POST UTME ESUT 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
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 3
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 = 4
C. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 4
Question 4
Solve the inequality $|x - 2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, -1 \) \cup (2, 5)
C. \( -\infty, 1 \) \cup \( 2, \infty \)
D. \( -\infty, 5 \) \cup \( 2, \infty \)
Question 5
Find the value of \( \frac{1}{2} \sin^{-1} \left\( \frac{3x}{5} \right \ \) ) if \( \tan x = \frac{3}{4} \).
A. 30
B. 45
C. 60
D. 90
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
C. \( x < -\frac{1}{2} \) or \( x < \frac{3}{2} \)
D. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 7
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)
B. \( 0, \frac{pi}{2}, \frac{3pi}{2} \)
C. ( 0, pi, 2pi )
D. \( \frac{pi}{2}, \frac{3pi}{2}, 2pi \)
Question 8
Solve the inequality $\frac{x^2 - 4}{x^2 - 9} > 0$.
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup \( 3, \infty \)
C. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \)
D. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \) \cup (0, 1)
Question 9
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{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 10
A sequence is defined recursively as \( a_n = 2a_{n-1} + 1 \) with \( a_1 = 3 \). Find the value of \( a_{10} \).
A. ( 1023 )
B. ( 1024 )
C. ( 1025 )
D. ( 1026 )
Question 11
Find the value of \( \frac{1}{2} \sin^{-1} \left\( \frac{3x}{5} \right \ \) ) if \( \tan x = \frac{3}{4} \).
A. 30
B. 45
C. 60
D. 90
Question 12
Find the area under the curve $y = x^2$ from $x = 0$ to $x = 4$.
A. 32
B. 64
C. 128
D. 256
Question 13
Determine the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{-2x^2}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2x^2}{\( x^2 + 1 \ \)^2} )
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. ( 8 )
C. ( 12 )
D. ( 16 )
Question 15
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

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