POST UTME VERITAS UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
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 4
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 5
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. Find the z-score of a score of 70.
A. 0.5
B. 1
C. 1.5
D. 2
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 12
B. 14
C. 16
D. 18
Question 7
Find the determinant of the matrix \( \begin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{pmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 8
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 9
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 10
Find the value of \( \sin\( 2x \ \) ) given that \( \sin\( x \ \) = \frac{3}{5} ) and \( \cos\( x \ \) = \frac{4}{5} ).
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{12}{25}
D. \frac{8}{25}
Question 11
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 12
A polynomial function has a degree of 4 and has roots at \( x = -2, 1, 3 \). Find the polynomial function.
A. \( x^4 + 6x^3 - 3x^2 - 18x + 18 \)
B. \( x^4 + 6x^3 - 3x^2 + 18x - 18 \)
C. \( x^4 - 6x^3 - 3x^2 + 18x + 18 \)
D. \( x^4 - 6x^3 + 3x^2 - 18x - 18 \)
Question 13
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)
B. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)
C. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2} \)
D. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)
Question 14
A circle has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the line pas\sing through the center of the circle and perp\endicular to the line \( y = x \).
A. \( y = -x + 5 \)
B. \( y = x + 5 \)
C. \( y = -x - 5 \)
D. \( y = x - 5 \)
Question 15
Find the equation of the circle with center $\left\( \frac{3}{2}, \frac{5}{4} \right \)$ and radius $\frac{5}{4}$.
A. $\left\( x - \frac{3}{2} \right \)^2 + \left\( y - \frac{5}{4} \right \)^2 = \left\( \frac{5}{4} \right \)^2$
B. $\left\( x - \frac{5}{4} \right \)^2 + \left\( y - \frac{3}{2} \right \)^2 = \left\( \frac{5}{4} \right \)^2$
C. $\left\( x - \frac{3}{2} \right \)^2 + \left\( y - \frac{5}{4} \right \)^2 = \left\( \frac{3}{2} \right \)^2$
D. $\left\( x - \frac{5}{4} \right \)^2 + \left\( y - \frac{3}{2} \right \)^2 = \left\( \frac{3}{2} \right \)^2$

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