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Key Facts: Concours e3a-Polytech Exam

4 filières

MP, MPI, PC and PSI second-year preparatory streams

e3a-polytech.fr

21–24 April 2026

Written papers; admissibilité published 3 June 2026 at 18:00

Calendrier e3a-Polytech 2026

240 €

Common dossier fee shared with CCINP (0 € for boursiers), plus per-concours supplements

e3a-Polytech / CCINP 2026

130 €

Supplement for the Concours Polytech, which alone offers 1,192 places across 33 schools in 2026

demain-ingenieur.fr, 2026

Since 2020

Français-philosophie, langue vivante and selected science papers mutualised with CCINP

e3a-polytech.fr

22 July 2026

Final classement published at 20:00; first integration offers 28 July 2026

Calendrier e3a-Polytech 2026

The primary competitive examination bank for CPGE MP, MPI, PC, and PSI students seeking admission to 67 engineering schools (including the Réseau Polytech, Avenir Prépas, and Ingéni'UP), featuring mutualised CCINP general papers alongside proprietary e3a-Polytech mathematics and physics examinations.

Sample Concours e3a-Polytech Practice Questions

Try these sample questions to review concepts for the Concours e3a-Polytech exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Calculate the determinant of the 2x2 real matrix M = [[3, -2], [4, 5]].
A.23
B.7
C.15
D.-23
Explanation: For any 2x2 matrix [[a, b], [c, d]], the determinant is given by det(M) = ad - bc. Here, det(M) = (3)(5) - (-2)(4) = 15 - (-8) = 15 + 8 = 23.
2Determine the eigenvalues of the matrix A = [[4, 1], [2, 3]] in M_2(R).
A.lambda = 1 and lambda = 6
B.lambda = 2 and lambda = 5
C.lambda = 3 and lambda = 4
D.lambda = -2 and lambda = -5
Explanation: The characteristic polynomial is det(A - lambda I) = (4 - lambda)(3 - lambda) - 2 = lambda^2 - 7 lambda + 12 - 2 = lambda^2 - 7 lambda + 10 = (lambda - 2)(lambda - 5). The roots are lambda_1 = 2 and lambda_2 = 5.
3Let A in M_3(R) be a diagonal matrix with diagonal entries 2, -1, and 3. What is the characteristic polynomial chi_A(X) = det(X I_3 - A)?
A.X^3 - 4X^2 - X + 6
B.X^3 + 4X^2 + X - 6
C.X^3 - 4X^2 + X + 6
D.X^3 - 6X^2 + 11X - 6
Explanation: For a diagonal matrix, chi_A(X) = (X - 2)(X + 1)(X - 3). Expanding: (X - 2)(X + 1) = X^2 - X - 2; then (X^2 - X - 2)(X - 3) = X^3 - 3X^2 - X^2 + 3X - 2X + 6 = X^3 - 4X^2 + X + 6.
4A 3x3 real matrix M has eigenvalues 1, 2, and -3. What are its trace tr(M) and determinant det(M)?
A.tr(M) = 6, det(M) = -6
B.tr(M) = 0, det(M) = 6
C.tr(M) = -6, det(M) = 0
D.tr(M) = 0, det(M) = -6
Explanation: The trace of a matrix is the sum of its eigenvalues: tr(M) = 1 + 2 + (-3) = 0. The determinant is the product of its eigenvalues: det(M) = (1)(2)(-3) = -6.
5Let A in M_2(R) be diagonalizable such that A = P D P^(-1) with D = diag(1, 2). For any integer k >= 1, what is D^k?
A.[[1, 0], [0, 2^k]]
B.[[k, 0], [0, 2k]]
C.[[1, 0], [0, 2^k + 1]]
D.[[1, 0], [0, 2]]
Explanation: Powers of a diagonal matrix are obtained by raising each diagonal entry to the power k: D^k = diag(1^k, 2^k) = [[1, 0], [0, 2^k]]. Consequently, A^k = P D^k P^(-1).
6Let f: R^5 -> R^3 be a linear map between real vector spaces. If dim(Ker f) = 2, what is the dimension of the image Im(f)?
A.2
B.3
C.5
D.1
Explanation: By the rank-nullity theorem (théorème du rang), dim(Ker f) + dim(Im f) = dim(E), where E = R^5. Thus, 2 + dim(Im f) = 5, which gives dim(Im f) = 3. Since the codomain is R^3 and dim(Im f) = 3, f is surjective.
7Calculate the inverse of the matrix B = [[2, 1], [5, 3]] in GL_2(R).
A.[[-3, 1], [5, -2]]
B.[[2, -1], [-5, 3]]
C.[[3, -1], [-5, 2]]
D.[[3, 1], [5, 2]]
Explanation: The determinant is det(B) = (2)(3) - (1)(5) = 6 - 5 = 1. For a 2x2 matrix [[a, b], [c, d]], B^(-1) = (1/det(B)) [[d, -b], [-c, a]]. Thus B^(-1) = [[3, -1], [-5, 2]].
8Apply d'Alembert's ratio test (règle de d'Alembert) to examine the convergence of the numerical series sum_{n=1}^infty (n! / 3^n). What is the conclusion?
A.The series converges because the ratio tends to 1/3
B.The series converges conditionally
C.The ratio test is inconclusive because the limit is 1
D.The series diverges because lim (u_{n+1} / u_n) = +infinity > 1
Explanation: Evaluating the ratio of consecutive terms: u_{n+1}/u_n = [(n+1)! / 3^(n+1)] / [n! / 3^n] = (n + 1)/3. As n -> +infinity, (n + 1)/3 -> +infinity. Since this limit exceeds 1, d'Alembert's test establishes that the series diverges grossièrement.
9Compute the sum of the convergent geometric series S = sum_{n=0}^infty (2/3)^n.
A.3
B.2
C.3/2
D.1/3
Explanation: For |q| < 1, the sum of a geometric series starting at n = 0 is S = 1 / (1 - q). With q = 2/3, S = 1 / (1 - 2/3) = 1 / (1/3) = 3.
10What is the radius of convergence R of the power series sum_{n=1}^infty (n! / n^n) x^n?
A.R = 1
B.R = e
C.R = 1/e
D.R = +infinity
Explanation: Using d'Alembert's ratio test on the coefficients a_n = n! / n^n: a_{n+1} / a_n = [(n+1)! / (n+1)^(n+1)] * [n^n / n!] = (n+1) n^n / (n+1)^(n+1) = [n / (n+1)]^n = 1 / (1 + 1/n)^n. As n -> infinity, (1 + 1/n)^n -> e, so a_{n+1} / a_n -> 1/e. The radius of convergence is R = 1 / lim |a_{n+1} / a_n| = 1 / (1/e) = e.

