POST UTME ACHIEVERS UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle pas\sing through the points ((2,3)), ((4,5)), and ((6,7)).
A. \( x^2 + y^2 - 12x - 6y + 36 = 0 \)
B. \( x^2 + y^2 - 8x - 4y + 16 = 0 \)
C. \( x^2 + y^2 - 10x - 5y + 25 = 0 \)
D. \( x^2 + y^2 - 14x - 7y + 49 = 0 \)
Question 2
Find the equation of the circle with center at $\( -2,3 \)$ and radius $4$.
A. \( x^2 + y^2 + 4x - 6y - 7 = 0 \)
B. \( x^2 + y^2 - 4x + 6y - 7 = 0 \)
C. \( x^2 + y^2 + 2x - 3y - 7 = 0 \)
D. \( x^2 + y^2 - 2x + 3y - 7 = 0 \)
Question 3
Find the derivative of ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x^2 - 2}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x^3 - 2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x^2 + 2}{\( x^2 + 1 \)^2} )
Question 4
Find the surface area of the sphere with radius 6 cm.
A. 288\pi cm^2
B. 288\pi cm^3
C. 288\pi cm^4
D. 288\pi cm^5
Question 5
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. \( \frac{32}{3} pi \)
B. \( \frac{64}{3} pi \)
C. \( \frac{128}{3} pi \)
D. \( \frac{256}{3} pi \)
Question 6
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
A. 18
B. 17
C. 16
D. 15
Question 7
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \( \frac{-x}{\( x^2 + 1 \ \)^{3/2}} )
B. \( \frac{x}{\( x^2 + 1 \ \)^{3/2}} )
C. \( \frac{1}{\( x^2 + 1 \ \)^{3/2}} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^{3/2}} )
Question 8
A binary operation \(* \) is defined as \( a * b = ab + 2a + 2b \). Find the value of \( 2 * 3 \).
A. 20
B. 22
C. 24
D. 26
Question 9
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( -∞, -3 \) ∪ (2, ∞)
B. \( -∞, -3 \) ∪ (2, 3)
C. \( -∞, -3 \) ∪ (3, ∞)
D. \( -∞, 3 \) ∪ (4, ∞)
Question 10
Find the equation of the circle with center (C(2, 3)) and radius \( r = 4 \).
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 11
Solve the system of equations \( egin{cases} x + y = 2 \ x - 2y = -3 \end{cases} \) u\sing substitution.
A. \( x = 1, y = 1 \)
B. \( x = 1, y = -1 \)
C. \( x = -1, y = 1 \)
D. \( x = -1, y = -1 \)
Question 12
Find the derivative of the function ( f(x) = \sin^2(x) ) u\sing the chain rule.
A. \( 2\sin\( x \)\cos(x \) )
B. \( \cos^2\( x \ \) )
C. \( \sin^2\( x \ \) )
D. \( \cos^2\( x \ \) - \sin^2(x) )
Question 13
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 32\pi
B. 64\pi
C. 96\pi
D. 128\pi
Question 14
Find the area under the curve [ y = \frac{1}{x^2 + 1} ] from [ x = 0 ] to [ x = 1 ].
A. \( int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{4} \)
B. \( int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{2} \)
C. \( int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{6} \)
D. \( int_0^1 \frac{1}{x^2 + 1} dx = arc\tan x Big|_0^1 = \frac{pi}{3} \)
Question 15
Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 4x + 4} > 0.
A. \( -\infty, -1 \) \cup \( 1, \infty \)
B. \( -\infty, -1 \) \cup (1, 2]
C. \( -\infty, 1 \) \cup \( 2, \infty \)
D. \( -\infty, 1] \cup \( 2, \infty \ \)

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