POST UTME SUMMIT UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 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
Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).
A. 6
B. 12
C. 18
D. 24
Question 4
In a certain number base, the number 1011 is equivalent to 11 in base 10. What is the value of the number base?
A. 5
B. 6
C. 7
D. 8
Question 5
Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$.
A. $-\frac{2x}{\( x^2 + 1 \)^2}$
B. $\frac{2x}{\( x^2 + 1 \)^2}$
C. $-\frac{2}{\( x^2 + 1 \)^2}$
D. $\frac{2}{\( x^2 + 1 \)^2}$
Question 6
Solve the equation \( x^2 + 5x - 6 = 0 \).
A. -6, 1
B. -3, 2
C. -2, 3
D. -1, 6
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
A circle has a radius of 4 cm. Find the area of the circle.
A. 50 cm²
B. 64 cm²
C. 100 cm²
D. 200 cm²
Question 9
Let \( A = egin{pmatrix} 2 & 1 \ 3 & 4 \end{pmatrix} \) and \( B = egin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \). Find the product ( AB ).
A. \( egin{pmatrix} 5 & 6 \ 12 & 16 \end{pmatrix} \)
B. \( egin{pmatrix} 5 & 8 \ 15 & 20 \end{pmatrix} \)
C. \( egin{pmatrix} 7 & 10 \ 21 & 28 \end{pmatrix} \)
D. \( egin{pmatrix} 9 & 12 \ 27 & 36 \end{pmatrix} \)
Question 10
Find the mean of the data set ( 10, 12, 14, 16, 18 ).
A. 14
B. 16
C. 18
D. 20
Question 11
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 12
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 13
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the prism?
A. 400 cm^3
B. 500 cm^3
C. 600 cm^3
D. 800 cm^3
Question 14
Solve the system of linear equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. \begin{bmatrix} x = 1 \ y = 2 \end{bmatrix}
B. \begin{bmatrix} x = 2 \ y = 1 \end{bmatrix}
C. \begin{bmatrix} x = 3 \ y = 4 \end{bmatrix}
D. \begin{bmatrix} x = 4 \ y = 3 \end{bmatrix}
Question 15
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

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