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POST UTME COAL CITY UNIVERSITY 2025 Mathematics | Objective

Are you preparing for POST UTME COAL CITY 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 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. 3

B. 4

C. 5

Correct D. 6

Correct Answer: D

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Question 2

A histogram of exam scores is shown below. If the mean score is 75, and the range is 20, what is the mode?

Correct A. 60

B. 70

C. 80

D. 90

Correct Answer: A

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Question 3

Solve for x in the equation \( 2^x + 5^x = 7^x \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 4

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 5

A polynomial function has a degree of 4 and a leading coefficient of 2. If the function has a root at x = 3, what is the product of the roots?

Correct A. -6

B. -12

C. -18

D. -24

Correct Answer: A

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Question 6

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

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 7

A survey of 100 students found that 60% preferred Mathematics, 20% preferred Science, and 20% preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?

Correct A. 0.8

B. 0.7

C. 0.6

D. 0.5

Correct Answer: A

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Question 8

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 9

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.

A. 65

B. 67

Correct C. 69

D. 71

Correct Answer: C

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Question 10

A set of 10 points is chosen at random from a circle of radius 5. What is the probability that the dis\tance between the two farthest points is less than 5?

A. 0.1

B. 0.2

C. 0.3

Correct D. 0.4

Correct Answer: D

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Question 11

Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).

A. \( -2, -1 \) ∪ (1, ∞)

Correct B. \( -∞, -2 \) ∪ (0, ∞)

C. \( -∞, -2 \) ∪ (1, ∞)

D. \( -∞, -1 \) ∪ (0, ∞)

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. 1/3

B. 1/6

C. 1/2

D. 2/3

Correct Answer: A

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Question 13

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

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

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

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

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

Correct Answer: B

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Question 14

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

A. 30 cm^3

B. 50 cm^3

Correct C. 60 cm^3

D. 70 cm^3

Correct Answer: C

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Question 15

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 16

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

A. 64

B. 80

Correct C. 96

D. 128

Correct Answer: C

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Question 17

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

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 18

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

A particle moves in a straight line with a velocity of \( 5 , \text{m/s} \) and an acceleration of \( 2 , \text{m/s}^2 \). Find its position after ( 3 ) seconds.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 20

A circle has a radius of ( 4 ) cm. Find the area of the circle.

A. 16

B. 25

Correct C. 36

D. 49

Correct Answer: C

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Question 21

Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 22

Solve the inequality \frac{x}{x-1} > 2.

A. x < -1 or x > 2

Correct B. x < 1 or x > 2

C. x < -1 or x < 2

D. x > -1 or x > 2

Correct Answer: B

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Question 23

A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.

Correct A. x^2 + y^2 = 16

B. x^2 + y^2 = 20

C. x^2 + y^2 = 24

D. x^2 + y^2 = 28

Correct Answer: A

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Question 24

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 25

A rec\tangular box has dimensions 3 cm x 4 cm x 5 cm. Find the surface area of the box.

A. 94 cm^2

B. 98 cm^2

Correct C. 102 cm^2

D. 106 cm^2

Correct Answer: C

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