POST UTME UNIBEN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2^x + 5^x geq 7^x \) for x.
A. -1
B. 0
C. 1
D. 2
Question 2
Solve the inequality $|x - 2| > 3$.
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, 1 \) ∪ (4, ∞)
C. \( -∞, -1 \) ∪ (1, 4)
D. \( -∞, 1 \) ∪ (1, 4)
Question 3
A sequence is defined by $a_n = 2n^2 + 3n - 1$. Find the sum of the first 5 terms of the sequence.
A. 65
B. 70
C. 75
D. 80
Question 4
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( x < -2 \) or \( x > 2 \)
B. \( x < -2 \) or \( x = 2 \)
C. \( x > -2 \) or \( x = 2 \)
D. \( x < -2 \) or \( x < 2 \)
Question 5
Find the value of x in the inequality \( |x - 2| > 3 \).
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -5 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (5, ∞)
D. \( -∞, -5 \) ∪ (1, ∞)
Question 6
A histogram of exam scores is shown below. If the mean score is 60, find the value of ( k ).
A. 40
B. 50
C. 60
D. 70
Question 7
The vectors \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \) are given. Find the vector ( mathbf{c} ) such that ( mathbf{c} ) is perp\endicular to both ( mathbf{a} ) and ( mathbf{b} ).
A. \( egin{pmatrix} 7 \ -2 \end{pmatrix} \)
B. \( egin{pmatrix} 2 \ -7 \end{pmatrix} \)
C. \( egin{pmatrix} -7 \ 2 \end{pmatrix} \)
D. \( egin{pmatrix} 2 \ 7 \end{pmatrix} \)
Question 8
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 1x + 1
B. y = 1x - 1
C. y = -1x + 1
D. y = -1x - 1
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 50.26
C. 50.28
D. 50.30
Question 10
Determine the value of k such that the equation \( x^2 + kx + 16 = 0 \) has roots that are in the ratio 2:3.
A. -8
B. -4
C. 8
D. 16
Question 11
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. 13
B. 14
C. 15
D. 16
Question 12
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x in [0, 2pi] ).
A. \( x = \frac{pi}{2} \) or \( x = \frac{3pi}{2} \)
B. \( x = \frac{pi}{4} \) or \( x = \frac{5pi}{4} \)
C. \( x = \frac{pi}{6} \) or \( x = \frac{11pi}{6} \)
D. \( x = \frac{pi}{3} \) or \( x = \frac{2pi}{3} \)
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \) or \( x > \frac{3}{2} \)
B. \( x < \frac{3}{2} \) or \( x > -\frac{5}{4} \)
C. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
Question 14
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} ) for \( x = 1, 2, 3 \). Find the expected value of ( X ).
A. 1
B. 2
C. 3
D. 4
Question 15
Evaluate the definite integral \( \int_{0}^{1} x^3 dx \).
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{1}{3}
D. \frac{1}{6}

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: