POST UTME VERITAS UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. 24π cm^3
B. 48π cm^3
C. 64π cm^3
D. 80π cm^3
Question 2
Solve the trigonometric equation \( 2\sin^2 x + 3\cos x - 1 = 0 \) for \( 0 \leq x \leq 2\pi \).
A. \frac{\pi}{6}, \frac{\pi}{2}, \frac{5\pi}{6}
B. \frac{\pi}{6}, \frac{\pi}{4}, \frac{5\pi}{4}
C. \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}
D. \frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}
Question 3
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 4
Solve the equation \( x^2 + 2x - 6 = 0 \) u\sing the quadratic formula.
A. x = 2 \pm \sqrt{7}
B. x = -2 \pm \sqrt{7}
C. x = 2 \pm \sqrt{5}
D. x = -2 \pm \sqrt{5}
Question 5
The mean of a set of numbers is 25. If one of the numbers is increased by 5, the mean becomes 26. How many numbers are in the set?
A. 5
B. 10
C. 15
D. 20
Question 6
Find the volume of the solid formed by revolving the region bounded by the curve [ y = x^2 \] and the line [ y = 2x \] about the x-axis.
A. 4\pi
B. 8\pi
C. 16\pi
D. 32\pi
Question 7
Find the area under the curve \( y = x^2 - 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{4}{3}
B. \frac{5}{3}
C. \frac{6}{3}
D. \frac{7}{3}
Question 8
In the diagram below, the circle with center O passes through points A, B, and C. What is the measure of angle AOC?
A. 60°
B. 90°
C. 120°
D. 150°
Question 9
Find the derivative of the function \( f(x) = \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{1}{\( x^2 + 1 \)^2}
D. \frac{-1}{\( x^2 + 1 \)^2}
Question 10
Solve for ( x ) in the equation \( 2^x = 16 \).
A. 2
B. 3
C. 4
D. 5
Question 11
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 0
C. x = -1
D. x = 1
Question 12
Solve the equation \log_{10} \( x^2 \) = 4.
A. 10^4
B. 10^2
C. 10^8
D. 10^12
Question 13
Find the mean deviation about the median of the data set ( 2, 4, 6, 8, 10 ).
A. 2
B. 3
C. 4
D. 5
Question 14
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 4
B. 6
C. 8
D. 10
Question 15
Determine the value of x in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \).
A. 2
B. 3
C. 4
D. 5

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