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Free Practice Questions for Senegal Concours École Polytechnique de Thiès (EPT)

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Key Facts: Senegal Concours École Polytechnique de Thiès (EPT) Exam

3 hours

Total duration of the standardized examination across all testing centres

École Polytechnique de Thiès (ept.sn)

7,000 FCFA

Non-refundable candidate application and registration fee

Avis d'ouverture du Concours EPT

5 years

Duration of the rigorous Cycle Ingénieur de Conception program upon admission

EPT curriculum documentation

Sample Senegal Concours École Polytechnique de Thiès (EPT) Practice Questions

Try these sample questions to review concepts for the Senegal Concours École Polytechnique de Thiès (EPT) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 92+ question experience with AI tutoring.

1What is the limit of f(x) = (sin(3x)) / (2x) as x approaches 0?
A.3/2
B.0
C.1
D.2/3
Explanation: Using the standard limit lim_{u->0} (sin u)/u = 1, we rewrite (sin(3x))/(2x) as (3/2) * (sin(3x))/(3x). As x -> 0, (sin(3x))/(3x) -> 1, so the limit is 3/2 * 1 = 3/2.
2What is the derivative of f(x) = ln(x^2 + 4) with respect to x?
A.2x / (x^2 + 4)
B.1 / (x^2 + 4)
C.2 / (x^2 + 4)
D.x / (x^2 + 4)
Explanation: Applying the chain rule for the natural logarithm d/dx [ln(u)] = u'/u, where u = x^2 + 4 and u' = 2x, yields f'(x) = 2x / (x^2 + 4).
3Evaluate the definite integral of (3x^2 - 2x + 1) dx from x = 0 to x = 2.
A.6
B.8
C.4
D.10
Explanation: The antiderivative is F(x) = x^3 - x^2 + x. Evaluating from 0 to 2 gives F(2) - F(0) = (2^3 - 2^2 + 2) - 0 = (8 - 4 + 2) = 6.
4What is the general solution of the first-order differential equation y' + 3y = 0?
A.y(x) = C * e^(-3x)
B.y(x) = C * e^(3x)
C.y(x) = C - 3x
D.y(x) = C * e^(-x/3)
Explanation: The differential equation y' + ay = 0 has the general solution y(x) = C * e^(-ax). With a = 3, y(x) = C * e^(-3x), where C is an arbitrary real constant.
5What is the modulus of the complex number z = 3 - 4i?
A.5
B.7
C.25
D.1
Explanation: The modulus of z = a + bi is |z| = sqrt(a^2 + b^2). Here, |z| = sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5.
6If a sequence (u_n) is defined by u_0 = 2 and u_{n+1} = 3 * u_n, what is the value of u_4?
A.162
B.54
C.486
D.81
Explanation: (u_n) is a geometric progression with first term u_0 = 2 and common ratio r = 3. Thus u_n = u_0 * r^n. For n = 4, u_4 = 2 * 3^4 = 2 * 81 = 162.
7What is the dot product of the vectors u = (2, -1, 3) and v = (4, 2, -1) in R^3?
A.3
B.9
C.-3
D.5
Explanation: The dot product is given by u . v = (2)(4) + (-1)(2) + (3)(-1) = 8 - 2 - 3 = 3.
8A fair six-sided die is rolled once. What is the probability of obtaining a prime number?
A.1/2
B.1/3
C.2/3
D.1/6
Explanation: The possible outcomes are {1, 2, 3, 4, 5, 6}. The prime numbers in this set are 2, 3, and 5 (note that 1 is not prime). There are 3 favorable outcomes out of 6, giving a probability of 3/6 = 1/2.
9What is the determinant of the 2x2 matrix M = [[4, 2], [1, 3]]?
A.10
B.14
C.12
D.2
Explanation: For a 2x2 matrix [[a, b], [c, d]], det(M) = ad - bc. Here, det(M) = (4)(3) - (2)(1) = 12 - 2 = 10.
10What is the equation of the tangent line to the curve y = x^2 at the point where x = 3?
A.y = 6x - 9
B.y = 6x + 9
C.y = 3x - 9
D.y = 6x - 18
Explanation: At x = 3, y = 3^2 = 9. The derivative is y' = 2x, so the slope at x = 3 is m = 2(3) = 6. Using point-slope form: y - 9 = 6(x - 3) => y = 6x - 18 + 9 => y = 6x - 9.

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