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EMIG Concours d'entrée — Cycle de Technicien Grade Licence (Niger)

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Key Facts: EMIG Concours Ingénieur Exam

Coefficient 4

Weight of the 4-hour Mathematics paper common to all options in the EMIG Master entrance competition

EMIG 2026 Master concours notice (emig-niger.org)

Coefficient 3

Weight of each of the two 3-hour specialty papers set for the candidate's option

EMIG 2026 Master concours notice (emig-niger.org)

10,000 FCFA

Non-refundable application fee for the EMIG Cycle d'Ingénieur competition

EMIG 2026 Master concours notice (emig-niger.org)

10 hours

Total duration of the three written papers across the two-day session

EMIG 2026 Master concours notice (emig-niger.org)

Free independent practice for EMIG Niamey's Cycle d'Ingénieur Grade Master entrance competition: English-language MCQs on the common mathematics paper (linear algebra, calculus, differential equations, series, numerical methods) and on option topics including structures, hydraulics, electrotechnics, software analysis and algorithms, geology, roads, and analytical chemistry.

Sample EMIG Concours Ingénieur Practice Questions

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

1What are the eigenvalues of the real symmetric matrix A = [[5, 2], [2, 2]]?

A.2 and 5

B.1 and 6

C.3 and 4

D.-1 and -6

Explanation: The characteristic equation is det(A - lambda*I) = (5 - lambda)(2 - lambda) - (2)(2) = lambda^2 - 7*lambda + 6 = 0. Factoring gives (lambda - 1)(lambda - 6) = 0, so the eigenvalues are lambda = 1 and lambda = 6. Check: their sum 7 equals the trace and their product 6 equals det(A) = 10 - 4.

2For the matrix A = [[4, 2], [1, 3]], which of the following is an eigenvector associated with the eigenvalue lambda = 5?

A.[2, 1]^T

B.[1, -1]^T

C.[1, 2]^T

D.[2, -1]^T

Explanation: For lambda = 5, we solve (A - 5*I)v = 0: [[-1, 2], [1, -2]][x, y]^T = [0, 0]^T. This yields the single independent equation -x + 2y = 0, or x = 2y. Choosing y = 1 gives the eigenvector v = [2, 1]^T.

3A real 3x3 symmetric matrix A has eigenvalues lambda_1 = 1, lambda_2 = 2, and lambda_3 = 3. What is the determinant of A^2?

A.6

B.14

C.12

D.36

Explanation: The determinant of A is the product of its eigenvalues: det(A) = 1 * 2 * 3 = 6. By determinant properties, det(A^2) = (det(A))^2 = 6^2 = 36.

4What is the rank of the 3x4 matrix M = [[1, 2, 3, 4], [2, 4, 6, 8], [1, 0, 1, 0]]?

A.1

B.3

C.2

D.4

Explanation: Notice that Row 2 is exactly 2 * Row 1, making Row 2 linearly dependent on Row 1. Row 3 is not proportional to Row 1. Row-reducing yields two non-zero rows, so the rank of M is 2.

5According to the Cayley-Hamilton theorem, which matrix identity holds for A = [[2, 1], [3, 4]]?

A.A^2 - 5*A + 6*I = 0

B.A^2 - 6*A + 5*I = 0

C.A^2 + 6*A - 5*I = 0

D.A^2 - 6*A - 5*I = 0

Explanation: The characteristic polynomial of A is det(lambda*I - A) = lambda^2 - tr(A)*lambda + det(A). Here tr(A) = 2 + 4 = 6 and det(A) = (2)(4) - (1)(3) = 8 - 3 = 5. By the Cayley-Hamilton theorem, every square matrix satisfies its own characteristic equation: A^2 - 6*A + 5*I = 0.

6What is the gradient vector of the scalar function f(x, y, z) = x^2 * y + y * z^3 at the point P(1, 2, -1)?

A.[4, 0, 6]^T

B.[4, 2, -6]^T

C.[2, 0, -3]^T

D.[4, -1, 6]^T

Explanation: The partial derivatives are: df/dx = 2*x*y, df/dy = x^2 + z^3, and df/dz = 3*y*z^2. Evaluating at P(1, 2, -1): df/dx = 2(1)(2) = 4; df/dy = 1^2 + (-1)^3 = 1 - 1 = 0; df/dz = 3(2)(-1)^2 = 6. Thus, grad(f)(1, 2, -1) = [4, 0, 6]^T.

