POST UTME UNILORIN 2025 Mathematics | Objective

Are you preparing for POST UTME UNILORIN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
Correct A. 10
B. 100
C. 1000
D. 10000

Correct Answer: A

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Question 2
A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers Mathematics or Science?
A. 0.7
Correct B. 0.8
C. 0.9
D. 1.0

Correct Answer: B

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Question 3
The histogram below shows the distribution of exam scores for a class of 50 students. What is the mean score?
A. 60
B. 70
Correct C. 80
D. 90

Correct Answer: C

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Question 4
Simplify the expression \( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} \).
A. 1
B. 2
C. 3
Correct D. 4

Correct Answer: D

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Question 5
Evaluate the definite integral \( \int_{0}^{2} x^2 dx \).
A. 4
B. 8
Correct C. 16
D. 32

Correct Answer: C

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Question 6
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{4pi}{3} \)
Correct B. \( \frac{5pi}{3} \)
C. \( \frac{2pi}{3} \)
D. \( \frac{pi}{3} \)

Correct Answer: B

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Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
Correct A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > -\frac{5}{4} \)
C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{3}{2} \) or \( x > \frac{5}{4} \)

Correct Answer: A

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Question 8
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix} \).
Correct A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )

Correct Answer: A

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Question 9
Determine the equation of the \tangent line to the curve \( y = \frac{1}{x} \) at the point ( (1, 1) ).
Correct A. \( y = x - 1 \)
B. \( y = x + 1 \)
C. \( y = -x + 1 \)
D. \( y = x - 2 \)

Correct Answer: A

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Question 10
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 90?
A. ( 0.1587 )
B. ( 0.3413 )
C. ( 0.5 )
Correct D. ( 0.8413 )

Correct Answer: D

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Question 11
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8 cm
Correct B. 12 cm
C. 14 cm
D. 16 cm

Correct Answer: B

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Question 12
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
Correct A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{1}{2}
D. \frac{3}{4}

Correct Answer: A

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Question 13
A cylindrical \tank has a height of 10 m and a radius of 4 m. Find the volume of the \tank in cubic meters.
A. 200\pi
B. 400\pi
Correct C. 800\pi
D. 1600\pi

Correct Answer: C

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Question 14
A set of 5 numbers has an average of 10. If one of the numbers is 15, what is the sum of the remaining 4 numbers?
Correct A. 40
B. 45
C. 50
D. 55

Correct Answer: A

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Question 15
A geometric sequence has a first term of 2 and a common ratio of 3. Find the sum of the first 5 terms.
A. 243
Correct B. 255
C. 267
D. 279

Correct Answer: B

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Question 16
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi
B. 32\pi
Correct C. 40\pi
D. 48\pi

Correct Answer: C

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Question 17
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
Correct A. \( -\infty, -3 \) \cup \( -3, 2 \) \cup \( 2, \infty \)
B. \( -\infty, -3 \) \cup \( 2, \infty \)
C. \( -3, 2 \)
D. \( -\infty, -3 \) \cup \( 2, \infty \)

Correct Answer: A

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Question 18
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 18
B. 20
Correct C. 22
D. 24

Correct Answer: C

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Question 19
Solve the system of equations \begin{align*} x + y &= 4 \ x - 2y &= 2 \end{align*}.
Correct A. \begin{pmatrix} 2 \ 2 \end{pmatrix}
B. \begin{pmatrix} 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} 4 \ 0 \end{pmatrix}

Correct Answer: A

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Question 20
Find the equation of the circle with center (2, 3) and radius 4.
Correct A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16

Correct Answer: A

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Question 21
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
Correct A. \( x < -2 \) or \( x > 2 \)
B. \( x > -2 \) or \( x < 2 \)
C. \( x < -2 \) or \( x = 2 \)
D. \( x > -2 \) or \( x = 2 \)

Correct Answer: A

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Question 22
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 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

Correct Answer: A

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Question 23
A fair six-sided die is rolled twice. What is the probability that the sum of the two numbers shown is greater than 9?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
Correct C. \( \frac{5}{36} \)
D. \( \frac{1}{2} \)

Correct Answer: C

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Question 24
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
Correct A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )

Correct Answer: A

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Question 25
Solve the equation \( 2^x + 2^{-x} = 3 \) for ( x in mathbb{R} ).
A. \( x = \log_2\( 2 \ \) )
Correct B. \( x = \log_2\( 3 \ \) )
C. \( x = \log_2\( 2 \ \) - \log_2(2) )
D. \( x = \log_2\( 2 \ \) + \log_2(2) )

Correct Answer: B

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