POST UTME ABU 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
Solve the inequality \( \frac{x + 1}{x - 1} > 0 \) for ( x ).
A. x < -1
B. x > 1
C. x < 1
D. x > -1
Question 3
Solve the equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \) for ( x ) in the interval ( [0, 2 pi] ).
A. \sin x = -1
B. \sin x = \frac{1}{2}
C. \sin x = \frac{2}{3}
D. \sin x = \frac{3}{2}
Question 4
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 5
Solve for x in the equation \( \frac{x}{2} + 5 = 11 \)
A. 6
B. 7
C. 8
D. 9
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( - \frac{5}{4}, \frac{3}{2} \right \)
B. \left\( - \frac{3}{2}, \frac{5}{4} \right \)
C. \left\( - \frac{5}{4}, \frac{3}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
D. \left\( - \frac{3}{2}, \frac{5}{4} \right \) \cup \left\( - \infty, \frac{3}{2} \right \)
Question 7
In the diagram below, the graph of the function ( f(x) = x^2 - 4x + 3 \) is shown. Find the x-coordinate of the vertex of the parabola.
A. 1
B. 2
C. 3
D. 4
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\infty, -1 \right \) \cup \left\( \frac{3}{2}, \infty \right \)
B. \left\( -\infty, 1 \right \) \cup \left\( 2, \infty \right \)
C. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)
D. \left\( -\infty, 2 \right \) \cup \left\( 3, \infty \right \)
Question 9
Solve the inequality \( x^2 - 4x + 3 > 0 \) for ( x ).
A. x < 1
B. x > 1
C. x < 3
D. x > 3
Question 10
Solve the equation \( x^2 + 4x + 4 = 0 \ \) u\sing the quadratic formula.
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 11
Find the value of x in the equation \( x^2 + 2x - 3 = 0 \)
A. 1
B. -1
C. 2
D. -2
Question 12
Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(2, 1) ) u\sing the formula for the area of a triangle.
A. \frac{1}{2} |\( 2 - 1 \)\( 4 - 2 \) - \( 3 - 1 \)\( 2 - 1 \) + \( 2 - 3 \)\( 4 - 1 \)|
B. \frac{1}{2} |\( 2 - 1 \)\( 4 - 2 \) + \( 3 - 1 \)\( 2 - 1 \) - \( 2 - 3 \)\( 4 - 1 \)|
C. \frac{1}{2} |\( 2 - 1 \)\( 4 - 2 \) - \( 3 - 1 \)\( 2 - 1 \) - \( 2 - 3 \)\( 4 - 1 \)|
D. \frac{1}{2} |\( 2 - 1 \)\( 4 - 2 \) + \( 3 - 1 \)\( 2 - 1 \) + \( 2 - 3 \)\( 4 - 1 \)|
Question 13
Find the value of ( x ) in the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 15
Find the value of y in the equation \( 2y^2 + 5y - 3 = 0 \)
A. 1
B. -1
C. 2
D. -2

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