7What is the directional derivative of f(x, y) = x^2 + 3*y^2 at point P(2, 1) in the direction of the unit vector u = [3/5, 4/5]^T?

A.12/5

B.10

C.2*sqrt(13)

D.36/5

Explanation: The gradient is grad(f) = [2x, 6y]^T. At P(2, 1), grad(f) = [4, 6]^T. The directional derivative is grad(f) . u = 4*(3/5) + 6*(4/5) = 12/5 + 24/5 = 36/5.

8What is the divergence of the vector field F(x, y, z) = [x^2 * y, y^2 * z, z^2 * x]^T at point P(1, 2, 3)?

A.16

B.28

C.22

D.11

Explanation: Divergence is div(F) = d(F_x)/dx + d(F_y)/dy + d(F_z)/dz = 2*x*y + 2*y*z + 2*z*x. At P(1, 2, 3): 2(1)(2) + 2(2)(3) + 2(3)(1) = 4 + 12 + 6 = 22.

9What is the curl of the vector field F(x, y, z) = [y * z, x * z, x * y]^T?

A.[x, y, z]^T

B.[0, 0, 0]^T

C.[z, x, y]^T

D.[2z, 2x, 2y]^T

Explanation: Curl(F) = [d(xy)/dy - d(xz)/dz, d(yz)/dz - d(xy)/dx, d(xz)/dx - d(yz)/dy]^T = [x - x, y - y, z - z]^T = [0, 0, 0]^T. The field is conservative (F = grad(xyz)).

10Evaluate the double integral I = double_integral_D (x + 2*y) dA, where D is the rectangle [0, 2] x [0, 1].

A.4

B.3

C.2

D.6

Explanation: Integrating with respect to y first: integral_0^1 (x + 2y) dy = [x*y + y^2]_0^1 = x + 1. Integrating with respect to x: integral_0^2 (x + 1) dx = [x^2/2 + x]_0^2 = (4/2 + 2) - 0 = 2 + 2 = 4.

About the EMIG Concours Ingénieur Exam

The Cycle d'Ingénieur Grade Master at EMIG Niamey offers six options: Génie Logiciel, Électromécanique, Bâtiments et Travaux Publics, Génie Géologique, Eau et Environnement, and Électrotechnique. Entry is by a written competition: a common Mathematics paper plus two specialty papers for the chosen option. This independent bank gives English-language MCQ practice on the mathematics and specialty topics; it is a study adaptation, not an official translation or format simulation.

Exam sponsor: École des Mines, de l'Industrie et de la Géologie (EMIG), Niamey. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Day 1 (28 August 2026): Mathematics, common to all options, 08:00–12:00 (4 hours, coefficient 4). Day 2 (29 August 2026): two 3-hour specialty papers, 08:30–11:30 and 15:00–18:00 (coefficient 3 each), set by option. Génie Logiciel: Analyse et conception; Algorithme et programmation. Électromécanique: Électrotechnique; Construction mécanique. Bâtiments et Travaux Publics: Bâtiments; Routes. Génie Géologique (Géotechnique, Hydrogéologie et Ressources Minérales): Géologie générale; Pétrographie-Minéralogie. Eau et Environnement: Hydraulique; Chimie analytique. Électrotechnique: Électrotechnique; Technologie d'électricité.

Time Limit

10 hours of written papers across 2 days (4 h Mathematics + two 3 h specialty papers)

Passing Score

No fixed pass mark is published; the August 2026 results list admitted candidates for each option in order of merit by a coefficient-weighted average (Mathematics x4, each specialty paper x3)

Exam / Certification Fees

10,000 FCFA non-refundable application fee

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

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.

