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Key Facts: Concours Centrale-Supélec Exam

15 schools

Grandes écoles recruiting through the Concours Centrale-Supélec

concours-centrale-supelec.fr

5 filières

MP, MPI, PC, PSI and TSI preparatory streams

concours-centrale-supelec.fr

10,270

Candidates registered in 2025, of whom 2,654 were declared admissible

SCEI 2025

4–7 May 2026

Written papers; orals and practicals run 22 June – 19 July 2026

Notices Centrale-Supélec 2026

140 €

Per Centrale school and IOGS; 135 € Arts et Métiers/ENSEA, 85 € EPF/ESTP, free for boursiers

Concours Centrale-Supélec 2026

SCEI

Registration via the national engineering-school concours portal

scei-concours.fr

The elite joint competitive gateway to 15 top French engineering grandes écoles (CentraleSupélec, Centrale Lyon/Nantes/Lille/Méditerranée, IOGS, Arts et Métiers, and partner schools) for CPGE students (MP, MPI, PC, PSI, TSI), comprising rigorous written problem papers in May and oral examinations in June–July.

Sample Concours Centrale-Supélec Practice Questions

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1In the infinite-dimensional real vector space E = C([0, 1], R), consider the norms ||f||_1 = \int_0^1 |f(t)| dt and ||f||_\infty = \sup_{t \in [0, 1]} |f(t)|. By testing the sequence of functions f_n(t) = t^n for n \ge 1, what can be concluded regarding the equivalence of these two norms?
A.The norms are equivalent because E is a normed space of continuous functions on a closed bounded interval.
B.There exists a constant C > 0 such that ||f||_\infty \le C ||f||_1 for all f in E.
C.The norms are not equivalent because ||f_n||_\infty = 1 while ||f_n||_1 = 1/(n + 1) -> 0 as n -> \infty.
D.The norms are not equivalent because ||f_n||_1 diverges to +\infty while ||f_n||_\infty remains bounded.
Explanation: Two norms are equivalent if and only if each is bounded by a constant multiple of the other. For f_n(t) = t^n on [0, 1], ||f_n||_\infty = 1 for all n, whereas ||f_n||_1 = \int_0^1 t^n dt = 1/(n+1), which tends to 0 as n -> \infty. Hence, no constant C satisfies ||f||_\infty \le C ||f||_1 on E, proving that in this infinite-dimensional space the norms are strictly non-equivalent.
2According to the spectral theorem for real symmetric matrices, the matrix A = [[2, 1], [1, 2]] admits an orthonormal basis of eigenvectors. What are the eigenvalues and an orthonormal eigenbasis for A?
A.\lambda_1 = 3 with v_1 = (1/\sqrt{2})(1, 1)^T, and \lambda_2 = 1 with v_2 = (1/\sqrt{2})(-1, 1)^T
B.\lambda_1 = 4 with v_1 = (1, 0)^T, and \lambda_2 = 0 with v_2 = (0, 1)^T
C.\lambda_1 = 3 with v_1 = (1, 1)^T, and \lambda_2 = 1 with v_2 = (-1, 1)^T (unnormalized)
D.\lambda_1 = 2 + \sqrt{2} with v_1 = (1/\sqrt{2})(1, -1)^T, and \lambda_2 = 2 - \sqrt{2} with v_2 = (1/\sqrt{2})(1, 1)^T
Explanation: The characteristic polynomial is det(A - \lambda I) = (2 - \lambda)^2 - 1 = \lambda^2 - 4\lambda + 3 = (\lambda - 3)(\lambda - 1) = 0, giving eigenvalues \lambda_1 = 3 and \lambda_2 = 1. Solving (A - 3I)v = 0 yields x = y, so v_1 = (1/\sqrt{2})(1, 1)^T, and solving (A - I)v = 0 yields x = -y, so v_2 = (1/\sqrt{2})(-1, 1)^T. These vectors are mutually orthogonal with unit norm.
3Consider the multivariable function f(x, y) = x^3 + y^3 - 3xy defined on R^2. Which statement correctly identifies its critical point in the first open quadrant (x > 0, y > 0) and determines its nature using the Hessian matrix?
