POST UTME UI 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -\infty, -3 \) \cup \( -3, 2 \) \cup \( 2, \infty \)
B. \( -\infty, -3 \) \cup \( 2, \infty \)
C. \( -3, 2 \)
D. \( -\infty, 2 \) \cup \( 2, \infty \)
Question 2
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. \( x < -1 \) or \( x > 3 \)
B. \( x < 1 \) or \( x > 3 \)
C. \( x < -3 \) or \( x > 1 \)
D. \( x < 3 \) or \( x > 1 \)
Question 3
Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 4
Solve the inequality \( |x - 3| > 2 \).
A. x < 1 or x > 5
B. x < -1 or x > 5
C. x < 1 or x > 3
D. x < -1 or x > 3
Question 5
Find the derivative of the function \(f(x) = \frac{1}{x^2 + 1}\).
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{1}{\( x^2 + 1 \)^2}
D. \frac{-1}{\( x^2 + 1 \)^2}
Question 6
A set ( S ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( S ) that contain exactly two elements.
A. 10
B. 15
C. 20
D. 25
Question 7
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. 4
B. 6
C. 8
D. 10
Question 8
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \frac{2x^2 - 4}{\( x - 2 \)^2}
B. \frac{2x^2 + 4}{\( x - 2 \)^2}
C. \frac{2x^2 - 4x}{\( x - 2 \)^2}
D. \frac{2x^2 + 4x}{\( x - 2 \)^2}
Question 9
Find the area under the curve y = x^2 + 2x - 3 from x = -2 to x = 1.
A. 4
B. 5
C. 6
D. 7
Question 10
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 11
A right circular cone has a height of 10 cm and a radius of 5 cm. Find the volume of the cone.
A. 250π
B. 500π
C. 750π
D. 1000π
Question 12
In the diagram below, a circle with center O passes through points A, B, and C. If the radius of the circle is 6 units, what is the area of the shaded region?
A. 36π
B. 72π
C. 108π
D. 144π
Question 13
Find the vector projection of \( vec{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \) onto \( vec{b} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \).
A. \( egin{pmatrix} 0.8 \ 1 \ 1.2 \end{pmatrix} \)
B. \( egin{pmatrix} 1 \ 1.2 \ 1.6 \end{pmatrix} \)
C. \( egin{pmatrix} 1.2 \ 1.6 \ 2 \end{pmatrix} \)
D. \( egin{pmatrix} 1.6 \ 2 \ 2.4 \end{pmatrix} \)
Question 14
Find the equation of the circle with center (2, 3) and radius 4.
A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
C. \left\( x - 4 \right \)^2 + \left\( y - 5 \right \)^2 = 16
D. \left\( x - 5 \right \)^2 + \left\( y - 4 \right \)^2 = 16
Question 15
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. 24π cm^3
B. 48π cm^3
C. 72π cm^3
D. 96π cm^3

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