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Free Practice Questions for CNC Maroc

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Sample CNC Maroc Practice Questions

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1What is the radius of convergence R of the real power series sum_{n=1}^inf (n^2 / 3^n) * x^n?
A.R = 3
B.R = 1/3
C.R = 9
D.R = inf
Explanation: Applying d'Alembert's ratio test to the coefficients a_n = n^2 / 3^n, we compute lim_{n->inf} |a_{n+1} / a_n| = lim_{n->inf} [((n+1)^2 / 3^(n+1)) * (3^n / n^2)] = lim_{n->inf} (1/3) * (1 + 1/n)^2 = 1/3. The radius of convergence is the reciprocal of this limit, giving R = 1 / (1/3) = 3.
2What is the sum of the alternating harmonic series sum_{n=1}^inf ((-1)^(n-1) / n) = 1 - 1/2 + 1/3 - 1/4 + ...?
A.ln(2)
B.1
C.e
D.1/2
Explanation: The Taylor series expansion of ln(1 + x) for |x| < 1 is sum_{n=1}^inf ((-1)^(n-1) / n) * x^n. By Leibniz's alternating series test, the series converges at x = 1, and by Abel's theorem on power series boundary convergence, the sum equals ln(1 + 1) = ln(2).
3For what values of the real parameter alpha does the Bertrand series sum_{n=2}^inf (1 / (n * (ln n)^alpha)) converge?
A.Converges for alpha >= 1 and diverges for alpha < 1
B.Converges if and only if alpha > 1
C.Converges for all alpha > 0
D.Diverges for all real values of alpha
Explanation: By the integral test of Cauchy, the series sum_{n=2}^inf (1 / (n * (ln n)^alpha)) has the same nature as the improper integral int_2^inf (1 / (x * (ln x)^alpha)) dx. Using the substitution u = ln x with du = dx / x, the integral becomes int_{ln 2}^inf (1 / u^alpha) du, which is a standard Riemann integral that converges if and only if alpha > 1.
4What is the asymptotic expansion of the harmonic series partial sum H_n = sum_{k=1}^n (1 / k) through the 1/n^2 term?
A.H_n = ln n + gamma + O(1/n)
B.H_n = n * ln n + gamma + O(1/n^2)
C.H_n = ln n + gamma + 1/(2n) - 1/(12n^2) + O(1/n^4)
D.H_n = ln n + 1/n + O(1/n^2)
Explanation: Using the Euler-Maclaurin summation formula or telescoping series comparison with the integral int_1^n (1/t) dt, the harmonic sum admits the asymptotic expansion H_n = ln n + gamma + 1/(2n) - 1/(12n^2) + O(1/n^4), where gamma approx 0.5772 is the Euler-Mascheroni constant.
5What is the value of the improper integral int_0^inf e^(-3t) dt?
A.3
B.1
C.0
D.1/3
Explanation: The primitive of e^(-3t) is -(1/3) * e^(-3t). Evaluating from 0 to infinity yields lim_{T->inf} [-(1/3) * e^(-3T)] - [-(1/3) * e^0] = 0 - (-1/3) = 1/3.
6What is the exact value of the improper integral int_0^inf t^3 * e^(-2t) dt?
A.3/8
B.3/4
C.3/16
D.6
Explanation: Using the substitution u = 2t, we have t = u/2 and dt = du/2. The integral transforms into int_0^inf (u/2)^3 * e^(-u) * (du/2) = (1/16) * int_0^inf u^3 * e^(-u) du = (1/16) * Gamma(4) = (1/16) * 3! = 6 / 16 = 3/8.
7What is the value of the Gaussian integral I = int_{-inf}^inf e^(-x^2 / 2) dx?
A.pi
B.sqrt(2 * pi)
C.sqrt(pi) / 2
D.2 * pi
Explanation: Evaluating I^2 in Cartesian coordinates yields int_{-inf}^inf int_{-inf}^inf e^(-(x^2 + y^2)/2) dx dy. Converting to polar coordinates (r, theta) gives int_0^(2*pi) dtheta * int_0^inf r * e^(-r^2 / 2) dr = 2*pi * [-e^(-r^2 / 2)]_0^inf = 2*pi * (0 - (-1)) = 2*pi. Taking the square root gives I = sqrt(2 * pi).
8What is the value of the Dirichlet integral int_0^inf (sin x / x) dx?
A.pi
B.1
C.pi / 2
D.pi / 4
Explanation: The Dirichlet integral can be computed using parameter differentiation on F(a) = int_0^inf e^(-a x) * (sin x / x) dx for a >= 0. Differentiating under the integral sign gives F'(a) = -int_0^inf e^(-a x) sin x dx = -1 / (1 + a^2). Integrating from 0 to infinity with lim_{a->inf} F(a) = 0 yields F(0) = int_0^inf (1 / (1 + a^2)) da = [arctan a]_0^inf = pi / 2.
9What is the general solution of the second-order homogeneous linear differential equation y'' - 5y' + 6y = 0?
A.y(t) = C1 * e^(-2t) + C2 * e^(-3t)
B.y(t) = (C1 + C2 * t) * e^(2.5t)
C.y(t) = C1 * cos(2t) + C2 * sin(3t)
D.y(t) = C1 * e^(2t) + C2 * e^(3t)
Explanation: The characteristic equation associated with the ODE is r^2 - 5r + 6 = 0. Factoring gives (r - 2)(r - 3) = 0, which yields two distinct real roots r1 = 2 and r2 = 3. Therefore, the general solution is y(t) = C1 * e^(2t) + C2 * e^(3t) where C1, C2 are arbitrary constants.
10What is a particular solution y_p(t) to the differential equation y'' + 4y = 8 * cos(2t)?
A.y_p(t) = 2t * sin(2t)
B.y_p(t) = 2 * cos(2t)
C.y_p(t) = -2t * cos(2t)
D.y_p(t) = 4t * sin(2t)
Explanation: The homogeneous equation has characteristic roots r = +-2i, so the forcing term 8*cos(2t) is at resonance. We seek a particular solution of the form y_p(t) = t * (A * cos(2t) + B * sin(2t)). Differentiating twice and substituting into y'' + 4y yields -4A * sin(2t) + 4B * cos(2t) = 8 * cos(2t). Equating coefficients gives -4A = 0 => A = 0 and 4B = 8 => B = 2, so y_p(t) = 2t * sin(2t).

