POST UTME IGBINEDION UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( x^2 + 5x - 6 = 0 \).
A. 2
B. 3
C. 4
D. 6
Question 2
Solve for ( x ) in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 3
Solve for ( x ) in the equation \( \log_{10}\( x \ \) = 2 ).
A. \( x = 10^2 \)
B. \( x = 10^3 \)
C. \( x = 10^4 \)
D. \( x = 10^5 \)
Question 4
Simplify the expression \( \frac{1}{2} \sqrt{4x^2 + 9} \) u\sing the properties of radicals.
A. \frac{1}{2} \sqrt{x^2 + \frac{9}{4}}
B. \frac{1}{2} \sqrt{x^2 + 4}
C. \frac{1}{2} \sqrt{x^2 + 9}
D. \frac{1}{2} \sqrt{x^2 - 9}
Question 5
A vector ( mathbf{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x-component of the vector.
A. 2.5
B. 5
C. 7.5
D. 10
Question 6
Solve the equation \( \sin x = \cos x \) for x.
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \\frac{3\\pi}{4}
D. x = \frac{\pi}{6}
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\\infty, -1 \) \\cup \( 3, \\infty \)
B. \( -\\infty, -3 \) \\cup \( 1, \\infty \)
C. \( -\\infty, 1 \) \\cup \( 3, \\infty \)
D. \( -\\infty, -3 \) \\cup \( 1, \\infty \)
Question 8
Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \).
A. -3
B. 0
C. 3
D. 6
Question 9
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \\frac{3\\pi}{4}
D. x = \frac{\pi}{6}
Question 10
Solve the equation \( 2^x + 3^x = 5^x \) for ( x ).
A. 1
B. 2
C. 3
D. 4
Question 11
Solve the equation \( \frac{dy}{dx} = \frac{2x}{y} \) with the initial condition y(0) = 1.
A. y = x^2 + 1
B. y = x^2 - 1
C. y = x^2 + x
D. y = x^2 - x
Question 12
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 64
B. 16
C. 32
D. 128
Question 13
Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the coordinate plane.
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 14
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 = 25 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 25 )
Question 15
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2, & 0 leq y leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that \( X + Y leq 1 \).
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}

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