POST UTME IMS U 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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
Question 2
Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).
A. x > 10
B. x < 10
C. x > 100
D. x < 100
Question 3
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 4
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 5
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 6
A car travels from city A to city B at an average speed of 60km/h and returns at an average speed of 40km/h. If the dis\tance between the two cities is 240km, find the average speed for the round trip.
A. \( 48 \text{ km/h} \ \)
B. \( 50 \text{ km/h} \ \)
C. \( 52 \text{ km/h} \ \)
D. \( 55 \text{ km/h} \ \)
Question 7
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 8
Solve the inequality \frac{x^2 - 4x + 3}{x^2 - 2x - 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 9
Find the value of ( x ) in the equation \( 2^x + 2^{x+1} = 2^{x+2} + 2^{x+3} \).
A. -3
B. -2
C. -1
D. 0
Question 10
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 11
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. \( 2 \sin x \cos x \)
B. \( \cos^2 x \)
C. \( \sin^2 x \)
D. \( \cos^2 x - \sin^2 x \)
Question 12
A histogram of exam scores is shown below. What is the mean score?
A. 60
B. 70
C. 80
D. 90
Question 13
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
Question 14
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 15
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y = 2x - 1 \ \)
B. \( y = 2x + 1 \ \)
C. \( y = x + 2 \ \)
D. \( y = x - 2 \ \)

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