POST UTME KSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 2
Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).
A. 0
B. 2
C. 4
D. 6
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 4
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) by factoring.
A. \( x - 3 \)\( x + 1 \ \) > 0 )
B. \( x - 1 \)\( x + 3 \ \) > 0 )
C. \( x + 3 \)\( x - 1 \ \) > 0 )
D. \( x + 1 \)\( x - 3 \ \) > 0 )
Question 5
Solve the inequality \( x^2 - 6x + 8 < 0 \) by factoring.
A. \( x - 2 \)\( x - 4 \ \) < 0 )
B. \( x - 4 \)\( x - 2 \ \) < 0 )
C. \( x + 2 \)\( x - 4 \ \) < 0 )
D. \( x + 4 \)\( x - 2 \ \) < 0 )
Question 6
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = \frac{2}{1}x + \frac{2}{1} \)
B. \( y = \frac{2}{1}x - \frac{2}{1} \)
C. \( y = \frac{2}{1}x + \frac{4}{1} \)
D. \( y = \frac{2}{1}x - \frac{4}{1} \)
Question 7
Solve the system of equations: \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 8
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}
Question 9
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).
A. x = \frac{pi}{2}
B. x = \frac{pi}{4}
C. x = \frac{3pi}{4}
D. x = \frac{5pi}{4}
Question 10
Solve the inequality \( \log_{10} \( x^2 \ \) > 2 ).
A. \( x > 10 \)
B. \( x < 10 \)
C. \( x > 100 \)
D. \( x < 100 \)
Question 11
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 12
Find the volume of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 4 - x \) about the x-axis.
A. \frac{32}{3} pi
B. \frac{64}{3} pi
C. \frac{128}{3} pi
D. \frac{256}{3} pi
Question 13
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 14
Find the derivative of the function ( f(x) = \frac{x^2 + 1}{x^2 - 1} ) u\sing the quotient rule.
A. \( \frac{2x}{\( x^2 - 1 \ \)^2} )
B. \( \frac{2x^2 + 2}{\( x^2 - 1 \ \)^2} )
C. \( \frac{2x^3 - 2x}{\( x^2 - 1 \ \)^2} )
D. \( \frac{2x^3 + 2x}{\( x^2 - 1 \ \)^2} )
Question 15
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. 4
B. 6
C. 8
D. 10

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