POST UTME COAL CITY UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -1 \ \) or \( x > \frac{3}{2} \ \)
B. \( x < -1 \ \) or \( x < \frac{3}{2} \ \)
C. \( x > -1 \ \) or \( x < \frac{3}{2} \ \)
D. \( x > -1 \ \) or \( x > \frac{3}{2} \ \)
Question 2
A function f(x) is defined as \(f(x) = 2x^2 + 3x - 1\). Find the derivative of f(x) u\sing the power rule.
A. 4x + 3
B. 2x + 3
C. 4x - 3
D. 2x - 3
Question 3
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{pmatrix} ].
A. -1
B. 1
C. 0
D. 2
Question 4
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is unknown, calculate the 95% confidence interval for the mean height of all students in the university.
A. 173.1 cm, 177.9 cm
B. 174.5 cm, 176.5 cm
C. 172.9 cm, 178.1 cm
D. 171.7 cm, 179.3 cm
Question 5
Determine the value of x in the equation \( \tan^2 x + 1 = sec^2 x \) for \( 0 leq x leq \frac{pi}{2} \).
A. \( \frac{\pi}{4} \)
B. \( \frac{\pi}{2} \)
C. \( \frac{3\pi}{4} \)
D. \( \frac{\pi}{6} \)
Question 6
If \( f(x) = \frac{1}{x^2 + 1} \), find \( f'(x) \) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 7
Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \ \).
A. \( 0 \ \)
B. \( 1 \ \)
C. \( 2 \ \)
D. \( 3 \ \)
Question 8
Solve for x in the equation \(\log_{10}\( x^2 \) = 4\).
A. 10^4
B. 10^8
C. 10^12
D. 10^16
Question 9
Solve for x in the equation [ 2x^2 + 5x - 3 = 0 ].
A. 1
B. -1
C. 2
D. -2
Question 10
Solve the system of equations \[ x + y = 2 \] and \[ x - y = 1 \].
A. x = 1, y = 1
B. x = 1, y = -1
C. x = -1, y = 1
D. x = -1, y = -1
Question 11
Find the volume of the cylinder with radius 6 and height 8.
A. 288\pi
B. 288\pi^2
C. 288\pi^3
D. 288\pi^4
Question 12
Solve the system of linear equations \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \ \).
A. \( x = 1, y = 1 \ \)
B. \( x = 2, y = 1 \ \)
C. \( x = 1, y = 2 \ \)
D. \( x = 2, y = 2 \ \)
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 3 \) \cup \( 1, \infty \)
Question 14
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{\( x^2 + 2x - 3 \)\( 2x + 2 \) - \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{\( x^2 + 2x - 3 \)\( 2x + 2 \) + \( x^2 - 4 \)(2x)}{\( x^2 - 4 \)^2}
Question 15
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}

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