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POST UTME COAL CITY UNIVERSITY 2021 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 2021 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Evaluate the definite integral \( int_{0}^{1} x^2 \sqrt{1-x^2} , dx \).

Correct A. \frac{1}{3}

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{1}{4}

Correct Answer: A

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Question 2

Find the equation of the circle with center \( -2, 3 \ \) ) and radius ( 5 ).

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

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

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

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

Correct Answer: A

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Question 3

Solve the system of linear equations \( egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \).

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 4

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

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

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

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

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

Correct Answer: A

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Question 5

Solve the inequality \( |x - 2| > 3 \).

Correct A. \( x < -1 \) or \( x > 5 \)

B. \( x > -1 \) or \( x < 5 \)

C. \( x < 1 \) or \( x > 5 \)

D. \( x > 1 \) or \( x < 5 \)

Correct Answer: A

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Question 6

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 cm^3

B. 48\pi cm^3

Correct C. 96\pi cm^3

D. 192\pi cm^3

Correct Answer: C

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Question 7

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. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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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

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

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 10

Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...

Correct A. 155

B. 165

C. 175

D. 185

Correct Answer: A

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Question 11

A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 12

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

A. 1000\pi cm^3

B. 1200\pi cm^3

Correct C. 1500\pi cm^3

D. 1800\pi cm^3

Correct Answer: C

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Question 13

If the matrix A = \begin{bmatrix} 2 & 1 \\ 4 & 3 \end{bmatrix} and B = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, find the product AB.

Correct A. \begin{bmatrix} 5 & 8 \\ 11 & 16 \end{bmatrix}

B. \begin{bmatrix} 7 & 10 \\ 13 & 18 \end{bmatrix}

C. \begin{bmatrix} 9 & 12 \\ 15 & 20 \end{bmatrix}

D. \begin{bmatrix} 11 & 14 \\ 17 & 22 \end{bmatrix}

Correct Answer: A

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Question 14

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 15

A sequence is defined as a_1 = 2, a_2 = 4, a_n = a_{n-1} + 2. Find the 10th term of the sequence.

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 16

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 59048

B. 59049

C. 59050

D. 59051

Correct Answer: A

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Question 17

Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.

Correct A. \( -\infty, -1 \) \cup \( 3, \infty \)

B. \( -\infty, -1 \) \cup \( 1, \infty \)

C. \( -\infty, 1 \) \cup \( 3, \infty \)

D. \( -\infty, 1 \) \cup \( 3, \infty \)

Correct Answer: A

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Question 18

A die is rolled 5 times. Find the probability that exactly 3 of the rolls result in an even number.

Correct A. \frac{125}{512}

B. \frac{1}{32}

C. \frac{5}{32}

D. \frac{1}{16}

Correct Answer: A

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Question 19

Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 20

Solve the system of linear equations \begin{align*} x + y &= 2 \ x - 2y &= -3 \end{align*}

Correct A. \left\( -1, \frac{5}{2} \right \)

B. \left\( 1, -1 \right \)

C. \left\( -1, -1 \right \)

D. \left\( 1, \frac{5}{2} \right \)

Correct Answer: A

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Question 21

Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 22

A particle moves along the curve y = x^3 - 6x^2 + 9x + 2. Find the equation of the \tangent line at the point where x = 1.

Correct A. y = 3x - 5

B. y = 3x - 7

C. y = 3x - 9

D. y = 3x - 11

Correct Answer: A

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Question 23

Find the area under the curve y = x^2 + 1 from x = 0 to x = 2.

A. 7

B. 9

Correct C. 11

D. 13

Correct Answer: C

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Question 24

A force of 3N is applied to an object at an angle of 30° to the horizontal. Find the horizontal and vertical components of the force.

Correct A. F_x = 2.6N, F_y = 1.5N

B. F_x = 1.5N, F_y = 2.6N

C. F_x = 2.6N, F_y = 2.6N

D. F_x = 1.5N, F_y = 1.5N

Correct Answer: A

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Question 25

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 = 16

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

Correct Answer: A

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