A.The critical point is (1, 1) and it is a saddle point because det(H_f(1, 1)) = -27 < 0.
B.The critical point is (1, 1) and it is a strict local minimum with f(1, 1) = -1 because det(H_f(1, 1)) = 27 > 0 and \partial^2 f / \partial x^2 (1, 1) = 6 > 0.
C.The critical point is (1, 1) and it is a strict local maximum because f(1, 1) = -1 and the trace of H_f(1, 1) is negative.
D.The critical point is (3, 3) and it is a strict local minimum with f(3, 3) = 27.
Explanation: Setting the gradient \nabla f = (3x^2 - 3y, 3y^2 - 3x) = (0, 0) gives y = x^2 and x = y^2 = x^4, so x(x^3 - 1) = 0. In the quadrant x > 0, y > 0, the unique critical point is (1, 1). The Hessian matrix is H_f(x, y) = [[6x, -3], [-3, 6y]], so H_f(1, 1) = [[6, -3], [-3, 6]]. Its determinant is rt - s^2 = 36 - 9 = 27 > 0 and r = 6 > 0, which confirms a strict local minimum with value f(1, 1) = 1 + 1 - 3 = -1.
4For a > 0, consider the parametric improper integral I(a) = \int_0^\infty e^{-ax} \frac{\sin x}{x} dx. By differentiating under the integral sign with respect to a, what is the exact analytical expression of I(a), and what is its value at a = 1?
A.I(a) = \ln(1 + a^2), and I(1) = \ln 2
B.I(a) = \frac{\pi}{2} - a, and I(1) = \frac{\pi}{2} - 1
C.I(a) = \frac{1}{a^2 + 1}, and I(1) = \frac{1}{2}
D.I(a) = \frac{\pi}{2} - \arctan a = \arctan(1/a), and I(1) = \frac{\pi}{4}
Explanation: Applying Leibniz's rule, I'(a) = -\int_0^\infty e^{-ax} \sin x dx = -\frac{1}{a^2 + 1}. Integrating with respect to a gives I(a) = -\arctan a + C. As a -> +\infty, the integrand is dominated by e^{-ax} and \lim_{a -> +\infty} I(a) = 0, which implies C = \pi/2. Therefore, I(a) = \pi/2 - \arctan a = \arctan(1/a). At a = 1, I(1) = \pi/2 - \pi/4 = \pi/4.
5Let X_1 and X_2 be two independent discrete random variables following Poisson distributions with parameters \lambda_1 = 2 and \lambda_2 = 3 respectively. What is the probability generating function (fonction génératrice) G_S(t) = E[t^S] of their sum S = X_1 + X_2?
A.G_S(t) = e^{5(t - 1)}
B.G_S(t) = e^{6(t - 1)}
C.G_S(t) = \frac{1}{(1 - 5t)^2}
D.G_S(t) = e^{2(t - 1)} + e^{3(t - 1)}
Explanation: The probability generating function of a Poisson variable X ~ P(\lambda) is G_X(t) = \sum_{k=0}^\infty t^k e^{-\lambda} \lambda^k / k! = e^{\lambda(t - 1)}. By independence, the generating function of the sum S = X_1 + X_2 is the product of their individual generating functions: G_S(t) = G_{X_1}(t) G_{X_2}(t) = e^{2(t - 1)} e^{3(t - 1)} = e^{(2 + 3)(t - 1)} = e^{5(t - 1)}, which confirms that S ~ P(5).
6Consider the ill-conditioned 2x2 linear system matrix A = [[10, 9], [9, 8]]. What is the spectral condition number \kappa_2(A) = ||A||_2 \cdot ||A^{-1}||_2 with respect to the Euclidean 2-norm?
A.\kappa_2(A) = 1
B.\kappa_2(A) = 19
C.\kappa_2(A) = 163 + 18\sqrt{82} \approx 325.99
D.\kappa_2(A) = 80
Explanation: Since A is real symmetric, ||A||_2 = \max |\lambda_i| and ||A^{-1}||_2 = 1 / \min |\lambda_i|. The characteristic equation is det(A - \lambda I) = (10 - \lambda)(8 - \lambda) - 81 = \lambda^2 - 18\lambda - 1 = 0. The eigenvalues are \lambda = (18 \pm \sqrt{324 + 4})/2 = 9 \pm \sqrt{82}. The magnitudes are |\lambda_1| = 9 + \sqrt{82} and |\lambda_2| = \sqrt{82} - 9 = 1/(9 + \sqrt{82}). Thus, \kappa_2(A) = |\lambda_1| / |\lambda_2| = (9 + \sqrt{82})^2 = 81 + 82 + 18\sqrt{82} = 163 + 18\sqrt{82} \approx 325.99.
