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POST UTME UNIPORT 2025 Mathematics | Objective

Are you preparing for POST UTME UNIPORT 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 \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 2

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.

Correct A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )

B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )

C. \( \frac{-2}{\( x^2 + 1 \ \)^2} )

D. \( \frac{2}{\( x^2 + 1 \ \)^2} )

Correct Answer: A

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Question 3

Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.

Correct A. \( x < -1 \) or \( x > \frac{3}{2} \)

B. \( x < -\frac{3}{2} \) or \( x > 1 \)

C. \( x < -1 \) or \( x < \frac{3}{2} \)

D. \( x > -1 \) or \( x < \frac{3}{2} \)

Correct Answer: A

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Question 4

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 5

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).

Correct A. 1023

B. 1024

C. 1025

D. 1026

Correct Answer: A

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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} ).

Correct A. \( \frac{4}{5} \)

B. \( \frac{3}{4} \)

C. \( \frac{5}{4} \)

D. \( \frac{4}{3} \)

Correct Answer: A

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Question 7

A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are of different colors?

Correct A. \( \frac{5}{8} \)

B. \( \frac{3}{8} \)

C. \( \frac{2}{5} \)

D. \( \frac{3}{5} \)

Correct Answer: A

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Question 8

Solve for x in the equation \( 2^x + 2^{x+1} = 100 \).

A. ( 4 )

Correct B. ( 5 )

C. ( 6 )

D. ( 7 )

Correct Answer: B

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Question 9

Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.

A. \( \frac{32pi}{3} \)

Correct B. \( \frac{64pi}{3} \)

C. \( \frac{128pi}{3} \)

D. \( \frac{256pi}{3} \)

Correct Answer: B

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Question 10

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).

A. ( 1023 )

Correct B. ( 1024 )

C. ( 1025 )

D. ( 1026 )

Correct Answer: B

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Question 11

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. 48\pi

B. 64\pi

Correct C. 80\pi

D. 96\pi

Correct Answer: C

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Question 12

Solve the inequality \frac{x}{x-1} > 0.

Correct A. x > 1

B. x < 1

C. x > 0

D. x < 0

Correct Answer: A

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Question 13

Find the equation of the line pas\sing through the points (2, 3) and (4, 5).

Correct A. y = 2x - 1

B. y = 2x + 1

C. y = x - 1

D. y = x + 1

Correct Answer: A

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Question 14

Solve the quadratic equation x^2 + 5x + 6 = 0.

A. x = -2

Correct B. x = -3

C. x = 2

D. x = 3

Correct Answer: B

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Question 15

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 16

Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17

A circle has a radius of 5 units. Find the area of the circle.

Correct A. 25\pi

B. 50\pi

C. 75\pi

D. 100\pi

Correct Answer: A

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Question 18

A histogram shows the distribution of exam scores. If the mean score is 60 and the s\tandard deviation is 10, find the probability that a randomly selected score is between 50 and 70.

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 19

Solve the equation \( \sin^2 x + \cos^2 x = 1 \).

A. x = \frac{\pi}{4}

B. x = \frac{\pi}{2}

C. x = \\frac{3\\pi}{4}

Correct D. x = \frac{\pi}{2} \text{ or } \frac{3\pi}{4}

Correct Answer: D

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Question 20

A random experiment has two indep\endent events, A and B. If the probability of event A is 0.4 and the probability of event B is 0.6, find the probability that both events occur.

Correct A. 0.2

B. 0.4

C. 0.6

D. 0.8

Correct Answer: A

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Question 21

A circle has a radius of 4 units. Find the length of the arc subt\ended by a central angle of 60 degrees.

A. 2\pi

Correct B. 4\pi

C. 6\pi

D. 8\pi

Correct Answer: B

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Question 22

A histogram shows the distribution of exam scores. If the mean score is 70 and the s\tandard deviation is 15, find the probability that a randomly selected score is between 50 and 90.

A. 0.6

B. 0.7

Correct C. 0.8

D. 0.9

Correct Answer: C

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Question 23

Solve the equation \( \cos^2 x - \sin^2 x = 0 \).

A. x = \frac{\pi}{4}

B. x = \frac{\pi}{2}

C. x = \\frac{3\\pi}{4}

Correct D. x = \frac{\pi}{2} \text{ or } \frac{3\pi}{4}

Correct Answer: D

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Question 24

Determine the value of k in the equation \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2k \ 3k \end{bmatrix} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 25

A histogram of exam scores for a class of 100 students is shown. What is the mean score?

A. 60

B. 70

Correct C. 80

D. 90

Correct Answer: C

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