POST UTME SKYLINE UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of linear equations \( \begin{cases} x + 2y - 3z = 7 \ x - 2y + 3z = -3 \ 2x + 4y - 6z = 12 \end{cases} \).
A. \begin{cases} x = 1 \ y = 2 \ z = 3 \end{cases}
B. \begin{cases} x = 2 \ y = 1 \ z = 4 \end{cases}
C. \begin{cases} x = 3 \ y = 2 \ z = 1 \end{cases}
D. \begin{cases} x = 4 \ y = 3 \ z = 2 \end{cases}
Question 2
Let X be a random variable with probability density function f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X lies between -1 and 1.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 3
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. 0.5
B. 1
C. 1.5
D. 2
Question 4
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for \( x \) in the interval \( [0, 2\pi] \).
A. \( x = \frac{\pi}{4}, \frac{3\pi}{4} \)
B. \( x = \frac{\pi}{2}, \frac{3\pi}{2} \)
C. \( x = \frac{\pi}{4}, \frac{5\pi}{4} \)
D. \( x = \frac{\pi}{2}, \frac{7\pi}{2} \)
Question 5
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are red?
A. \frac{1}{4}
B. \frac{1}{6}
C. \frac{1}{8}
D. \frac{1}{10}
Question 6
Solve the equation \( x^2 + 2x + 1 = 0 \).
A. x = 0
B. x = -1
C. x = 1
D. x = -2
Question 7
Find the volume of the solid formed by revolving the region bounded by the curve y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 8
In the interval $[0, 2pi]$, find the value of $\int_0^{2\pi} \frac{\sin^2 x}{1 + \cos^2 x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{8}
D. \frac{\pi}{16}
Question 9
Find the vector \( \mathbf{a} \times \mathbf{b} \) given that \( \mathbf{a} = 2\mathbf{i} + 3\mathbf{j} \) and \( \mathbf{b} = -4\mathbf{i} + 5\mathbf{j} \).
A. -10\mathbf{i} + 14\mathbf{j}
B. 10\mathbf{i} - 14\mathbf{j}
C. -14\mathbf{i} + 10\mathbf{j}
D. 14\mathbf{i} - 10\mathbf{j}
Question 10
Find the value of \( \sin left\( \frac{pi}{4} + \frac{pi}{6} \right \ \) ).
A. \( \frac{\sqrt{3}}{2} \)
B. \( \frac{1}{2} \)
C. \( \frac{\sqrt{2}}{2} \)
D. \( \frac{1}{\sqrt{2}} \)
Question 11
Solve for x in the equation \frac{1}{x+1} + \frac{1}{x-1} = \frac{3}{2}
A. 1
B. 2
C. 3
D. 4
Question 12
Solve the trigonometric equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \).
A. \sin x = -1
B. \sin x = 1
C. \sin x = -\frac{1}{2}
D. \sin x = \frac{1}{2}
Question 13
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 1950
B. 1960
C. 1970
D. 1980
Question 14
Find the area under the curve \( y = \frac{1}{x} \) between \( x = 1 \) and \( x = 2 \).
A. 0.693
B. 0.693
C. 0.693
D. 0.693
Question 15
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 2 \)

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