About the Concours e3a-Polytech Exam

The Concours e3a-Polytech is one of the cornerstone competitive examination pools (banques d'épreuves) in the French Classes Préparatoires aux Grandes Écoles (CPGE) system. Tailored for second-year scientific prep students (Mathématiques Spéciales) in the MP (Maths-Physique), MPI (Maths-Physique-Informatique), PC (Physique-Chimie), and PSI (Physique et Sciences de l'Ingénieur) streams, the concours acts as the single gateway to 67 prestigious engineering schools across France, collectively offering more than 2,300 accredited engineering places (titre d'ingénieur diplômé, accredited by the CTI). Participating networks include the 16 university engineering schools of the Réseau Polytech (such as Polytech Sorbonne, Polytech Paris-Saclay, Polytech Lyon, and Polytech Nantes), the Avenir Prépas consortium (ECE, EPF, ESTACA, ESILV), the Ingéni'UP network (formerly FESIC Prépa, including ECAM LaSalle, HEI, ISEN, ISEP, and ICAM), and notable independent military and civilian institutions like ESM Saint-Cyr. Registration takes place via the SCEI national portal between December and January. Since the 2020 mutualisation reform with the Concours Commun INP (CCINP), general written tests (Français-Philosophie and Langue Vivante A) and certain stream-specific scientific papers are shared between CCINP and e3a-Polytech, sparing candidates duplicated examinations while preserving specific Mathematics and Physique-Chimie papers created directly by the Banque e3a-Polytech.

Exam sponsor: Banque e3a-Polytech (managed in cooperation with CCINP and SCEI). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written phase (écrits) over four days, 21–24 April 2026, for the MP, MPI, PC and PSI streams. Since 2020 the français-philosophie paper, the langue vivante paper and one to two science papers per filière are mutualised with the CCINP bank and sat only once, while the e3a-Polytech mathematics and physique-chimie papers are specific to this bank. Admissibilité is published on 3 June 2026 at 18:00; admissible candidates then sit the orals of the sub-concours they entered (Concours Polytech, Avenir Prépas, Ingéni'UP and others). The final classement is published on 22 July 2026 at 20:00, with the first integration offers on 28 July 2026.

