POST UTME UNILAG 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of numbers is defined as \( S = \{ 1, 2, 3, 4, 5 \} \ \). Find the number of subsets of S.
A. 5
B. 10
C. 15
D. 20
Question 2
Solve the inequality \( x^2 - 4x + 3 > 0 \) u\sing the quadratic formula.
A. \left\( 1, 3 \right \)
B. \left\( -1, -3 \right \)
C. \left\( 1, -3 \right \)
D. \left\( -1, 3 \right \)
Question 3
Find the sum of the first 10 terms of the geometric series \( 2x^2 - 3x + 1 \) with common ratio \( r = \frac{1}{2} \).
A. -1
B. 1
C. 2
D. 3
Question 4
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 5
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 6
Solve the inequality \frac{x^2 - 4}{x + 2} > 0.
A. x < -2 \text{ or } x > 2
B. x > -2 \text{ and } x < 2
C. x < -2 \text{ and } x > 2
D. x > -2 \text{ or } x < 2
Question 7
Find the derivative of the function ( f(x) = x^2 \sin x ) u\sing the product rule.
A. \left\( 2x \sin x + x^2 \cos x \right \)
B. \left\( 2x \sin x - x^2 \cos x \right \)
C. \left\( 2x \sin x + x^2 \cos x \right \)
D. \left\( 2x \sin x - x^2 \cos x \right \)
Question 8
A histogram represents the distribution of exam scores. If the mean score is 60 and the s\tandard deviation is 10, what is the probability that a randomly selected score is between 50 and 70?
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 9
Find the area of the region bounded by the curve y = x^3 - 6x^2 + 9x + 2, the x-axis, and the lines x = 0 and x = 3.
A. 18
B. 36
C. 54
D. 72
Question 10
A circle with center (0, 0) and radius 4 is revolved about the x-axis. Find the volume of the solid formed.
A. 256\pi
B. 128\pi
C. 64\pi
D. 32\pi
Question 11
Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.
A. \begin{align*} x &= 3 \ y &= 1 \end{align*}
B. \begin{align*} x &= 2 \ y &= 2 \end{align*}
C. \begin{align*} x &= 1 \ y &= 3 \end{align*}
D. \begin{align*} x &= 4 \ y &= 0 \end{align*}
Question 12
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 6x - 2
C. 3x^2 + 2
D. 3x^2 - 2
Question 13
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. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 14
Find the equation of the plane pas\sing through the points (1, 2, 3), (4, 5, 6), and (7, 8, 9).
A. x - y + z = 0
B. x + y - z = 0
C. x - y + z = 0
D. x + y + z = 0
Question 15
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 12
B. 15
C. 18
D. 20

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