POST UTME IMS U 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 )
A. 10
B. 100
C. 1000
D. 10000
Question 2
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 2x about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 3
Find the volume of the solid formed by revolving the region bounded by y = x^2, x = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \)
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 5
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. -2
B. -3
C. 2
D. 3
Question 6
Solve the matrix equation \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}
A. \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}
B. \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}
C. \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}
D. \\begin{bmatrix} 4 \\\\ 3 \\end{bmatrix}
Question 7
Solve the inequality $\frac{x^2 - 4x + 3}{x^2 - 2x - 3} > 0$.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -3 \) \cup \( -1, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup (1, 3)
Question 8
Solve for x in the equation \( \log_{2}\( x^2 \ \) = 4 ).
A. \( x = 16 \)
B. \( x = 8 \)
C. \( x = 4 \)
D. \( x = 2 \)
Question 9
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 10
In the diagram below, ( ABC ) is a right-angled triangle with \( AB = 3 \) and \( BC = 4 \). Find the length of ( AC ).
A. 5
B. 6
C. 7
D. 8
Question 11
A binary operation ( odot ) is defined as \( a odot b = ab + 2 \). Find the value of ( 3 odot 4 ).
A. 14
B. 16
C. 18
D. 20
Question 12
Solve the equation \( \sin^2 x + \cos^2 x = 1 \)
A. x = 0
B. x = π/2
C. x = π
D. x = 2π
Question 13
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}{6}
D. \frac{\pi}{8}
Question 14
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}
A. \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}
B. \\begin{bmatrix} 2 \\\\ 3 \\end{bmatrix}
C. \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}
D. \\begin{bmatrix} 4 \\\\ 5 \\end{bmatrix}
Question 15
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

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