POST UTME CALEB UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
Simplify the expression \frac{\sqrt{12}}{\sqrt{3}}.
A. 2\sqrt{3}
B. \sqrt{3}
C. \sqrt{12}
D. \sqrt{3} + \sqrt{12}
Question 3
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{5\pi}{4}
D. x = \frac{7\pi}{4}
Question 4
Find the value of \( \frac{1}{2} \sin^2 \( \frac{\pi}{3} \ \) + \frac{1}{2} \cos^2 \( \frac{\pi}{3} \) ).
A. 0
B. \frac{1}{2}
C. \frac{1}{4}
D. \frac{3}{4}
Question 5
A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from this set is greater than 12.
A. 0.25
B. 0.5
C. 0.75
D. 0.9
Question 6
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 7
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \( \frac{5}{8} \)
B. \( \frac{3}{8} \)
C. \( \frac{2}{8} \)
D. \( \frac{1}{8} \)
Question 8
Solve the equation $\frac{x^2}{x-1} = 2$.
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Question 9
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \( x = \frac{-5 \pm \sqrt{25 + 6}}{1} \ \)
B. \( x = \frac{-5 \pm \sqrt{25 - 6}}{1} \ \)
C. \( x = \frac{-5 \pm \sqrt{25 + 12}}{1} \ \)
D. \( x = \frac{-5 \pm \sqrt{25 - 12}}{1} \ \)
Question 10
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 11
Solve the inequality $|x-2| > 3$.
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -1 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (5, ∞)
D. \( -∞, -1 \) ∪ (2, ∞)
Question 12
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. \( -\infty, 1 \) \cup \( 3, \infty \)
Question 13
A histogram shows the distribution of exam scores. If the mean score is 80 and the s\tandard deviation is 10, what is the probability that a randomly selected score will be between 70 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 14
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 15
Solve the trigonometric equation \sin^2(x) + \cos^2(x) = 1 for x.
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{3\pi}{4}

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