POST UTME ESUT 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \log_2 \( x^2 \) = 4 \)
A. 16
B. 8
C. 4
D. 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{-2}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2}{\( x^2 + 1 \ \)^2} )
Question 3
A circle has a radius of 4 cm. What is the area of the circle?
A. 50.24
B. 100.48
C. 200.96
D. 50.24
Question 4
Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0.
A. \boxed{(2, 3) \cup \( 5, \infty \)}
B. \boxed{\( -\infty, -1 \) \cup (1, 3)}
C. \boxed{\( -\infty, -3 \) \cup (1, 5)}
D. \boxed{(2, 5)}
Question 5
Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. \boxed{\frac{32\pi}{3}}
B. \boxed{\frac{64\pi}{3}}
C. \boxed{\frac{128\pi}{3}}
D. \boxed{\frac{256\pi}{3}}
Question 6
Solve the system of equations u\sing matrices: \begin{align*} x + 2y &= 6 \ 3x - 2y &= -3 \end{align*}
A. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 2 \ 2 \end{pmatrix}
B. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 1 \end{pmatrix}
C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 3 \end{pmatrix}
D. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 4 \ 0 \end{pmatrix}
Question 7
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. x = -2, x = -3
B. x = 2, x = 3
C. x = -1, x = -6
D. x = 1, x = 6
Question 8
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 9
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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 10
Solve the equation \log_2 \( x + 1 \) + \log_2 \( x - 1 \) = 2.
A. \boxed{x = 3}
B. \boxed{x = 5}
C. \boxed{x = 7}
D. \boxed{x = 9}
Question 11
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 12
Solve for ( x ) in the equation \( 2^x = 16 \).
A. \( x = 2 \)
B. \( x = 4 \)
C. \( x = 8 \)
D. \( x = 16 \)
Question 13
A sequence is defined by the formula \( a_n = 2n^2 - 5n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 120
B. 130
C. 140
D. 150
Question 14
A probability experiment has two indep\endent events, A and B. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 15
Find the derivative of ( 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{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )

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