POST UTME DELSU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2}
B. \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2}
C. \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2}
D. \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2}
Question 2
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{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}
Question 3
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < -1 or x > 3
B. x > -1 or x < 3
C. x < 1 or x > 3
D. x > 1 or x < 3
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( \frac{-5 + \sqrt{49}}{4}, \frac{-5 - \sqrt{49}}{4}\right \)
B. \left\( \frac{-5 - \sqrt{49}}{4}, \frac{-5 + \sqrt{49}}{4}\right \)
C. \left\( \frac{-5 + \sqrt{49}}{4}, \frac{-5 - \sqrt{49}}{4}\right \)
D. \left\( \frac{-5 - \sqrt{49}}{4}, \frac{-5 - \sqrt{49}}{4}\right \)
Question 5
A histogram of exam scores for a class of 50 students is shown below. If the mean score is 75, what is the median score?
A. 70
B. 75
C. 80
D. 85
Question 6
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3, 4, 5 \). Find the expected value of ( X ).
A. 3
B. 4
C. 5
D. 6
Question 7
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 14
B. 16
C. 18
D. 20
Question 8
Solve the trigonometric equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) for x in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{3pi}{4} \)
C. \( x = \frac{5pi}{4} \)
D. \( x = \frac{7pi}{4} \)
Question 9
Solve the equation $x^2 + 4x + 4 = 0$.
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 10
The area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) is given by the definite integral \( \int_{0}^{2} x^2 dx \). Evaluate the integral.
A. \frac{8}{3}
B. \frac{16}{3}
C. \frac{32}{3}
D. \frac{64}{3}
Question 11
Find the volume of the cylinder with radius 6 and height 8.
A. ( 384pi )
B. ( 384pi )
C. ( 384pi )
D. ( 384pi )
Question 12
Simplify the expression \( \frac{1}{2} \times 3^2 + 2 \times 3^3 \) u\sing the rules of exponents.
A. \( 3^4 + 2 \)
B. \( 3^4 - 2 \)
C. \( 3^4 \times 2 \)
D. \( 3^4 div 2 \)
Question 13
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 14
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 15
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

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