7In the topological space M_n(R) equipped with any norm, consider the general linear group GL_n(R) = {M \in M_n(R) : \det(M) \ne 0}. Which statement regarding its topological properties is correct?
A.GL_n(R) is compact and connected.
B.GL_n(R) is an open subset of M_n(R) with exactly two connected components: GL_n^+(R) and GL_n^-(R).
C.GL_n(R) is a closed, dense subvector space of M_n(R).
D.GL_n(R) is connected because any two invertible matrices can be joined by a continuous straight line segment.
Explanation: The determinant mapping \det: M_n(R) -> R is polynomial, hence continuous. Because R^* = (-\infty, 0) \cup (0, +\infty) is open in R, GL_n(R) = \det^{-1}(R^*) is open in M_n(R). Furthermore, the continuous image of a connected set is connected; since \det(GL_n(R)) = R^* is disconnected into two components, GL_n(R) is disconnected into exactly two connected components: GL_n^+(R) = \det^{-1}((0, +\infty)) and GL_n^-(R) = \det^{-1}((-\infty, 0)).
8Consider the series of functions \sum_{n=1}^\infty u_n(x) with u_n(x) = \frac{x}{n^2 + x^2} for x \ge 0. On which domain does this series converge normally (convergence normale)?
A.It converges normally on all of [0, +\infty).
B.It does not converge for any positive value of x.
C.It converges uniformly on [0, +\infty) but not pointwise on (0, +\infty).
D.It converges normally on every compact interval [0, A] (where A > 0), but does not converge normally on [0, +\infty).
Explanation: On any bounded interval [0, A], |u_n(x)| \le A / n^2, and \sum A/n^2 converges, so normal convergence holds on [0, A]. On [0, +\infty), the supremum of u_n(x) occurs at x = n, where u_n(n) = n / (2n^2) = 1/(2n). Because \sum 1/(2n) diverges (harmonic series), \sum ||u_n||_{\infty, [0, +\infty)} diverges, meaning normal convergence fails on [0, +\infty).
9Let A be an n x n real symmetric matrix with eigenvalues arranged in increasing order: \lambda_1 \le \lambda_2 \le \dots \le \lambda_n. According to the Rayleigh quotient and the Courant-Fischer min-max theorem, what is the value of \max_{x \in R^n, x \ne 0} \frac{x^T A x}{x^T x}?
A.\lambda_1
B.\mathrm{Tr}(A)
C.\lambda_n
D.\frac{1}{2}(\lambda_1 + \lambda_n)
Explanation: By the spectral theorem, there exists an orthonormal basis (e_1, ..., e_n) of eigenvectors with A e_i = \lambda_i e_i. Decomposing any x \ne 0 as x = \sum c_i e_i gives x^T A x = \sum \lambda_i c_i^2 \le \lambda_n \sum c_i^2 = \lambda_n ||x||^2. Equality is attained at x = e_n, proving that the maximum of the Rayleigh quotient is the largest eigenvalue \lambda_n.
10Using the method of Lagrange multipliers, minimize the Euclidean squared distance f(x, y, z) = x^2 + y^2 + z^2 subject to the affine hyperplane constraint x + 2y + 2z = 9 in R^3. What is the minimum value of f?
A.f_{min} = 3
B.f_{min} = 9
C.f_{min} = 81
D.f_{min} = 27
Explanation: Set the Lagrangian L(x, y, z, \lambda) = x^2 + y^2 + z^2 - \lambda(x + 2y + 2z - 9). The stationarity conditions give \nabla f = \lambda \nabla g, so (2x, 2y, 2z) = \lambda(1, 2, 2). This yields x = \lambda/2, y = \lambda, z = \lambda. Substituting into the constraint gives \lambda/2 + 2\lambda + 2\lambda = 9\lambda/2 = 9, so \lambda = 2. Thus (x, y, z) = (1, 2, 2), and f_{min} = 1^2 + 2^2 + 2^2 = 1 + 4 + 4 = 9. Geometrically, the distance from the origin to the plane is |9|/\sqrt{1^2+2^2+2^2} = 9/3 = 3, so the squared distance is 3^2 = 9.

