100+ Free Concours ENSPY Practice Questions

Prepare for the Concours ENSPY — École Nationale Supérieure Polytechnique de Yaoundé (Cameroon) exam with instant access — no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately

100+ Questions

100% Free

Loading practice questions...

2026 Statistics

Key Facts: Concours ENSPY Exam

20,000 FCFA

Non-refundable Concours Registration Fee

MINESUP Concours Arrêté

4 x 3 Hours

Written papers of equal weight, with no oral examination

MINESUP Communiqué opening the concours

400 places

First-year engineering places opened for 2026/2027

MINESUP Communiqué, 13 May 2026

The Concours ENSPY is Cameroon's most competitive engineering entrance examination: four 3-hour written papers of equal weight in Mathematics and Physics, no oral, set on the common ground of the Première and Terminale science programmes, with 400 first-year engineering places opened for 2026/2027.

Sample Concours ENSPY Practice Questions

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

1Let $z_1 = 1 + i\sqrt{3}$ and $z_2 = 1 - i$. What is the trigonometric/polar form of the quotient $Z = \frac{z_1}{z_2}$?

A.Z = \sqrt{2} \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right)

B.Z = \sqrt{2} \left(\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)\right)

C.Z = 2 \left(\cos\left(\frac{7\pi}{12}\right) + i \sin\left(\frac{7\pi}{12}\right)\right)

D.Z = 1 \left(\cos\left(\frac{5\pi}{12}\right) + i \sin\left(\frac{5\pi}{12}\right)\right)

Explanation: $|z_1| = \sqrt{1 + 3} = 2$ and $\arg(z_1) = \frac{\pi}{3}$. $|z_2| = \sqrt{1 + 1} = \sqrt{2}$ and $\arg(z_2) = -\frac{\pi}{4}$. Thus, $|Z| = \frac{|z_1|}{|z_2|} = \frac{2}{\sqrt{2}} = \sqrt{2}$. The argument is $\arg(Z) = \arg(z_1) - \arg(z_2) = \frac{\pi}{3} - \left(-\frac{\pi}{4}\right) = \frac{4\pi + 3\pi}{12} = \frac{7\pi}{12}$. Therefore, $Z = \sqrt{2} e^{i 7\pi/12}$.

2What is the determinant of the $3 \times 3$ real matrix $A = \begin{pmatrix} 2 & 1 & 3 \\ 0 & 4 & -1 \\ 0 & 0 & 5 \end{pmatrix}$?

A.40

B.0

C.20

D.11

Explanation: Matrix $A$ is upper triangular. The determinant of any triangular matrix is simply the product of its main diagonal elements: $\det(A) = 2 \times 4 \times 5 = 40$.

3A geometric sequence $(u_n)$ of positive terms satisfies $u_2 = 12$ and $u_5 = 96$. What is its common ratio $q$ and its first term $u_0$?

A.q = 2 and u_0 = 3

B.q = 2 and u_0 = 6

C.q = 4 and u_0 = 3

D.q = 8 and u_0 = 1.5

Explanation: For a geometric sequence, $u_5 = u_2 \cdot q^{3}$, so $q^3 = \frac{u_5}{u_2} = \frac{96}{12} = 8$ and therefore $q = 2$. Working back from $u_2 = u_0 \cdot q^2$: $12 = u_0 \times 4$, so $u_0 = 3$. Checking: the sequence runs $3, 6, 12, 24, 48, 96$.

4Find the eigenvalues $\lambda$ of the matrix $M = \begin{pmatrix} 3 & 1 \\ 2 & 2 \end{pmatrix}$.

A.λ₁ = 4 and λ₂ = 1

B.λ₁ = 3 and λ₂ = 2

C.λ₁ = 5 and λ₂ = 0

D.λ₁ = 2 and λ₂ = -1

Explanation: Characteristic polynomial: $P(\lambda) = \det(M - \lambda I) = (3 - \lambda)(2 - \lambda) - (1)(2) = \lambda^2 - 5\lambda + 6 - 2 = \lambda^2 - 5\lambda + 4 = 0$. Factoring gives $(\lambda - 4)(\lambda - 1) = 0 \implies \lambda_1 = 4, \lambda_2 = 1$. (Check: $\text{Tr}(M) = 3 + 2 = 5 = 4 + 1$; $\det(M) = 6 - 2 = 4 = 4 \times 1$).

5What is the cross product $\vec{u} \times \vec{v}$ of vectors $\vec{u} = (1, 2, 3)$ and $\vec{v} = (4, 5, 6)$ in $\mathbb{R}^3$?

