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POST UTME CALEB UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME CALEB 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.

Practice these randomly selected questions to test your readiness.

Question 1

Determine the mean of the following dataset: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 2

Solve for x in the equation \( 2^x + 5^x = 10^x \).

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 3

A histogram of exam scores is shown below. If the mean score is 60, what is the median?

A. 60

Correct B. 65

C. 70

D. 75

Correct Answer: B

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Question 4

Find the value of x in the equation \( \frac{x}{2} + 3 = 7 \).

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 5

A vector ( vec{a} ) has a magnitude of 5 and makes an angle of 30 degrees with the positive x-axis. Find the x-component of ( vec{a} ).

Correct A. 3.54

B. 4.24

C. 4.65

D. 5.12

Correct Answer: A

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Question 6

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

Correct A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )

B. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 3 )

C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - 2 )

D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + 2 )

Correct Answer: A

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Question 7

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

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

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

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

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

Correct Answer: B

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Question 8

Solve the system of linear equations: \( 2x + 3y = 7 \) and \( x - 2y = -3 \).

Correct A. \( x = 1, y = 2 \)

B. \( x = 2, y = 1 \)

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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Question 9

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. \( -1 \)

D. ( 2 )

Correct Answer: A

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Question 10

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 11

Determine the value of x in the equation \( \frac{x}{2} + \frac{5}{3} = \frac{7}{6} \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 12

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 13

A die is rolled twice. What is the probability that the sum of the two numbers is 7?

Correct A. 1/6

B. 1/12

C. 1/2

D. 2/3

Correct Answer: A

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Question 14

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -1 \) ∪ (1, ∞)

D. \( -∞, 3 \) ∪ (1, ∞)

Correct Answer: A

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Question 15

Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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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. 48\pi

Correct C. 96\pi

D. 192\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. \( 2, \infty \)

Correct Answer: A

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Question 18

Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 1 \ 4 & 3 & 2 \ 3 & 2 & 1 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

Solve the equation x^2 + 4x + 4 = 0.

Correct A. x = -2

B. x = -1

C. x = 1

D. x = 2

Correct Answer: A

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Question 20

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 21

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 5 \).

Correct A. x^2 + y^2 - 6x - 2y + 12 = 0

B. x^2 + y^2 + 6x - 2y + 12 = 0

C. x^2 + y^2 - 6x + 2y + 12 = 0

D. x^2 + y^2 + 6x + 2y + 12 = 0

Correct Answer: A

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Question 22

A particle moves in a straight line with a velocity of 5 m/s. If the acceleration is 2 m/s^2, find the dis\tance traveled in 4 seconds.

A. 20 m

B. 30 m

Correct C. 40 m

D. 50 m

Correct Answer: C

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Question 23

A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?

A. 1/2

B. 1/3

Correct C. 2/3

D. 1/6

Correct Answer: C

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Question 24

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

Correct A. 6x + 2

B. 6x - 2

C. 6x^2 + 2x

D. 6x^2 - 2x

Correct Answer: A

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Question 25

Solve the equation \sin(x) = \cos(x) for 0 ≤ x ≤ 2π.

Correct A. π/4

B. 3π/4

C. π/2

D. 5π/4

Correct Answer: A

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