POST UTME BELLS UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Let $A = \begin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix}$. Find the eigenvalues of $A^2$.
A. -3
B. -1
C. 1
D. 3
Question 2
Solve the inequality |x - 2| > 3
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, 1 \) ∪ (4, ∞)
C. \( -∞, 1 \) ∪ (2, 4)
D. \( -∞, -1 \) ∪ (2, 4)
Question 3
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. ( f'(x) = \frac{2x\( x^2 + 1 \) - 2x^2}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x^2}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x^2 + 2}{\( x^2 + 1 \)^2} )
Question 4
In a 3x3 matrix, if the determinant is 0, what can be concluded about the linear indep\endence of the column vectors?
A. The column vectors are linearly dep\endent
B. The column vectors are linearly indep\endent
C. The determinant is not 0
D. The matrix is \singular
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. ( 8 )
B. ( 16 )
C. ( 32 )
D. ( 64 )
Question 6
Find the area under the curve $y = \frac{1}{x^2 + 1}$ from $x = 0$ to $x = 1$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 7
A histogram is shown below. Find the mean of the data.
A. 30
B. 35
C. 40
D. 45
Question 8
A vector \( \vec{a} \) is represented by the diagram below. What is the magnitude of \( \vec{a} \)?
A. 5
B. 10
C. 15
D. 20
Question 9
Find the derivative of the function \( y = \sin^2\( x \ \) ) u\sing the chain rule.
A. \( \cos^2\( x \ \) )
B. \( 2\sin\( x \)\cos(x \) )
C. \( 2\sin\( x \)\cos(x \) )
D. \( 2\sin^2\( x \)\cos(x \) )
Question 10
A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.
A. 6
B. 10
C. 12
D. 15
Question 11
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 12
Solve the system of equations x + y = 4 and x - y = 2
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 13
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \ \)
B. \( x = 2 \ \)
C. \( x = -1 \ \)
D. \( x = 1 \ \)
Question 14
Let $f(x) = \frac{x^2 - 4}{x - 2}$. Find the domain of $f(x)$.
A. \( -\infty, 2 \) \cup \( 2, \infty \)
B. \( -\infty, 2 \) \cup (2, 4]
C. \( -\infty, 2 \) \cup \( 4, \infty \)
D. (2, 4]
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
D. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)

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