POST UTME UNIOSUN 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A binary operation $\oplus$ is defined as $a\oplus b = a^2 + b^2$. Find the value of $a\oplus \( a\oplus b \)$.
A. a^2 + b^2
B. a^4 + b^2
C. a^2 + b^4
D. a^4 + b^4
Question 2
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{4}{5}
Question 3
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{64}{3} \)
B. \( \frac{128}{3} \)
C. \( \frac{256}{3} \)
D. \( \frac{512}{3} \)
Question 4
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 5
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
Question 6
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 7
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. ( 3099 )
B. ( 3098 )
C. ( 3097 )
D. ( 3096 )
Question 8
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 = 4 )
C. \( x-2 \ \)^2 + \( y-3 \)^2 = 9 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )
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
A circle with center $O$ and radius $3$ is inscribed in a square with side length $6$. Find the area of the shaded region.
A. 12
B. 18
C. 24
D. 36
Question 11
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 12
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix}.
A. -120
B. 120
C. 0
D. -60
Question 13
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 14
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 15
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

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