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100+ Free EXETAT Math-Physique Practice Questions

Prepare for the Examen d'État — Option Mathématiques-Physique (DR Congo) exam with instant access — no signup required.

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2026 Statistics

Key Facts: EXETAT Math-Physique Exam

4 days

Length of the EXETAT session ordinaire, held 22-25 June in 2026

Ministère de l'Éducation Nationale et Nouvelle Citoyenneté

50%

Minimum overall mark required for the Diplôme d'État

Ministère de l'Éducation Nationale et Nouvelle Citoyenneté

1,079,675

Cycle-long candidates registered for the 2026 EXETAT session

Ministère de l'Éducation Nationale et Nouvelle Citoyenneté

3,268

EXETAT examination centres used for the 2026 session, including 14 abroad

Ministère de l'Éducation Nationale et Nouvelle Citoyenneté

Comprehensive 100-question practice bank for DR Congo's EXETAT Math-Physique option, covering advanced calculus, linear algebra, Newtonian mechanics, electromagnetism, optics, chemistry, and Congolese civic culture.

Sample EXETAT Math-Physique Practice Questions

Try these sample questions to test your EXETAT Math-Physique exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Evaluate the algebraic limit: lim(x→4) (√(2x + 1) - 3) / (x - 4).
A.1/3
B.1/6
C.2/3
D.1/2
Explanation: Multiplying numerator and denominator by the conjugate (√(2x + 1) + 3) yields ((2x + 1) - 9) / ((x - 4)(√(2x + 1) + 3)) = 2(x - 4) / ((x - 4)(√(2x + 1) + 3)). Cancelling the non-zero factor (x - 4) gives 2 / (√(2(4) + 1) + 3) = 2 / (3 + 3) = 2/6 = 1/3.
2Let f(x) = ln((x² + 1) / (x² - 1)) for x > 1. Compute f'(2).
A.-8/15
B.8/15
C.-4/15
D.-16/15
Explanation: Rewrite f(x) as ln(x² + 1) - ln(x² - 1). Differentiating gives f'(x) = 2x/(x² + 1) - 2x/(x² - 1) = 2x((x² - 1) - (x² + 1)) / (x⁴ - 1) = -4x / (x⁴ - 1). Evaluating at x = 2 gives f'(2) = -4(2) / (16 - 1) = -8/15.
3Evaluate the definite integral ∫₀¹ x · e^(2x) dx.
A.(e² + 1) / 4
B.(e² - 1) / 4
C.(2e² + 1) / 4
D.(e² + 1) / 2
Explanation: Using integration by parts with u = x and dv = e^(2x) dx gives du = dx and v = (1/2)e^(2x). Then ∫₀¹ x e^(2x) dx = [(x/2)e^(2x)]₀¹ - ∫₀¹ (1/2)e^(2x) dx = (1/2)e² - [(1/4)e^(2x)]₀¹ = (1/2)e² - ((1/4)e² - 1/4) = (1/4)e² + 1/4 = (e² + 1)/4.
4Solve the initial value problem dy/dx + 2y = 4x with y(0) = 1. What is the value of y(1)?
A.1 + 2e⁻²
B.2 + 2e⁻²
C.1 - 2e⁻²
D.2 - e⁻²
Explanation: The integrating factor is I(x) = e^(∫2dx) = e^(2x). Multiplying through gives d/dx [y e^(2x)] = 4x e^(2x). Integrating by parts yields y e^(2x) = 2x e^(2x) - e^(2x) + C, so y(x) = 2x - 1 + C e^(-2x). Applying y(0) = 1 gives -1 + C = 1 => C = 2. Thus y(1) = 2(1) - 1 + 2e^(-2) = 1 + 2e^(-2).
5Find the unique solution to the second-order ODE y'' - 4y' + 13y = 0 satisfying y(0) = 2 and y'(0) = 4.
A.y(t) = 2e^(2t) cos(3t)
B.y(t) = e^(2t)(2 cos(3t) + 4 sin(3t))
C.y(t) = 2e^(2t) sin(3t)
D.y(t) = e^(2t)(2 cos(3t) + 2 sin(3t))
