POST UTME UNILORIN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the vector equation \( \mathbf{a} \cdot \( \mathbf{b} \times \mathbf{c} \ \) = \mathbf{b} \cdot \( \mathbf{c} \times \mathbf{a} \) ).
A. 0
B. \mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{a}
C. \mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{a}
D. \mathbf{a} \cdot \mathbf{b} = \mathbf{a} \times \mathbf{b}
Question 2
Find the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{5}{6} \).
A. 1
B. 2
C. 3
D. 4
Question 3
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x in the interval ( [0, 2pi] ).
A. 0
B. \frac{\pi}{4}
C. \frac{\pi}{2}
D. \frac{3\pi}{4}
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 5
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \frac{x}{\( 1 - x^2 \)^{3/2}}
B. \frac{-x}{\( 1 - x^2 \)^{3/2}}
C. \frac{1}{\( 1 - x^2 \)^{3/2}}
D. \frac{2x}{\( 1 - x^2 \)^{3/2}}
Question 6
A die is rolled twice. Find the probability that the sum of the two numbers obtained is 7.
A. 1/6
B. 1/12
C. 1/18
D. 1/24
Question 7
Find the determinant of the matrix \( \begin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 5 & 1 & 2 \end{pmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 8
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 9
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first five terms of the sequence.
A. ( 15 )
B. ( 25 )
C. ( 35 )
D. ( 45 )
Question 10
Solve the system of linear equations u\sing matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -3 \end{align*}
A. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 2 \ 1 \end{pmatrix}
B. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 2 \end{pmatrix}
C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 4 \end{pmatrix}
D. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 4 \ 3 \end{pmatrix}
Question 11
Determine the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \( \frac{8}{15} pi \)
B. \( \frac{16}{15} pi \)
C. \( \frac{32}{15} pi \)
D. \( \frac{64}{15} pi \)
Question 12
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 13
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 14
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( -∞, -3 \) ∪ (2, ∞)
B. \( -∞, -3 \) ∪ (2, 3)
C. \( -∞, -3 \) ∪ (3, ∞)
D. \( -∞, 3 \) ∪ (3, ∞)
Question 15
Find the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \), given that \( \sin x = \frac{3}{5} \).
A. 0
B. π/2
C. π
D. 3π/2

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