Free Practice Questions for Bac Série E Côte d'Ivoire

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Key Facts: Bac Série E Côte d'Ivoire Exam

5,000 FCFA

Official candidate registration fee via TrésorPay/TrésorMoney

DECO MENA

240 / 480

Passing threshold score (10/20 weighted average)

DECO METFPA

Lycée Technique

Specialized technical institutions offering Série E in Côte d'Ivoire

METFPA

Free 100-question English MCQ study bank for Bac Série E Côte d'Ivoire. Official exam: French written papers in technical maths, mechanics, and design; pass with ≥240/480. Not an official-format simulation.

Sample Bac Série E Côte d'Ivoire Practice Questions

Try these sample questions to review concepts for the Bac Série E Côte d'Ivoire exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the derivative f'(x) of the function f(x) = (3x^2 - 5x + 2) e^(2x)?

A.(6x^2 - 4x - 1) e^(2x)

B.(6x - 5) e^(2x)

C.(6x^2 - 10x + 4) e^(2x)

D.(3x^2 + x - 3) e^(2x)

Explanation: Using the product rule (u·v)' = u'v + uv' with u(x) = 3x^2 - 5x + 2 and v(x) = e^(2x): u'(x) = 6x - 5 and v'(x) = 2e^(2x). Therefore, f'(x) = (6x - 5)e^(2x) + (3x^2 - 5x + 2)(2e^(2x)) = e^(2x)[(6x - 5) + (6x^2 - 10x + 4)] = (6x^2 - 4x - 1)e^(2x).

2Using integration by parts, what is the exact value of the definite integral I = ∫[0 to 1] x e^(-x) dx?

A.1 - 1/e

B.1 - 2/e

C.2/e

D.1 + 1/e

Explanation: Let u = x and dv = e^(-x) dx, so du = dx and v = -e^(-x). Applying integration by parts: ∫ x e^(-x) dx = [-x e^(-x)]_0^1 - ∫_0^1 (-e^(-x)) dx = -e^(-1) - [e^(-x)]_0^1 = -1/e - (e^(-1) - e^0) = -1/e - 1/e + 1 = 1 - 2/e.

3What is the value of the limit L = lim(x -> 0) [ln(1 + 3x) / sin(2x)]?

A.2/3

B.1

C.3/2

D.0

Explanation: As x -> 0, standard equivalents give ln(1 + 3x) ~ 3x and sin(2x) ~ 2x. Alternatively, by L'Hôpital's rule: lim(x -> 0) [ (3/(1 + 3x)) / (2 cos(2x)) ] = (3/1) / (2·1) = 3/2.

4What are the modulus and principal argument of the complex number z = -2 + 2i√3?

A.|z| = 4, arg(z) = π/3 rad

B.|z| = 2√3, arg(z) = 5π/6 rad

C.|z| = 4, arg(z) = -2π/3 rad

D.|z| = 4, arg(z) = 2π/3 rad

Explanation: The modulus is |z| = √((-2)^2 + (2√3)^2) = √(4 + 12) = √16 = 4. Factoring 4: z = 4(-1/2 + i√3/2). Since cos(θ) = -1/2 and sin(θ) = √3/2, the principal argument in the second quadrant is θ = 2π/3 rad.

5What are the solutions to the quadratic equation z^2 - (2√3)z + 4 = 0 in the set of complex numbers C?

A.z1 = 2 e^(iπ/6) and z2 = 2 e^(-iπ/6)

B.z1 = 4 e^(iπ/3) and z2 = 4 e^(-iπ/3)

C.z1 = 2 e^(iπ/3) and z2 = 2 e^(-iπ/3)

D.z1 = √3 e^(iπ/6) and z2 = √3 e^(-iπ/6)

Explanation: The discriminant is Δ = (-2√3)^2 - 4(1)(4) = 12 - 16 = -4 = (2i)^2. Thus, z = (2√3 ± 2i)/2 = √3 ± i. The modulus is r = √(3 + 1) = 2. Since √3 + i = 2(√3/2 + i/2) = 2 e^(iπ/6), the two conjugate solutions are z1 = 2 e^(iπ/6) and z2 = 2 e^(-iπ/6).