About the Concours Centrale-Supélec Exam

The Concours Centrale-Supélec is one of the premier joint competitive entrance examinations in France, offering admission into 15 prestigious engineering grandes écoles. Administered by CentraleSupélec on behalf of the Groupe des Écoles Centrale and partner institutions, the concours recruits top students from the French Classes Préparatoires aux Grandes Écoles (CPGE) across five scientific filières: MP (Mathématiques-Physique), MPI (Mathématiques, Physique et Informatique), PC (Physique-Chimie), PSI (Physique et Sciences de l'Ingénieur), and TSI (Technologie et Sciences Industrielles). Participating schools include CentraleSupélec, École Centrale de Lyon, École Centrale de Nantes, École Centrale de Lille, École Centrale Méditerranée, Institut d'Optique Graduate School (IOGS), Arts et Métiers ParisTech, ENSEA, EPF, ESTP Paris, and École Navale. Candidates register nationally through the SCEI portal (Session 2026: registration 8 December 2025 – 12 January 2026 at 17:00, document upload and payment deadline 20 January 2026 at 17:00). Written eligibility papers (épreuves écrites) are held nationwide from 4 to 7 May 2026 (27 to 30 April 2026 for TSI). Admissible candidates proceed to oral examinations (épreuves orales) and TIPE presentations from 22 June to 19 July 2026. School ranking preferences (vœux) run from 1 March to 24 July 2026, with admissions offers released from 28 July 2026. This practice bank is an English-language MCQ study adaptation designed to reinforce core mathematical, physical, chemical, computational, and analytical concepts required across the shared CPGE curriculum.

Exam sponsor: CentraleSupélec — Service du Concours Centrale-Supélec. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written phase (écrits) over four days, 4–7 May 2026 (TSI 27–30 April 2026), for the MP, MPI, PC, PSI and TSI streams: two Mathématiques papers, Physique-chimie 1 and 2, Rédaction, Langue vivante, and an option paper (S2I or Informatique in MP; Informatique in MPI; Chimie in PC; S2I in PSI), each of four hours. Admissible candidates sit oral and practical examinations in the Paris region from 22 June to 19 July 2026 (TSI to 5 July, MPI from 6 July), including mathematics, physics-chemistry, a three-hour physics-chemistry TP specific to Centrale-Supélec, a modern language and the TIPE. Each school chooses which tests it uses for its own ranking.

Time Limit

3 to 4 hours per written paper; 30 to 45 minutes per oral examination

Passing Score

Competitive ranking based on weighted scores across written eligibility tests (admissibilité) and oral admission tests (admission); each member school applies its own specific coefficients and determines cutoffs.

Exam / Certification Fees

140 € per school for the Centrale group schools (CentraleSupélec, Centrale Lyon, Centrale Nantes, Centrale Lille, Centrale Méditerranée) and Institut d'Optique (IOGS); 135 € for Arts et Métiers and ENSEA; 85 € for EPF and ESTP; 0 € for École navale; free (full fee waiver) for French government scholarship holders (boursiers de l'État).

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.

30%

Mathématiques

Normed vector spaces, topology in finite and infinite dimensions, spectral decomposition of real symmetric and Hermitian operators, multivariable calculus (gradients, differentials, extrema under constraints), parametric integrals, series of functions, discrete random variables, probability generating functions, and linear system solvers.

25%

Physique

Analytical mechanics (Lagrangian, generalized coordinates, conservation laws), electromagnetism in linear and magnetized media, Faraday and Maxwell-Ampère induction, wave propagation in dispersive media, optical interference and Fraunhofer diffraction gratings, and statistical thermodynamics.

15%

Chimie et Sciences de la Matière

Solid-state chemistry and crystallography (BCC, FCC, hexagonal packing, interstitial sites, density calculations), chemical thermodynamics (standard enthalpy, entropy, free energy, chemical potential, Ellingham diagrams), reaction kinetics (activation energy, steady-state approximation), and organic reaction mechanisms.

15%

Informatique et Sciences Industrielles

Core computer science algorithms (graph traversal BFS/DFS, Dijkstra's shortest path, dynamic programming, binary search trees), feedback system theory (linear time-invariant systems, Laplace domain transfer functions, Bode plots, gain/phase stability margins, PID tuning, and state-space models).

15%

Français-Philosophie et Langue Vivante

Argumentative essay structuring (dissertation), epistemological and ethical debates linked to the official national CPGE theme, literary analysis of classical and contemporary texts, and advanced English scientific reading comprehension and nuance identification.

