Free Practice Questions for UNIKIN Polytechnique Admission Test

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Key Facts: UNIKIN Polytechnique Admission Test Exam

Premier Engineering School

Top polytechnic institution in the DR Congo

UNIKIN Academic Board

30 September 2026

Date fixed for the B1 and L1 concours outside Médecine humaine, 2026-2027 intake

Université de Kinshasa concours calendar

USD 20

Concours participation fee in CDF equivalent for faculties other than Médecine humaine

Université de Kinshasa 2026-2027 enrolment notice

Free 100-question practice bank for the UNIKIN Faculté Polytechnique Entrance Test (DR Congo). Covers engineering mathematics, applied physics, and technical reasoning with step-by-step calculations.

Sample UNIKIN Polytechnique Admission Test Practice Questions

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

1Evaluate the limit: lim(x→0) [sin(5x) / (3x + tan(2x))].

A.5/5

B.5/3

C.1

D.0

Explanation: Divide the numerator and denominator by x: lim(x→0) [ (sin(5x)/x) / (3 + (tan(2x)/x)) ]. Using standard limits lim(x→0) sin(kx)/x = k and lim(x→0) tan(kx)/x = k, the expression becomes 5 / (3 + 2) = 5/5 = 1.

2Find the value of the limit: lim(x→∞) [√(4x² + 3x) − 2x].

A.3/4

B.3/2

C.0

D.∞

Explanation: Multiply and divide by the conjugate √(4x² + 3x) + 2x: [(4x² + 3x) − 4x²] / [√(4x² + 3x) + 2x] = 3x / [x(√(4 + 3/x) + 2)]. As x → ∞, this reduces to 3 / (√4 + 2) = 3 / (2 + 2) = 3/4.

3Let f(x) = x³ ln(x) for x > 0. Determine f''(1).

A.3

B.5

C.6

D.2

Explanation: Compute the first derivative using the product rule: f'(x) = 3x² ln(x) + x³(1/x) = 3x² ln(x) + x². Compute the second derivative: f''(x) = (6x ln(x) + 3x²(1/x)) + 2x = 6x ln(x) + 3x + 2x = 6x ln(x) + 5x. Evaluating at x = 1 gives f''(1) = 6(1)(0) + 5(1) = 5.

4Find the equation of the tangent line to the folium curve defined implicitly by x³ + y³ = 9xy at the point (2, 4).

A.4x − 5y + 12 = 0

B.5x − 4y + 6 = 0

C.5x + 4y − 26 = 0

D.x − 2y + 6 = 0

Explanation: Differentiate implicitly with respect to x: 3x² + 3y²(dy/dx) = 9y + 9x(dy/dx). Rearrange to solve for dy/dx: dy/dx = (3y − x²) / (y² − 3x). Substitute (x, y) = (2, 4): dy/dx = (3(4) − 2²) / (4² − 3(2)) = (12 − 4) / (16 − 6) = 8/10 = 4/5. Using point-slope form: y − 4 = (4/5)(x − 2) ⇒ 5(y − 4) = 4(x − 2) ⇒ 4x − 5y + 12 = 0.

5A cylindrical tank with an open top has a fixed volume of 27π m³. Find the radius r that minimizes the total surface area of the tank.

A.3 m

B.3.5 m

C.4 m

D.√27 m

Explanation: The volume is V = π r² h = 27π ⇒ h = 27 / r². The open-top surface area is A = π r² + 2π r h = π r² + 2π r (27 / r²) = π r² + 54π / r. Differentiate with respect to r and set to 0: dA/dr = 2π r − 54π / r² = 0 ⇒ 2 r³ = 54 ⇒ r³ = 27 ⇒ r = 3 m. The second derivative 2π + 108π/r³ is positive, confirming a minimum.

6Evaluate the definite integral: ∫[0 to 1] (x² e^(2x)) dx.

