POST UTME MOUNTAIN TOP UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x - 5 > 3x + 2 \).
A. x < -3
B. x > -3
C. x < 3
D. x > 3
Question 2
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. \( x > 3 \ \)
B. \( x < 3 \ \)
C. \( x = 3 \ \)
D. \( x = 2 \ \)
Question 3
Find the sum of the first 5 terms of the geometric progression ( 2, 6, 18, 54, ... ).
A. 120
B. 130
C. 140
D. 150
Question 4
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{2}
B. x = \frac{\pi}{4}
C. x = \frac{\pi}{6}
D. x = \frac{\pi}{8}
Question 5
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \( x = 1, y = 2 \ \)
B. \( x = 2, y = 1 \ \)
C. \( x = 3, y = 4 \ \)
D. \( x = 4, y = 3 \ \)
Question 6
Solve the system of equations \( x + y = 4 \) and \( x - y = 2 \).
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 7
The mean of a set of numbers is 15. If the mean of a subset of these numbers is 20, what is the mean of the remaining numbers?
A. 10
B. 12
C. 15
D. 18
Question 8
Solve for x in the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 9
Solve the system of equations \( \begin{cases} x + y = 4 \ x - 2y = -2 \end{cases} \).
A. \( x = 2, y = 2 \ \)
B. \( x = 3, y = 1 \ \)
C. \( x = 1, y = 3 \ \)
D. \( x = 4, y = 0 \ \)
Question 10
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the derivative of ( f(x) ) u\sing the quotient rule.
A. \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2}
B. \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2}
C. \frac{2x\( x - 2 \) - \( x^2 - 4 \)}{\( x - 2 \)^2}
D. \frac{2x\( x - 2 \) + \( x^2 - 4 \)}{\( x - 2 \)^2}
Question 11
Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 1 \end{bmatrix}.
A. 0
B. 2
C. 4
D. 6
Question 12
Solve the equation \frac{x^2 - 4}{x + 2} = 2.
A. x = 0
B. x = 2
C. x = -2
D. x = 4
Question 13
Find the sum of the first 10 terms of the geometric series 2 + 6 + 18 + ...
A. 3120
B. 3240
C. 3360
D. 3480
Question 14
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = x \) about the x-axis.
A. \( \frac{\pi}{12} \ \)
B. \( \frac{\pi}{6} \ \)
C. \( \frac{\pi}{4} \ \)
D. \( \frac{\pi}{2} \ \)
Question 15
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)

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