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POST UTME COAL CITY UNIVERSITY 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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 2

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 is between 60 and 90?

A. 0.68

Correct B. 0.85

C. 0.95

D. 0.99

Correct Answer: B

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Question 3

Solve the system of linear equations u\sing matrices:

Correct A. \begin{bmatrix} 2 \ 3 \end{bmatrix}

B. \begin{bmatrix} 3 \ 2 \end{bmatrix}

C. \begin{bmatrix} 1 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 1 \end{bmatrix}

Correct Answer: A

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Question 4

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 = 20

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 24

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 28

Correct Answer: A

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Question 5

Solve the quadratic 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 6

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{array} ].

Correct A. -6

B. 6

C. -12

D. 12

Correct Answer: A

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Question 7

A circle has a radius of 5 cm. Find the area of the circle.

A. 50\pi

Correct B. 25\pi

C. 100\pi

D. 75\pi

Correct Answer: B

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Question 8

Find the volume of a rec\tangular prism with dimensions 5 cm, 6 cm, and 7 cm.

Correct A. 210

B. 210\pi

C. 210\pi^2

D. 210\pi^3

Correct Answer: A

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Question 9

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

Correct A. 6x + 2

B. 6x - 2

C. 6x^2 + 2

D. 6x^2 - 2

Correct Answer: A

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Question 10

Solve the equation 2x + 5 = 11.

Correct A. 3

B. 2

C. 1

D. 4

Correct Answer: A

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Question 11

In a set of 10 consecutive integers, the sum of the first and last term is 51. If the sum of the second and ninth term is 47, find the sum of the third and eighth term.

A. 48

B. 49

Correct C. 50

D. 51

Correct Answer: C

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Question 12

Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the line \( y = 4 \), and the ( y )-axis about the ( x )-axis.

A. 32π

Correct B. 64π

C. 128π

D. 256π

Correct Answer: B

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Question 13

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

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 14

Find the surface area of the solid formed by revolving the region bounded by the curve \( y = \sqrt{x} \), the line \( y = 2 \), and the ( y )-axis about the ( x )-axis.

A. 16π

B. 32π

Correct C. 64π

D. 128π

Correct Answer: C

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Question 15

Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 2

B. 4

Correct C. 8

D. 16

Correct Answer: C

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Question 16

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 17

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

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 18

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 120

B. 150

C. 180

Correct D. 210

Correct Answer: D

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Question 19

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the chain rule.

Correct A. 3x^2 - 4x + 3

B. 3x^2 - 4x + 2

C. 3x^2 - 4x - 1

D. 3x^2 - 4x - 2

Correct Answer: A

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Question 20

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

Correct A. x < 1 or x > 3

B. x < 3 or x > 1

C. x < 1 or x < 3

D. x > 1 or x > 3

Correct Answer: A

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Question 21

Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1 and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.

Correct A. 1/4

B. 1/2

C. 3/4

D. 1

Correct Answer: A

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Question 22

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

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 23

The equation of a circle is given by \( x^2 + y^2 + 2gx + 2fy + c = 0 \). Find the equation of the circle with center \( -2, 3 \) and radius 4.

Correct A. \( x^2 + y^2 - 4x + 12y - 20 = 0 \)

B. \( x^2 + y^2 + 4x - 12y - 20 = 0 \)

C. \( x^2 + y^2 - 4x - 12y - 20 = 0 \)

D. \( x^2 + y^2 + 4x + 12y - 20 = 0 \)

Correct Answer: A

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Question 24

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

Correct A. \( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} \)

B. \( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} \)

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

D. \( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} \)

Correct Answer: A

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Question 25

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

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

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

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

D. \( x = \frac{7\pi}{4} \)

Correct Answer: A

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