)/∂x + ∂(yz)/∂y + ∂(zx)/∂z = y + z + x. At P(2, 3, 4), div(F) = 3 + 4 + 2 = 9.

6Consider the vector field F(x, y, z) = (2xy + z^3, x^2 + 2y, 3xz^2). Which statement correctly describes its curl and conservation property on ℝ^3?

A.curl(F) = (0, 0, 0); F is conservative with scalar potential φ(x, y, z) = x^2 y + y^2 + x z^3

B.curl(F) = (2x, 3z^2, 2y); F is non-conservative

C.curl(F) = (0, 0, 0); but F cannot possess a potential function

D.curl(F) = (0, 0, 2xy); F is rotational

Explanation: Compute curl(F) = ∇ × F: Component 1: ∂(3xz^2)/∂y - ∂(x^2 + 2y)/∂z = 0 - 0 = 0. Component 2: ∂(2xy + z^3)/∂z - ∂(3xz^2)/∂x = 3z^2 - 3z^2 = 0. Component 3: ∂(x^2 + 2y)/∂x - ∂(2xy + z^3)/∂y = 2x - 2x = 0. Since curl(F) = (0, 0, 0) on the simply connected domain ℝ^3, F is conservative. Integrating yields φ = x^2 y + y^2 + x z^3 + C.

7What is the total surface area of a sphere of radius a, computed via the surface integral ∬_S 1 dS?

A.4π a^2

B.(4/3)π a^3

C.2π a^2

D.π a^2

Explanation: In spherical coordinates on the surface r = a, the surface area element is dS = a^2 sin(θ) dθ dφ for 0 <= θ <= π and 0 <= φ <= 2π. The integral is ∬_S dS = ∫_0^{2π} dφ ∫_0^π a^2 sin(θ) dθ = (2π) * a^2 * [-cos(θ)]_0^π = 2π a^2 (1 - (-1)) = 4π a^2.

8Which set of conditions (Dirichlet conditions) guarantees that the Fourier series of a 2L-periodic function f(x) converges to f(x) at all points of continuity and to [f(x^+) + f(x^-)] / 2 at jump discontinuities?

A.f(x) is piecewise continuous on [-L, L], has a finite number of finite discontinuities, and has a finite number of local extrema

B.f(x) is infinitely differentiable on ℝ

C.f(x) is strictly positive and monotonically increasing everywhere

D.f(x) is a polynomial of degree at most 2

Explanation: Dirichlet's theorem states that if a periodic function f(x) is piecewise continuous on [-L, L], possesses only a finite number of finite jump discontinuities in any single period, and has a finite number of local maxima and minima, its Fourier series converges everywhere. At points of continuity, it converges to f(x); at jump discontinuities, it converges to the arithmetic mean of the one-sided limits [f(x^+) + f(x^-)]/2.

9What is the Fourier transform F(ω) = ∫_{-∞}^∞ f(t) e^{-iωt} dt of the Gaussian function f(t) = e^{-a t^2} (a > 0)?

A.√(π / a) e^{-ω^2 / (4a)}

B.√(a / π) e^{-a ω^2}

C.1 / (a^2 + ω^2)

D.2a / (a^2 + ω^2)

Explanation: Compute the integral by completing the square in the exponent: -a t^2 - i ω t = -a (t + i ω / (2a))^2 - ω^2 / (4a). Substituting u = √a (t + i ω / (2a)) and using the known Gaussian integral ∫_{-∞}^∞ e^{-u^2} du = √π yields F(ω) = e^{-ω^2 / (4a)} * (1 / √a) ∫_{-∞}^∞ e^{-u^2} du = √(π / a) e^{-ω^2 / (4a)}. A Gaussian in time transforms into a Gaussian in frequency.

10For any harmonic function u(x, y) satisfying Laplace's equation ∇^2 u = 0 in an open domain Ω, what does the Mean Value Property state for any disk D(z_0, R) ⊂ Ω centered at z_0 = (x_0, y_0)?

