POST UTME COAL CITY UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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
C. 64π
D. 128π
Question 2
Find the equation of the line pas\sing through the points (1, 2) and (3, 4).
A. y = 2x - 2
B. y = 2x + 2
C. y = -2x + 2
D. y = -2x - 2
Question 3
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for \( x \).
A. \( x = \frac{\pi}{4} \)
B. \( x = \frac{3\pi}{4} \)
C. \( x = \frac{5\pi}{4} \)
D. \( x = \frac{7\pi}{4} \)
Question 4
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
B. 64π
C. 128π
D. 256π
Question 5
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
B. 0.85
C. 0.95
D. 0.99
Question 6
Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).
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
Question 7
Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...
A. 120
B. 150
C. 180
D. 210
Question 8
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 9
Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the chain rule.
A. 3x^2 - 4x + 3
B. 3x^2 - 4x + 2
C. 3x^2 - 4x - 1
D. 3x^2 - 4x - 2
Question 10
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 11
Given that ( f(x) = x^3 - 6x^2 + 11x - 6 ), find the value of ( f(2) ).
A. 0
B. 2
C. 4
D. 6
Question 12
Find the value of \( \sin\( 2x \ \) ) if \( \cos\( x \ \) = \frac{3}{5} ) and \( \sin\( x \ \) = \frac{4}{5} ).
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{12}{25}
D. \frac{8}{25}
Question 13
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}
Question 14
If \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \) and \( B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix} \), find ( AB ) if it exists.
A. \begin{bmatrix} 19 & 22 \ 43 & 50 \end{bmatrix}
B. \begin{bmatrix} 11 & 14 \ 23 & 26 \end{bmatrix}
C. \begin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}
D. \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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