35% of this local bank (35 questions)

Applied Mathematics (common paper)

Linear algebra and eigenvalues, multivariable and vector calculus, differential equations, Laplace transforms, Fourier and power series, numerical methods, and probability

24% of this local bank (24 questions)

Mechanics, Structures, Hydraulics, and Geotechnics

Statics and dynamics, strength of materials and beam bending, fluid statics, Bernoulli and pipe flow, and soil effective stress and shear strength (Bâtiments, Construction mécanique, and Hydraulique topics)

16% of this local bank (16 questions)

Software Analysis, Algorithms, and Digital Systems

Algorithm complexity, searching and sorting, data structures, object-oriented design and UML, development life cycles, Boolean logic, and PLC basics (Analyse et conception and Algorithme et programmation topics)

15% of this local bank (15 questions)

Electrotechnics and Mechanical Construction

DC and AC circuit analysis, resonance, three-phase power and power-factor correction, transformers, induction and DC machines, and rolling-bearing life (Électrotechnique, Technologie d'électricité, and Construction mécanique topics)

5% of this local bank (5 questions)

Geology and Mineralogy

Igneous textures, Bowen's reaction series, Mohs hardness, silicate structures, and stratigraphic principles (Géologie générale and Pétrographie-Minéralogie topics)

3% of this local bank (3 questions)

Road Engineering

Horizontal curve radius, flexible pavement layers, and the California Bearing Ratio test (Routes topics)

2% of this local bank (2 questions)

Analytical Chemistry

Acid-base titration calculations and Beer-Lambert spectrophotometry (Chimie analytique topics)

Preparing for the EMIG Concours Ingénieur Exam

What You Need to Know

Passing score: No fixed pass mark is published; the August 2026 results list admitted candidates for each option in order of merit by a coefficient-weighted average (Mathematics x4, each specialty paper x3)
Assessment: Day 1 (28 August 2026): Mathematics, common to all options, 08:00–12:00 (4 hours, coefficient 4). Day 2 (29 August 2026): two 3-hour specialty papers, 08:30–11:30 and 15:00–18:00 (coefficient 3 each), set by option. Génie Logiciel: Analyse et conception; Algorithme et programmation. Électromécanique: Électrotechnique; Construction mécanique. Bâtiments et Travaux Publics: Bâtiments; Routes. Génie Géologique (Géotechnique, Hydrogéologie et Ressources Minérales): Géologie générale; Pétrographie-Minéralogie. Eau et Environnement: Hydraulique; Chimie analytique. Électrotechnique: Électrotechnique; Technologie d'électricité.
Time limit: 10 hours of written papers across 2 days (4 h Mathematics + two 3 h specialty papers)
Exam / certification fees: 10,000 FCFA non-refundable application fee Official sources

Using Our Practice Resources

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EMIG Concours Ingénieur: Suggested Study Strategy

1Give the common Mathematics paper the most time: it carries coefficient 4, against 3 for each specialty paper. Revise eigenvalues, multivariable calculus, differential equations, Laplace transforms, and series.

2Check your option's two specialty papers in the official notice and study those first, for example Hydraulique and Chimie analytique for Eau et Environnement.

3For Bâtiments, Construction mécanique, and Hydraulique, practise worked calculations: bending moments, stresses and deflection, Bernoulli's equation with head loss, and Reynolds number.

4For Électrotechnique and Technologie d'électricité, drill three-phase power, power-factor correction, transformer tests, and induction-motor slip.

5For Génie Logiciel, review algorithm complexity, sorting and searching, data structures, and UML class-diagram relationships; for Génie Géologique, review igneous textures, Bowen's series, and silicate structures.

Frequently Asked Questions

Is the EMIG Cycle d'Ingénieur concours a multiple-choice exam?

EMIG's 2026 notice lists timed written papers with their titles, durations, and coefficients; it does not describe a multiple-choice format or publish an item count. This bank is an independent English-language MCQ study adaptation for practising the underlying knowledge and calculations. It does not simulate the written papers or their French-language setting.

Which papers make up the 2026 Master entrance competition?

A 4-hour Mathematics paper common to all options (coefficient 4) on 28 August 2026, then two 3-hour specialty papers on 29 August (coefficient 3 each) that depend on the option, for example Bâtiments and Routes for Bâtiments et Travaux Publics, or Géologie générale and Pétrographie-Minéralogie for Génie Géologique. The notice lists no oral or interview stage.

Who is eligible to sit the EMIG Master entrance competition?

The 2026 notice opens the competition to holders of a scientific, technical, or professional Licence, or any other diploma judged equivalent. Applications were filed at EMIG from 6 to 20 August 2026 with a non-refundable 10,000 FCFA fee.