6In the complex plane, a direct plane similitude S is defined by the complex expression z' = (1 + i√3)z + 2. What are its scaling ratio k, rotation angle θ, and center invariant point Ω?

A.k = √3, θ = π/6 rad, Ω has affix ω = 1 + i√3

B.k = 2, θ = π/3 rad, Ω has affix ω = i(2√3/3)

C.k = 2, θ = -π/3 rad, Ω has affix ω = 2 - 2i

D.k = 4, θ = π/3 rad, Ω has affix ω = 2i

Explanation: For S(z) = a·z + b with a = 1 + i√3 and b = 2: ratio k = |a| = √(1 + 3) = 2. Rotation angle θ = arg(a) = π/3 rad. The invariant center point Ω satisfies ω = a·ω + b <=> ω(1 - a) = b <=> ω(1 - 1 - i√3) = 2 <=> -i√3·ω = 2 <=> ω = 2 / (-i√3) = 2i / √3 = i(2√3/3).

7What is the unique solution to the first-order differential equation y' + 2y = 4e^(-2x) satisfying the initial condition y(0) = 3?

A.y(x) = (2x + 3) e^(-2x)

B.y(x) = 4x e^(-2x) + 3 e^(2x)

C.y(x) = (4x + 3) e^(-2x)

D.y(x) = 3 e^(-2x) + 4

Explanation: The integrating factor is e^(∫ 2 dx) = e^(2x). Multiplying both sides gives (y e^(2x))' = 4. Integrating yields y e^(2x) = 4x + C, so y(x) = (4x + C)e^(-2x). Applying y(0) = 3 gives C = 3. Thus, y(x) = (4x + 3)e^(-2x).

8What is the solution to the second-order differential equation y'' + 4y' + 13y = 0 subject to initial conditions y(0) = 1 and y'(0) = -2?

A.y(x) = e^(-2x) (cos(3x) + sin(3x))

B.y(x) = e^(2x) cos(3x)

C.y(x) = e^(-2x) sin(3x)

D.y(x) = e^(-2x) cos(3x)

Explanation: The characteristic equation is r^2 + 4r + 13 = 0, which has roots r = (-4 ± √(16 - 52))/2 = (-4 ± 6i)/2 = -2 ± 3i. The general solution is y(x) = e^(-2x)[A cos(3x) + B sin(3x)]. Condition y(0) = 1 gives A = 1. The derivative is y'(x) = -2e^(-2x)[cos(3x) + B sin(3x)] + e^(-2x)[-3 sin(3x) + 3B cos(3x)]. At x = 0: y'(0) = -2(1) + 3B = -2 => 3B = 0 => B = 0. Therefore, y(x) = e^(-2x) cos(3x).

9An undamped mechanical oscillator is modeled by y''(t) + ω0^2 y(t) = F0 cos(ω t). What happens to the particular solution when the excitation pulsation ω equals the natural pulsation ω0 (resonance)?

A.The particular solution has an amplitude that grows proportionally with time t: y_p(t) = (F0 / (2ω0)) t sin(ω0 t)

B.The response remains bounded with constant amplitude Y = F0 / (ω0^2 - ω^2)

C.The system immediately decays exponentially to zero

D.The system undergoes frequency doubling with y_p(t) = F0 cos(2ω0 t)

Explanation: When ω = ω0, the driving force is in resonance with the natural frequency of the undamped system. The standard trial solution fails because ±iω0 are roots of the characteristic equation. Multiplying by t yields the secular resonant response y_p(t) = (F0 / (2ω0)) t sin(ω0 t), whose amplitude increases linearly without bound.

10What is the determinant of the 3x3 matrix A = [[2, 1, 0], [3, -1, 4], [1, 2, -1]]?

A.7

B.-7

C.-14

D.0

Explanation: Expanding along the first row: det(A) = 2 · det([[-1, 4], [2, -1]]) - 1 · det([[3, 4], [1, -1]]) + 0 = 2 · ((-1)(-1) - (4)(2)) - 1 · ((3)(-1) - (4)(1)) = 2 · (1 - 8) - 1 · (-3 - 4) = 2(-7) - 1(-7) = -14 + 7 = -7.