A.(-3, 6, -3)

B.(3, -6, 3)

C.(32, 32, 32)

D.(0, 0, 0)

Explanation: Using determinant expansion: $\vec{u} \times \vec{v} = \begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ 1 & 2 & 3 \\ 4 & 5 & 6 \end{vmatrix} = \vec{i}(12 - 15) - \vec{j}(6 - 12) + \vec{k}(5 - 8) = -3\vec{i} + 6\vec{j} - 3\vec{k} = (-3, 6, -3)$.

6What is the distance from point $P(2, -1, 3)$ to the plane $\mathcal{P}: 2x - y + 2z - 5 = 0$ in 3D Euclidean space?

A.2.0 (d = |2(2) - (-1) + 2(3) - 5| / √(2² + (-1)² + 2²))

B.6.0

C.1.5

D.3.0

Explanation: The distance formula is $d = \frac{|A x_0 + B y_0 + C z_0 + D|}{\sqrt{A^2 + B^2 + C^2}}$. Substituting: $d = \frac{|2(2) - (-1) + 2(3) - 5|}{\sqrt{2^2 + (-1)^2 + 2^2}} = \frac{|4 + 1 + 6 - 5|}{\sqrt{4 + 1 + 4}} = \frac{|6|}{\sqrt{9}} = \frac{6}{3} = 2.0$.

7A committee of 4 students must be chosen from a class of 10 students. How many different committees are possible if the order of selection does not matter?

A.210

B.5040

C.40

D.24

Explanation: Because the committee is an unordered selection, the count is the combination $\binom{10}{4} = \frac{10!}{4! \, 6!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = \frac{5040}{24} = 210$.

8What is the remainder $R(X)$ in the Euclidean division of polynomial $P(X) = X^4 - 3X^3 + 2X^2 - 5X + 7$ by $(X - 2)$?

A.-11

B.-3

C.+5

D.0

Explanation: By the Remainder Theorem, the remainder of dividing $P(X)$ by $(X - a)$ is $R = P(a)$. Evaluating at $a = 2$: $P(2) = 2^4 - 3(2^3) + 2(2^2) - 5(2) + 7 = 16 - 3(8) + 2(4) - 10 + 7 = 16 - 24 + 8 - 10 + 7 = 0 - 10 + 7 = -3$.

9Solve the system of 3 linear equations using Gaussian elimination: $\begin{cases} x + y + z = 6 \\ 2x - y + z = 3 \\ x + 2y - z = 2 \end{cases}$. What is $(x, y, z)$?

A.(1, 2, 3)

B.(2, 1, 3)

C.(1, 3, 2)

D.(3, 2, 1)

Explanation: Adding eq 1 and eq 3: $(x+y+z) + (x+2y-z) = 6 + 2 \implies 2x + 3y = 8$. Subtracting eq 1 from eq 2: $(2x-y+z) - (x+y+z) = 3 - 6 \implies x - 2y = -3 \implies x = 2y - 3$. Substitute into $2(2y-3) + 3y = 8 \implies 4y - 6 + 3y = 8 \implies 7y = 14 \implies y = 2$. Then $x = 2(2) - 3 = 1$. From eq 1: $1 + 2 + z = 6 \implies z = 3$. The unique solution is $(x, y, z) = (1, 2, 3)$.

10A workshop has two machines. Machine A produces 60% of the parts and 3% of its output is defective; machine B produces the remaining 40% and 5% of its output is defective. A part drawn at random is found to be defective. What is the probability that it came from machine A?

A.9/19 ≈ 0.474

B.3/100 = 0.030

C.3/5 = 0.600

D.10/19 ≈ 0.526

Explanation: Total probability of a defective part: $P(D) = P(A)P(D|A) + P(B)P(D|B) = 0.60 \times 0.03 + 0.40 \times 0.05 = 0.018 + 0.020 = 0.038$. Bayes' rule then gives $P(A|D) = \frac{P(A)P(D|A)}{P(D)} = \frac{0.018}{0.038} = \frac{18}{38} = \frac{9}{19} \approx 0.474$.

About the Concours ENSPY Exam

The Concours d'Entrée à l'École Nationale Supérieure Polytechnique de Yaoundé (ENSPY) is Cameroon's premier and most competitive engineering grand school entrance examination. Organized annually by MINESUP and the University of Yaoundé I, it admits the nation's top mathematical and scientific talents into the 5-year engineering cycle (Diplôme d'Ingénieur de Conception) across fields including Civil, Electrical, Mechanical, Telecommunications, Computer, Industrial, and Chemical Engineering. This 100-question practice bank drills the calculus, algebra and geometry, mechanics, electromagnetism, optics and thermal physics of the Première and Terminale science programmes that the communiqué names as the examinable syllabus, with complete worked solutions. Format note: the official concours consists of written problem sets in French and English; this bank is an English-language MCQ study adaptation designed to build speed and analytical precision, not an official translation or a format simulation.

