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POST UTME VERITAS UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME VERITAS UNIVERSITY 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

In the diagram below, the equation of the circle is given by \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the center of the circle is at ( (h, k) = (2, 3) ) and the radius is 4, find the equation of the circle.

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 2

Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. \( x = 2 \)

Correct B. \( x = 3 \)

C. \( x = 4 \)

D. \( x = 5 \)

Correct Answer: B

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Question 3

A matrix ( A ) is given by \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of ( A ).

A. ( det(A) = 2 )

B. ( det(A) = 4 )

C. ( det(A) = 6 )

Correct D. ( det(A) = 8 )

Correct Answer: D

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Question 4

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the player wins. If the number rolled is odd, the player loses. What is the probability that the player wins?

Correct A. \( P\( \text{win} \ \) = \frac{1}{2} )

B. \( P\( \text{win} \ \) = \frac{1}{3} )

C. \( P\( \text{win} \ \) = \frac{2}{3} )

D. \( P\( \text{win} \ \) = \frac{3}{4} )

Correct Answer: A

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Question 5

A polynomial function ( f(x) ) is defined by ( f(x) = x^3 - 2x^2 + 3x - 1 ). Find the value of ( f(2) ).

A. ( f(2) = 1 )

B. ( f(2) = 3 )

Correct C. ( f(2) = 5 )

D. ( f(2) = 7 )

Correct Answer: C

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Question 6

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 7

Solve the inequality \( x^2 - 4x + 3 > 0 \).

Correct A. \( -∞, 1 \) ∪ (3, ∞)

B. \( -∞, 3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∩ (3, ∞)

D. \( -∞, 3 \) ∩ (1, ∞)

Correct Answer: A

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Question 8

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

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

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

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

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

Correct Answer: B

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Question 9

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 10

A water \tank has a capacity of 1000 liters. Water is flowing into the \tank at a rate of 5 liters per minute. Find the time taken to fill the \tank.

Correct A. 200 minutes

B. 100 minutes

C. 50 minutes

D. 20 minutes

Correct Answer: A

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Question 11

Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \) u\sing the formula ( det(A) = ad - bc ).

A. 1

Correct B. -1

C. 2

D. 3

Correct Answer: B

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Question 12

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 will be between 60 and 90?

Correct A. 0.6827

B. 0.3413

C. 0.8413

D. 0.1587

Correct Answer: A

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Question 13

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.

Correct A. 6x + 2

B. 6x^2 + 2

C. 6x^2 + 2x

D. 6x^2 - 2x

Correct Answer: A

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Question 14

Solve the inequality \( 2x^2 + 5x - 3 > 0 \) by factoring.

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -3 \) \cup \( 1, \infty \)

C. \( -\infty, 1 \) \cup \( 3, \infty \)

D. \( -\infty, -3 \) \cup \( -1, \infty \)

Correct Answer: A

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Question 15

A population of bacteria grows according to the equation ( P(t) = 2000e^{0.2t} ), where ( t ) is time in hours. Find the rate of growth of the population at \( t = 5 \) hours.

Correct A. 400e^{0.2(5)}

B. 400e^{0.2(10)}

C. 400e^{0.2(15)}

D. 400e^{0.2(20)}

Correct Answer: A

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Question 16

In a set of 10 consecutive integers, the mean is 20. If the smallest number is x, find the value of x.

Correct A. 9

B. 10

C. 11

D. 12

Correct Answer: A

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Question 17

A histogram is constructed with 5 classes of equal width. The frequency of the first class is 10, and the frequency of the second class is 15. If the total frequency is 50, find the width of each class.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 18

The sum of the first n terms of an arithmetic progression is given by the formula: \[ S_n = \frac{n}{2} \( 2a + \( n-1 \ \)d) \]. If the sum of the first 5 terms is 25, and the first term is 3, find the common difference d.

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 19

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 20

A sequence is given by the formula: \[ a_n = 2n^2 + 3n - 1 \]. Find the value of the 6th term.

A. 109

Correct B. 119

C. 129

D. 139

Correct Answer: B

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Question 21

Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 22

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 23

Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).

Correct A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16

C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16

D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16

Correct Answer: A

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Question 24

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 25

A line passes through the points ( (2, 3) ) and ( (4, 5) ). Find the equation of the line in slope-intercept form.

Correct A. y = x + 1

B. y = x - 1

C. y = -x + 1

D. y = x + 2

Correct Answer: A

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