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POST UTME COVENANT UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME COVENANT 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

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

A. 0

B. -1

Correct C. 1

D. 2

Correct Answer: C

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Question 2

If \( f(x) = \frac{1}{x^2 + 1} \), find \( f'(x) \).

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 3

Find the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 2 \).

Correct A. 0.693

B. 0.693

C. 1.098

D. 1.098

Correct Answer: A

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Question 4

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

Correct A. \left( -\infty, \frac{-5 - \sqrt{61}}{4} \right] \cup \left[ \frac{-5 + \sqrt{61}}{4}, \infty \right]

B. \left( -\infty, \frac{-5 + \sqrt{61}}{4} \right] \cup \left[ \frac{-5 - \sqrt{61}}{4}, \infty \right]

C. \left( -\infty, \frac{-5 - \sqrt{61}}{4} \right] \cup \left[ \frac{-5 + \sqrt{61}}{4}, \infty \right]

D. \left( -\infty, \frac{-5 + \sqrt{61}}{4} \right] \cup \left[ \frac{-5 - \sqrt{61}}{4}, \infty \right]

Correct Answer: A

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Question 5

Find the value of \( x \) in the equation \( 2^x + 3^x = 5^x \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 6

Solve for x in 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 7

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 8

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

Correct A. x < -1 or x > 3

B. x < 1 or x > 3

C. x < -1 or x < 3

D. x > 1 or x > 3

Correct Answer: A

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Question 9

Find the sum of the first 5 terms of the geometric series \( 2 + 6 + 18 + ... \).

Correct A. 62

B. 64

C. 66

D. 68

Correct Answer: A

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Question 10

Solve the system of linear equations \( x + y = 4 \) and \( x - y = 2 \).

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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Question 11

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

Correct A. 2x/\( x^2 + 1 \)^2

B. -2x/\( x^2 + 1 \)^2

C. 2/\( x^2 + 1 \)^2

D. -2/\( x^2 + 1 \)^2

Correct Answer: A

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Question 12

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 13

The equation of a circle is given by \( x^2 + y^2 = 4 \). Find the equation of the \tangent line to the circle at the point \( 1, \sqrt{3} \ \) ).

Correct A. y = -\sqrt{3}x + 2\sqrt{3}

B. y = \sqrt{3}x + 2\sqrt{3}

C. y = -\sqrt{3}x - 2\sqrt{3}

D. y = \sqrt{3}x - 2\sqrt{3}

Correct Answer: A

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Question 14

A histogram is shown below. Find the mean of the data.

A. 10

B. 15

Correct C. 20

D. 25

Correct Answer: C

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Question 15

Evaluate the definite integral \( \int_0^1 x^2 dx \).

A. 1/3

Correct B. 1/2

C. 2/3

D. 1

Correct Answer: B

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Question 16

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

Correct A. \( \frac{-x}{\( 1 - x^2 \ \)^{3/2}} )

B. \( \frac{x}{\( 1 - x^2 \ \)^{3/2}} )

C. \( \frac{1}{\( 1 - x^2 \ \)^{3/2}} )

D. \( \frac{-1}{\( 1 - x^2 \ \)^{3/2}} )

Correct Answer: A

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Question 17

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

Correct A. \( x = \frac{pi}{4} \)

B. \( x = \frac{3pi}{4} \)

C. \( x = \frac{pi}{2} \)

D. \( x = \frac{5pi}{4} \)

Correct Answer: A

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Question 18

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 = 4 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )

Correct Answer: A

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Question 19

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 90.

Correct A. 0.1587

B. 0.3413

C. 0.5

D. 0.8413

Correct Answer: A

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Question 20

Simplify the expression \( \frac{2^3 cdot 3^2}{2^2 cdot 3^4} \).

Correct A. \( \frac{1}{3} \)

B. \( \frac{1}{9} \)

C. \( \frac{1}{27} \)

D. \( \frac{1}{81} \)

Correct Answer: A

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Question 21

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 1/2.

Correct A. 1023/512

B. 2047/1024

C. 4095/2048

D. 8191/4096

Correct Answer: A

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Question 22

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, calculate their total daily profit in naira.

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: A

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Question 23

In the diagram below, what is the area of the triangle ABC?

A. 6

Correct B. 12

C. 18

D. 24

Correct Answer: B

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Question 24

Solve for x in the equation 2^x + 2^x = 128.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 25

A car travels from city A to city B at an average speed of 60 km/h. If the dis\tance between the two cities is 240 km, how long does the journey take in hours?

A. 4

Correct B. 4.5

C. 5

D. 5.5

Correct Answer: B

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