POST UTME MADONNA UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with centre at ((2,3)) and pas\sing through the point ((6,7)).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 5^2 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 7^2 )
C. \( x-3 \ \)^2 + \( y-2 \)^2 = 5^2 )
D. \( x-3 \ \)^2 + \( y-2 \)^2 = 7^2 )
Question 2
Find the derivative of the function \( y = 3x^2 + 2x - 5 \) u\sing the chain rule.
A. 6x + 2
B. 6x^2 + 2
C. 6x^2 + 2x
D. 6x^2 + 2x - 2
Question 3
Solve for x: \( 2^x = 32 \).
A. \( x = 4 \)
B. \( x = 5 \)
C. \( x = 6 \)
D. \( x = 7 \)
Question 4
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 5
If \sin(x) = 3/5, and \cos(x) = 4/5, what is the value of \tan(x)?
A. 3/4
B. 4/3
C. 3/4
D. 4/3
Question 6
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 16 )
B. ( 20 )
C. ( 24 )
D. ( 28 )
Question 7
If the volume of a rec\tangular prism is 120 cubic units, and the length and width are in the ratio 3:2, what is the height of the prism?
A. 4
B. 5
C. 6
D. 8
Question 8
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 50
C. 60
D. 70
Question 9
Find the equation of the circle with center at ((2,3)) and radius 4.
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-3 \ \)^2 + \( y-2 \)^2 = 16 )
C. \( x-4 \ \)^2 + \( y-2 \)^2 = 16 )
D. \( x-2 \ \)^2 + \( y-4 \)^2 = 16 )
Question 10
A histogram of exam scores is shown below. Find the mean score.
A. 50
B. 55
C. 60
D. 65
Question 11
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 12
A circle has a radius of 4 cm. Find its area.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )
B. \( \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \ \) )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )
Question 14
Solve the inequality \frac{x^2 - 4}{x^2 - 9} > 0.
A. \( -3, -2 \) \cup (2, 3)
B. \( -3, -2 \) \cup \( 2, \infty \)
C. \( -\infty, -3 \) \cup \( -2, 2 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( -2, 2 \) \cup (3, 4)
Question 15
Find the derivative of the function \( y = \sin^2 x \).
A. \( y' = 2 \sin x \cos x \)
B. \( y' = 2 \sin^2 x \)
C. \( y' = 2 \cos^2 x \)
D. \( y' = 2 \sin x \)

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