Time Limit

3 to 4 hours per paper (4-day written session: 21–24 April 2026)

Passing Score

Competitive ranking: eligibility thresholds (admissibilité) are determined by school-specific coefficient weighting of written marks; final admission depends on subsequent oral interrogations (oraux) and national SCEI ranking.

Exam / Certification Fees

240 € common dossier fee shared with CCINP (0 € for boursiers de l'État) plus sub-concours fees: Concours Polytech 130 €, Avenir Prépas 65 €, Ingéni'UP 50 €.

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

Linear algebra (vector spaces, matrix reduction, eigenvalues, eigenvectors, trace, determinants, orthogonal matrices), analysis (convergence of numerical series, power series radius and sum, linear differential equations of order 1 and 2, multivariate calculus, directional derivatives), and discrete probability spaces (random variables, expectation, variance, binomial, geometric, and Poisson distributions).

25%

Physique

Point-particle Newtonian mechanics, harmonic and damped oscillators, energy balance theorems, angular momentum in central force fields, wave phenomena, interference in Young's double-slit and Michelson setups, thin-lens optics, Maxwell's equations and static fields (Gauss's law, Ampère's theorem, Lorentz force), classical thermodynamics (first and second laws, state functions, PV cycles, heat engine efficiency), and RLC transient and sinusoidal circuit regimes.

15%

Chimie

Aqueous chemical equilibria, acid-base pairs, Henderson-Hasselbalch relations, pH buffer solutions, precipitation equilibria (solubility product Ks), coordination complexes (formation constants Kf), oxidation-reduction equilibria, the Nernst equation, electrochemical cells and titrations, chemical kinetics (reaction orders, rate constants, Arrhenius law), and foundational organic reaction mechanisms.

15%

Sciences Industrielles & Informatique

Linear time-invariant (LTI) continuous system modeling, Laplace transform fundamentals, canonical first- and second-order transfer functions, transient step-response metrics (rise time, settling time, damping factor, percent overshoot), frequency-domain Bode plots, combinational logic, and Python programming (control structures, list slicing, algorithm complexity, and numerical algorithms including Euler integration and Newton-Raphson).

15%

Français-Philosophie & Langue Vivante

Methodology of the CPGE dissertation on the annual national French-philosophy theme, structural analysis of philosophical arguments, evaluation of thesis-antithesis-synthesis coherence, textual analysis, and advanced modern English comprehension focusing on grammar, scientific idiom, vocabulary precision, and logical discourse markers.

Preparing for the Concours e3a-Polytech Exam

What You Need to Know

  • Passing score: Competitive ranking: eligibility thresholds (admissibilité) are determined by school-specific coefficient weighting of written marks; final admission depends on subsequent oral interrogations (oraux) and national SCEI ranking.
  • Assessment: Written phase (écrits) over four days, 21–24 April 2026, for the MP, MPI, PC and PSI streams. Since 2020 the français-philosophie paper, the langue vivante paper and one to two science papers per filière are mutualised with the CCINP bank and sat only once, while the e3a-Polytech mathematics and physique-chimie papers are specific to this bank. Admissibilité is published on 3 June 2026 at 18:00; admissible candidates then sit the orals of the sub-concours they entered (Concours Polytech, Avenir Prépas, Ingéni'UP and others). The final classement is published on 22 July 2026 at 20:00, with the first integration offers on 28 July 2026.
  • Time limit: 3 to 4 hours per paper (4-day written session: 21–24 April 2026)
  • Exam / certification fees: 240 € common dossier fee shared with CCINP (0 € for boursiers de l'État) plus sub-concours fees: Concours Polytech 130 €, Avenir Prépas 65 €, Ingéni'UP 50 €. Official sources

Using Our Practice Resources

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Concours e3a-Polytech: Suggested Study Strategy

