POST UTME COAL CITY UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a certain town, 60% of the people are right-handed, and 40% are left-handed. If 100 people are randomly selected from the town, how many are expected to be left-handed?
A. 30
B. 40
C. 50
D. 60
Question 2
Solve the system of linear equations \( egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} \).
A. (1, 2)
B. (2, 1)
C. (3, 4)
D. (4, 5)
Question 3
In the set A = {1, 2, 3, 4, 5}, find the number of subsets with exactly 3 elements.
A. 5
B. 10
C. 15
D. 20
Question 4
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment is terminated. What is the probability that the experiment will be terminated on the first roll?
A. \frac{1}{2}
B. \frac{2}{3}
C. \frac{3}{4}
D. \frac{4}{5}
Question 5
In the complex plane, if z = 3 + 4i and w = 2 - 5i, find the value of |z + w|.
A. 5
B. 7
C. 10
D. 13
Question 6
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 7
Find the area under the curve y = \( \sin^2\( x \ \)) from 0 to \( \frac{pi}{2} \) u\sing integration by substitution.
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{2} \)
C. \( \frac{3pi}{4} \)
D. \( \frac{5pi}{4} \)
Question 8
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-2}{\( x^2 + 1 \ \)^2} )
Question 9
A histogram is shown below. What is the mean of the data set?
A. 5
B. 6
C. 7
D. 8
Question 10
Solve for $x$ in the equation $\log_2 \( x^2 + 1 \) = 3$.
A. \sqrt{7}
B. \sqrt{8}
C. \sqrt{9}
D. \sqrt{10}
Question 11
Find the equation of the circle with center \( -2, 3 \ \) ) and radius 5.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 25 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 25 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 25 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 12
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is 6, what is the sum of the data set?
A. 20
B. 30
C. 40
D. 50
Question 13
A cylindrical \tank with a radius of 4m and a height of 6m is filled with water. Find the volume of water in the \tank.
A. ( 96pi ) cubic meters
B. ( 192pi ) cubic meters
C. ( 384pi ) cubic meters
D. ( 576pi ) cubic meters
Question 14
Find the area under the curve y = x^2 + 2x + 1 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36
Question 15
Use the chain rule to find the derivative of the function f(x) = \( 2x + 1 \ \)^3).
A. f'(x) = 6\( 2x + 1 \)^2
B. f'(x) = 6\( 2x + 1 \)
C. f'(x) = 12\( 2x + 1 \)
D. f'(x) = 24\( 2x + 1 \)

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