About the CNC Maroc Exam

The CNC is the current national competition through which Morocco's CPGE candidates compete for engineering-school places. Official CPGE materials identify MP, PSI, and TSI variants, common written admissibility testing, and a mandatory TIPE oral for admissible candidates. This independent English-language MCQ bank reviews cross-stream concepts; it is not an official translation, a paper-by-paper blueprint, or a substitute for written derivations and the TIPE presentation and discussion.

Exam sponsor: Moroccan Ministry of Higher Education through the CPGE portal and the annual organizing school. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Written admissibility stage plus mandatory TIPE oral for admissible MP, PSI, and TSI candidates.

Time Limit

Current paper durations were not published in the reviewed official overview.

Passing Score

Competitive ranking; no fixed pass mark published in the reviewed official overview.

Exam / Certification Fees

Not published in the reviewed current official CNC overview.

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.

Varies by MP, PSI, or TSI paper

Mathematics

Analysis, algebra, probability, differential equations, and geometry.

Varies by stream

Physics and Chemistry

Mechanics, electricity, electromagnetism, waves, thermodynamics, and chemistry.

Varies by stream

Engineering Science and Computing

Systems, mechanics, control, algorithms, and programming concepts.

Written and oral components

Languages, Humanities, and TIPE

Communication, synthesis, scientific inquiry, presentation, and discussion.

Preparing for the CNC Maroc Exam

What You Need to Know

  • Passing score: Competitive ranking; no fixed pass mark published in the reviewed official overview.
  • Assessment: Written admissibility stage plus mandatory TIPE oral for admissible MP, PSI, and TSI candidates.
  • Time limit: Current paper durations were not published in the reviewed official overview.
  • Exam / certification fees: Not published in the reviewed current official CNC overview. 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

CNC Maroc: Suggested Study Strategy

1Follow the official MP, PSI, or TSI program.
2Practice complete written solutions under timed conditions.
3Prepare the TIPE presentation and discussion separately from MCQ practice.

Frequently Asked Questions

Is the CNC only a written examination?

No. The official overview requires a common TIPE oral for admissible MP, PSI, and TSI candidates.

Does this bank simulate a specific stream?

No. It is a cross-stream concept review; candidates should use the official program for their own stream.