1Linear Algebra Reduction: Master eigenvalues, eigenspaces, characteristic polynomials, and the diagonalization criterion (P^-1 A P = D) for 3x3 matrices; practice computing matrix powers A^k using spectral decomposition.
2Series and Sequences: Systematically verify hypotheses for d'Alembert's ratio test, Cauchy's root test, and the alternating series test (théorème des séries alternées) before declaring convergence.
3Differential Equations and Oscillators: Practice finding general solutions for linear 2nd-order ODEs with constant coefficients by solving the characteristic equation, identifying the resonant frequency, and computing the quality factor Q.
4Thermodynamics & Carnot Cycles: Memorize state function relationships for ideal gases (dU = Cv dT, dH = Cp dT, Mayer's relation Cp - Cv = R) and practice calculating efficiency eta = 1 - Tc/Th for reversible thermodynamic cycles.
5Aqueous Equilibria & Electrochemistry: Apply the Henderson-Hasselbalch equation (pH = pKa + log([A-]/[HA])) and the Nernst equation (E = E° + (0.059/n) log(Ox/Red)) swiftly under time constraints.
6Control Systems (SII): Identify damping ratios zeta and undamped natural frequencies omega_0 directly from canonical transfer functions H(s) = K / (1 + 2*zeta*s/omega_0 + s^2/omega_0^2) to predict transient step overshoot.
7Python Algorithmic Complexity: Understand big-O runtimes for search, sort, and recursion in Python, and practice stepping through iterative approximations (e.g. dichotomy, Newton's method).

Frequently Asked Questions

What is the Concours e3a-Polytech and which engineering schools recruit through it?

The Concours e3a-Polytech is a major French competitive entrance examination bank (banque d'épreuves) that enables students in scientific preparatory classes (CPGE MP, MPI, PC, and PSI) to compete for entry into 67 Grandes Écoles d'Ingénieurs. The member schools include the 16 university-based engineering schools of the Réseau Polytech (e.g., Polytech Sorbonne, Polytech Lyon, Polytech Paris-Saclay), private and associative engineering schools belonging to Concours Avenir Prépas (such as EPF, ESTACA, and ESILV), the Ingéni'UP federation (such as ECAM LaSalle, HEI, ISEN, and ISEP), and various specialized independent institutes across France.

How does the mutualisation between Concours e3a-Polytech and CCINP work?

Since the 2020 examination session, the Banque e3a-Polytech and the Concours Commun INP (CCINP) have mutualised several written examinations to reduce candidate fatigue. Specifically, the Français-Philosophie (4-hour essay) and Langue Vivante A (3-hour modern language test) papers are shared and sat only once by candidates registered for both concours. Additionally, stream-specific papers such as the Informatique paper in MPI or the Sciences Industrielles paper in PSI are mutualised. However, the core Mathematics and Physique-Chimie tests are authored independently by e3a-Polytech.

What is the fee structure for registering for Concours e3a-Polytech in 2026?

Candidates pay a common dossier management fee of 240 € via the SCEI portal, which is shared with CCINP (free for French government scholarship recipients / boursiers). In addition, candidates pay specific supplementary fees depending on the school clusters they select: 130 € to apply to all 32 schools recruiting via Concours Polytech (0 € for boursiers), 65 € for Concours Avenir Prépas, 50 € for Ingéni'UP, plus modest variable fees for individual independent schools.

What are the key dates for the 2026 examination session?

For Session 2026, registration opens on the national SCEI platform (scei-concours.fr) on 8 December 2025 and closes on 12 January 2026 at 17:00 CET. The national written examinations (épreuves écrites) are sat between 21 April and 24 April 2026. Admissibility results (admissibilité) are published on 3 June 2026 at 18:00 CET. Oral examinations (oraux) occur throughout June and early July. The final national ranking (classement) is released on 22 July 2026 at 20:00 CET, followed by the first round of SCEI integration offers on 28 July 2026.

What format do the actual written and oral examinations take?

The official Concours e3a-Polytech written papers consist of rigorous, multi-hour handwritten problem-solving exams (épreuves de synthèse) lasting 3 to 4 hours each. Candidates must write out complete mathematical proofs, derive physical and chemical formulas, and construct structured philosophical essays in French. Admissible candidates then sit oral interrogations (oraux) and present their Travaux d'Initiative Personnelle Encadrés (TIPE) research projects before examination juries. This practice question bank is an English-language MCQ study adaptation crafted to provide rapid conceptual drills, calculation training, and syllabus review.

Which foreign modern languages are available in the written examination?

Under the mutualised CCINP / e3a-Polytech regulations, candidates may sit their mandatory Langue Vivante A (LVA) paper in one of seven official languages: German (allemand), English (anglais), Arabic (arabe), Spanish (espagnol), Italian (italien), Portuguese (portugais), or Russian (russe). The paper assesses reading comprehension, translation (version), and guided essay composition.