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Key Facts: Concours National Ingénieurs Tunisie Exam

4 concours

M-P, P-C, T and B-G

Guide du candidat 2026

44

Total coefficient of the M-P papers (46 for Concours T)

Guide du candidat 2026

+15 pts

Ranking bonus for admitted candidates with at most two years of preparatory cycle

Guide du candidat 2026

1 June 2026

Start of the 2026 written papers

concours-ingenieurs.rnu.tn

Tunisia's national engineering concours ranks candidates by a coefficient-weighted score on written papers in four concours (M-P, P-C, T, B-G). This independent English-language bank offers 100 conceptual MCQs on the mathematics, physics, chemistry, automated systems and computing content shared by the M-P, P-C and T concours.

Sample Concours National Ingénieurs Tunisie Practice Questions

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

1Let E and F be finite-dimensional real vector spaces with dim(E) = 7 and dim(F) = 4. Let f: E -> F be a linear transformation whose kernel has dimension 3 (dim(ker f) = 3). What is the dimension of the image of f (dim(Im f))?
A.4
B.3
C.7
D.1
Explanation: According to the Rank-Nullity Theorem (théorème du rang), for any linear map f: E -> F defined on a finite-dimensional space E, dim(E) = dim(ker f) + dim(Im f). Substituting the given values yields 7 = 3 + dim(Im f), which gives dim(Im f) = 4. Since dim(Im f) equals dim(F) = 4, f is also a surjective linear transformation.
2Let A be an n x n square matrix with real coefficients. Which of the following conditions is both necessary and sufficient for A to be invertible?
A.The trace of A is non-zero, and all diagonal entries are strictly positive.
B.The determinant of A is non-zero, and 0 is not an eigenvalue of A.
C.A is symmetric and has at least one non-zero eigenvalue.
D.The minimal polynomial of A has degree equal to n.
Explanation: A square matrix A is invertible if and only if its determinant is non-zero (det(A) != 0), which is equivalent to saying that its kernel is trivial and 0 is not an eigenvalue of A. If 0 were an eigenvalue, there would exist a non-zero vector v such that Av = 0, violating injectivity.
3Let A in M_n(C) be an n x n complex matrix. Which of the following conditions guarantees that A is diagonalizable over the complex field C?
A.Its characteristic polynomial has at least one root of multiplicity 1.
B.All entries of A are purely imaginary numbers.
C.Its minimal polynomial is split over C with simple roots.
D.The trace of A equals the sum of the diagonal elements of its inverse.
Explanation: In endomorphism reduction theory, an endomorphism of a finite-dimensional vector space is diagonalizable if and only if its minimal polynomial is split (factors completely into linear factors) with only simple roots. Over C, every polynomial is split, so the condition reduces precisely to the minimal polynomial having no repeated roots.
4Let u be a nilpotent endomorphism on an n-dimensional real vector space E, such that u^k = 0 for some integer k >= 1. Which statement regarding the eigenvalues and trace of u is correct?
A.The eigenvalues of u are +1 and -1, and tr(u) = 0.
B.The only eigenvalue of u in C is 0, and tr(u) = 0.
C.u has n distinct non-zero eigenvalues whose sum is 0.
D.The trace of u equals the dimension n of the vector space E.
Explanation: If lambda is an eigenvalue of u with eigenvector v != 0, then u(v) = lambda * v, which implies u^k(v) = lambda^k * v = 0. Since v != 0, lambda^k = 0, which implies lambda = 0. Therefore, 0 is the unique eigenvalue of u. Because the trace of an endomorphism is the sum of its eigenvalues counted with algebraic multiplicities, tr(u) = 0.
5Let E be a real inner product space equipped with inner product <u, v> and associated norm ||u|| = sqrt(<u, u>). What does the Cauchy-Schwarz inequality state, and under what condition does equality hold?
A.|<u, v>| >= ||u|| * ||v||, with equality if and only if u and v are orthogonal.
B.|<u, v>|^2 <= <u, u> + <v, v>, with equality if and only if u = v.
C.||u + v|| <= ||u|| - ||v||, with equality if and only if u and v are unit vectors.
D.|<u, v>| <= ||u|| * ||v||, with equality if and only if u and v are linearly dependent.
Explanation: The Cauchy-Schwarz inequality states that for all vectors u and v in an inner product space, |<u, v>| <= ||u|| * ||v||. Equality holds if and only if one of the vectors is a scalar multiple of the other (that is, u and v are linearly dependent/collinear).
6In R^3 equipped with the standard Euclidean dot product, let v_1 = (1, 1, 0) and v_2 = (1, 0, 1). Using the Gram-Schmidt orthogonalization process, what is the orthogonal projection of v_2 onto the subspace spanned by v_1?
A.(1/2, 1/2, 0)
B.(1, 1, 0)
C.(1/2, -1/2, 1)
D.(0, 1/2, 1/2)
Explanation: The orthogonal projection of v_2 onto v_1 is given by proj_{v_1}(v_2) = (<v_2, v_1> / <v_1, v_1>) * v_1. The inner product is <v_2, v_1> = (1)(1) + (0)(1) + (1)(0) = 1. The squared norm of v_1 is <v_1, v_1> = 1^2 + 1^2 + 0^2 = 2. Therefore, the projection is (1/2) * (1, 1, 0) = (1/2, 1/2, 0).
7Let A be a real symmetric matrix of size n. What does the spectral theorem guarantee?
A.A is invertible, since its eigenvalues are real
B.A is diagonalizable in an orthonormal basis
C.All eigenvalues of A are real and strictly positive
D.A has n pairwise distinct real eigenvalues
Explanation: The spectral theorem states that a symmetric endomorphism of a Euclidean space, or equivalently a real symmetric matrix, has real eigenvalues and is diagonalizable in an orthonormal basis: E is the orthogonal direct sum of the eigenspaces, and there is an orthogonal matrix P (P⁻¹ = Pᵀ) such that PᵀAP is diagonal.
8A matrix A ∈ M_n(R) satisfies A² − 3A + 2I_n = 0, and A is neither I_n nor 2I_n. What can be concluded?
A.A is nilpotent
B.A is not diagonalizable, because its minimal polynomial has degree 2
C.A is diagonalizable with spectrum {1, 2}
D.A is invertible with A⁻¹ = A − 3I_n
Explanation: The polynomial X² − 3X + 2 = (X − 1)(X − 2) annuls A and is split with simple roots, so A is diagonalizable and its eigenvalues lie in {1, 2}. Since A is neither I_n nor 2I_n, its minimal polynomial is exactly (X − 1)(X − 2), so both values are eigenvalues, and the kernel decomposition lemma gives Rⁿ = Ker(A − I_n) ⊕ Ker(A − 2I_n).
9Let A in M_2(R) be a 2 x 2 matrix with real entries. Using the Cayley-Hamilton theorem, which expression correctly relates the trace of A^2 to the trace and determinant of A?
A.tr(A^2) = (tr A)^2 - det(A)
B.tr(A^2) = (tr A)^2 + 2 det(A)
C.tr(A^2) = (tr A)^2 - 2 det(A)
D.tr(A^2) = tr(A) * det(A)
Explanation: The characteristic polynomial of a 2x2 matrix A is chi_A(X) = X^2 - (tr A) X + det(A). By the Cayley-Hamilton theorem, A satisfies its own characteristic equation: A^2 - (tr A) A + det(A) I_2 = 0. Taking the trace of both sides and using linearity gives tr(A^2) - (tr A) tr(A) + det(A) tr(I_2) = 0. Since tr(I_2) = 2, we have tr(A^2) - (tr A)^2 + 2 det(A) = 0, which yields tr(A^2) = (tr A)^2 - 2 det(A).
10Let u and v be two endomorphisms of a finite-dimensional complex vector space E. Assume that both u and v are diagonalizable and that they commute (u o v = v o u). What fundamental algebraic conclusion follows?
A.The product u o v is nilpotent.
B.Either u or v must be a scalar multiple of the identity.
C.All eigenvalues of u must also be eigenvalues of v.
D.u and v are diagonalizable in a common basis.
Explanation: A central theorem of linear algebra establishes that a family of commuting diagonalizable endomorphisms is simultaneously diagonalizable (codiagonalisable). Because u and v commute, each eigenspace of u is stable under v. The restriction of v to each eigenspace of u remains diagonalizable, allowing one to construct a basis of simultaneous eigenvectors for both u and v across all of E.

About the Concours National Ingénieurs Tunisie Exam

The Concours Nationaux d'Entrée aux Cycles de Formation d'Ingénieurs are Tunisia's national competitive entrance examinations to engineering schools, organized by the Ministère de l'Enseignement Supérieur et de la Recherche Scientifique through four concours: Mathématiques et Physique (M-P), Physique et Chimie (P-C), Technologie (T) and Biologie et Géologie (B-G). They are open to second-year preparatory-cycle students and to selected second-year LMD licence students in science and technology. Admission is decided by rank from written papers, and admitted candidates are assigned to programmes at schools such as EPT, ENIT, SUP'COM, ENSI and ENSIT according to their rank and stated choices. This resource is an independent English-language MCQ study adaptation covering the shared M-P, P-C and T content (mathematics, physics, chemistry, automated technical systems and computing); it does not cover the B-G biology and geology papers.

Exam sponsor: Ministère de l'Enseignement Supérieur et de la Recherche Scientifique (MESRS), République Tunisienne. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written papers only, anonymous and double-marked. Concours M-P: Mathématiques I (coef. 10, 4 h), Mathématiques II (6, 3 h), Physique (10, 4 h), Chimie inorganique (4, 2 h), Informatique (4, 2 h), Systèmes techniques automatisés (4, 3 h), Français (3, 2 h) and Anglais (3, 2 h), total 44. Concours P-C drops Mathématiques II, adds Chimie organique (3) and weights Mathématiques I at 11 and Physique at 12 (total 44); Concours T adds Conception et fabrication mécanique (6, 4 h) and weights STA at 6 (total 46); Concours B-G is built around biology and geology papers (total 44).

Time Limit

2–4 hours per written paper (M-P: Mathématiques I and Physique 4 h, Mathématiques II and Systèmes techniques automatisés 3 h, other papers 2 h); the 2026 written papers began on 1 June 2026

Passing Score

Competitive ranking: score = sum of marks out of 20 × paper coefficients; the jury publishes a merit-ranked list of admitted candidates within the places open (plus an optional complementary list); a zero in any paper can lead to elimination

Exam / Certification Fees

Paid online during registration at concours-ingenieurs.rnu.tn; the amount is set in each session's official communiqué and is not stated in the 2026 Guide du candidat

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% of this bank

Higher Mathematics

Linear algebra and reduction with annihilating polynomials, Euclidean spaces and the spectral theorem, power series and series of functions, integrals with a parameter and dominated convergence, differential calculus, differential equations, and discrete probability with generating functions.

30% of this bank

Physics

Mechanics (energy theorems, central forces, rigid bodies, oscillators), Maxwell's equations and electromagnetic waves, thermodynamics, wave optics and introductory quantum physics.

15% of this bank

Chemistry

Chemical thermodynamics and equilibria, Ellingham diagrams, electrochemistry and corrosion, Pourbaix E-pH diagrams, solution equilibria and kinetics.

13% of this bank

Systèmes Techniques Automatisés

Laplace transforms, first- and second-order systems, block diagrams and feedback, stability criteria, Bode diagrams, steady-state error and PID correction.

12% of this bank

Computer Science

Python programming, stacks and queues, object-oriented programming, sorting, relational algebra and SQL through sqlite3, Gaussian elimination, cryptography (Vigenère, RSA) and Lagrange interpolation.

Preparing for the Concours National Ingénieurs Tunisie Exam

What You Need to Know

  • Passing score: Competitive ranking: score = sum of marks out of 20 × paper coefficients; the jury publishes a merit-ranked list of admitted candidates within the places open (plus an optional complementary list); a zero in any paper can lead to elimination
  • Assessment: Written papers only, anonymous and double-marked. Concours M-P: Mathématiques I (coef. 10, 4 h), Mathématiques II (6, 3 h), Physique (10, 4 h), Chimie inorganique (4, 2 h), Informatique (4, 2 h), Systèmes techniques automatisés (4, 3 h), Français (3, 2 h) and Anglais (3, 2 h), total 44. Concours P-C drops Mathématiques II, adds Chimie organique (3) and weights Mathématiques I at 11 and Physique at 12 (total 44); Concours T adds Conception et fabrication mécanique (6, 4 h) and weights STA at 6 (total 46); Concours B-G is built around biology and geology papers (total 44).
  • Time limit: 2–4 hours per written paper (M-P: Mathématiques I and Physique 4 h, Mathématiques II and Systèmes techniques automatisés 3 h, other papers 2 h); the 2026 written papers began on 1 June 2026
  • Exam / certification fees: Paid online during registration at concours-ingenieurs.rnu.tn; the amount is set in each session's official communiqué and is not stated in the 2026 Guide du candidat Official sources

Using Our Practice Resources

  • Work through all 100 available questions
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Concours National Ingénieurs Tunisie: Suggested Study Strategy

1Practice diagonalization with annihilating polynomials and the kernel decomposition lemma, and apply the spectral theorem to real symmetric matrices.
2Rework Maxwell's equations, Poynting energy flow and boundary conditions for electromagnetic waves.
3Drill thermodynamic potentials and the Maxwell relations derived from them.
4For the Systèmes techniques automatisés paper, practise Laplace-domain analysis of first- and second-order systems, stability and Bode margins.
5Write and trace short Python programs using stacks, queues and classes, and run SQL queries through sqlite3.
6Combine chemical thermodynamics with Ellingham and Pourbaix diagrams.

Frequently Asked Questions

What are the Concours Nationaux d'Entrée aux Cycles de Formation d'Ingénieurs?

They are the national competitive examinations, organized each year by the Tunisian Ministry of Higher Education and Scientific Research (MESRS), through which candidates are ranked and assigned to programmes at public and partner engineering schools.

Which concours exist?

There are four: Mathématiques et Physique (M-P), Physique et Chimie (P-C), Technologie (T) and Biologie et Géologie (B-G). Each has its own set of written papers and coefficients, which are common to all the schools it gives access to.

Who can sit the concours?

Second-year students of a Tunisian preparatory cycle presented by their institution (type 1-a), second-year students of a foreign preparatory cycle (1-b), Tunisian preparatory students presented in one of the two previous years who have not confirmed an earlier admission (1-c), and high-achieving second-year LMD licence students in science and technology who have not repeated a year (type 2).

How are candidates scored and admitted?

Each candidate's score is the sum of their marks out of 20 multiplied by the paper coefficients. The jury publishes a merit-ranked list of admitted candidates within the places open, and possibly a complementary list. Admitted candidates who spent at most two years in the preparatory cycle receive a 15-point bonus in the preferential ranking used when programmes are chosen, and assignment follows rank and the candidates' choice forms.

What is the registration fee?

The fee is paid online when registering on concours-ingenieurs.rnu.tn. Its amount is set in each session's official communiqué; the 2026 Guide du candidat does not state it, so check the current communiqué.

Why is this practice bank in English and multiple-choice format?

The official papers are written problems in French (the Anglais paper in English). This resource is an independent English-language MCQ study adaptation for drilling definitions, theorems and methods; it is not an official translation and does not replace practice with full written derivations.

Does this resource replace official past papers?

No. Working through complete past concours papers under timed conditions remains essential. This bank is a supplementary conceptual drill.