POST UTME COAL CITY UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. x < 1 or x > 3
B. x < 3 or x > 1
C. x < 1 or x < 3
D. x > 1 or x > 3
Question 2
Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{array} ].
A. -6
B. 6
C. -12
D. 12
Question 3
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 4
Given that ( f(x) = \frac{x^2 - 4}{x + 2} ), find the derivative of ( f(x) ) u\sing the quotient rule.
A. \frac{2x\( x + 2 \) - \( x^2 - 4 \)(1)}{\( x + 2 \)^2}
B. \frac{\( x + 2 \)\( 2x - 1 \)}{\( x + 2 \)^2}
C. \frac{\( x + 2 \)^2}{x^2 - 4}
D. \frac{x^2 - 4}{\( x + 2 \)^2}
Question 5
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.
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. \( x^2 + y^2 + 4x + 12y - 20 = 0 \)
Question 6
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \left\( -2, -2\right \)
B. \left\( -2, \infty\right \) \cup \left\( -\infty, -2\right \)
C. \left\( -\infty, -2\right \) \cup \left\( -2, \infty\right \)
D. \left\( -\infty, \infty\right \)
Question 7
Find the equation of the circle with center ( (2, 3) ) and radius 4.
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
Question 8
If \( A = egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \), find the value of \( |A| \).
A. 0
B. 1
C. 2
D. 3
Question 9
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 10
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and \( -1, 1 \).
A. \left\( x - 1 \right \)^2 + \left\( y - 2 \right \)^2 = 10
B. \left\( x + 1 \right \)^2 + \left\( y - 2 \right \)^2 = 10
C. \left\( x - 1 \right \)^2 + \left\( y + 2 \right \)^2 = 10
D. \left\( x + 1 \right \)^2 + \left\( y + 2 \right \)^2 = 10
Question 11
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 12
A circle has a radius of 5 cm. Find the area of the circle.
A. 50\pi
B. 25\pi
C. 100\pi
D. 75\pi
Question 13
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 14
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 15
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
C. 50
D. 51

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