Assessment

Two written Mathematics papers and two written Physics papers, three hours each and of equal weight, sat over two consecutive days; the communiqué states explicitly that there is no oral examination. The examinable syllabus is the common ground of the Première and Terminale programmes of series C, D, E, TI and F (or Lower and Upper Sixth science for anglophone candidates). Admission is by merit ranking against the number of places opened by the communiqué. Separately, candidates who registered with a complete dossier and earned a mention 'Très Bien' in the 2026 Baccalauréat C or E, an 'Excellent' in the 2026 Baccalauréat D, TI or F, or five grade-A subjects at the 2026 GCE A-Level, may be admitted directly on title.

Time Limit

12 hours total across four 3-hour written papers, six hours per day over two consecutive days (16 and 17 July in the 2026 session)

Passing Score

No published pass mark; admission is by merit ranking against the places opened (400 engineering places for 2026/2027)

Exam Fee

20,000 FCFA (Ministère de l'Enseignement Supérieur (MINESUP) & Université de Yaoundé I)

Concours ENSPY Exam Content Outline

25%

Mathématiques 1: Analyse, Calcul Intégral, Suites & Nombres Complexes

Functions of a real variable, limits, continuity, differentiability, integration techniques (by parts, partial fractions, trigonometric substitution), ordinary differential equations (first/second order linear ODEs with constant coefficients), sequences, and complex numbers in algebra/geometry.

25%

Mathématiques 2: Algèbre Linéaire, Géométrie dans l'Espace & Probabilités

Vector spaces, subspaces, linear transformations, matrices, determinants, systems of linear equations (Gaussian elimination), dot and cross products in 3D Euclidean space, lines and planes, combinatorics, conditional probability, Bayes' theorem, and standard random variables.

25%

Physique 1: Mécanique Newtonienne, Oscillations, Gravitation & Énergie

Kinematics in Cartesian, polar, and intrinsic coordinates, Newton's laws of motion, work-kinetic energy theorem, conservative forces and potential energy, momentum and collisions, center of mass, rotational dynamics (torque, moment of inertia, angular momentum), and harmonic oscillations.

25%

Physique 2: Électromagnétisme, Circuits RLC, Optique Ondulatoire & Thermodynamique

Electrostatics (Coulomb's law, electric field/potential), magnetostatics (Biot-Savart, Lorentz force), electromagnetic induction (Faraday-Lenz law), AC circuits, RLC series resonance and quality factor, wave optics (Young's double slit interference, diffraction), first and second laws of thermodynamics, and ideal gas cycles.

How to Pass the Concours ENSPY Exam

What You Need to Know

Passing score: No published pass mark; admission is by merit ranking against the places opened (400 engineering places for 2026/2027)
Assessment: Two written Mathematics papers and two written Physics papers, three hours each and of equal weight, sat over two consecutive days; the communiqué states explicitly that there is no oral examination. The examinable syllabus is the common ground of the Première and Terminale programmes of series C, D, E, TI and F (or Lower and Upper Sixth science for anglophone candidates). Admission is by merit ranking against the number of places opened by the communiqué. Separately, candidates who registered with a complete dossier and earned a mention 'Très Bien' in the 2026 Baccalauréat C or E, an 'Excellent' in the 2026 Baccalauréat D, TI or F, or five grade-A subjects at the 2026 GCE A-Level, may be admitted directly on title.
Time limit: 12 hours total across four 3-hour written papers, six hours per day over two consecutive days (16 and 17 July in the 2026 session)
Exam fee: 20,000 FCFA

Keys to Passing

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

Frequently Asked Questions

What is the Concours ENSPY?

The Concours ENSPY is the national competitive entrance examination for admission into the five-year engineering diploma program (Cycle Ingénieur) at the École Nationale Supérieure Polytechnique de Yaoundé (ENSPY), affiliated with the University of Yaoundé I under the Ministry of Higher Education (MINESUP).

What are the subjects and format of the Concours ENSPY?

The concours consists of two written Mathematics papers and two written Physics papers, three hours each and of equal weight, sat over two consecutive days. There is no oral examination. The communiqué does not assign separate topic titles to the individual papers, and the examinable syllabus is the common ground of the Première and Terminale programmes of series C, D, E, TI and F.

Who is eligible to sit the Concours ENSPY?

Eligible candidates include students holding or preparing a Baccalauréat (Series C, D, E, F, or TI) or GCE Advanced Level (at least two scientific subjects in one sitting including Pure Mathematics and Physics) who are at most 29 years old on January 1 of the examination year.

What is the passing score and admission rule for ENSPY?

There is no published passing grade or eliminatory minimum. Candidates are ranked by total score and admitted against the number of places opened by the ministerial communiqué — 400 first-year engineering places in Sciences et Technologies for 2026/2027, plus 70 on the engineering-sciences bachelor track. Top 2026 Baccalauréat and GCE A-Level performers may instead be admitted directly on title.