About the Bac Série E Côte d'Ivoire Exam

Série E is Côte d'Ivoire's high-level technical mathematics Baccalauréat stream, taught primarily in specialized institutions such as the Lycée Technique d'Abidjan (Cocody) and Lycée Technique de Bouaké. It bridges rigorous mathematical analysis with mechanical engineering, strength of materials (RDM), kinematics, and industrial technology. Official examinations are written analytical problem sets and technical designs in French. This bank provides 100 English-language MCQs covering applied mechanics, engineering mathematics, and industrial physics.

Exam sponsor: Direction des Examens et Concours (DECO) / Ministère de l'Éducation Nationale, de l'Alphabétisation et de l'Enseignement Technique (MENAET). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written and design papers in Mathématiques, Physique-Chimie, Construction Mécanique (Mécanique appliquée & Dessin industriel), Français, Philosophie, Histoire-Géo, and Anglais.

Time Limit

Multi-day examination session (written and technical design papers held in June/July over 4 to 5 days, preceded by oral and physical tests).

Passing Score

Graded out of 480 total points; admission requires at least 240/480 (a 10/20 weighted average). Official candidates in Série E scoring 192–239 may be repêchés by the jury if they reach the pass mark in one matière spécifique and hold an annual school average (moyenne générale annuelle) of at least 10/20.

Exam / Certification Fees

5,000 FCFA (official candidate registration fee via TrésorPay/TrésorMoney; optional subjects +1,000 FCFA each)

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.

Study emphasis ~30%

Applied Mathematics

Differential equations, integral calculus, complex numbers, Laplace transforms, vectors, and linear systems.

Study emphasis ~25%

Applied Physics & Electrotechnics

Kinematics of rigid bodies, dynamics, torque, work-energy theorem, single and three-phase AC power, transformers.

Study emphasis ~25%

Mechanical Construction & Strength of Materials

Statics, beam deflection, shear and bending moment diagrams, torsion, stress-strain relations, fits and tolerances, transmission ratios.

Study emphasis ~10%

Automation & Electronics

Logic gates, combinational and sequential systems, GRAFCET specification, sensors and actuators.

Study emphasis ~10%

General Subjects

Technical French, philosophy of technology and ethics, and technical English.

Preparing for the Bac Série E Côte d'Ivoire Exam

What You Need to Know

Passing score: Graded out of 480 total points; admission requires at least 240/480 (a 10/20 weighted average). Official candidates in Série E scoring 192–239 may be repêchés by the jury if they reach the pass mark in one matière spécifique and hold an annual school average (moyenne générale annuelle) of at least 10/20.
Assessment: Written and design papers in Mathématiques, Physique-Chimie, Construction Mécanique (Mécanique appliquée & Dessin industriel), Français, Philosophie, Histoire-Géo, and Anglais.
Time limit: Multi-day examination session (written and technical design papers held in June/July over 4 to 5 days, preceded by oral and physical tests).
Exam / certification fees: 5,000 FCFA (official candidate registration fee via TrésorPay/TrésorMoney; optional subjects +1,000 FCFA each) Official sources

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Bac Série E Côte d'Ivoire: Suggested Study Strategy

1Master beam statics: practice drawing shear force (V) and bending moment (M) diagrams accurately.

2Calculate gear train ratios, torque transmission, and efficiency in compound gear systems.

3Review AC power formulas (active, reactive, apparent power, power factor correction with capacitors).

4Drill differential equations of motion for damped and forced mechanical oscillators.

Frequently Asked Questions

Is the official Bac Série E multiple-choice?

No. Official examinations involve complex mechanical drawings, calculation problem sets, and essays in French. This bank is an English MCQ study adaptation.

What is the difference between Série E and Séries F in Côte d'Ivoire?

Série E maintains a much higher level of theoretical mathematics and physics comparable to Série C, combined with broad mechanical engineering, while Séries F focus more deeply on specific industrial sub-fields (F1 mechanics, F2 electronics, F3 electrical, F4 civil).

What score is needed to pass Bac Série E in Côte d'Ivoire?

Candidates must achieve at least 240 points out of 480 (a weighted average of 10/20) across all written and practical subjects.

Free Practice Questions for Bac Série E Côte d'Ivoire

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