Explanation: The characteristic equation is r² - 4r + 13 = 0, with roots r = (4 ± √(16 - 52))/2 = 2 ± 3i. The general solution is y(t) = e^(2t)(C₁ cos(3t) + C₂ sin(3t)). Using y(0) = 2 gives C₁ = 2. Differentiating gives y'(0) = 2C₁ + 3C₂ = 4(1) + 3C₂ = 4 => 3C₂ = 0 => C₂ = 0. Therefore, y(t) = 2e^(2t) cos(3t).
6Find the Cartesian equation of the oblique asymptote of the function f(x) = (2x³ - 3x² + 5) / (x² + 1) as x → ±∞.
A.y = 2x - 3
B.y = 2x + 3
C.y = 2x - 1
D.y = x - 3
Explanation: Performing polynomial long division: (2x³ - 3x² + 5) / (x² + 1) = (2x - 3) + (-2x + 8) / (x² + 1). As x → ±∞, the remainder term (-2x + 8)/(x² + 1) approaches 0. Therefore, the oblique asymptote is the linear quotient y = 2x - 3.
7Evaluate the definite integral ∫₀² 1 / √(4 - x²) dx.
A.π/2
B.π/4
C.π
D.2π
Explanation: The standard antiderivative of 1/√(a² - x²) is arcsin(x/a). Here a = 2, so ∫₀² 1/√(4 - x²) dx = [arcsin(x/2)]₀² = arcsin(1) - arcsin(0) = π/2 - 0 = π/2.
8Calculate the arc length of the plane curve y = (2/3)x^(3/2) from x = 0 to x = 3.
A.14/3
B.16/3
C.7/3
D.8/3
Explanation: The derivative is y' = (2/3)(3/2)x^(1/2) = √x. The arc length formula gives L = ∫₀³ √(1 + (y')²) dx = ∫₀³ √(1 + x) dx = [(2/3)(1 + x)^(3/2)]₀³ = (2/3)(4^(3/2) - 1^(3/2)) = (2/3)(8 - 1) = 14/3.
9What is the coefficient of x⁴ in the Maclaurin series expansion of f(x) = 1 / (1 + 2x²)?
A.4
B.-4
C.2
D.-2
Explanation: Using the geometric power series 1/(1 - u) = 1 + u + u² + u³ + ... with u = -2x² gives 1/(1 + 2x²) = 1 + (-2x²) + (-2x²)² + ... = 1 - 2x² + 4x⁴ - 8x⁶ + ... The coefficient of x⁴ is (-2)² = 4.
10Find the volume of the solid generated by revolving the region bounded by y = √x, y = 0, and x = 4 around the x-axis.
A.8π
B.16π
C.4π
D.32π/3
Explanation: By the disk method, V = π ∫₀⁴ y² dx = π ∫₀⁴ (√x)² dx = π ∫₀⁴ x dx = π [x²/2]₀⁴ = π(16/2 - 0) = 8π.

About the EXETAT Math-Physique Exam

The Examen d'État (EXETAT) is the Democratic Republic of the Congo's high-stakes national secondary exit examination and university entrance qualification. The Mathématiques-Physique (Math-Physique) option within the Humanités Scientifiques stream is the elite STEM track designed for aspiring engineers, physicists, and mathematicians. Administered nationwide by the Ministère de l'Éducation Nationale et Nouvelle Citoyenneté (EDU-NC), candidates are assessed on advanced calculus, differential equations, linear algebra, mechanics, electromagnetism, wave physics, thermodynamics, chemistry, and general civic culture. This 100-question English study prep bank adapts key Congolese curriculum concepts into rigorous quantitative and conceptual MCQs.

Assessment

Hors-session tests in May (dissertation, traditional papers for the technical options, oral French and — new from the 2026 session — oral English, and professional practice), followed by the four-day session ordinaire: Day 1 Culture générale, Day 2 Sciences, Day 3 Options, Day 4 Langues.

