POST UTME ELIZADE UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
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
Find the surface area of the sphere with a radius of 4 cm.
A. 201.06
B. 314.16
C. 502.65
D. 804.25
Question 4
Solve the equation \frac{1}{x+1} + \frac{1}{x-2} = \frac{3}{2x-1} for x.
A. x = -1
B. x = 2
C. x = \frac{1}{2}
D. x = -\frac{1}{2}
Question 5
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}} )
B. ( f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}} )
D. ( f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}} )
Question 6
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the surface area of the prism.
A. 88
B. 92
C. 96
D. 100
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 blue?
A. 3/8
B. 1/2
C. 3/5
D. 5/8
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 9
Solve the equation \log_{10} \( x^2 \) = 4.
A. x = \pm 10
B. x = \pm 100
C. x = \pm 1000
D. x = \pm 10000
Question 10
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 = 4
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
Question 11
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 12
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 14
A vector \overrightarrow{a} has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x-component of the vector.
A. 2.5
B. 3.75
C. 4.33
D. 5.00
Question 15
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ).
A. \frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x^2}{\( x^2 + 1 \)^2}
C. \frac{x^2 + 1}{x^2}
D. \frac{x^2 - 1}{x^2 + 1}

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