POST UTME OAU 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of 10 numbers has a mean of 20 and a s\tandard deviation of 5. What is the probability that a randomly selected number from this set is greater than 25?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 2
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 3
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 4
Find the derivative of the function \( f(x) = 3x^2 + 2x - 5 \) u\sing the power rule.
A. f'(x) = 6x + 2
B. f'(x) = 6x - 2
C. f'(x) = 6x + 1
D. f'(x) = 6x - 1
Question 5
Find the derivative of the function f(x) = x^3 - 2x^2 + 5x - 1.
A. 3x^2 - 4x + 5
B. x^3 - 2x^2 + 5x - 1
C. 3x^2 + 4x - 5
D. x^3 + 2x^2 - 5x + 1
Question 6
Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, 54, ... ).
A. 190
B. 200
C. 210
D. 220
Question 7
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 8
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \left\( x + 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 2 \right \)^2 + \left\( y + 3 \right \)^2 = 16
C. \left\( x + 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
D. \left\( x - 3 \right \)^2 + \left\( y + 2 \right \)^2 = 16
Question 9
A histogram shows the distribution of exam scores for a class of 50 students. The histogram has 5 bars, each representing a score range. The heights of the bars are 8, 12, 15, 10, and 5 units, respectively. What is the mean score of the class?
A. 11.2
B. 12.1
C. 13.5
D. 14.8
Question 10
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm. The frustum is cut off by a plane parallel to the base of the cone.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3
Question 11
Find the derivative of the function [ f(x) = \frac{1}{x^2} \] u\sing the chain rule.
A. \frac{-2}{x^3}
B. \frac{2}{x^3}
C. \frac{-1}{x^3}
D. \frac{1}{x^3}
Question 12
A histogram of exam scores is shown below. What is the mean score?
A. 40
B. 50
C. 60
D. 70
Question 13
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = \frac{\pi}{2}
C. x = \frac{\pi}{4}
D. x = \frac{3\pi}{4}
Question 14
A vector ( mathbf{a} ) has a magnitude of 5 and is directed at an angle of 30° to the x-axis. Find the x and y components of ( mathbf{a} ).
A. 3, 4
B. 4, 3
C. 5, 5
D. 6, 6
Question 15
Solve the inequality [ 2x^2 + 5x - 3 \geq 0 \].
A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
D. \left\( -\infty, \frac{3}{2} \right \) \cup \left\( -\frac{1}{2}, \infty \right \)

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