POST UTME FUTA 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Simplify the expression \( \sqrt[3]{64x^3y^3} \).
A. \( 4x^3y^3 \)
B. \( 4xy^3 \)
C. \( 4x^3y \)
D. \( 4x^3y^3 \)
Question 4
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 5
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 6
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 7
Find the value of ( x ) in the equation \( x^2 + 2x - 6 = 0 \).
A. \frac{-2 + \sqrt{4 + 24}}{2}
B. \frac{-2 - \sqrt{4 + 24}}{2}
C. \frac{-2 + \sqrt{4 + 24}}{2}
D. \frac{-2 - \sqrt{4 + 24}}{2}
Question 8
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6827
Question 9
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. \( -1 \)
D. ( 2 )
Question 10
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with a_1 = 3. Find the value of a_5.
A. 33
B. 35
C. 37
D. 39
Question 11
In a circle with center ( O ) and radius 6 cm, a chord ( AB ) is drawn such that \( AB = 8 cm \). Find the dis\tance from ( O ) to the midpoint of ( AB ).
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm
Question 12
Solve the system of linear equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \).
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 0 \)
C. \( x = 0, y = 2 \)
D. \( x = 1, y = 2 \)
Question 13
Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.
A. 300\pi
B. 400\pi
C. 500\pi
D. 600\pi
Question 14
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) )
Question 15
Find the derivative of ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{\( x^2 - 4 \)\( 2x + 2 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}

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