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POST UTME COAL CITY UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

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 View Details

A histogram of exam scores has a mean of 75 and a standard 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 View Details

Solve the system of linear equations using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the volume of a rectangular 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 View Details

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 View Details

Solve the equation \(2x + 5 = 11\).

Correct A. 3

B. 2

C. 1

D. 4

Correct Answer: A

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Question 11 View Details

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 View Details

Find the volume of the solid formed by revolving the region bounded by the parabola (y = \(x^2\)\), the line \(y = 4\\((y = x^2), the line\), 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 View Details

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 View Details

Find the surface area of the solid formed by revolving the region bounded by the curve (y = \(\sqrt{x}\)\), the line \\((y = sqrt{x}\(y = 2\), 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the derivative of the function ( f(x) = \(x^3 - 2x^2 + 3x - 1\) ) using 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 View Details

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 View Details

Let X and Y be independent 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 \(X + Y < 1\\((0 < y) < 1. Find the probability that\).

Correct A. \(1/4\)

B. \(1/2\)

C. \(3/4\)

D. 1

Correct Answer: A

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Question 22 View Details

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 View Details

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

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

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 View Details

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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