POST UTME CALEB UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).
A. \( -2, -1 \) ∪ (1, ∞)
B. \( -∞, -2 \) ∪ \( -1, 1 \) ∪ (1, ∞)
C. \( -∞, -2 \) ∪ (1, ∞)
D. \( -2, -1 \) ∪ (1, ∞)
Question 2
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{2}
B. x = \frac{\pi}{4}
C. x = \frac{3\pi}{4}
D. x = \frac{5\pi}{4}
Question 3
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 8
C. 10
D. 12
Question 4
Solve the following system of linear equations u\sing matrices:
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
C. \begin{bmatrix} 5 \\ 11 \end{bmatrix}
D. \begin{bmatrix} 7 \\ 13 \end{bmatrix}
Question 5
Find the derivative of the function (f(x) = \frac{x^2 + 2x - 3}{x^2 - 4}) u\sing the quotient rule.
A. (f'(x) = \frac{\( 2x + 2 \)\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2})
B. (f'(x) = \frac{\( 2x + 2 \)\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2})
C. (f'(x) = \frac{\( 2x + 2 \)\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2})
D. (f'(x) = \frac{\( 2x + 2 \)\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2})
Question 6
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 population mean.
A. 168.3 cm, 182.7 cm
B. 170.1 cm, 180.9 cm
C. 172.9 cm, 178.1 cm
D. 174.5 cm, 176.5 cm
Question 7
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the Rational Root Theorem.
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 8
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 9
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( \cos x \)
C. \( \sin x \)
D. \( \cos^2 x \)
Question 10
Find the sum of the first 10 terms of the geometric series \( 2, 6, 18, \ldots \).
A. 1950
B. 1960
C. 1970
D. 1980
Question 11
A random sample of 25 students from a population of 1000 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the probability that the sample mean height of a new random sample of 20 students will be less than 165 cm.
A. 0.001
B. 0.01
C. 0.1
D. 0.5
Question 12
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 13
Solve the inequality 2x^2 + 5x - 3 > 0 for x.
A. x < -1 or x > 3/2
B. x < -3/2 or x > 1
C. x < 1 or x > -3/2
D. x < -3/2 or x < 1
Question 14
Find the determinant of the matrix [ egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{pmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 15
Solve the equation [ \sin^2 x + \cos^2 x = 1 \] for [ 0 \leq x \leq 2 \pi \].
A. x = \frac{\pi}{2}
B. x = \frac{3\pi}{2}
C. x = \pi
D. x = 0

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: