POST UTME OSUSTECH 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \( x = -2, -3 \)
B. \( x = 2, 3 \)
C. \( x = -3, 2 \)
D. \( x = 3, -2 \)
Question 2
A histogram is shown below. If the area under the curve is 20, what is the value of ( x )?
A. 5
B. 10
C. 15
D. 20
Question 3
Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. \frac{32\pi}{5}
B. \frac{64\pi}{5}
C. \frac{128\pi}{5}
D. \frac{256\pi}{5}
Question 4
Find the derivative of $f(x)=\frac{1}{x^2+1}$.
A. -\frac{2x}{\( x^2+1 \)^2}
B. \frac{2x}{\( x^2+1 \)^2}
C. -\frac{1}{\( x^2+1 \)^2}
D. \frac{1}{\( x^2+1 \)^2}
Question 5
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 6
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 7
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is between 60 and 90.
A. 0.9772
B. 0.9849
C. 0.9915
D. 0.9986
Question 8
Solve the inequality $|x-2|>3$.
A. \( -\infty,-5)\cup\( 8,\infty \ \)
B. \( -\infty,5)\cup\( 8,\infty \ \)
C. \( -\infty,-5)\cup\( 2,8 \ \)
D. \( -\infty,5)\cup\( 2,8 \ \)
Question 9
Solve the quadratic equation: x^2 + 5x + 6 = 0
A. -2
B. -3
C. 1
D. 2
Question 10
A line passes through the points (2,3) and (4,5). Find the equation of the line in slope-intercept form.
A. y = 1x + 1
B. y = 2x + 1
C. y = 3x + 1
D. y = 4x + 1
Question 11
Let X and Y be indep\endent random variables with means 2 and 3, respectively. If E(XY) = 7, find the variance of X + Y.
A. 10
B. 12
C. 15
D. 20
Question 12
Find the derivative of the function: f(x) = 3x^2 + 2x - 5
A. 6x + 2
B. 3x^2 + 2
C. 2x - 5
D. x^2 + 2x
Question 13
Find the derivative of the function ( f(x) = \frac{1}{x^2} \) u\sing the chain rule.
A. -2x^{-3}
B. 2x^{-3}
C. -x^{-3}
D. x^{-3}
Question 14
Determine the value of $\int_0^\pi\frac{1}{1+\sin^2x}dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{1}
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.
A. ( f'(x) = -\frac{2}{x^3} )
B. ( f'(x) = \frac{2}{x^3} )
C. ( f'(x) = -\frac{1}{x^3} )
D. ( f'(x) = \frac{1}{x^3} )

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