POST UTME IMS U 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
B. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
C. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
D. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
Question 2
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 3
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
A. 30
B. 50
C. 60
D. 70
Question 4
A random variable X has a probability distribution given by P\( X = 1 \) = 1/4, P\( X = 2 \) = 1/2, and P\( X = 3 \) = 1/4. Find the expected value of X.
A. 1.5
B. 2
C. 2.5
D. 3
Question 5
Solve the inequality \( \frac{x}{x - 1} > 1 \).
A. \( x < -1 \) or \( x > 1 \)
B. \( x < 0 \) or \( x > 1 \)
C. \( x < 0 \) or \( x > 2 \)
D. \( x < -1 \) or \( x > 2 \)
Question 6
Let X be a random variable with probability density function f(x) = \\begin{cases} 2x & 0 < x < 1 \\ 0 & \text{otherwise} \\end{cases}. Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 7
Find the value of ( k ) in the equation \( 2x^2 + 3x - 4 = k\( x + 2 \)\( x - 1 \ \) ).
A. 5
B. 6
C. 7
D. 8
Question 8
A circle has equation \( x - 3 \ \)^2 + \( y + 2 \)^2 = 16 ). Find the equation of the \tangent line at point \( 5, -1 \ \) ).
A. y = -x + 8
B. y = x - 3
C. y = -x - 2
D. y = x + 2
Question 9
Evaluate the integral \( int_{0}^{1} x^2 \sin x , dx \).
A. \( -\cos x^2 + 2x \sin x + 2 \cos x \)
B. \( -\cos x^2 - 2x \sin x - 2 \cos x \)
C. \( \cos x^2 - 2x \sin x + 2 \cos x \)
D. \( \cos x^2 + 2x \sin x - 2 \cos x \)
Question 10
Solve the equation $\frac{1}{2} \log_{10} \( x^2 \) = 4$ for $x$.
A. 10
B. 20
C. 40
D. 80
Question 11
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the probability that ( X ) is greater than 2.
A. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{2} \)
Question 12
Solve the equation \\tan x + \\cot x = 3.
A. \\frac{\pi}{4}
B. \\frac{\pi}{3}
C. \\frac{\pi}{2}
D. \\frac{\pi}{6}
Question 13
A die is rolled twice. What is the probability that the sum of the two numbers shown on the dice is 7?
A. \frac{1}{6}
B. \frac{1}{12}
C. \frac{1}{36}
D. \frac{1}{24}
Question 14
Find the area of the triangle with vertices $(0, 0), (3, 0),$ and $(0, 2)$.
A. 6
B. 12
C. 18
D. 24
Question 15
In the diagram below, what is the value of $x$?
A. 30
B. 45
C. 60
D. 90

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