POST UTME UNIBEN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -\frac{3}{2} \text{ or } x > \frac{1}{2}
B. x < -\frac{1}{2} \text{ or } x > \frac{3}{2}
C. x < -\frac{3}{2} \text{ or } x < \frac{1}{2}
D. x > -\frac{3}{2} \text{ or } x > \frac{1}{2}
Question 2
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 256\pi\text{ cm}^3
B. 512\pi\text{ cm}^3
C. 768\pi\text{ cm}^3
D. 1024\pi\text{ cm}^3
Question 3
Find the derivative of the function f(x) = \frac{x^2}{x^2 + 1} u\sing the chain rule.
A. \frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2}
B. \frac{2x^3 - 2x}{\( x^2 + 1 \)^2}
C. \frac{2x^3 + 2x}{\( x^2 + 1 \)^2}
D. \frac{2x^3 - 2x^2}{\( x^2 + 1 \)^2}
Question 4
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) u\sing the identity \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. \( x = \frac{\pi}{2} + 2k\pi \)
B. \( x = \frac{\pi}{4} + 2k\pi \)
C. \( x = \frac{3\pi}{4} + 2k\pi \)
D. \( x = \frac{5\pi}{4} + 2k\pi \)
Question 5
Find the mean of the data set \( \{ 2, 4, 6, 8, 10 \} \).
A. 5
B. 6
C. 7
D. 8
Question 6
A random variable X has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3 \). Find the probability that X is greater than 2.
A. \frac{1}{2}
B. \frac{1}{4}
C. \frac{3}{4}
D. \frac{1}{4} + \frac{1}{2}
Question 7
Find the derivative of ( f(x) = \frac{1}{2x^2 + 3x - 1} ) u\sing the chain rule.
A. \frac{-4x + 3}{\( 2x^2 + 3x - 1 \)^2}
B. \frac{4x + 3}{\( 2x^2 + 3x - 1 \)^2}
C. \frac{2x + 3}{\( 2x^2 + 3x - 1 \)^2}
D. \frac{-2x + 3}{\( 2x^2 + 3x - 1 \)^2}
Question 8
A fair six-sided die is rolled. Find the probability that the number showing is a multiple of 3.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{1}{6}
D. \frac{2}{3}
Question 9
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.
A. ( f'(x) = 6x + 2 )
B. ( f'(x) = 6x - 2 )
C. ( f'(x) = 6x + 4 )
D. ( f'(x) = 6x - 4 )
Question 10
Solve the inequality \( 2x^2 - 5x + 3 > 0 \).
A. \( -\infty, \frac{1}{2} \) \cup \( 3, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, 1 \) \cup \( 2, \infty \)
D. \( -\infty, 3 \) \cup \( 4, \infty \)
Question 11
Find the sum of the first 5 terms of the geometric progression \( 2, 6, 18, 54, \ldots \).
A. 124
B. 126
C. 128
D. 130
Question 12
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{bmatrix} \) u\sing the formula for the determinant of a 3x3 matrix.
A. -5
B. 5
C. 10
D. -10
Question 13
Solve the differential equation \( \frac{dy}{dx} = 2x \) u\sing separation of variables.
A. \( y = x^2 + C \)
B. \( y = 2x + C \)
C. \( y = x^3 + C \)
D. \( y = x^4 + C \)
Question 14
A circle passes through the points (2, 3), (4, 5), and (6, 7). Find the equation of the circle.
A. x^2 + y^2 - 4x - 6y + 5 = 0
B. x^2 + y^2 - 2x - 4y + 3 = 0
C. x^2 + y^2 + 2x - 6y + 4 = 0
D. x^2 + y^2 - 6x + 2y - 3 = 0
Question 15
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 = 25 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 36 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 49 )

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