POST UTME COAL CITY UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 2
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. \( \frac{1}{2} \)
B. \( \frac{3}{4} \)
C. \( \frac{1}{4} \)
D. \( \frac{3}{8} \)
Question 3
Find the mean and s\tandard deviation of the data set ( { 2, 4, 6, 8, 10 } ).
A. Mean: 6, S\tandard Deviation: 2
B. Mean: 5, S\tandard Deviation: 2
C. Mean: 6, S\tandard Deviation: 3
D. Mean: 5, S\tandard Deviation: 3
Question 4
Solve the equation \( \sin 2x = \cos x \) for ( 0 leq x leq 2pi ).
A. \( x = \frac{pi}{6} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{pi}{3} \)
D. \( x = \frac{pi}{2} \)
Question 5
Find the area under the curve \( y = \sin^2 x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{2} \)
D. \( \frac{3pi}{4} \)
Question 6
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is greater than 70?
A. \( \frac{1}{4} \)
B. \( \frac{1}{2} \)
C. \( \frac{3}{4} \)
D. \( \frac{3}{5} \)
Question 7
A histogram of exam scores for a class of 100 students is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 8
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4}, \frac{3pi}{4} \)
B. \( x = \frac{pi}{4}, \frac{5pi}{4} \)
C. \( x = \frac{pi}{4}, \frac{7pi}{4} \)
D. \( x = \frac{pi}{4}, \frac{9pi}{4} \)
Question 9
A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.
A. ( 100pi ) cm^3
B. ( 200pi ) cm^3
C. ( 300pi ) cm^3
D. ( 400pi ) cm^3
Question 10
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. \frac{\pi}{4}
B. \frac{3\pi}{4}
C. \frac{5\pi}{4}
D. \frac{7\pi}{4}
Question 11
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 12
Solve the equation \( x^2 + 6x + 8 = 0 \) u\sing the quadratic formula.
A. \frac{-6 \pm \sqrt{6^2 - 4(1)(8)}}{2(1)}
B. \frac{-6 \pm \sqrt{6^2 - 4(1)(8)}}{2(1)}
C. \frac{-6 \pm \sqrt{6^2 - 4(1)(8)}}{2(1)}
D. \frac{-6 \pm \sqrt{6^2 - 4(1)(8)}}{2(1)}
Question 13
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)
Question 14
Find the magnitude of the vector \( egin{pmatrix} 3 \ 4 \ 0 \end{pmatrix} \).
A. 5
B. \sqrt{5}
C. \sqrt{29}
D. \sqrt{41}
Question 15
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{2x\( x^2 + 1 \) - x^2(2x)}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x^2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x^3}{\( x^2 + 1 \)^2} )

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