POST UTME AAUA 2024 Mathematics | Objective

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Question 1
A 3x3 matrix A has the following elements: a11 = 2, a12 = 3, a13 = 4, a21 = 5, a22 = 6, a23 = 7, a31 = 8, a32 = 9, a33 = 10. If B = A^2, what is the value of b11?
A. 17
B. 19
C. 21
D. 23
Question 2
Find the area under the curve \( y = \sin^2\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{2} \)
D. \( \frac{3pi}{4} \)
Question 3
A circle has a radius of 4 cm. If the area of the circle is 50.24 cm^2, what is the value of π?
A. 3.14
B. 3.15
C. 3.16
D. 3.17
Question 4
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{8}{3}
B. \frac{16}{3}
C. \frac{32}{3}
D. \frac{64}{3}
Question 5
Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{6}
Question 6
Determine the value of $x$ in the equation $2x^2 + 5x - 3 = 0$ u\sing the quadratic formula.
A. -1
B. 1
C. 2
D. 3
Question 7
Solve the inequality \( |x^2 - 4x + 3| geq 2 \).
A. \( x leq -1 \) or ( x geq 3 )
B. ( x leq 1 ) or ( x geq 3 )
C. \( x leq -1 \) or ( x geq 1 )
D. \( x leq -3 \) or ( x geq 1 )
Question 8
Solve the system of equations \( x + y = 2 \) and \( xy = 3 \).
A. \left\( 1, 1\right \)
B. \left\( 1, 3\right \)
C. \left\( 3, 1\right \)
D. \left\( 3, 3\right \)
Question 9
Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ).
A. 3x^2 - 4x + 1
B. 3x^2 - 4x + 2
C. 3x^2 - 4x - 1
D. 3x^2 - 4x - 2
Question 10
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 11
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If a student scored 80, what is the z-score of this score?
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 12
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ).
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{-x}{\( x^2 + 1 \ \)^2} )
D. \( \frac{x}{\( x^2 + 1 \ \)^2} )
Question 13
Solve for ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 14
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \).
A. \( x \in \( -\infty, -1 \ \) \cup [3, \infty) \)
B. \( x \in \( -\infty, -3 \ \) \cup [1, \infty) \)
C. \( x \in \( -\infty, 1 \ \) \cup [3, \infty) \)
D. \( x \in \( -\infty, -3 \ \) \cup [1, \infty) \)
Question 15
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. \( x = 1, y = 1 \ \)
B. \( x = 1, y = -1 \ \)
C. \( x = -1, y = 1 \ \)
D. \( x = -1, y = -1 \ \)

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