A.u(x_0, y_0) equals both the average of u over the boundary circle and the average of u over the interior of the disk

B.u(x_0, y_0) must be identically zero

C.u(x_0, y_0) equals the maximum value of u on the boundary circle

D.The gradient ∇u must vanish everywhere inside the disk

Explanation: The Mean Value Theorem for harmonic functions states that the value of u at the center of any ball/disk equals the average of u over the boundary sphere/circle: u(z_0) = (1 / 2π) ∫_0^{2π} u(x_0 + R cos θ, y_0 + R sin θ) dθ. Integrating with respect to radius r shows that u(z_0) also equals the area average over the interior of the disk: u(z_0) = (1 / (π R^2)) ∬_D u dA.

About the ENSTP Access Contest Exam

The Concours d’Accès au Second Cycle de l’ENSTP is the school-specific competitive entrance examination for admission to the three-year civil engineering and public works engineering cycle (ingénieur d'État) at the École Nationale Supérieure des Travaux Publics in Kouba, Algiers. Candidates sit two compulsory two-hour written papers: Paper 1 covers Mathematical Analysis (12/20) and Numerical Analysis (8/20); Paper 2 covers General Physics (12/20) and Chemistry (8/20). The official 2026 results list names 50 candidates admitted after the written examination. 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) and Numerical Analysis (8/20) from 09:00 to 11:00; Paper 2 covers General Physics (12/20) and Chemistry (8/20) from 11:30 to 13:30.

Time Limit

4 hours total (two 2-hour written papers held on 27 June 2026)

Passing Score

Competitive ranking; the official 2026 results list names 50 admitted candidates, but no fixed minimum pass mark is published in the 2026 ENSTP materials.

Exam Fee

No separate candidate exam fee is published in the 2026 ENSTP contest notices or flyer. (École Nationale Supérieure des Travaux Publics Francis Jeanson (ENSTP Kouba))

ENSTP 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 ENSTP Access Contest Exam

What You Need to Know

Passing score: Competitive ranking; the official 2026 results list names 50 admitted candidates, but no fixed minimum pass mark is published in the 2026 ENSTP materials.
Assessment: Two compulsory two-hour written papers, each coefficient 1: Paper 1 covers Mathematical Analysis (12/20) and Numerical Analysis (8/20) from 09:00 to 11:00; Paper 2 covers General Physics (12/20) and Chemistry (8/20) from 11:30 to 13:30.
Time limit: 4 hours total (two 2-hour written papers held on 27 June 2026)
Exam fee: No separate candidate exam fee is published in the 2026 ENSTP contest notices or flyer.

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

ENSTP Access Contest Study Tips from Top Performers

1Master multivariable calculus and vector fields: compute line, surface, and volume integrals using Green's, divergence, and Stokes' theorems.

2Study numerical algorithms in linear algebra and root-finding: practise matrix conditioning, LU factorization, and iterative solver convergence.

3Review harmonic and wave phenomena: analyse damped/forced oscillators, normal modes, string vibrations, and acoustic/EM wave propagation.

4Strengthen chemical equilibrium calculations: master pH calculations for complex buffers, solubility product precipitation criteria, and electrochemical potentials.

5Review organic reaction mechanisms: understand electronic effects on aromatic substitution and stereochemical outcomes in nucleophilic substitutions.

Frequently Asked Questions

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

The contest was held on Saturday 27 June 2026 at the ENSTP campus in Kouba, Algiers. It comprised two compulsory two-hour written papers, each with coefficient 1: Paper 1 combined Mathematical Analysis (12/20) and Numerical Analysis (8/20) from 09:00 to 11:00; Paper 2 combined General Physics (12/20) and Chemistry (8/20) from 11:30 to 13:30.

Who is eligible to participate in the ENSTP 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 without repeating, subject to dossier review. The official results page lists 50 admitted candidates.

What language is used for the examination papers?

The official ENSTP announcements and flyer do not explicitly confirm the delivery language of the actual question papers; this bank provides English-language MCQs as a study adaptation across the common ST preparatory syllabus.

Is there an oral or practical examination?

No oral, practical, assignment, or case-study component is published in the official 2026 ENSTP notices. Selection is based strictly on pedagogical eligibility validation and performance on the written papers.

Is this bank an official-format simulation?

No. The official competition consists of two written examination papers, but the official materials do not publish their item types or delivery language. This bank is an English-language MCQ study adaptation designed to strengthen theoretical mastery and problem-solving abilities.

Is there an examination fee for candidates?

No separate candidate examination fee is published in the official 2026 ENSTP event notices, flyer, or results announcements.