A.(e² + 1) / 4

B.(e² − 1) / 4

C.(3e² − 1) / 4

D.e² / 2

Explanation: Use integration by parts twice. Let u = x², dv = e^(2x) dx ⇒ du = 2x dx, v = (1/2)e^(2x). First step: [ (1/2)x² e^(2x) ][0 to 1] − ∫[0 to 1] x e^(2x) dx = (1/2)e² − ∫[0 to 1] x e^(2x) dx. Integrate ∫ x e^(2x) dx by parts: let u = x, dv = e^(2x) dx ⇒ [ (1/2)x e^(2x) − (1/4)e^(2x) ][0 to 1] = ((1/2)e² − (1/4)e²) − (0 − 1/4) = (1/4)e² + 1/4. Subtracting this from (1/2)e² gives (1/2)e² − ((1/4)e² + 1/4) = (1/4)e² − 1/4 = (e² − 1) / 4.

7Evaluate the integral: ∫ [1 / (x² + 4x + 13)] dx.

A.(1/3) arctan((x + 2)/3) + C

B.(1/2) arctan((x + 2)/2) + C

C.ln|x² + 4x + 13| + C

D.(1/9) arctan((x + 2)/3) + C

Explanation: Complete the square in the denominator: x² + 4x + 13 = (x + 2)² + 9 = (x + 2)² + 3². The integral becomes ∫ [1 / ((x + 2)² + 3²)] dx. Using the standard formula ∫ 1/(u² + a²) du = (1/a) arctan(u/a) + C with u = x + 2 and a = 3, we obtain (1/3) arctan((x + 2)/3) + C.

8Compute the area of the region enclosed between the parabola y = 4 − x² and the line y = x + 2.

A.9/2

B.16/3

C.7/2

D.11/2

Explanation: Find intersection points: 4 − x² = x + 2 ⇒ x² + x − 2 = 0 ⇒ (x + 2)(x − 1) = 0, so x = −2 and x = 1. The parabola is above the line on [-2, 1]. Area = ∫[−2 to 1] ((4 − x²) − (x + 2)) dx = ∫[−2 to 1] (2 − x − x²) dx = [ 2x − x²/2 − x³/3 ][−2 to 1]. At x = 1: 2 − 1/2 − 1/3 = 7/6. At x = −2: 2(−2) − (−2)²/2 − (−2)³/3 = −4 − 2 + 8/3 = −6 + 8/3 = −10/3. Area = 7/6 − (−10/3) = 7/6 + 20/6 = 27/6 = 9/2.

9Determine the general solution to the first-order linear differential equation: dy/dx + 2y = 4e^(3x).

A.y(x) = (4/5) e^(3x) + C e^(−2x)

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

C.y(x) = 4 e^(3x) + C e^(−2x)

D.y(x) = (4/5) e^(−2x) + C e^(3x)

Explanation: The integrating factor is I(x) = e^(∫ 2 dx) = e^(2x). Multiply both sides: d/dx [y e^(2x)] = 4e^(3x) e^(2x) = 4e^(5x). Integrate both sides: y e^(2x) = ∫ 4e^(5x) dx = (4/5)e^(5x) + C. Divide by e^(2x): y(x) = (4/5)e^(3x) + C e^(−2x).

10Solve the initial value problem: y'' − 4y' + 4y = 0, with y(0) = 2 and y'(0) = 7.

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

B.y(x) = (2 + 5x) e^(2x)

C.y(x) = 2 e^(2x) + 3 e^(−2x)

D.y(x) = (2 + 7x) e^(2x)

Explanation: The characteristic equation is r² − 4r + 4 = 0 ⇒ (r − 2)² = 0, giving a repeated root r = 2. The general solution is y(x) = (c₁ + c₂ x) e^(2x). Using y(0) = 2: c₁ = 2. Compute y'(x) = c₂ e^(2x) + 2(c₁ + c₂ x) e^(2x). Using y'(0) = 7: c₂ + 2c₁ = 7 ⇒ c₂ + 2(2) = 7 ⇒ c₂ = 3. Therefore, y(x) = (2 + 3x) e^(2x).

About the UNIKIN Polytechnique Admission Test Exam

The Faculté Polytechnique at the Université de Kinshasa (UNIKIN) is the Democratic Republic of the Congo's premier engineering faculty. Admission to the Bachelor 1 (Preparatory / B1 Ingénieur) program is strictly competitive through the annual Concours d'Admission. The exam rigorously evaluates candidates on advanced secondary mathematics (analysis, linear algebra, complex numbers), university-preparatory physics (Newtonian mechanics, electromagnetism, thermodynamics, wave optics), and technical-logical reasoning. This free English MCQ practice bank provides 100 detailed calculation and conceptual problems covering topics from the UNIKIN Polytechnique curriculum.

