100+ Free Concours INP-HB Cycle Ingénieur Practice Questions

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2026 Statistics

Key Facts: Concours INP-HB Cycle Ingénieur Exam

24,000 FCFA

Total cost of entering one INP-HB Cycle Ingénieur concours via TrésorPay

INP-HB Fiche info concours Ingénieur 2026

20,000 FCFA

Droit d'inscription charged per concours entered

INP-HB Fiche info concours Ingénieur 2026

25 years

Maximum candidate age on 31 December of the competition year

INP-HB Bureau Central des Concours

4 concours

Concours directs offered: CAE, GIN, GCN and A2GP

INP-HB Concours Ingénieur 2026

3 years

Duration of the INP-HB cycle Ingénieur following the cycle préparatoire

INP-HB règlement de scolarité

Free 100-question English MCQ study bank for the INP-HB Cycle Ingénieur entrance concours. The official exam is a set of French-language written papers (mathematics, physics, chemistry, computing, engineering sciences, French, English) set to the CPGE syllabus, with rank-based admission and no published pass mark. This bank is an English-language study adaptation, not an official-format simulation or translation.

Sample Concours INP-HB Cycle Ingénieur Practice Questions

Try these sample questions to test your Concours INP-HB Cycle Ingénieur exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Let A be a 3x3 real matrix with eigenvalues λ₁ = 1, λ₂ = 2, and λ₃ = -3. What is the determinant of the matrix B = A³ - 2A + I?

A.0

B.-100

C.84

D.-203

Explanation: By the spectral mapping theorem, if λ is an eigenvalue of A, then P(λ) is an eigenvalue of P(A). Here P(x) = x³ - 2x + 1. Evaluating P at the eigenvalues: P(1) = 1 - 2 + 1 = 0; P(2) = 8 - 4 + 1 = 5; P(-3) = -27 + 6 + 1 = -20. Since det(B) is the product of its eigenvalues, det(B) = 0 * 5 * (-20) = 0. The key observation is that λ = 1 is a root of P, so B is singular.

2What is the general solution to the second-order non-homogeneous differential equation y'' - 6y' + 9y = 18x + 3?

A.y(x) = (C₁ + C₂ x)e^(3x) + 2x + 5/3

B.y(x) = C₁ e^(3x) + C₂ e^(-3x) + 2x + 1

C.y(x) = (C₁ + C₂ x)e^(3x) + 18x + 3

D.y(x) = C₁ cos(3x) + C₂ sin(3x) + 2x + 5/3

Explanation: The characteristic equation is r² - 6r + 9 = (r - 3)² = 0, giving double root r = 3. Thus the homogeneous solution is y_h(x) = (C₁ + C₂ x)e^(3x). For the particular solution, try y_p(x) = Ax + B. Then y_p' = A and y_p'' = 0. Substituting gives 0 - 6A + 9(Ax + B) = 9Ax + (9B - 6A) = 18x + 3. Equating coefficients: 9A = 18 ⇒ A = 2; 9B - 12 = 3 ⇒ 9B = 15 ⇒ B = 5/3. Thus y(x) = (C₁ + C₂ x)e^(3x) + 2x + 5/3.

3Evaluate the line integral ∮_C [(y³ - 3y) dx + (3x - x³) dy] along the positively oriented unit circle C: x² + y² = 1.

A.9π / 2

B.6π

C.0

D.3π / 2

Explanation: By Green's Theorem, ∮_C (P dx + Q dy) = ∬_D (∂Q/∂x - ∂P/∂y) dA. Here P = y³ - 3y and Q = 3x - x³, so ∂Q/∂x = 3 - 3x² and ∂P/∂y = 3y² - 3. The integrand is (3 - 3x²) - (3y² - 3) = 6 - 3(x² + y²). Converting to polar coordinates over D (r from 0 to 1, θ from 0 to 2π): ∬_D (6 - 3r²) r dr dθ = 2π ∫₀¹ (6r - 3r³) dr = 2π [3r² - 3r⁴/4]₀¹ = 2π (3 - 3/4) = 2π (9/4) = 9π/2.

4What is the Laplace transform L{t e^(2t) sin(3t)} for s > 2?

