POST UTME SKYLINE UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of 5 numbers has a mean of 10. If 5 is added to each number, what is the new mean?
A. 12
B. 15
C. 18
D. 20
Question 2
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval \( [0, 2\pi] \).
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{3\pi}{4}
D. \pi
Question 3
A rec\tangular prism has a length of 6 units, a width of 4 units, and a height of 3 units. Find the volume of the prism.
A. 72
B. 96
C. 120
D. 144
Question 4
A circle has a radius of 5 units. Find the area of the circle.
A. 25π
B. 50π
C. 75π
D. 100π
Question 5
Convert the number 1011 from base 2 to base 10.
A. 3
B. 5
C. 7
D. 9
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the quotient rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{x^2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{1}{\( x^2 + 1 \)^2} )
Question 7
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( P\( X > 4 \ \) = \frac{1}{6} )
B. \( P\( X > 4 \ \) = \frac{1}{3} )
C. \( P\( X > 4 \ \) = \frac{2}{3} )
D. \( P\( X > 4 \ \) = \frac{5}{6} )
Question 8
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^4 \)
B. \( x = 10^2 \)
C. \( x = 10^{-4} \)
D. \( x = 10^{-2} \)
Question 9
Solve for x in the quadratic equation \( x^2 + 5x + 6 = 0 \)
A. x = -2
B. x = -3
C. x = 2
D. x = 3
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > \frac{5}{4} \)
C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x > \frac{3}{2} \)
Question 11
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = x + 1
B. y = x - 1
C. y = 2x - 1
D. y = 2x + 1
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \)
A. x < -1 or x > 3/2
B. x < 1 or x > -3/2
C. x < -3/2 or x > 1
D. x < 3/2 or x > -1
Question 13
Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 14
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the cross product formula.
A. \( egin{pmatrix} 0 \ 0 \ 0 \end{pmatrix} \)
B. \( egin{pmatrix} 6 \ -4 \ 0 \end{pmatrix} \)
C. \( egin{pmatrix} 0 \ 0 \ 6 \end{pmatrix} \)
D. \( egin{pmatrix} 0 \ 0 \ -6 \end{pmatrix} \)
Question 15
A random experiment has two indep\endent events, A and B, with probabilities 0.4 and 0.6, respectively. Find the probability that both events occur.
A. 0.24
B. 0.48
C. 0.64
D. 0.76

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