Exam sponsor: Université de Kinshasa (UNIKIN) — Faculté Polytechnique. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Not published. The concours is organised by the Faculté Polytechnique itself on the date fixed in the UNIKIN concours calendar (30 September 2026 for the 2026-2027 B1 and L1 intake in the faculties and schools other than Médecine humaine), and all admission and concours activity closes on 15 October 2026.

Time Limit

Single sitting; for the 2026-2027 intake the B1/L1 concours for the faculties and schools other than Médecine humaine was scheduled for 30 September 2026

Passing Score

Not published — admission is by competitive ranking against the faculty intake quota; UNIKIN does not publish a fixed cut-off mark

Exam / Certification Fees

Concours participation fee for faculties other than Médecine humaine: the equivalent of USD 20 in Congolese francs, plus CDF 150,000 registration (UNIKIN 2026-2027 notice)

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 ~45%

Engineering Mathematics

Limits, derivatives, definite integrals, differential equations, vectors, matrix algebra, determinants, and complex analysis.

Study emphasis ~40%

Applied Engineering Physics

Kinematics, Newton's laws, rotational dynamics, Coulomb's law, DC circuits, Kirchhoff's laws, ideal gases, thermodynamics, and Snell's law.

Study emphasis ~15%

Logical Reasoning & Technical Aptitude

Pattern recognition, deductive logic, engineering dimensional analysis, and technical passage interpretation.

Preparing for the UNIKIN Polytechnique Admission Test Exam

What You Need to Know

Passing score: Not published — admission is by competitive ranking against the faculty intake quota; UNIKIN does not publish a fixed cut-off mark
Assessment: Not published. The concours is organised by the Faculté Polytechnique itself on the date fixed in the UNIKIN concours calendar (30 September 2026 for the 2026-2027 B1 and L1 intake in the faculties and schools other than Médecine humaine), and all admission and concours activity closes on 15 October 2026.
Time limit: Single sitting; for the 2026-2027 intake the B1/L1 concours for the faculties and schools other than Médecine humaine was scheduled for 30 September 2026
Exam / certification fees: Concours participation fee for faculties other than Médecine humaine: the equivalent of USD 20 in Congolese francs, plus CDF 150,000 registration (UNIKIN 2026-2027 notice) Official sources

Using Our Practice Resources

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UNIKIN Polytechnique Admission Test: Suggested Study Strategy

1Master step-by-step calculus: integration by parts, trigonometric substitutions, and solving first- and second-order differential equations.

2Practice multi-step physics mechanics problems involving energy conservation, projectile kinematics, and rotational equilibrium.

3Solve DC circuit problems with Kirchhoff's voltage and current laws, capacitor charging, and equivalent resistances under timed conditions.

4Review dimensional analysis, vector cross products, and matrix determinants to quickly eliminate distractor options.

Frequently Asked Questions

What is the UNIKIN Faculté Polytechnique Concours d'Admission?

It is the entrance competition for the first year of engineering (B1) at the Université de Kinshasa. UNIKIN's enrolment notice lists Polytechnique — alongside Médecine, Médecine Dentaire and the Mathematics-Computer Science department — among the faculties where the concours is compulsory for every applicant, whatever their EXETAT percentage; elsewhere only candidates below 60% must sit it.

What subjects are tested on the UNIKIN Polytechnique exam?

The examination tests advanced Mathematics (calculus, algebra, geometry, trigonometry), General Physics (mechanics, electricity, electromagnetism, thermodynamics, optics), and Technical Comprehension/Aptitude.

What is the official language and format of the test?

The official test is written and sat in French. This bank is an English-language multiple-choice study adaptation: it rehearses the same mathematics, physics and reasoning, but it is not an official translation and it does not reproduce the official paper format, which UNIKIN does not publish.

What score is required to gain admission?

UNIKIN does not publish a fixed cut-off. Admission is decided by competitive ranking against the number of places the faculty opens, so the effective threshold moves from year to year with the size and strength of the candidate field.