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100+ Free UB Concours d'Entrée Practice Questions

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2026 Statistics

Key Facts: UB Concours d'Entrée Exam

70%

Only candidates who scored 70% or more at the Examen d'État may sit the competition.

MENRS (mesrs.gov.bi), launch of the 2025 edition

4 pôles

The competition covers medicine, engineering sciences, agronomy and bio-engineering, and applied statistics.

MENRS (mesrs.gov.bi), 10 November 2025

400

400 laureates are retained: the top 100 study free at the Université du Burundi and 300 are placed across designated private universities.

MENRS (mesrs.gov.bi), 10 November 2025

2 days

The written competition is sat over two days.

MENRS reports on the 2021 and 2025 editions

1,798

1,798 candidates were expected at the 2025 edition, 36% of them women.

MENRS (mesrs.gov.bi), 10 November 2025

The Concours d'entrée aux pôles universitaires d'excellence is a two-day written competition run by MENRS with the Université du Burundi for candidates who scored 70% or more at the Examen d'État. It selects 400 laureates for four fields - medicine, engineering sciences, agronomy and bio-engineering, and applied statistics - with the 100 highest-ranked studying free at the Université du Burundi and the remaining 300 placed across designated private universities. This practice bank is an independent English-language MCQ study adaptation, not an official paper or a format simulation.

Sample UB Concours d'Entrée Practice Questions

Try these sample questions to test your UB Concours d'Entrée exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate the trigonometric limit: \lim_{x \to 0} \frac{\sin(5x)}{\tan(2x)}.
A.5/2
B.2/5
C.0
D.5/3
Explanation: Applying standard trigonometric limits or L'Hôpital's rule, \lim_{x \to 0} \frac{\sin(5x)}{\tan(2x)} = \lim_{x \to 0} \left(\frac{\sin(5x)}{5x} \cdot \frac{2x}{\tan(2x)} \cdot \frac{5}{2}\right) = 1 \cdot 1 \cdot \frac{5}{2} = \frac{5}{2}. Differentiating numerator and denominator directly gives 5\cos(0) / (2\sec^2(0)) = 5/2.
2Find the indefinite integral \int x e^{3x} dx.
A.\frac{e^{3x}(x - 1)}{3} + C
B.\frac{e^{3x}(3x - 1)}{9} + C
C.\frac{e^{3x}(3x + 1)}{9} + C
D.\frac{x^2 e^{3x}}{6} + C
Explanation: Using integration by parts with u = x and dv = e^{3x} dx, we obtain du = dx and v = \frac{1}{3}e^{3x}. Then \int x e^{3x} dx = \frac{1}{3}x e^{3x} - \int \frac{1}{3}e^{3x} dx = \frac{1}{3}x e^{3x} - \frac{1}{9}e^{3x} + C = \frac{e^{3x}(3x - 1)}{9} + C.
3Calculate the definite integral \int_0^1 \frac{2x}{x^2 + 1} dx.
A.2\ln(2)
B.\frac{1}{2}\ln(2)
C.\ln(2)
D.\ln(4)
Explanation: Let u = x^2 + 1, so du = 2x dx. When x = 0, u = 1; when x = 1, u = 2. The integral transforms into \int_1^2 \frac{1}{u} du = [\ln|u|]_1^2 = \ln(2) - \ln(1) = \ln(2).
4Find the general solution to the homogeneous second-order differential equation y'' - 4y' + 13y = 0.
A.y(x) = C_1 e^{2x} + C_2 e^{-3x}
B.y(x) = e^{3x}(C_1 \cos(2x) + C_2 \sin(2x))
C.y(x) = e^{-2x}(C_1 \cos(3x) + C_2 \sin(3x))
D.y(x) = e^{2x}(C_1 \cos(3x) + C_2 \sin(3x))
Explanation: The characteristic equation is r^2 - 4r + 13 = 0. Solving with the quadratic formula gives r = \frac{4 \pm \sqrt{16 - 52}}{2} = \frac{4 \pm \sqrt{-36}}{2} = 2 \pm 3i. For complex conjugate roots \alpha \pm i\beta = 2 \pm 3i, the general solution is y(x) = e^{2x}(C_1 \cos(3x) + C_2 \sin(3x)).
5Compute the first derivative of f(x) = \ln(x^2 + 4).
A.\frac{2x}{x^2 + 4}
B.\frac{1}{x^2 + 4}
C.\frac{2}{x^2 + 4}
D.\frac{x}{x^2 + 4}
Explanation: Applying the chain rule for natural logarithms, \frac{d}{dx}[\ln(u(x))] = \frac{u'(x)}{u(x)}. Setting u(x) = x^2 + 4 gives u'(x) = 2x, which yields f'(x) = \frac{2x}{x^2 + 4}.
6Evaluate the indefinite integral \int \frac{5x - 1}{x^2 - x - 2} dx.
A.2\ln|x - 2| + 3\ln|x + 1| + C
B.3\ln|x - 2| + 2\ln|x + 1| + C
C.5\ln|x^2 - x - 2| + C
D.\ln|x - 2| - 2\ln|x + 1| + C
Explanation: Factoring the denominator gives (x - 2)(x + 1). Expressing in partial fractions: \frac{5x - 1}{(x - 2)(x + 1)} = \frac{A}{x - 2} + \frac{B}{x + 1}. Setting x = 2 gives 9 = 3A \implies A = 3. Setting x = -1 gives -6 = -3B \implies B = 2. Integrating term by term yields 3\ln|x - 2| + 2\ln|x + 1| + C.
7Find the eigenvalues of the matrix A = \begin{pmatrix} 4 & 1 \\ 2 & 3 \end{pmatrix}.
A.\lambda_1 = 4, \lambda_2 = 3
B.\lambda_1 = 6, \lambda_2 = 1
C.\lambda_1 = 5, \lambda_2 = 2
D.\lambda_1 = 7, \lambda_2 = -2
Explanation: The characteristic polynomial is \det(A - \lambda I) = (4 - \lambda)(3 - \lambda) - (1)(2) = \lambda^2 - 7\lambda + 12 - 2 = \lambda^2 - 7\lambda + 10 = 0. Factoring yields (\lambda - 5)(\lambda - 2) = 0, giving eigenvalues \lambda_1 = 5 and \lambda_2 = 2.
8Compute the determinant of the 3 \times 3 matrix M = \begin{pmatrix} 1 & 2 & 0 \\ 0 & 3 & 4 \\ 2 & 0 & 1 \end{pmatrix}.
A.11
B.-13
C.15
D.19
Explanation: Expanding along the first row: \det(M) = 1 \cdot \det\begin{pmatrix} 3 & 4 \\ 0 & 1 \end{pmatrix} - 2 \cdot \det\begin{pmatrix} 0 & 4 \\ 2 & 1 \end{pmatrix} + 0 = 1(3 - 0) - 2(0 - 8) = 3 - 2(-8) = 3 + 16 = 19.
9What is the principal argument \text{Arg}(z) of the complex number z = -\sqrt{3} + i?
A.5\pi/6
B.\pi/6
C.2\pi/3
D.7\pi/6
Explanation: The number lies in the second quadrant because \text{Re}(z) = -\sqrt{3} < 0 and \text{Im}(z) = 1 > 0. The reference angle is \arctan(1/\sqrt{3}) = \pi/6, so \text{Arg}(z) = \pi - \pi/6 = 5\pi/6, which lies in the principal range (-\pi, \pi].
10Solve the initial value problem \frac{dy}{dx} = 2xy^2 with initial condition y(0) = 1.
A.y(x) = \frac{1}{1 + x^2}
B.y(x) = \frac{1}{1 - x^2}
C.y(x) = e^{x^2}
D.y(x) = \sqrt{x^2 + 1}
Explanation: Separating variables gives y^{-2} dy = 2x dx. Integrating both sides yields -\frac{1}{y} = x^2 + C. Substituting y(0) = 1 gives -1 = 0 + C \implies C = -1. Therefore, -\frac{1}{y} = x^2 - 1 \implies \frac{1}{y} = 1 - x^2 \implies y(x) = \frac{1}{1 - x^2}.

