POST UTME CRAWFORD UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < -3/2 or x > 1
C. x < 1 or x > -3/2
D. x < -3/2 or x < 1
Question 2
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 3
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} x = 2 \).
A. 2
B. 4
C. 6
D. 8
Question 4
Solve the system of equations u\sing matrices:\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \)
A. \( egin{bmatrix} 1 \ 2 \end{bmatrix} \)
B. \( egin{bmatrix} -1 \ 1 \end{bmatrix} \)
C. \( egin{bmatrix} 2 \ -1 \end{bmatrix} \)
D. \( egin{bmatrix} -2 \ 1 \end{bmatrix} \)
Question 5
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{-x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{x}{\( x^2 + 1 \)^2} )
Question 6
Find the area of the triangle with vertices (0, 0), (4, 0), and (0, 3).
A. 6
B. 8
C. 10
D. 12
Question 7
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm and upper base radius 2cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3
Question 8
A company produces 200 units of a product per day. If the production \cost is $150 per unit, what is the total \cost of producing 500 units?
A. ₦75,000
B. ₦80,000
C. ₦85,000
D. ₦90,000
Question 9
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = 0
C. x = -1 or x = -3
D. x = 2 or x = -2
Question 10
Find the mean and s\tandard deviation of the data set $\{2, 4, 6, 8, 10\}$.
A. \bar{x} = 6, \sigma = 2
B. \bar{x} = 6, \sigma = 4
C. \bar{x} = 6, \sigma = 6
D. \bar{x} = 6, \sigma = 8
Question 11
A box contains 5 red balls and 3 blue balls. If 2 balls are drawn at random, what is the probability that both balls are blue?
A. 1/7
B. 1/10
C. 1/14
D. 1/21
Question 12
The equation of a circle is \( x^2 + y^2 - 4x + 6y + 9 = 0 \). Find the coordinates of the center of the circle.
A. \( -2, -3 \)
B. \( -1, -2 \)
C. (2, 3)
D. (1, 2)
Question 13
In the number base $8$, what is the value of the expression $[5]_8 + [7]_8$?
A. 12
B. 14
C. 16
D. 18
Question 14
Solve the system of equations \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 15
A set of exam scores has a mean of 80 and a s\tandard deviation of 10. Find the z-score of a score of 90.
A. 0.5
B. 1
C. 1.5
D. 2

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