POST UTME SUMMIT UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < -1 or x > \frac{3}{2}
B. x < -1 or x < \frac{3}{2}
C. x > -1 or x > \frac{3}{2}
D. x > -1 or x < \frac{3}{2}
Question 4
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 5
Solve for x in the equation \(\log_{2}(x) + \log_{2}\( x-1 \) = 3\).
A. 8
B. 9
C. 10
D. 11
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 sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + \cdots \).
A. \frac{2x\( 1 - x^5 \)}{1 - x}
B. \frac{2x\( 1 - x^5 \)}{1 + x}
C. \frac{2x\( 1 - x^5 \)}{1 - x^2}
D. \frac{2x\( 1 - x^5 \)}{1 + x^2}
Question 8
In the complex plane, the points $z_1 = 2 + 3i$ and $z_2 = 4 - 5i$ are represented by vectors $mathbf{z}_1$ and $mathbf{z}_2$. If $z_3 = z_1 + z_2$, find the magnitude of $z_3$.
A. \sqrt{10}
B. \sqrt{11}
C. \sqrt{12}
D. \sqrt{13}
Question 9
A geometric sequence is defined as follows: a_1 = 2, r = 2. Find the value of a_{10}.
A. 1024
B. 512
C. 256
D. 128
Question 10
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 11
Solve the equation [ \frac{\tan x}{1 - \tan x} = \frac{1}{3} \] for [ 0 \leq x \leq \frac{\pi}{2} \].
A. \frac{\pi}{6}
B. \frac{\pi}{3}
C. \frac{\pi}{4}
D. \frac{\pi}{2}
Question 12
A sequence is defined as $a_n = 2n + 1$. Find the sum of the first 10 terms of the sequence.
A. 210
B. 220
C. 230
D. 240
Question 13
A binary operation \( \ast \) is defined as \( a \ast b = a^2 + b^2 \). Find the value of \( 2 \ast 3 \).
A. 13
B. 14
C. 15
D. 16
Question 14
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \boxed{\frac{1}{3}}
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{1}{6}
Question 15
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}

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