POST UTME UNILAG 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 11 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 2
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 32π
B. 64π
C. 128π
D. 256π
Question 3
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the quotient rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{1}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^2} )
Question 4
A histogram of exam scores is shown below. What is the mean score?
A. 50
B. 60
C. 70
D. 80
Question 5
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 6
A histogram is constructed from the following data: 2, 4, 5, 6, 8, 9, 10. Find the mean and median of the data.
A. 5.5, 6
B. 6, 5.5
C. 6.5, 6
D. 7, 6
Question 7
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 8
Solve the inequality x^2 + 4x + 4 > 0.
A. x < -2 or x > 0
B. x > -2 or x < 0
C. x < 0 or x > 2
D. x > 0 or x < 2
Question 9
Solve for x in the equation [ \sin^2 x + \cos^2 x = 1 ].
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{\pi}{6}
D. x = \frac{\pi}{3}
Question 10
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 4 - x^2 \) about the x-axis.
A. \frac{32\pi}{3}
B. \frac{64\pi}{3}
C. \frac{128\pi}{3}
D. \frac{256\pi}{3}
Question 11
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{array} ].
A. -2
B. 4
C. 6
D. 8
Question 12
Find the vector ( mathbf{a} ) such that \( mathbf{a} cdot mathbf{b} = 5 \) and \( mathbf{a} cdot mathbf{c} = 3 \), where \( mathbf{b} = \( 2, 1, 3 \ \) ) and \( mathbf{c} = \( 1, 2, 1 \ \) ).
A. (1, 2, 3)
B. (2, 1, 3)
C. (3, 2, 1)
D. (1, 3, 2)
Question 13
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. \( x > 2 \ \)
B. \( x < 2 \ \)
C. \( x = 2 \ \)
D. \( x \leq 2 \ \)
Question 14
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 15
A 3x3 matrix is given by A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]. Find the determinant of the matrix.
A. 0
B. 1
C. 2
D. 3

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