POST UTME NOUN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
If \( x^2 + 4x + 4 = 0 \), find the value of ( x ).
A. -2
B. -1
C. 1
D. 2
Question 2
Solve the system of linear equations: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}
A. \begin{pmatrix} 1 \ 2 \end{pmatrix}
B. \begin{pmatrix} 2 \ 1 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} 4 \ 2 \end{pmatrix}
Question 3
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 4
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 5
Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 - 2x + 3 \) about the x-axis, from \( x = 1 \) to \( x = 3 \).
A. \( \frac{1}{2} pi \( 3^2 - 1^2 \ \) \( 3 + 1 \) )
B. \( \frac{1}{2} pi \( 3^2 - 1^2 \ \) \( 3 - 1 \) )
C. \( \frac{1}{2} pi \( 3^2 - 1^2 \ \) \( 3 + 2 \) )
D. \( \frac{1}{2} pi \( 3^2 - 1^2 \ \) \( 3 - 2 \) )
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 60
C. 80
D. 100
Question 7
Find the mean of the data set: \{ 2, 4, 6, 8, 10 \}.
A. 5
B. 6
C. 7
D. 8
Question 8
Find the equation of the circle with center at ((2,3)) and pas\sing through the point ((6,7)).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 36 )
C. \( x-2 \ \)^2 + \( y-3 \)^2 = 49 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 64 )
Question 9
Simplify the expression \( \frac{2x^2 + 5x - 3}{x^2 + 2x - 3} \).
A. 2x - 1
B. x + 3
C. 2x + 3
D. x - 1
Question 10
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{3\pi}{4}
D. x = \frac{\pi}{6}
Question 11
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. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x > -3 \) or \( x < \frac{1}{2} \)
B. \( x < -3 \) or \( x > \frac{1}{2} \)
C. \( x > -3 \) or \( x < \frac{1}{2} \)
D. \( x < -3 \) or \( x > \frac{1}{2} \)
Question 13
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( x in \( -infty, -3 \ \) cup (3, infty) )
B. \( x in \( -infty, -3 \ \) cup (3, infty) cup {0} )
C. \( x in \( -infty, -3 \ \) cup (3, infty) cup {4} )
D. \( x in \( -infty, -3 \ \) cup (3, infty) cup {0, 4} )
Question 14
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \( x = \frac{\pi}{6} \) or \( x = \frac{5\pi}{6} \)
B. \( x = \frac{\pi}{4} \) or \( x = \frac{3\pi}{4} \)
C. \( x = \frac{\pi}{3} \) or \( x = \frac{2\pi}{3} \)
D. \( x = \frac{\pi}{2} \) or \( x = \frac{3\pi}{2} \)
Question 15
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \) u\sing the formula for 3x3 matrices.
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )

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