POST UTME SUMMIT UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 256\pi \text{ cm}^3
B. 512\pi \text{ cm}^3
C. 768\pi \text{ cm}^3
D. 1024\pi \text{ cm}^3
Question 2
Given the vectors \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \), find the magnitude of the vector \( mathbf{a} + mathbf{b} \).
A. 5
B. 6
C. 7
D. 8
Question 3
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. x < -3/2 or x > 1
B. x < -1 or x > 3
C. x < 1 or x > 3
D. x < -3/2 or x < 1
Question 4
Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.
A. 1
B. -1
C. -2
D. 2
Question 5
Find the volume of the solid formed by revolving the region bounded by y = x^2, x = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 6
In the number system with base 8, what is the value of the expression \( 5 \times 8^2 + 3 \times 8^1 + 2 \times 8^0 \)?
A. 42
B. 48
C. 52
D. 58
Question 7
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{-2x}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 8
A vector is defined as: \vec{a} = 3\hat{i} + 4\hat{j}. Find the magnitude of the vector.
A. 5
B. 10
C. 15
D. 20
Question 9
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the co\sine rule.
A. 8 cm
B. 12 cm
C. 16 cm
D. 20 cm
Question 10
A solid cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone.
A. 32π cm³
B. 64π cm³
C. 128π cm³
D. 256π cm³
Question 11
Evaluate the definite integral \int_{0}^{1} x^2 dx.
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{4}
Question 12
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \frac{1}{3}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{4}{5}
Question 13
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{3}
Question 14
Find the value of \( \sin\( 2\theta \ \) ) given that \( \sin\( \theta \ \) = \frac{3}{5} ) and \( \cos\( \theta \ \) = \frac{4}{5} ).
A. \frac{24}{25}
B. \frac{16}{25}
C. \frac{20}{25}
D. \frac{12}{25}
Question 15
Solve for x in the equation \( \tan^2 x + 2 \tan x - 6 = 0 \).
A. x = -2π/3, x = π/3
B. x = 2π/3, x = -π/3
C. x = π/3, x = -π/3
D. x = 2π/3, x = π/3

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