A.6(s - 2) / ((s - 2)² + 9)²

B.3 / ((s - 2)² + 9)

C.6 / ((s - 2)² + 9)²

D.3(s - 2) / ((s - 2)² + 9)²

Explanation: First, L{sin(3t)} = 3 / (s² + 9). Using the multiplication-by-t rule L{t f(t)} = -d/ds F(s): -d/ds [3(s² + 9)⁻¹] = 3(2s)(s² + 9)⁻² = 6s / (s² + 9)². Finally, applying the frequency shift theorem L{e^(at) g(t)} = G(s - a) with a = 2 gives 6(s - 2) / ((s - 2)² + 9)².

5For a system of 4 linear equations in 6 unknowns represented by Ax = b, suppose rank(A) = 3 and b is in the column space of A. What is the dimension of the solution space?

A.3

B.1

C.2

D.4

Explanation: By the Rank-Nullity Theorem, for a matrix A with n columns, dim(Ker A) = n - rank(A). Here n = 6 and rank(A) = 3, so dim(Ker A) = 6 - 3 = 3. Since b is in the column space (Col A), the system is consistent and its solution set is an affine subspace of dimension equal to nullity(A) = 3.

6What is the radius of convergence R of the power series ∑_{n=1}^∞ ((n!)^2 / (2n)!) x^n?

A.4

B.1/4

C.1

D.+∞

Explanation: Use D'Alembert's ratio test: a_{n+1} / a_n = [((n+1)!)^2 / (2n+2)!] / [(n!)^2 / (2n)!] = (n+1)^2 / [(2n+2)(2n+1)] = (n+1)^2 / [2(n+1)(2n+1)] = (n+1) / [2(2n+1)]. As n → ∞, this limit L = lim (n+1)/(4n+2) = 1/4. The radius of convergence is R = 1/L = 4.

7Let X be a continuous random variable following an exponential distribution with parameter λ = 0.5 h⁻¹. What is the conditional probability P(X > 6 | X > 2)?

A.e^(-2)

B.e^(-3)

C.e^(-1)

D.1 - e^(-2)

Explanation: By the memoryless property of the exponential distribution, P(X > s + t | X > s) = P(X > t). Here s = 2 and s + t = 6, so t = 4. Thus P(X > 6 | X > 2) = P(X > 4) = e^(-λt) = e^(-0.5 * 4) = e^(-2).

8Find the directional derivative of f(x, y, z) = x² y + y z² at the point P(1, 2, -1) in the direction of vector v = (2, -1, 2).

A.-2/3

B.2/3

C.-2

D.4/3

Explanation: First compute the gradient: ∇f = (2xy, x² + z², 2yz). At P(1, 2, -1), ∇f(1, 2, -1) = (2(1)(2), 1² + (-1)², 2(2)(-1)) = (4, 2, -4). The unit direction vector is u = v / ||v|| = (2, -1, 2) / √(2² + (-1)² + 2²) = (2/3, -1/3, 2/3). The directional derivative is D_u f = ∇f · u = 4(2/3) + 2(-1/3) + (-4)(2/3) = (8 - 2 - 8) / 3 = -2/3.

9What is the value of the line integral ∮_C (z dx + x dy + y dz) along the triangle C connecting (1,0,0) to (0,1,0) to (0,0,1) and back to (1,0,0), oriented counterclockwise when viewed from above?

A.3/2

B.-3/2

C.0

D.3

Explanation: Apply Stokes' Theorem: ∮_C F · dr = ∬_S (curl F) · n dS. For F = (z, x, y), curl F = (∂F_z/∂y - ∂F_y/∂z, ∂F_x/∂z - ∂F_z/∂x, ∂F_y/∂x - ∂F_x/∂y) = (1, 1, 1). Take S as the flat triangle on the plane x + y + z = 1, whose unit normal is n = (1, 1, 1)/√3 and whose area element is dS = √3 dA over the xy-projection. Then curl F · n = 3/√3 = √3, so ∬_S curl F · n dS = √3 · √3 · Area(D) = 3 · Area(D). The projection D is the triangle with vertices (0,0), (1,0), (0,1), of area 1/2, giving 3 · (1/2) = 3/2. The orientation is consistent: projecting the path (1,0,0) → (0,1,0) → (0,0,1) onto the xy-plane gives (1,0) → (0,1) → (0,0), whose signed area is +1/2, i.e. counterclockwise seen from above, which is exactly the upward normal used here. Hence the integral is +3/2.

10Which of the following matrices is diagonalizable over ℝ?

A.[[1, 2], [2, 1]]

B.[[1, 1], [0, 1]]

C.[[0, -1], [1, 0]]

D.[[2, 1, 0], [0, 2, 1], [0, 0, 2]]

Explanation: The matrix [[1, 2], [2, 1]] is real symmetric. By the Spectral Theorem, every real symmetric matrix is orthogonally diagonalizable over ℝ. Its eigenvalues are roots of (1-λ)² - 4 = 0 ⇒ λ = 3 and λ = -1, which are distinct real numbers.

About the Concours INP-HB Cycle Ingénieur Exam

The Concours d'Entrée à l'INP-HB — Cycle Ingénieur is Côte d'Ivoire's most selective engineering entrance competition, run by the Bureau Central des Concours of the Institut National Polytechnique Félix Houphouët-Boigny in Yamoussoukro. It is open to students in the second year of a Classe Préparatoire aux Grandes Écoles, to holders of a Diplôme de Technicien Supérieur at licence grade, and to holders of specified Licences or equivalent diplomas, all aged 25 at most on 31 December of the competition year. It is organised as four concours directs — CAE at the École Supérieure de Commerce et d'Administration des Entreprises, GIN at the École Supérieure d'Industrie, GCN as a joint INP-HB / Université de San-Pedro competition, and A2GP covering agronomy, mines and geology, and process engineering — leading to the three-year cycle Ingénieur. This practice bank delivers 100 English-language MCQs on the knowledge the written papers draw on: advanced calculus and linear algebra, mechanics and strength of materials, thermodynamics, electrical circuits and control, chemistry and process engineering, computing, and technical English.

Assessment

Four separate concours directs run by the Bureau Central des Concours: CAE (Commerce et Administration des Entreprises, at ESCAE), GIN (Génies Industriel et Numérique, at ESI), GCN (Génies Civil et Naval, a concours commun INP-HB/Université de San-Pedro known as CCGIU), and A2GP (Agronomie, Géo-Ressources et Génie des Procédés). Each concours offers two or three options keyed to a CPGE filière. Selection is by written papers only — there is no separate admissibility jury: online pre-registration and file deposit are followed directly by composition and then by publication of the admission results. In the 2026 session, GIN and GCN composed on 13, 15 and 16 April, A2GP on 13, 14 and 15 April, and CAE on 17-18 April, with results published on 13 May 2026.

Time Limit

Registration (online pre-registration plus physical file deposit) followed by a single written composition stage of two to three days per concours. Individual papers run from 2 hours (Anglais 2, Informatique 2) to 5 hours (Mathématiques 2, Physique 1 and 2); a typical A2GP option totals 18 hours of examination.

Passing Score

Rank-ordered competitive quota admission (concours direct). No pass mark is published; selection depends strictly on the cumulative written score and ranking within the seats available in each filière.

Exam Fee

24,000 FCFA for one concours: 20,000 FCFA droit d'inscription per concours plus a 3,000 FCFA frais de dossier and a 1,000 FCFA frais de photo, each payable once regardless of the number of concours entered (all via TrésorPay). Two concours cost 44,000 FCFA. (Institut National Polytechnique Félix Houphouët-Boigny (INP-HB) — Bureau Central des Concours, Yamoussoukro)

Concours INP-HB Cycle Ingénieur Exam Content Outline

Study emphasis ~30%

Applied Mathematics & Linear Algebra

Matrices, eigenvalues, eigenvectors, quadratic forms, multivariable integration, differential equations, Fourier/Laplace transforms, and probability distributions.

Study emphasis ~25%

Physics & Mechanics of Materials

Newtonian mechanics, rotational dynamics, work-energy theorems, beam bending, torsion, Mohr's circle, stress analysis, and thermodynamic cycles.

Study emphasis ~20%

Applied Engineering Sciences, Chemistry & Systems

Three-phase electrical systems, RLC response, semiconductor and op-amp fundamentals, linear feedback control (Bode, Routh-Hurwitz, phase margin), algorithms and data structures for the Informatique paper, and chemistry/process engineering (Raoult's law, reactor design, heat exchangers).

