POST UTME MADONNA UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center at (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 2
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 = 16
C. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 3
A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.
A. 256π cm³
B. 128π cm³
C. 512π cm³
D. 2048π cm³
Question 4
In a circle of radius 5 cm, a chord of length 8 cm subt\ends an angle of 60° at the centre. Find the area of the sector.
A. ( 20pi ) cm²
B. ( 30pi ) cm²
C. ( 40pi ) cm²
D. ( 50pi ) cm²
Question 5
Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.
A. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)
B. \left\( -\infty, 1 \right \) \cup \left\( 3, \infty \right \)
C. \left\( -\infty, -3 \right \) \cup \left\( 1, \infty \right \)
D. \left\( -\infty, 1 \right \) \cup \left\( 3, \infty \right \)
Question 6
A set of 5 consecutive integers has a median of 8. Find the sum of the integers.
A. 40
B. 50
C. 60
D. 70
Question 7
If f(x) = 3x^2 + 2x - 5, find the derivative of f(x) u\sing the chain rule.
A. 6x + 2
B. 6x^2 + 2x
C. 6x^2 + 2
D. 6x + 2x^2
Question 8
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 9
Solve for x in the equation \( \frac{1}{x} + 2 = \frac{3}{x} \).
A. \( x = -\frac{1}{2} \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = \frac{1}{2} \)
Question 10
A function ( f(x) = 2x^3 - 5x^2 + x - 1 ) is given. Find the derivative of ( f(x) ) u\sing the chain rule.
A. 6x^2 - 10x + 1
B. 6x^2 - 10x + 2
C. 6x^2 - 10x - 1
D. 6x^2 - 10x - 2
Question 11
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. \frac{64}{3}
B. \frac{32}{3}
C. \frac{16}{3}
D. \frac{8}{3}
Question 12
Solve for x in the equation \tan x = \frac{1}{\sqrt{3}}.
A. \frac{\pi}{6}
B. \frac{\pi}{3}
C. \frac{\pi}{2}
D. \frac{2\pi}{3}
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
C. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
D. \( x > -\frac{1}{2} \) or \( x < \frac{3}{2} \)
Question 14
A matrix ( A ) is given by \( A = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \). Find the determinant of ( A ).
A. 0
B. 1
C. 2
D. 3
Question 15
Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ).
A. ( f'(x) = 3x^2 - 4x + 1 )
B. ( f'(x) = x^2 - 2x + 1 )
C. ( f'(x) = 3x^2 - 4x - 1 )
D. ( f'(x) = x^2 - 2x - 1 )

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