About the UB Concours d'Entrée Exam

Burundi's competitive national entrance examination for the four university pôles d'excellence - medicine, engineering sciences, agronomy and bio-engineering, and applied statistics - open to the strongest Examen d'État candidates.

Assessment

Question count not published by the exam provider

Time Limit

2 days of written papers

Passing Score

No published pass mark; selection is by competitive rank with 400 laureates retained, and eligibility requires 70% or more at the Examen d'État

Exam Fee

Not published (Université du Burundi (UB) & Ministère de l'Éducation Nationale et de la Recherche Scientifique (MENRS))

UB Concours d'Entrée Exam Content Outline

~25% of this local bank

Advanced Mathematics and Calculus

Differential calculus, integrals, differential equations, vectors, matrix algebra, complex numbers, and probability

~25% of this local bank

Physics for Engineering and Health Sciences

Newtonian mechanics, work and energy, thermodynamics, fluid statics/dynamics, circuits, electromagnetism, and optics

~20% of this local bank

General and Organic Chemistry

Chemical kinetics, equilibrium, acid-base solutions, buffers, electrochemistry, and organic reaction mechanisms

~20% of this local bank

Cellular Biology, Genetics and Human Physiology

Molecular biology, DNA replication, gene regulation, cellular respiration, human organ physiology, and immunology

~10% of this local bank

Scientific Logic and Quantitative Reasoning

Data analysis, graph interpretation, deductive reasoning, and quantitative problem solving

How to Pass the UB Concours d'Entrée Exam

What You Need to Know

  • Passing score: No published pass mark; selection is by competitive rank with 400 laureates retained, and eligibility requires 70% or more at the Examen d'État
  • Assessment: Question count not published by the exam provider
  • Time limit: 2 days of written papers
  • Exam fee: Not published

Keys to Passing

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

UB Concours d'Entrée Study Tips from Top Performers

1Focus on rigorous calculus and differential equation problems with precise numerical and algebraic steps.
2Review classical mechanics, rotational dynamics, and electrical circuits in physics.
3Master equilibrium constants, pH and buffer calculations, and organic functional group transformations.
4Review molecular genetics, enzyme kinetics, and cardiovascular and renal physiology for the medical track.

Frequently Asked Questions

Who can sit the pôles d'excellence entrance competition?

Only candidates who passed the Examen d'État with a mark of 70% or more. Identity is checked at the centre against the attestation de réussite and the national identity card.

Which fields does the competition cover?

Four: the faculty of medicine, the faculty of engineering sciences, the faculty of agronomy and bio-engineering, and the institute of applied statistics.

How many candidates are selected?

400 laureates are retained. The 100 highest-ranked study free of charge at the Université du Burundi, and the remaining 300 are distributed across designated private universities, with a cap on the number each may enrol.

What is the pass mark?

There is no published pass mark. Places are awarded by competitive rank order until the 400 places are filled, so the effective cut-off depends on how the cohort performs in a given year.

Is this practice bank an official exam?

No. MENRS publishes no syllabus, item count or mark scheme for this competition. This bank is an independent English-language MCQ study adaptation of the scientific competencies the four pôles rely on, and is not an official paper, a translation, or a simulation of the real format.