POST UTME COAL CITY UNIVERSITY 2021 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. 0.3
C. 0.4
D. 0.5
Question 2
Solve for x in the equation \( \frac{x}{2} + 5 = 3x - 2 \) u\sing the method of substitution.
A. \( x = 4 \)
B. \( x = -2 \)
C. \( x = 2 \)
D. \( x = -4 \)
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{3}{2} \) or \( x > 1 \)
C. \( x < 1 \) or \( x > -\frac{3}{2} \)
D. \( x < -\frac{3}{2} \) or \( x < 1 \)
Question 4
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 5
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 6
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{-x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{x}{\( x^2 + 1 \)^2} )
Question 7
A sequence is defined as a_1 = 2, a_2 = 4, a_n = a_{n-1} + 2. Find the 10th term of the sequence.
A. 20
B. 22
C. 24
D. 26
Question 8
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.5 cm
C. 4.5 cm
D. 5.5 cm
Question 9
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 10
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the surface area of the prism.
A. 62
B. 64
C. 66
D. 68
Question 11
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 12
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. \( x - 3 \)^2 + \( y - 2 \)^2 = 25
Question 13
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...
A. 155
B. 165
C. 175
D. 185
Question 14
A die is rolled 5 times. Find the probability that exactly 3 of the rolls result in an even number.
A. \frac{125}{512}
B. \frac{1}{32}
C. \frac{5}{32}
D. \frac{1}{16}
Question 15
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3

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