POST UTME COAL CITY UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -1 \) ∪ (1, ∞)
Question 2
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, 1 \) ∪ (5, ∞)
C. \( -∞, -5 \) ∪ (1, ∞)
D. \( -∞, -1 \) ∪ (1, ∞)
Question 3
A histogram shows the distribution of exam scores in a class of 50 students. The histogram has 5 bars, with heights 8, 12, 15, 10, and 5. What is the mean of the exam scores?
A. 10
B. 12
C. 15
D. 18
Question 4
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 5
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = 5 \end{cases} \).
A. \( x = 3, y = 1 \)
B. \( x = 1, y = 3 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 0 \)
Question 6
Find the value of x in the equation \( 2^x = 16 \).
A. 2
B. 3
C. 4
D. 5
Question 7
Find the derivative of the function ( 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} + \frac{\( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} - \frac{\( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 8
A circle has a radius of 4 units and a centre at the origin. Find the equation of the circle.
A. \( x^2 + y^2 = 16 \)
B. \( x^2 + y^2 = 4 \)
C. \( x^2 - y^2 = 16 \)
D. \( x^2 - y^2 = 4 \)
Question 9
A cone has a radius of 4 cm and a height of 6 cm. Find its volume.
A. 32π
B. 64π
C. 96π
D. 128π
Question 10
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 11
Find the area under the curve \( y = x^2 \) from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 12
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
A. 72
B. 80
C. 96
D. 108
Question 13
A random variable X has a probability density function (pdf) given by ( f(x) = egin{cases} 2x & \text{if } 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. \( int_{0.5}^{1} 2x , dx \)
B. \( int_{0}^{1} 2x , dx \)
C. \( int_{0}^{0.5} 2x , dx \)
D. \( int_{0}^{1} 2x , dx - int_{0}^{0.5} 2x , dx \)
Question 14
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y - 3 = \frac{2}{2}\( x - 2 \ \) )
B. \( y - 5 = \frac{2}{2}\( x - 4 \ \) )
C. \( y - 3 = \frac{2}{2}\( x - 4 \ \) )
D. \( y - 5 = \frac{2}{2}\( x - 2 \ \) )
Question 15
Evaluate the definite integral: \int_0^1 \( 2x^2 + 3x - 1 \) dx.
A. 7/3
B. 11/3
C. 13/3
D. 17/3

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