POST UTME UNIOSUN 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = -\frac{2}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
Question 2
Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )
B. ( f'(x) = \frac{1}{2}x^{-\frac{3}{2}} )
C. ( f'(x) = -\frac{1}{2}x^{-\frac{1}{2}} )
D. ( f'(x) = \frac{1}{2}x^{-\frac{1}{2}} )
Question 3
Determine the value of $x$ in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 4
In a circle with center $C$ and radius $5$, a chord $AB$ is drawn such that $AC = 3$. Find the length of $AB$.
A. 4
B. 6
C. 8
D. 10
Question 5
A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.7
B. 0.75
C. 0.8
D. 0.85
Question 6
Two events are indep\endent if the occurrence of one does not affect the probability of the other. If event A has probability 0.4 and event B has probability 0.6, are events A and B indep\endent?
A. Yes
B. No
C. Maybe
D. Not enough information
Question 7
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).
A. \( x = 0, pi, 2pi \)
B. \( x = \frac{pi}{2}, \frac{3pi}{2} \)
C. \( x = pi, 2pi \)
D. \( x = 0, 2pi \)
Question 8
The volume of a rec\tangular prism is given by \( V = lwh \). If the length, width, and height of the prism are in the ratio 2:3:4, and the volume is 288 cubic units, find the length of the prism.
A. 6
B. 8
C. 12
D. 16
Question 9
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( x = 2, y = 3 \)
B. \( x = 3, y = 2 \)
C. \( x = 4, y = 5 \)
D. \( x = 5, y = 4 \)
Question 10
Find the volume of the solid formed by revolving the region bounded by the curves $y=x^3$ and $y=2x^2$ about the x-axis.
A. \frac{16}{5}
B. \frac{32}{5}
C. \frac{64}{5}
D. \frac{128}{5}
Question 11
Find the volume of the solid formed by revolving the region bounded by \( y = x^2 \) and \( y = 4 \) about the x-axis.
A. \( \frac{32pi}{3} \)
B. \( \frac{64pi}{3} \)
C. \( \frac{128pi}{3} \)
D. \( \frac{256pi}{3} \)
Question 12
In a triangle $ABC$, $AB = 5$, $BC = 6$, and $\angle B = 60^\circ$. Find the length of $AC$.
A. 4
B. 5
C. 6
D. 7
Question 13
Find the equation of the circle pas\sing through the points $(2,3)$ and $(4,5)$.
A. x^2 + y^2 + 6x - 8y + 11 = 0
B. x^2 + y^2 + 4x - 6y + 11 = 0
C. x^2 + y^2 - 6x + 4y + 11 = 0
D. x^2 + y^2 + 2x - 4y + 11 = 0
Question 14
Determine the value of x in the equation \( \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2} \).
A. 1
B. 2
C. 3
D. 4
Question 15
Find the equation of the circle pas\sing through the points (1, 2), (3, 4), and (5, 6).
A. x^2 + y^2 - 4x - 6y + 9 = 0
B. x^2 + y^2 - 2x - 4y + 4 = 0
C. x^2 + y^2 + 2x - 6y + 9 = 0
D. x^2 + y^2 - 6x + 2y + 9 = 0

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