POST UTME FUTA 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle with center ( C(3, 4) ) and radius \( r = 5 \) is drawn in the coordinate plane. Find the equation of the line pas\sing through the point ( P(6, 1) ) and perp\endicular to the radius of the circle at point ( P ).
A. y = -\frac{1}{5}x + \frac{31}{5}
B. y = \frac{1}{5}x + \frac{21}{5}
C. y = -\frac{1}{5}x + \frac{21}{5}
D. y = \frac{1}{5}x + \frac{31}{5}
Question 2
In the coordinate plane, the equation of a circle is given by \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 ). Find the equation of the line pas\sing through the center of the circle and perp\endicular to the line \( y = \frac{1}{2}x + 2 \).
A. y = -2x + 11
B. y = 2x - 7
C. y = -\frac{1}{2}x + 5
D. y = \frac{1}{2}x + 1
Question 3
The equation of a circle is given by \(\( x - 2 \)^2 + \( y - 3 \)^2 = 4\). Find the equation of the \tangent line at the point \(\( 3, 5)\ \).
A. y - 5 = -\frac{1}{2}\( x - 3 \)
B. y - 5 = \frac{1}{2}\( x - 3 \)
C. y - 5 = 2\( x - 3 \)
D. y - 5 = -2\( x - 3 \)
Question 4
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. \boxed{x^2 + y^2 - 7x + 5y + 12 = 0}
B. x^2 + y^2 - 9x + 3y + 16 = 0
C. x^2 + y^2 - 5x - 3y + 4 = 0
D. x^2 + y^2 + 3x - 7y + 9 = 0
Question 5
Find the equation of the circle pas\sing through the points ( (2,3) ), ( (4,5) ), and ( (6,7) ).
A. \( x^2 + y^2 - 10x - 16y + 39 = 0 \)
B. \( x^2 + y^2 - 12x - 20y + 36 = 0 \)
C. \( x^2 + y^2 - 14x - 24y + 53 = 0 \)
D. \( x^2 + y^2 - 16x - 28y + 70 = 0 \)
Question 6
Solve the system of equations x + y = 4 and x - y = 2.
A. \boxed{x = 3, y = 1}
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 7
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. f'(x) = \frac{2x - 4}{\( x - 2 \)^2}
B. f'(x) = \frac{2x + 4}{\( x - 2 \)^2}
C. f'(x) = \frac{2x^2 - 8}{\( x - 2 \)^2}
D. f'(x) = \frac{2x^2 + 8}{\( x - 2 \)^2}
Question 8
Find the equation of the circle with center (2, 3) and radius 4.
A. \boxed{\( x - 2 \)^2 + \( y - 3 \)^2 = 16}
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 8
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 12
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 20
Question 9
Find the volume of the solid formed by revolving the region bounded by the parabola \[ y = x^2 \] and the line \[ y = 2x \] about the x-axis.
A. \[ V = \frac{16\pi}{3} \]
B. \[ V = \frac{32\pi}{3} \]
C. \[ V = \frac{64\pi}{3} \]
D. \[ V = \frac{128\pi}{3} \]
Question 10
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 11
A matrix ( A ) is given by \( A = egin{bmatrix} 2 & 1 \ 3 & 4 \end{bmatrix} \). Find the determinant of ( A ).
A. det(A) = 5
B. det(A) = 7
C. det(A) = 9
D. det(A) = 11
Question 12
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 0.375
B. 0.5
C. 0.625
D. 0.75
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 60
C. 80
D. 100
Question 14
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. \boxed{\frac{16\pi}{3}}
B. \frac{8\pi}{3}
C. \frac{12\pi}{3}
D. \frac{20\pi}{3}
Question 15
Solve the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = π/2
C. x = π
D. x = 2π

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