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Sample Concours passerelle ENSAM Rabat Practice Questions

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

1What is the limit of the indeterminate form (1 - cos(4x)) / x^2 as x approaches 0?
A.8
B.4
C.16
D.2
Explanation: Using the Taylor expansion cos(u) = 1 - u^2/2 + o(u^2) with u = 4x, we have 1 - cos(4x) = (4x)^2 / 2 + o(x^2) = 8x^2 + o(x^2). Dividing by x^2 yields a limit of 8 as x approaches 0. L'Hôpital's rule applied twice also yields (4*sin(4x))/(2x) -> (16*cos(4x))/2 = 8.
2Consider the piecewise function f(x) defined by f(x) = sin(3x) / x for x != 0, and f(0) = k. For which value of k is f continuous at x = 0?
A.0
B.3
C.1
D.1/3
Explanation: A function f is continuous at x = 0 if and only if lim_(x->0) f(x) = f(0). Since lim_(x->0) sin(3x) / x = 3 * lim_(x->0) sin(3x) / (3x) = 3 * 1 = 3, we must set k = 3 to maintain continuity.
3What is the first derivative of the function f(x) = x^2 * ln(x) for all x > 0?
A.2x * ln(x)
B.x * (ln(x) + 1)
C.x * (2*ln(x) + 1)
D.2x
Explanation: Applying the product rule (u*v)' = u'*v + u*v' with u(x) = x^2 and v(x) = ln(x), we obtain f'(x) = 2x * ln(x) + x^2 * (1/x) = 2x*ln(x) + x. Factoring out x gives x*(2*ln(x) + 1).
4What is the horizontal asymptote of the rational function f(x) = (3x^2 - 5x + 2) / (2x^2 + 7x - 1) as x approaches +infinity?
A.y = 0
B.y = 3
C.y = 2/3
D.y = 3/2
Explanation: For a rational function where the degree of the numerator equals the degree of the denominator (both degree 2), the horizontal asymptote is given by the ratio of leading coefficients. Here, lim_(x->+infinity) (3x^2)/(2x^2) = 3/2, which gives the horizontal line y = 3/2.
5By the Mean Value Theorem applied to f(x) = x^3 on the closed interval [0, 3], there exists a number c in (0, 3) such that f'(c) = (f(3) - f(0)) / (3 - 0). What is the exact value of c?
A.sqrt(3)
B.3/2
C.sqrt(2)
D.2
Explanation: Evaluating the average rate of change gives (f(3) - f(0)) / (3 - 0) = (27 - 0) / 3 = 9. Setting the derivative f'(c) = 3c^2 equal to 9 yields 3c^2 = 9, so c^2 = 3. Since c must lie in the open interval (0, 3), we have c = sqrt(3).
6What is the equation of the slant (oblique) asymptote of f(x) = (2x^2 + 5x + 1) / (x + 1) as x approaches +infinity?
A.y = 2x + 5
B.y = 2x + 3
C.y = 2x - 3
D.y = 2x + 1
Explanation: Performing polynomial long division of 2x^2 + 5x + 1 by x + 1 gives 2x^2 + 5x + 1 = (2x + 3)(x + 1) - 2. Thus, f(x) = 2x + 3 - 2/(x + 1). As x -> +infinity, the remainder term -2/(x + 1) approaches 0, establishing y = 2x + 3 as the oblique asymptote.
7What is the value of the definite integral I = int_0^1 x * e^(2x) dx?
A.(e^2 - 1) / 4
B.e^2 / 2
C.(e^2 + 1) / 4
D.(e^2 + 1) / 2
Explanation: Using integration by parts with u = x and dv = e^(2x) dx, we have du = dx and v = (1/2)*e^(2x). Then I = [x/2 * e^(2x)]_0^1 - int_0^1 (1/2)*e^(2x) dx = (1/2)*e^2 - [(1/4)*e^(2x)]_0^1 = (e^2 / 2) - (e^2 / 4 - 1/4) = (e^2 + 1) / 4.
8Evaluate the definite integral J = int_0^(pi/4) tan(x) * sec^2(x) dx.
A.1
B.1/4
C.2
D.1/2
Explanation: Substitute u = tan(x), which gives du = sec^2(x) dx. The integration limits transform from x = 0 to u = tan(0) = 0, and from x = pi/4 to u = tan(pi/4) = 1. The integral becomes int_0^1 u du = [u^2 / 2]_0^1 = 1/2.
9What is the value of the integral int_0^1 (1 / (x^2 + 3x + 2)) dx?
A.ln(4/3)
B.ln(3/2)
C.ln(2)
D.ln(5/4)
Explanation: Factoring the denominator gives (x + 1)(x + 2). Partial fraction decomposition yields 1 / ((x+1)(x+2)) = 1/(x+1) - 1/(x+2). The primitive is ln|(x+1)/(x+2)|. Evaluating between 0 and 1 gives ln(2/3) - ln(1/2) = ln((2/3) / (1/2)) = ln(4/3).
10For which real values of the parameter p does the improper integral int_1^(+infinity) (1 / x^p) dx converge?
A.p >= 1
B.p > 1
C.p < 1
D.p > 0
Explanation: For p != 1, int_1^R x^(-p) dx = [x^(1-p) / (1-p)]_1^R = (R^(1-p) - 1) / (1-p). As R -> +infinity, R^(1-p) converges to 0 if and only if 1 - p < 0, which requires p > 1. For p = 1, the integral is [ln(x)]_1^R = ln(R) -> +infinity, which diverges.

About the Concours passerelle ENSAM Rabat Exam

The official 2026 notice covers a Bac+2/Bac+3 passerelle into the first engineering-cycle year for eligible DEUG, DEUP, DEUST, DUT, and Licence profiles mapped to the announced engineering streams. The written competition was scheduled for 21 July 2026. This identity is not the post-Baccalauréat network route. This bank is an independent English-language MCQ adaptation; it preserves French and English skill prompts where relevant but does not simulate the official written papers or replace extended technical solutions.

Exam sponsor: ENSAM Rabat, Université Mohammed V de Rabat. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Dossier preselection followed by Mathematics, Culture and Languages (French/English), and stream-specific Engineering Sciences written papers.

Time Limit

7 hours total

Passing Score

Competitive ranking; no fixed pass mark stated.

Exam / Certification Fees

Not stated in the reviewed official notice.

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.

Official: 2 hours; practice bank: 35 questions

Mathematics

Analysis and algebra.

Official: 2 hours; practice bank: 20 questions

Culture and Languages

French and English comprehension, grammar, argument, and professional communication.

Official: 3 hours; practice bank: 45 questions

Stream-specific Engineering Sciences

Physics and engineering-science concepts selected across the announced streams.

Preparing for the Concours passerelle ENSAM Rabat Exam

What You Need to Know

  • Passing score: Competitive ranking; no fixed pass mark stated.
  • Assessment: Dossier preselection followed by Mathematics, Culture and Languages (French/English), and stream-specific Engineering Sciences written papers.
  • Time limit: 7 hours total
  • Exam / certification fees: Not stated in the reviewed official notice. 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 passerelle ENSAM Rabat: Suggested Study Strategy

1Use the engineering-science outline for your eligible stream.
2Practice extended written calculations in addition to MCQs.
3Prepare both French and English language tasks.

Frequently Asked Questions

Is this the post-Baccalauréat ENSAM network route?

No. It covers ENSAM Rabat's distinct 2026 Bac+2/Bac+3 passerelle competition.

Why are some prompts in French or English?

The official Culture and Languages paper explicitly tests French and English; exact target-language text is retained where it is the skill being assessed.