POST UTME SKYLINE UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 2
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = -\frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
Question 3
Find the sum of the first 5 terms of the arithmetic progression ( 2, 5, 8, ldots ).
A. ( 20 )
B. ( 25 )
C. ( 30 )
D. ( 35 )
Question 4
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
A. \( S = \frac{1}{2} \)
B. \( S = \frac{1}{4} \)
C. \( S = \frac{1}{8} \)
D. \( S = \frac{1}{16} \)
Question 5
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 6
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.
A. \begin{pmatrix} -15 \ 12 \end{pmatrix}
B. \begin{pmatrix} 12 \ -15 \end{pmatrix}
C. \begin{pmatrix} 15 \ -12 \end{pmatrix}
D. \begin{pmatrix} -12 \ 15 \end{pmatrix}
Question 7
A box 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. 2/3
D. 3/4
Question 8
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 9
A line passes through points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line.
A. y = x + 1
B. y = x - 1
C. y = -x + 3
D. y = x - 3
Question 10
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 11
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. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 12
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 13
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 14
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. \( x = 2, y = 2 \)
B. \( x = 3, y = 1 \)
C. \( x = 1, y = 3 \)
D. \( x = 4, y = 0 \)
Question 15
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

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