Preparing for the Concours Centrale-Supélec Exam

What You Need to Know

  • Passing score: Competitive ranking based on weighted scores across written eligibility tests (admissibilité) and oral admission tests (admission); each member school applies its own specific coefficients and determines cutoffs.
  • Assessment: Written phase (écrits) over four days, 4–7 May 2026 (TSI 27–30 April 2026), for the MP, MPI, PC, PSI and TSI streams: two Mathématiques papers, Physique-chimie 1 and 2, Rédaction, Langue vivante, and an option paper (S2I or Informatique in MP; Informatique in MPI; Chimie in PC; S2I in PSI), each of four hours. Admissible candidates sit oral and practical examinations in the Paris region from 22 June to 19 July 2026 (TSI to 5 July, MPI from 6 July), including mathematics, physics-chemistry, a three-hour physics-chemistry TP specific to Centrale-Supélec, a modern language and the TIPE. Each school chooses which tests it uses for its own ranking.
  • Time limit: 3 to 4 hours per written paper; 30 to 45 minutes per oral examination
  • Exam / certification fees: 140 € per school for the Centrale group schools (CentraleSupélec, Centrale Lyon, Centrale Nantes, Centrale Lille, Centrale Méditerranée) and Institut d'Optique (IOGS); 135 € for Arts et Métiers and ENSEA; 85 € for EPF and ESTP; 0 € for École navale; free (full fee waiver) for French government scholarship holders (boursiers de l'État). Official sources

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Concours Centrale-Supélec: Suggested Study Strategy

1For Mathematics, focus on rigorous proofs in normed vector space topology (compactness, completeness, equivalent norms in finite dimensions) and master spectral decomposition of symmetric matrices.
2Work through complete multi-step physics problems connecting analytical mechanics (Lagrangian equations of motion) with electromagnetic wave propagation and Maxwell's equations in matter.
3In Chemistry, practice quantitative calculations: atomic packing fraction and density in crystalline lattices (BCC, FCC), free energy delta G vs T lines on Ellingham diagrams, and multi-step organic reaction pathways.
4In Computer Science and Engineering, practice tracing graph algorithms (Dijkstra, BFS) and determining stability margins (gain margin, phase margin) from asymptotic Bode plots.
5For Français-Philosophie, construct clear, balanced three-part essay outlines addressing the annual CPGE theme with precise philosophical concepts and textual citations.

Frequently Asked Questions

What is the Concours Centrale-Supélec and which schools does it admit to?

The Concours Centrale-Supélec is a joint competitive entrance examination that selects students from scientific CPGE preparatory classes for admission into 15 prestigious French engineering grandes écoles, including CentraleSupélec (Paris-Saclay, Rennes, Metz), École Centrale de Lyon, École Centrale de Nantes, École Centrale de Lille, École Centrale Méditerranée, Institut d'Optique Graduate School (IOGS), Arts et Métiers ParisTech, ENSEA, EPF, ESTP Paris, and École Navale.

Which preparatory class filières are eligible for the Concours Centrale-Supélec?

Candidates sit the concours through their respective scientific tracks: MP (Mathématiques-Physique), MPI (Mathématiques, Physique et Informatique), PC (Physique-Chimie), PSI (Physique et Sciences de l'Ingénieur), and TSI (Technologie et Sciences Industrielles). Each filière has tailored examination papers and school intake quotas.

What are the key dates for the 2026 session of the Concours Centrale-Supélec?

Registration opens on the SCEI platform on 8 December 2025 and closes on 12 January 2026 at 17:00 CET. Supporting documentation and fee payments must be finalized by 20 January 2026 at 17:00 CET. Written examinations (épreuves écrites) take place from 4 to 7 May 2026 (27 to 30 April 2026 for TSI). Oral examinations (épreuves orales) take place from 22 June to 19 July 2026. Ranking lists and preference submissions (vœux) run from 1 March to 24 July 2026, with first-round offers published on 28 July 2026.

What are the registration fees for the concours?

Application fees are charged per school applied to: 140 € per school for the Centrale group institutions and Institut d'Optique (IOGS), 135 € for Arts et Métiers and ENSEA, 85 € for EPF and ESTP, and 0 € for École Navale. Candidates holding a French government scholarship (boursiers de l'État) receive a 100% fee waiver across all participating schools.

Is the official exam a multiple-choice test?

No. The official Concours Centrale-Supélec consists of long-form, multi-part open-ended written problem sets lasting 3 to 4 hours each, followed by rigorous oral examinations (colles/interrogations orales) in front of an examination jury. This practice bank is an English-language MCQ study adaptation developed to test core conceptual principles, mathematical derivations, and physical computations from the CPGE syllabus.

What is the role of the TIPE (Travaux d'Initiative Personnelle Encadrés)?

The TIPE is an independent research project conducted by candidates over the CPGE cycle centered around a designated national theme. Evaluated during the oral examination phase through a formal presentation and question session before a specialized jury, the TIPE score carries significant weight across multiple member schools.