POST UTME SUMMIT UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A cylindrical \tank with a radius of 7m and a height of 10m is filled with water. If the water level is raised by 2m, what is the increase in the volume of water in the \tank?
A. 140\pi m^3
B. 280\pi m^3
C. 420\pi m^3
D. 560\pi m^3
Question 2
Solve the inequality [ 2x^2 + 5x - 3 \geq 0 \].
A. x \leq -1 \text{ or } x \geq \frac{3}{2}
B. x \leq -1 \text{ or } x \leq \frac{3}{2}
C. x \geq -1 \text{ or } x \geq \frac{3}{2}
D. x \geq -1 \text{ or } x \leq \frac{3}{2}
Question 3
Find the equation of the circle with center at ((2, 3)) and radius 4.
A. \boxed{\( x - 2 \)^2 + \( y - 3 \)^2 = 16}
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
Question 4
A random experiment consists of rolling two fair six-sided dice. If the sum of the numbers on the dice is even, the outcome is a success. Find the probability of success.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 5
A histogram is constructed from the following data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. Find the mean of the data.
A. 9
B. 10
C. 11
D. 12
Question 6
A circle has a radius of 5cm. What is the area of the circle?
A. 25\pi cm^2
B. 50\pi cm^2
C. 75\pi cm^2
D. 100\pi cm^2
Question 7
Find the volume of the frustum of a cone with height 6 cm, and radii of the top and bottom bases 3 cm and 6 cm respectively.
A. 36\pi
B. 72\pi
C. 108\pi
D. 144\pi
Question 8
Find the derivative of the function (f(x) = \frac{x^2}{x^2 + 1}).
A. \boxed{\frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2}}
B. \frac{2x^2 - 2x^3}{\( x^2 + 1 \)^2}
C. \frac{2x^3 - 2x^2}{\( x^2 + 1 \)^2}
D. \frac{2x^2 + 2x^3}{\( x^2 + 1 \)^2}
Question 9
A set S is defined as follows: S = {x | x is a positive integer and x < 10}. Find the value of \bigcup_{n=1}^{10} S_n, where S_n = {x | x is a positive integer and x < n}.
A. {1, 2, 3, 4, 5, 6, 7, 8, 9}
B. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C. {1, 2, 3, 4, 5, 6, 7, 8}
D. {1, 2, 3, 4, 5, 6}
Question 10
A sequence is defined as follows: a_1 = 2, a_n = 3a_{n-1} for n > 1. Find the value of a_{10}.
A. 2
B. 3
C. 6
D. 9
Question 11
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 3, with a_1 = 2. Find the value of a_5.
A. 47
B. 49
C. 51
D. 53
Question 12
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. f'(x) = -\frac{1}{2x^{3/2}}
B. f'(x) = \frac{1}{2x^{3/2}}
C. f'(x) = \frac{1}{x^{3/2}}
D. f'(x) = -\frac{1}{x^{3/2}}
Question 13
Find the area of the region bounded by the parabola y = x^2, the line y = 4, and the x-axis.
A. 16
B. 32
C. 48
D. 64
Question 14
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \boxed{\( -3, -1 \) \cup (1, 3)}
B. \( -3, 1 \)
C. \( -1, 3 \)
D. \( -3, 3 \)
Question 15
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{7}{8}

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