POST UTME MOUNTAIN TOP UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In the triangle ABC, angle A = 30°, angle B = 60°, and side AB = 6 cm. Find the length of side AC.
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Question 2
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 3
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].
A. 1
B. -1
C. 2
D. 3
Question 4
Find the derivative of ( f(x) = x^2 \sin x ) u\sing the product rule.
A. x^2 \cos x + 2x \sin x
B. x^2 \cos x - 2x \sin x
C. x^2 \cos x + 2x \sin x
D. x^2 \cos x - 2x \sin x
Question 5
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. 2
C. -1
D. 1
Question 6
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 7
Find the derivative of ( f(x) = \sin (2x) ) u\sing the chain rule.
A. 2 \cos (2x)
B. 2 \sin (2x)
C. 2 \cos (2x)
D. 2 \sin (2x)
Question 8
Solve the trigonometric equation \sin^2 x + \cos^2 x = 1.
A. x = \frac{\pi}{2}
B. x = \frac{\pi}{4}
C. x = \frac{3\pi}{4}
D. x = \frac{5\pi}{4}
Question 9
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < -1 or x < 3/2
D. x > -1 or x > 3/2
Question 10
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 11
Solve the equation \( 2^x + 3^x = 5^x \) for ( x ).
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 12
Let \( S = \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of ( S ) that contain exactly 3 elements.
A. 5
B. 10
C. 15
D. 20
Question 13
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 14
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. \( x > 3 \ \)
B. \( x < 3 \ \)
C. \( x = 3 \ \)
D. \( x = 2 \ \)
Question 15
Solve the equation \frac{x^2 - 4}{x + 2} = 2.
A. x = 0
B. x = 2
C. x = -2
D. x = 4

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