POST UTME EKSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{\pi}{2} \).
A. \frac{1}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}
Question 2
In the diagram below, [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ] is a matrix. Find the determinant of the matrix.
A. 0
B. 1
C. 2
D. 3
Question 3
Solve the system of linear equations: \[ \begin{cases} x + y + z = 6 \ x + 2y + 3z = 14 \ 2x + 3y + 4z = 20 \end{cases} \]
A. \{ (1, 2, 3) \}
B. \{ (2, 3, 1) \}
C. \{ (3, 1, 2) \}
D. \{ (1, 3, 2) \}
Question 4
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 5
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{pmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 6
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3, 4 \). Find the probability that ( X ) is greater than 2.
A. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{2} \)
Question 7
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis about the x-axis.
A. 16π/3
B. 16π/5
C. 16π/7
D. 16π/9
Question 8
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \( \frac{-1}{2x^{3/2}} \)
B. \( \frac{1}{2x^{3/2}} \)
C. \( \frac{1}{x^{3/2}} \)
D. \( \frac{-1}{x^{3/2}} \)
Question 9
Find the derivative of the function [ f(x) = 3x^2 \sin (2x) ] u\sing the product rule.
A. 6x^2 \sin (2x) + 12x \cos (2x)
B. 6x^2 \sin (2x) - 12x \cos (2x)
C. 12x^2 \sin (2x) + 6x \cos (2x)
D. 12x^2 \sin (2x) - 6x \cos (2x)
Question 10
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. -1
D. 2
Question 11
Find the derivative of the function ( f(x) = \sin \( x^2 \) ) u\sing the chain rule.
A. \( 2x \cos \( x^2 \ \) )
B. \( 2x \sin \( x^2 \ \) )
C. \( \cos \( x^2 \ \) )
D. \( \sin \( x^2 \ \) )
Question 12
Solve the equation \( \log_{10} \( x^2 \ \) = 4 ) for ( x ).
A. \( x = 10^4 \)
B. \( x = 10^{-4} \)
C. \( x = 10^2 \)
D. \( x = 10^{-2} \)
Question 13
Evaluate the integral \[ \int_0^1 \frac{1}{x^2 + 1} \, dx \].
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 14
Find the surface area of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis about the x-axis.
A. 16π
B. 32π
C. 64π
D. 128π
Question 15
Find the equation of the circle with center at ( (2, 3) ) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 20
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 24
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 28

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