POST UTME VERITAS UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center (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 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16
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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 4
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 5
Solve the equation x^2 + 4x + 4 = 0.
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 6
Determine the value of $\sum_{n=1}^{\infty} \frac{1}{n^2}$ u\sing the properties of infinite geometric series.
A. $\frac{\pi^2}{6}$
B. $\frac{\pi^2}{12}$
C. $\frac{\pi^2}{24}$
D. $\frac{\pi^2}{48}$
Question 7
Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.
A. \( 2\sin x \cos x \)
B. \( \cos x \)
C. \( \sin x \)
D. \( \cos^2 x \)
Question 8
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the rational root theorem.
A. 1
B. 2
C. 3
D. 4
Question 9
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. 40
C. 50
D. 60
Question 10
A set of data has mean \( ar{x} = 25 \) and s\tandard deviation \( sigma = 3 \). Find the probability that a randomly selected value from the set lies between 20 and 30.
A. \( P\( 20 < X < 30 \ \) = 0.6827 )
B. \( P\( 20 < X < 30 \ \) = 0.6827 )
C. \( P\( 20 < X < 30 \ \) = 0.6827 )
D. \( P\( 20 < X < 30 \ \) = 0.6827 )
Question 11
Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. x = -1.5, x = 2
B. x = 1, x = -3
C. x = -2, x = 1.5
D. x = 1.5, x = -2
Question 12
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. \( \frac{2x\( x^2 + 1 \ \) - 2x^2}{\( x^2 + 1 \)^2} )
B. \( \frac{2x^2}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2x^2 + 2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2x^2 - 2}{\( x^2 + 1 \ \)^2} )
Question 13
Find the derivative of the function (f(x) = \frac{1}{x^2 + 1}) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 14
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 15
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000

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