POST UTME SKYLINE UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi
B. 64\pi
C. 80\pi
D. 96\pi
Question 2
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -5 \) ∪ (1, ∞)
C. \( -∞, -5 \) ∪ (1, ∞)
D. \( -∞, -1 \) ∪ (5, ∞)
Question 3
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - y = 3 \end{cases} \).
A. {(1, 3), (2, 2)}
B. {(1, 2), (2, 3)}
C. {(1, 3), (2, 1)}
D. {(2, 2), (1, 3)}
Question 4
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( \frac{5 + \sqrt{109}}{4}, \infty\right \)
B. \left\( -\infty, \frac{5 - \sqrt{109}}{4}\right \)
C. \left\( \frac{5 - \sqrt{109}}{4}, \frac{5 + \sqrt{109}}{4}\right \)
D. \left\( -\infty, \frac{5 + \sqrt{109}}{4}\right \)
Question 5
Find the sum of the first 5 terms of the arithmetic sequence ( 2, 5, 8, ldots ).
A. 25
B. 30
C. 35
D. 40
Question 6
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for \( x \) in the interval \( [0, 2\pi] \).
A. 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}
B. \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}
C. \frac{\pi}{6}, \frac{\pi}{3}, \frac{2\pi}{3}, \frac{5\pi}{6}
D. \frac{\pi}{8}, \frac{3\pi}{8}, \frac{5\pi}{8}, \frac{7\pi}{8}
Question 7
A binary operation \ast on the set of integers is defined as a \ast b = ab + 1. Find the value of 2 \ast 3.
A. 7
B. 9
C. 11
D. 13
Question 8
Find the equation of the line pas\sing through the points (2, 3) and (4, 5)
A. y = 1x + 1
B. y = 1x - 1
C. y = -1x + 1
D. y = -1x - 1
Question 9
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.
A. 64
B. 128
C. 192
D. 256
Question 10
Find the magnitude of the vector \( \vec{a} = 3\hat{i} + 4\hat{j} \) and the angle it makes with the positive x-axis.
A. \sqrt{5}
B. \sqrt{10}
C. \sqrt{20}
D. \sqrt{25}
Question 11
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. {\( -2, 0 \)}
B. {\( 0, -2 \)}
C. {\( -2, -2 \)}
D. {(2, 2)}
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 24
B. 32
C. 40
D. 48
Question 13
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 14
A sequence is defined recursively by $a_1=1$ and $a_n=a_{n-1}+2$ for $n>1$. Find the value of $a_{10}$.
A. 21
B. 22
C. 23
D. 24
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \)
B. ( 3 )
C. ( 4 )
D. ( 6 )

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