POST UTME IMS U 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).
A. x > 10
B. x < 10
C. x > 100
D. x < 100
Question 2
Find the value of \( \frac{d}{dx} \( x^3 - 6x^2 + 11x - 6 \ \) ).
A. 3x^2 - 12x + 11
B. 3x^2 - 12x + 6
C. 3x^2 - 12x - 6
D. 3x^2 + 12x - 6
Question 3
A cylindrical \tank with a radius of 4m and height of 10m is filled with water. Find the volume of water in the \tank.
A. \( 1600 \pi \text{ m}^3 \ \)
B. \( 3200 \pi \text{ m}^3 \ \)
C. \( 4000 \pi \text{ m}^3 \ \)
D. \( 8000 \pi \text{ m}^3 \ \)
Question 4
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi cm^3
B. 48\pi cm^3
C. 72\pi cm^3
D. 96\pi cm^3
Question 5
Solve the inequality \( \frac{x-2}{x+1} > 0 \) for \( x in \( -infty, -1 \ \) cup \( -1, 2 \) cup (2, infty) ).
A. \( -\infty, -1 \) \cup \( 2, \infty \)
B. \( -\infty, -1 \) \cup \( -1, 2 \) \cup \( 2, \infty \)
C. \( -\infty, -1 \) \cup \( -1, 2 \)
D. \( -\infty, -1 \) \cup \( 2, \infty \)
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) )
B. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) + \frac{1}{2} )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) - \frac{1}{2} )
D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - left\( \frac{1}{2} cdot 0^2 + 3 cdot 0 - 2 \right \) + \frac{1}{2} )
Question 7
A set ( S ) contains the elements ( {1, 2, 3, 4, 5, 6} ). Find the number of subsets of ( S ) that contain exactly three elements.
A. 10
B. 15
C. 20
D. 25
Question 8
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \) u\sing interval notation.
A. \( -infty, -3 \ \) cup \( -3, -1 \) cup (1, infty) )
B. \( -infty, -3 \ \) cup \( -1, 1 \) cup (3, infty) )
C. \( -infty, -3 \ \) cup \( -1, 1 \) cup (3, infty) )
D. \( -infty, -3 \ \) cup \( -1, 1 \) cup (3, infty) )
Question 9
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(5, 6) ).
A. 10
B. 20
C. 30
D. 40
Question 11
Find the area under the curve \( y = x^3 \) from x = 0 to x = 2.
A. 16/5
B. 32/5
C. 64/5
D. 128/5
Question 12
Find the derivative of the function ( f(x) = \frac{x^2 + 3x - 2}{x^2 - 4} ) u\sing the quotient rule.
A. \( \frac{\( x^2 - 4 \)\( 2x + 3 \ \) - \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )
B. \( \frac{\( x^2 - 4 \)\( 2x + 3 \ \) + \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )
C. \( \frac{\( x^2 - 4 \)\( 2x + 3 \ \) - \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )
D. \( \frac{\( x^2 - 4 \)\( 2x + 3 \ \) + \( x^2 + 3x - 2 \)(2x)}{\( x^2 - 4 \)^2} )
Question 13
A company produces x units of a product, where the \cost function is given by ( C(x) = 2x^2 + 5x + 1 ). Find the value of x that minimizes the \cost.
A. 1
B. 2
C. 3
D. 4
Question 14
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 15
Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}.
A. 0
B. 1
C. -1
D. 2

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