POST UTME UNN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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} )
D. \( \frac{\( x^2 - 4 \)\( 2x + 2 \ \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
Question 2
A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.
A. y = x + 1
B. y = x - 1
C. y = -x + 2
D. y = x + 2
Question 3
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 4
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. \frac{x}{\( x^2 + 1 \)^{3/2}}
C. \frac{1}{\( x^2 + 1 \)^{3/2}}
D. \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 5
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. x = -2, x = -3
B. x = 2, x = 3
C. x = -1, x = 6
D. x = 1, x = 4
Question 6
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. \left\( x, \, y \right \) = \left\( 3, \, 1 \right \)
B. \left\( x, \, y \right \) = \left\( 1, \, 3 \right \)
C. \left\( x, \, y \right \) = \left\( 2, \, 2 \right \)
D. \left\( x, \, y \right \) = \left\( 4, \, 0 \right \)
Question 7
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 8
Find the area under the curve \( y = \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{pi}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{8} \)
D. \( \frac{pi}{16} \)
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
C. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x > \frac{3}{2} \)
Question 10
Find the derivative of ( 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 11
Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \frac{-5 + \sqrt{109}}{4}
B. \frac{-5 - \sqrt{109}}{4}
C. \frac{5 + \sqrt{109}}{4}
D. \frac{5 - \sqrt{109}}{4}
Question 12
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. 2.5
C. 3.5
D. 4.5
Question 13
In the diagram below, a circle with center O and radius 6 cm is \tangent to the x-axis at point A. If the point P(8, 3) lies on the circle, find the area of the shaded region.
A. 36π cm^2
B. 24π cm^2
C. 48π cm^2
D. 60π cm^2
Question 14
A histogram represents the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a range of scores. The heights of the bars are 8, 12, 15, 10, and 5 units. Calculate the mean score of the class.
A. 70
B. 75
C. 80
D. 85
Question 15
A circle has a radius of 5 cm. Find the area of the circle.
A. 78.5
B. 78.5
C. 78.5
D. 78.5

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