POST UTME ELIZADE UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation [ 2x^2 + 5x - 3 = 0 ].
A. x = -1.5, x = 2
B. x = 1, x = -3
C. x = -2, x = 1.5
D. x = 3, x = -1
Question 2
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 3
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 4
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 5
A binary operation ( ast ) is defined as \( a \ast b = a^2 + b^2 \). Find the value of \( 2 \ast 3 \).
A. 13
B. 14
C. 15
D. 16
Question 6
A right triangle has a hypotenuse of length 10 and one leg of length 6. What is the length of the other leg?
A. \( \sqrt{64} \)
B. \( \sqrt{56} \)
C. \( \sqrt{36} \)
D. \( \sqrt{16} \)
Question 7
A binary operation \ast on the set of integers is defined as a \ast b = ab + 1 for all integers a and b. Find the value of 2 \ast 3.
A. 7
B. 9
C. 11
D. 13
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 9
Find the value of ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. 1
B. -1
C. 2
D. -2
Question 10
Find the volume of the solid formed by revolving the region bounded by the curve y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 11
A right circular cone has a height of 12 cm and a base radius of 8 cm. Find the volume of the cone in cubic centimeters.
A. 256\pi
B. 512\pi
C. 768\pi
D. 1024\pi
Question 12
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 13
A survey of 100 students found that 60% of them preferred Mathematics as their favorite subject. If 20% of the students who preferred Mathematics were female, what is the probability that a student chosen at random from the group of students who preferred Mathematics is female?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 14
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 15
Find the volume of the sphere [ x^2 + y^2 + z^2 = 4 ].
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi

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