POST UTME MADONNA UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 )
Question 3
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. 16π
B. 32π
C. 64π
D. 128π
Question 4
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 5
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 6
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 7
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 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 = 16
C. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
Question 9
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < -1 or x < 3/2
D. x > -1 or x > 3/2
Question 10
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = -2x + 1 \)
D. \( y = -2x - 1 \)
Question 11
A die is rolled twice. What is the probability that the sum of the numbers on the two dice is 7?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 12
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 13
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 14
Find the volume of the frustum of the cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 256\pi cm^3
B. 512\pi cm^3
C. 768\pi cm^3
D. 1024\pi cm^3
Question 15
A histogram is given below. Find the mean of the data.
A. 10
B. 20
C. 30
D. 40

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