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Sample Concours ENA Meknès Practice Questions

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

1What is the value of the limit lim_{x -> +infinity} [sqrt(x^2 + 4x + 1) - x]?
A.0
B.2
C.4
D.+infinity
Explanation: Multiplying and dividing by the conjugate expression yields [x^2 + 4x + 1 - x^2] / [sqrt(x^2 + 4x + 1) + x] = (4x + 1) / [x * (sqrt(1 + 4/x + 1/x^2) + 1)]. Factoring out x in both the numerator and denominator gives (4 + 1/x) / (sqrt(1 + 4/x + 1/x^2) + 1), which converges to 4 / (1 + 1) = 2 as x approaches +infinity.
2Determine the value of the limit lim_{x -> 0} [(e^(3x) - 1) / sin(2x)].
A.1
B.2/3
C.3/2
D.3
Explanation: Using standard Baccalauréat calculus limits, we rewrite the expression as [(e^(3x) - 1) / (3x)] * [(2x) / sin(2x)] * (3 / 2). Since lim_{u -> 0} (e^u - 1)/u = 1 and lim_{v -> 0} v/sin(v) = 1, the overall limit is 1 * 1 * (3/2) = 3/2.
3Let f be the real-valued function defined on ]-1/2, +infinity[ by f(x) = ln((2x + 1) / (x + 2)). What is the value of the first derivative f'(1)?
A.1/3
B.2/3
C.-1/3
D.1
Explanation: Expressing f(x) as ln(2x + 1) - ln(x + 2), differentiation with respect to x gives f'(x) = 2 / (2x + 1) - 1 / (x + 2). Evaluating at x = 1 yields f'(1) = 2 / (2*1 + 1) - 1 / (1 + 2) = 2/3 - 1/3 = 1/3.
4What is the Cartesian equation of the tangent line to the curve representing f(x) = (3x - 2) * e^(2x) at the point of abscissa x = 0?
A.y = -x + 2
B.y = 3x - 2
C.y = -2x - 2
D.y = -x - 2
Explanation: At x = 0, f(0) = (0 - 2) * e^0 = -2. The derivative is f'(x) = 3 * e^(2x) + 2 * (3x - 2) * e^(2x) = (6x - 1) * e^(2x). Evaluating at x = 0 gives f'(0) = (0 - 1) * 1 = -1. The tangent equation is y = f'(0)*(x - 0) + f(0), which simplifies to y = -x - 2.
5Consider the function f(x) = x^3 + 3x - 5 defined on R. According to the Intermediate Value Theorem (Théorème des Valeurs Intermédiaires), how many real roots does f(x) = 0 have on the open interval ]1, 2[?
A.Zero roots
B.Exactly one root
C.Exactly two roots
D.Infinitely many roots
Explanation: The function f is continuous and strictly differentiable on R with derivative f'(x) = 3x^2 + 3 > 0 for all x in R, making f strictly increasing. Evaluating the endpoints gives f(1) = 1 + 3 - 5 = -1 < 0 and f(2) = 8 + 6 - 5 = 9 > 0. Because f is continuous, strictly monotonic, and changes sign across ]1, 2[, it has exactly one unique real root in this interval.
6Using integration by parts, calculate the definite integral I = integral_{1}^{e} [x * ln(x)] dx.
A.(e^2 + 1) / 4
B.(e^2 - 1) / 4
C.(3e^2 + 1) / 4
D.e^2 / 2
Explanation: Set u(x) = ln(x) and v'(x) = x, which implies u'(x) = 1/x and v(x) = x^2 / 2. Integration by parts gives I = [ (x^2 / 2) * ln(x) ]_{1}^{e} - integral_{1}^{e} [ (x^2 / 2) * (1/x) ] dx = [ (e^2 / 2) * 1 - 0 ] - [ x^2 / 4 ]_{1}^{e} = e^2 / 2 - (e^2 / 4 - 1/4) = (e^2 + 1) / 4.
7Which of the following functions represents the general primitive (antiderivative) of f(x) = (2x - 3) / (x^2 - 3x + 5) on R?
A.F(x) = (x^2 - 3x) / (x^2 - 3x + 5) + C
B.F(x) = arctan(x^2 - 3x + 5) + C
C.F(x) = ln(x^2 - 3x + 5) + C
D.F(x) = 1 / (x^2 - 3x + 5)^2 + C
Explanation: Notice that the numerator is precisely the derivative of the denominator: d/dx (x^2 - 3x + 5) = 2x - 3. The discriminant of the denominator is Delta = (-3)^2 - 4*1*5 = 9 - 20 = -11 < 0, meaning x^2 - 3x + 5 > 0 for all x in R. Therefore, the primitive of u'(x)/u(x) is ln(u(x)) + C = ln(x^2 - 3x + 5) + C.
8Compute the definite integral J = integral_{0}^{1} [x / (x^2 + 1)^2] dx.
A.1/2
B.1/8
C.ln(2) / 2
D.1/4
Explanation: Substitute u = x^2 + 1, so du = 2x dx, or x dx = du / 2. When x = 0, u = 1; when x = 1, u = 2. The integral becomes (1/2) * integral_{1}^{2} u^(-2) du = (1/2) * [ -1/u ]_{1}^{2} = (1/2) * [ -1/2 - (-1) ] = (1/2) * (1/2) = 1/4.
9What is the area (in area units) of the planar region bounded by the curve y = e^(2x), the horizontal x-axis, and the vertical lines x = 0 and x = 1?
A.e^2 - 1
B.(e^2 - 1) / 2
C.(e^2 + 1) / 2
D.e^2 / 2
Explanation: Since e^(2x) > 0 for all x, the area is given directly by the definite integral integral_{0}^{1} e^(2x) dx = [ e^(2x) / 2 ]_{0}^{1} = e^2 / 2 - e^0 / 2 = (e^2 - 1) / 2.
10What is the limit of the numerical sequence (u_n)_{n >= 1} defined by u_n = (5n^3 - 2n + 4) / (2n^3 + 7n^2 - 1) as n approaches +infinity?
A.5/2
B.0
C.+infinity
D.-4
Explanation: Factoring out the highest power n^3 from both the numerator and denominator gives u_n = [n^3 * (5 - 2/n^2 + 4/n^3)] / [n^3 * (2 + 7/n - 1/n^3)] = (5 - 2/n^2 + 4/n^3) / (2 + 7/n - 1/n^3). As n -> +infinity, all fractional terms vanish, leaving 5/2.

About the Concours ENA Meknès Exam

This identity is the school's post-Baccalauréat competition for first-year admission, whose 2026 written test was scheduled for 23 July 2026. It is distinct from ENA Meknès's Bac+2 competition for first-year engineering-cycle admission, which has a written test and a mandatory oral. This independent English-language MCQ bank supports science review and is not an official translation or a substitute for the official written test.

Exam sponsor: École Nationale d'Agriculture de Meknès. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Dossier preselection followed by one written test covering Mathematics, Physics-Chemistry, and Life and Earth Sciences.

Time Limit

3 hours

Passing Score

Competitive ranking; no fixed pass mark published.

Exam / Certification Fees

100 MAD application-processing fee

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 questions in this practice bank; official weight not published

Mathematics

Algebra, analysis, probability, and geometry.

35 questions in this practice bank; official weight not published

Physics-Chemistry

Mechanics, electricity, thermodynamics, waves, and chemistry.

35 questions in this practice bank; official weight not published

Life and Earth Sciences

Cell biology, genetics, physiology, ecology, geology, soils, and plant science.

Preparing for the Concours ENA Meknès Exam

What You Need to Know

  • Passing score: Competitive ranking; no fixed pass mark published.
  • Assessment: Dossier preselection followed by one written test covering Mathematics, Physics-Chemistry, and Life and Earth Sciences.
  • Time limit: 3 hours
  • Exam / certification fees: 100 MAD application-processing fee Official sources

Using Our Practice Resources

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

Concours ENA Meknès: Suggested Study Strategy

1Balance revision across all three official science areas.
2Practice quantitative work without relying on the site's multiple-choice format.
3Verify annual eligibility and dates on the official admission page.

Frequently Asked Questions

Is this the Bac+2 engineering-cycle competition?

No. This bank is for the distinct post-Baccalauréat first-year route.

Does the official page publish a fixed MCQ count?

No. This site's MCQ format is a study adaptation.