POST UTME FUTA 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector \( \vec{a} \) has a magnitude of 5 units and makes an angle of 60\circ with the positive x-axis. Find the x and y components of \( \vec{a} \).
A. 2.5, 4.33
B. 4.33, 2.5
C. 3.54, 3.54
D. 2.5, 2.5
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 3
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \frac{-5 + \sqrt{49}}{4}
B. \frac{-5 - \sqrt{49}}{4}
C. \frac{-5 + \sqrt{49}}{4}
D. \frac{-5 - \sqrt{49}}{4}
Question 4
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 5
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 6
A random variable X follows a binomial distribution with parameters n = 10 and p = 0.4. Find the probability that X is greater than 6.
A. 0.011
B. 0.032
C. 0.063
D. 0.094
Question 7
Determine the mean of the following dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. If the mean is 12, what is the value of the unknown variable x in the dataset?
A. 10
B. 12
C. 14
D. 16
Question 8
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( -3, -1 \) \cup (1, 3)
B. \( -3, -1 \) \cup (1, 3) \cup \( 3, \infty \)
C. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \)
D. \( -3, -1 \) \cup (1, 3) \cup \( -\infty, -3 \) \cup \( 3, \infty \) \cup (0, 1)
Question 9
A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.
A. 512\pi
B. 256\pi
C. 128\pi
D. 64\pi
Question 10
Solve the equation \( x^3 + 2x^2 - 7x - 12 = 0 \) u\sing the factor theorem.
A. \text{No real roots}
B. \text{One real root}
C. \text{Two real roots}
D. \text{Three real roots}
Question 11
Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).
A. 12
B. 16
C. 20
D. 24
Question 12
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).
A. x^2 + y^2 - 6x - 2y + 12 = 0
B. x^2 + y^2 + 6x - 2y + 12 = 0
C. x^2 + y^2 - 6x + 2y + 12 = 0
D. x^2 + y^2 + 6x + 2y + 12 = 0
Question 13
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 14
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )
B. ( f'(x) = \frac{1}{2}x^{-\frac{3}{2}} )
C. ( f'(x) = -\frac{1}{2}x^{-\frac{1}{2}} )
D. ( f'(x) = \frac{1}{2}x^{-\frac{1}{2}} )
Question 15
Solve the inequality \( \frac{x^2 - 4}{x + 2} geq 0 \) for ( x in mathbb{R} ).
A. \( -infty, -2 \ \) cup [0, infty) )
B. \( -infty, -2 \ \) cup \( -2, 0 \) cup (0, infty) )
C. \( -infty, 0 \ \) cup (0, infty) )
D. \( -infty, -2 \ \) cup [2, infty) )

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