POST UTME UI 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\sin (2x)$ given that $\sin x = \frac{1}{2}$.
A. \frac{1}{2}
B. \frac{\sqrt{3}}{2}
C. \frac{\sqrt{5}}{2}
D. \frac{\sqrt{7}}{2}
Question 2
Solve the equation $\log_{10} \( x^2 \) = 4$.
A. 10
B. 100
C. 1000
D. 10000
Question 3
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 4
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, and P\( X = 3 \) = 0.3. If Y is another random variable such that Y = 2X - 1, find the probability P\( Y = 3 \).
A. 0.4
B. 0.3
C. 0.2
D. 0.1
Question 5
Solve the inequality \( \frac{x - 2}{x + 1} > 0 \).
A. \( -∞, -1 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (1, 2)
C. \( -∞, -1 \) ∪ (2, ∞)
D. \( -∞, 1 \) ∪ (2, ∞)
Question 6
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
B. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
C. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
D. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
Question 7
Find the equation of the plane pas\sing through the points ( (1, 2, 3) ), ( (2, 3, 4) ), and ( (3, 4, 5) ).
A. \( 2x + 3y - z + 1 = 0 \)
B. \( 2x + 3y - z + 2 = 0 \)
C. \( 2x + 3y - z + 3 = 0 \)
D. \( 2x + 3y - z + 4 = 0 \)
Question 8
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis about the x-axis.
A. 32π
B. 64π
C. 128π
D. 256π
Question 9
A set of 5 points is chosen at random from the set ( {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ). Find the probability that the 5 points form an arithmetic sequence.
A. \( \frac{1}{252} \)
B. \( \frac{1}{126} \)
C. \( \frac{1}{63} \)
D. \( \frac{1}{32} \)
Question 10
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 11
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 12
Find the derivative of the function ( 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} )
Question 13
A circle has a radius of 4 cm. What is the area of the circle?
A. 16\pi
B. 20\pi
C. 24\pi
D. 32\pi
Question 14
Find the equation of the line pas\sing through the points (1,2) and (3,4).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)
Question 15
Evaluate the integral \( int_{0}^{1} \frac{1}{x^2 + 1} dx \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{2} \)
D. \( \frac{3pi}{4} \)

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: