POST UTME UNIBEN 2025 Mathematics | Objective

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Question 1 View Details
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\pitext{ cm}^3
B. 512\pitext{ cm}^3
Correct C. 768\pitext{ cm}^3
D. 1024\pitext{ cm}^3

Correct Answer: C

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Question 2 View Details
A circle passes through the points (2, 3), (4, 5), and (6, 7). Find the equation of the circle.
Correct 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\)\(= 0\)\)

Correct Answer: A

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Question 3 View Details
Find the derivative of the function f(x) = \(\frac{x^2}{x\)^2 + 1}\)\) using the chain rule.
Correct 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}\)\)

Correct Answer: A

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Question 4 View Details
Solve the inequality \\((2x^2 + 5x - 3\)\(> 0.\)\)
Correct 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 }\(x >\)\(\frac{1}{2}\)\)

Correct Answer: A

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Question 5 View Details
A fair six-sided die is rolled. Find the probability that the number showing is a multiple of 3.
A. \(\frac{1}{2}\)\)
B. \(\frac{1}{3}\)\)
Correct C. \(\frac{1}{6}\)\)
D. \(\frac{2}{3}\)\)

Correct Answer: C

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Question 6 View Details
Find the derivative of ( f(x) = \(\frac{1}{2x^2 + 3x - 1}\)\)\) ) using the chain rule.
Correct 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}\)\)

Correct Answer: A

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Question 7 View Details
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. \(\frac{1}{4}\)\)
Correct C. \(\frac{3}{4}\)\)
D. \(\frac{1}{4}\)\) + \(\frac{1}{2}\)\)

Correct Answer: C

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Question 8 View Details
Find the mean of the data set \(\{2, 4, 6, 8, 10 \}\).
A. 5
Correct B. 6
C. 7
D. 8

Correct Answer: B

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Question 9 View Details
Solve the inequality \(2x^2 - 5x + 3 > 0\).
Correct A. \(-\infty, \frac{1}{2}\) \cup \(3, \infty\)
B. \(-\infty, 1\) \cup \(3, \infty\)
C. \(-\infty, 1\) \cup \(2, \infty\)
D. \(-\infty, 3\) \cup \(4, \infty\)

Correct Answer: A

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Question 10 View Details
Find the sum of the first 5 terms of the geometric progression \(2, 6, 18, 54, \ldots\).
A. 124
Correct B. 126
C. 128
D. 130

Correct Answer: B

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Question 11 View Details
Solve for x in the equation \(\sin^2 x \\) + \\(\cos^2(x)\) = 1 ) using the identity \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)
Correct A. \(x = \frac{\pi}{2} + 2k\pi\)
B. \(x = \frac{\pi}{4} + 2k\pi\)
C. \(x = \frac{3\pi}{4} + 2k\pi\)
D. \(x = \frac{5\pi}{4} + 2k\pi\)

Correct Answer: A

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Question 12 View Details
Find the determinant of the matrix \(\begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{bmatrix}\) using the formula for the determinant of a 3x3 matrix.
A. -5
Correct B. 5
C. 10
D. -10

Correct Answer: B

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Question 13 View Details
Find the equation of the circle with center ( (2, 3) ) and radius 4.
Correct 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 + \(y - 3\)^\(2 = 49\) )

Correct Answer: A

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Question 14 View Details
Solve the differential equation \(\frac{dy}{dx} = 2x\) using separation of variables.
Correct A. \(y = x^2 + C\)
B. \(y = 2x + C\)
C. \(y = x^3 + C\)
D. \(y = x^4 + C\)

Correct Answer: A

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Question 15 View Details
Find the derivative of the function ( f(x) = \(3x^2 + 2x - 5\) ) using the power rule.
Correct A. ( f'\((x) = 6x + 2 )\)
B. ( f'\((x) = 6x - 2 )\)
C. ( f'\((x) = 6x + 4 )\)
D. ( f'\((x) = 6x - 4 )\)

Correct Answer: A

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