POST UTME SUMMIT UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the mean of the data set ( 10, 12, 14, 16, 18 ).
A. 14
B. 16
C. 18
D. 20
Question 2
The volume of a rec\tangular prism is given by V = lwh. If the length is tripled, the width is doubled, and the height is halved, what is the new volume?
A. \( l/2 \)\( w/3 \)\( h/3 \)
B. (3l)\( 2w)\( h/2 \ \)
C. (3l)\( 2w)\( h/2 \ \)
D. \( l/3 \)\( w/2 \)\( h/6 \)
Question 3
Solve for x in the equation: 2^x + 5^x = 10^x.
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 4
Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = x \) about the x-axis.
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
Question 5
Solve the system of equations $\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}$.
A. $x = 1, y = 2$
B. $x = 2, y = 1$
C. $x = -1, y = 3$
D. $x = 3, y = -1$
Question 6
A vector α has magnitude 5 and direction 60°. A vector β has magnitude 3 and direction 120°. Find the magnitude of the sum of α and β.
A. 4
B. 5
C. 6
D. 7
Question 7
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 9
Find the sum of the first $n$ terms of the geometric series $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$.
A. 1 - \frac{1}{2^n}
B. 1 - \frac{1}{2^{n+1}}
C. 1 + \frac{1}{2^n}
D. 1 + \frac{1}{2^{n+1}}
Question 10
Let ( X ) and ( Y ) be indep\endent random variables with probability density functions \( f_X\( x \ \) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ) and \( f_Y\( y \ \) = egin{cases} 3y^2 & 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that \( X + Y leq 1 \).
A. \( \frac{5}{24} \)
B. \( \frac{1}{6} \)
C. \( \frac{1}{4} \)
D. \( \frac{5}{12} \)
Question 11
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{2}
B. \frac{2}{5}
C. \frac{3}{5}
D. \frac{4}{5}
Question 12
A survey of 100 students found that 60 students preferred coffee, 30 students preferred tea, and 10 students preferred both. What is the probability that a randomly selected student prefers coffee or tea?
A. 0.7
B. 0.75
C. 0.8
D. 0.85
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 16
B. 32
C. 64
D. 128
Question 14
Determine the value of $x$ in the equation $left\( \frac{1}{2} \right \)^x = \frac{1}{64}$.
A. 2
B. 3
C. 4
D. 5
Question 15
A histogram is constructed with 5 classes of equal width. The class boundaries are 0, 10, 20, 30, and 40. The frequencies of the classes are 3, 5, 8, 10, and 7 respectively. Find the mean of the data.
A. 20
B. 22
C. 24
D. 26

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