Are the practice percentages official coefficients?

No. UGB confirms the four subjects, but the reviewed 2026 notice does not give their relative weights. The 30/30/25/15 split is a curated study allocation.

Is this a multiple-choice simulation of the concours?

No. The accessible official notice does not establish a pure MCQ format. These questions support subject study; follow the current official instructions for actual test format and performance requirements.

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Sample Concours IPSL — Saint-Louis Practice Questions

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1Evaluate lim(x→0) (e^(5x)−1)/x.

A.5

B.1

C.0

D.1/5

Explanation: Write the expression as 5(e^(5x)−1)/(5x). The standard exponential quotient tends to 1, giving the limit 5.

2In the complex plane, what locus is defined by |z+2−3i|=4?

A.Circle centered at (2,−3), radius 4

B.Circle centered at (−2,3), radius 4

C.Circle centered at (−2,3), radius 16

D.Line through (−2,3)

Explanation: The expression is |z−(−2+3i)|=4. It specifies a constant distance of 4 from the point with coordinates (−2,3), hence a circle.

3Evaluate ∫₁^(e²) (ln x)/x dx.

A.1

B.4

C.2

D.e²−1

Explanation: A primitive is (ln x)²/2. Evaluation gives 2²/2−0=2.

4Let u0=2 and u(n+1)=(2un+3)/(un+4). Define vn=(un−1)/(un+3). Which statement is correct? The sequences are well defined.

A.v(n+1)=5vn and un→+∞

B.v(n+1)=vn/2 and un→3

C.vn is constant and un→2

D.v(n+1)=vn/5 and un→1

Explanation: Subtracting 1 from the recurrence and adding 3 gives v(n+1)=(un−1)/(5(un+3))=vn/5. Since v0=1/5, vn tends to zero, and un=(1+3vn)/(1−vn) tends to 1.

5What is the oblique asymptote of (3x²+2x+1)/(x+1) at infinity?

A.y=3x−1

B.y=3x+2

C.y=3x+1

D.y=3x−2

Explanation: Polynomial division gives 3x−1+2/(x+1). The final fraction tends to zero at either infinity, leaving asymptote y=3x−1.

6Solve z²+6z+13=0 in ℂ.

A.3±2i

B.−3±2i

C.−6±4i

D.−3±4i

Explanation: The discriminant is 36−52=−16. Thus z=(−6±4i)/2=−3±2i.

7A function is continuous on [1,5] and differentiable on (1,5), with f(1)=3 and f(5)=15. Which derivative value is guaranteed somewhere in (1,5)?

A.12

B.4

C.3

D.15/4

Explanation: The mean value theorem gives f'(c)=(15−3)/(5−1)=3. Its assumptions concern continuity on the closed interval and differentiability in its interior.

8Solve y'+y=3 with y(0)=5.

A.3+5e^(−x)

B.5+3e^(−x)

C.3+2e^x

D.3+2e^(−x)

Explanation: A constant particular solution is 3, so the general solution is 3+Ce^(−x). The initial condition gives C=2.

9How many unordered pairs can be selected from eight distinct students?

A.28

B.56

C.16

D.64

Explanation: There are 8×7 ordered choices of two different students. Dividing by two for the two orders of each pair gives 28.

10Find the area between y=9−x² and the x-axis where the parabola is nonnegative.

A.18

B.36

C.54

D.27

Explanation: The roots are −3 and 3. The area is ∫₋₃³(9−x²)dx=[9x−x³/3]₋₃³=36 square units.

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