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POST UTME COAL CITY UNIVERSITY 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.

Correct A. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

B. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

C. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} + \frac{\( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

D. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} - \frac{\( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

Correct Answer: A

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Question 2

Solve the inequality \( |x + 2| > 5 \).

Correct A. x < -7 or x > 3

B. x < -3 or x > 7

C. x < -7 or x > -3

D. x < 3 or x > 7

Correct Answer: A

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Question 3

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 4

Solve the system of equations \( x + y = 3 \) and \( xy = 2 \).

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 1, y = 1

D. x = 2, y = 2

Correct Answer: A

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Question 5

Find the sum of the first 10 terms of the geometric series \( 2x^2 + 3x + 1 \).

Correct A. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1

B. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

C. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

D. 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + ... + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1

Correct Answer: A

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Question 6

Find the value of k such that the equation \( x^2 + kx + 16 = 0 \) has equal roots.

Correct A. -8

B. 8

C. -4

D. 4

Correct Answer: A

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Question 7

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

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

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

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

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

Correct Answer: A

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Question 8

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 9

Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).

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 10

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

Correct A. -2

B. 2

C. -1

D. 1

Correct Answer: A

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Question 11

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. 112

Correct Answer: C

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Question 12

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -1 \) ∪ (1, ∞)

Correct Answer: A

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Question 13

A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.

Correct A. 72

B. 80

C. 96

D. 108

Correct Answer: A

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Question 14

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

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

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

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

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

Correct Answer: A

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Question 15

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. \( -2, 0 \)

B. \( -1, 0 \)

C. \( 0, -2 \)

D. \( 0, -1 \)

Correct Answer: A

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Question 16

A cone has a radius of 4 cm and a height of 6 cm. Find its volume.

A. 32π

B. 64π

Correct C. 96π

D. 128π

Correct Answer: C

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Question 17

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

Correct A. \( y = x + 1 \)

B. \( y = x - 1 \)

C. \( y = -x + 3 \)

D. \( y = x + 3 \)

Correct Answer: A

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Question 18

Solve the inequality \( x^2 - 4x - 5 > 0 \).

Correct A. \( -∞, -1 \) ∪ (5, ∞)

B. \( -∞, 1 \) ∪ (5, ∞)

C. \( -∞, -5 \) ∪ (1, ∞)

D. \( -∞, -1 \) ∪ (1, ∞)

Correct Answer: A

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Question 19

A sphere has a radius of 3 cm. Find its volume.

A. 36π

B. 54π

Correct C. 72π

D. 90π

Correct Answer: C

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Question 20

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 21

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

Correct A. x < -1 or x > 3/2

B. x < 1 or x > -3/2

C. x < -3/2 or x > 1

D. x < 3/2 or x > -1

Correct Answer: A

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Question 22

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 23

A histogram shows the distribution of exam scores in a class of 50 students. The histogram has 5 bars, with heights 8, 12, 15, 10, and 5. What is the mean of the exam scores?

A. 10

Correct B. 12

C. 15

D. 18

Correct Answer: B

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Question 24

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. 6x + 2

B. 3x + 1

C. 2x - 1

D. x - 3

Correct Answer: A

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Question 25

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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