Study emphasis ~15%

General Culture & Industrial Economy

Background for the CAE concours papers in Culture générale, Économie générale and Histoire-Géographie-Géopolitique: Ivorian infrastructure policy (PND), West African Power Pool, mining and energy transitions, and ethical engineering practice.

Study emphasis ~10%

Scientific & Technical English

Engineering terminology, technical passage comprehension, syntax in scientific reporting, and discourse connectors.

How to Pass the Concours INP-HB Cycle Ingénieur Exam

What You Need to Know

Passing score: Rank-ordered competitive quota admission (concours direct). No pass mark is published; selection depends strictly on the cumulative written score and ranking within the seats available in each filière.
Assessment: Four separate concours directs run by the Bureau Central des Concours: CAE (Commerce et Administration des Entreprises, at ESCAE), GIN (Génies Industriel et Numérique, at ESI), GCN (Génies Civil et Naval, a concours commun INP-HB/Université de San-Pedro known as CCGIU), and A2GP (Agronomie, Géo-Ressources et Génie des Procédés). Each concours offers two or three options keyed to a CPGE filière. Selection is by written papers only — there is no separate admissibility jury: online pre-registration and file deposit are followed directly by composition and then by publication of the admission results. In the 2026 session, GIN and GCN composed on 13, 15 and 16 April, A2GP on 13, 14 and 15 April, and CAE on 17-18 April, with results published on 13 May 2026.
Time limit: Registration (online pre-registration plus physical file deposit) followed by a single written composition stage of two to three days per concours. Individual papers run from 2 hours (Anglais 2, Informatique 2) to 5 hours (Mathématiques 2, Physique 1 and 2); a typical A2GP option totals 18 hours of examination.
Exam fee: 24,000 FCFA for one concours: 20,000 FCFA droit d'inscription per concours plus a 3,000 FCFA frais de dossier and a 1,000 FCFA frais de photo, each payable once regardless of the number of concours entered (all via TrésorPay). Two concours cost 44,000 FCFA.

Keys to Passing

Work through all 100 available questions
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Concours INP-HB Cycle Ingénieur Study Tips from Top Performers

1Master linear algebra and differential equations: practice calculating eigenvalues, matrix exponentiation, and solving non-homogeneous second-order ODEs without assistance.

2Review strength of materials (RDM): focus on shear force and bending moment diagrams, normal stress calculation in beams, and Mohr's stress circle.

3Consolidate thermodynamics, chemistry and electrical circuits: study Carnot and Brayton cycles, acid-base and vapour-liquid equilibria, three-phase active and reactive power, and RLC response.

4Stay informed on West African industrial developments, including Côte d'Ivoire's major transport corridors, energy grids, and mining extraction frameworks.

Frequently Asked Questions

Is the INP-HB Cycle Ingénieur entrance examination multiple-choice?

No. The official competition consists of open-ended written problem papers, mathematical derivations, and essays, sat in French to the CPGE syllabus. This bank is an English-language MCQ study adaptation, not a translation of the official paper or a simulation of its format.

Who is eligible to sit the INP-HB Cycle Ingénieur concours?

Candidates must be aged 25 at most on 31 December of the examination year and must either be enrolled in the second year of the CPGE filière required by their chosen concours and option (ECG, MP, PC, PSI or BCPST), or hold a Diplôme de Technicien Supérieur at licence grade, or hold one of the Licences listed for that concours, or hold a diploma admitted by equivalence.

What does the INP-HB Cycle Ingénieur competition cost?

24,000 FCFA for a single concours: a 20,000 FCFA droit d'inscription per concours, plus a 3,000 FCFA frais de dossier and a 1,000 FCFA frais de photo that are each paid only once. Entering two concours costs 44,000 FCFA. All payments go through TrésorPay.

Which concours make up the INP-HB Cycle Ingénieur competition?

Four concours directs: CAE (Commerce et Administration des Entreprises, at ESCAE), GIN (Génies Industriel et Numérique, at ESI), GCN (Génies Civil et Naval, run jointly with the Université de San-Pedro), and A2GP (Agronomie, Géo-Ressources et Génie des Procédés).