Time Limit

Four-day written session (22–25 June for the 2026 edition), preceded by hors-session tests in May; each épreuve booklet carries its own duration, typically 2 to 5 hours

Passing Score

50% overall for the Diplôme d'État; 60% or more exempts the holder from the admission tests run by universities such as UNIKIN and UNILU

Exam Fee

Fixed per province by governor's decree, not nationally: for the 2026 session the hors-session fee ranged from about CDF 52,000 to CDF 100,000 and the session ordinaire fee from about CDF 40,000 to CDF 90,000 (Kinshasa: CDF 80,000 + CDF 60,000). Candidates in Nord-Kivu and Sud-Kivu were exempted by the government. (Ministère de l'Éducation Nationale et Nouvelle Citoyenneté (EDU-NC))

EXETAT Math-Physique Exam Content Outline

Study emphasis ~45%

Advanced Mathematics

Limits, derivatives, integrals, differential equations, sequences, matrices, determinants, complex numbers, analytic geometry, and probability.

Study emphasis ~35%

Physics

Newtonian mechanics, kinematics, dynamics, work-energy, fluid statics, electrostatics, DC/AC circuits, electromagnetic induction, optics, and thermodynamics.

Study emphasis ~10%

Chemistry

Acid-base equilibria, buffers, redox reactions, electrochemistry, stoichiometry, and reaction kinetics.

Study emphasis ~10%

General Culture & Civics

DR Congo geography, history, constitutional institutions, national symbols, and French scientific terminology.

How to Pass the EXETAT Math-Physique Exam

What You Need to Know

  • Passing score: 50% overall for the Diplôme d'État; 60% or more exempts the holder from the admission tests run by universities such as UNIKIN and UNILU
  • Assessment: Hors-session tests in May (dissertation, traditional papers for the technical options, oral French and — new from the 2026 session — oral English, and professional practice), followed by the four-day session ordinaire: Day 1 Culture générale, Day 2 Sciences, Day 3 Options, Day 4 Langues.
  • Time limit: Four-day written session (22–25 June for the 2026 edition), preceded by hors-session tests in May; each épreuve booklet carries its own duration, typically 2 to 5 hours
  • Exam fee: Fixed per province by governor's decree, not nationally: for the 2026 session the hors-session fee ranged from about CDF 52,000 to CDF 100,000 and the session ordinaire fee from about CDF 40,000 to CDF 90,000 (Kinshasa: CDF 80,000 + CDF 60,000). Candidates in Nord-Kivu and Sud-Kivu were exempted by the government.

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

EXETAT Math-Physique Study Tips from Top Performers

1Master calculus techniques: drill integration by parts, partial fractions, limits with conjugate multiplication, and first/second-order linear ODEs daily.
2Memorize and derive core physics formulas for projectile motion, RLC resonant circuits, Lorentz force, Faraday induction, and Snell's law.
3Practice rapid numeric calculations and unit conversions without relying heavily on graphic calculators.
4Review Congolese geography, historical milestones (such as June 30, 1960 independence), and constitutional institutions for the Culture Générale session.

Frequently Asked Questions

What is the official format of the EXETAT examination in DR Congo?

The session ordinaire runs over four consecutive days — Culture générale, Sciences, Options, Langues — using multiple-choice booklets answered on optical scan grids, with five lettered choices plus a 'none of these' box. It is preceded by hors-session tests in May: the dissertation, traditional papers for technical options, oral French and, from 2026, oral English, and professional practice.

What score is required to obtain the Diplôme d'État in the Math-Physique option?

A minimum weighted overall mark of 50% across all testing papers and school-year internal marks is required to pass and receive the Diplôme d'État. Scores of 60% or higher ('lauréat' tier) confer direct admission to premier public engineering and science university faculties.

Is this practice bank an official test paper?

No. This question bank is an independent English-language educational adaptation designed to test core STEM and civic competencies evaluated on the Congolese national syllabus.