POST UTME CRAWFORD UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for y in the equation \( y = \frac{1}{2} \tan^{-1} \left\( \frac{2x}{1-x^2} \right \ \) ).
A. \frac{1}{2} \tan^{-1} (2x)
B. \frac{1}{2} \tan^{-1} \left\( \frac{2x}{1-x^2} \right \)
C. \tan^{-1} (2x)
D. \tan^{-1} \left\( \frac{2x}{1-x^2} \right \)
Question 2
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \( \frac{2}{3} \)
B. \( \frac{3}{4} \)
C. \( \frac{4}{5} \)
D. \( \frac{5}{6} \)
Question 3
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 4
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{6}
B. \frac{2}{6}
C. \frac{3}{6}
D. \frac{4}{6}
Question 5
Solve the inequality \( x^2 - 4x - 5 > 0 \).
A. \( -∞, -1 \) ∪ (5, ∞)
B. \( -∞, -5 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (5, ∞)
D. \( -∞, -5 \) ∪ (1, ∞)
Question 6
Find the volume of the frustum of the cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64π cm³
B. 128π cm³
C. 256π cm³
D. 512π cm³
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \left\( \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \ \) - \left\( \frac{1}{2} \cdot 0^2 + 3 \cdot 0 - 2 \right \)
B. \( \frac{1}{2} \left\( \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \ \) + \left\( \frac{1}{2} \cdot 0^2 + 3 \cdot 0 - 2 \right \)
C. \( \frac{1}{2} \left\( \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \ \)
D. \( \frac{1}{2} \left\( \frac{4^3}{3} + 3 \cdot 4^2 - 2 \cdot 4 \right \ \) + 2 \)
Question 8
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 9
Solve the inequality \( \frac{1}{x+1} + \frac{1}{x-1} \geq \frac{1}{2} \ \).
A. \( x \leq -1 \ \) or \( x \geq 1 \ \)
B. \( x > -1 \ \) and \( x < 1 \ \)
C. \( x < -1 \ \) or \( x > 1 \ \)
D. \( x \geq -1 \ \) and \( x \leq 1 \ \)
Question 10
A vector [ mathbf{a} = egin{bmatrix} 2 \ 3 \ 4 \end{bmatrix} ] is rotated by 90° about the x-axis. Find the new vector [ mathbf{a}' ].
A. [ egin{bmatrix} 2 \ -3 \ 4 \end{bmatrix} ]
B. [ egin{bmatrix} 2 \ 3 \ -4 \end{bmatrix} ]
C. [ egin{bmatrix} 2 \ 4 \ 3 \end{bmatrix} ]
D. [ egin{bmatrix} 2 \ -4 \ 3 \end{bmatrix} ]
Question 11
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 = 20
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 12
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 8
Question 12
Solve for x in the equation \( 2^x = 16 \).
A. \( x = 2 \)
B. \( x = 4 \)
C. \( x = 8 \)
D. \( x = 16 \)
Question 13
Solve for x in the equation \frac{1}{2} \log_{10} x^2 = 3.
A. \boxed{x = 1000}
B. x = 100
C. x = 10
D. x = 1
Question 14
A population of bacteria doubles every 2 hours. If there are initially 100 bacteria, how many bacteria will there be after 6 hours?
A. 1000
B. 2000
C. 4000
D. 8000
Question 15
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = π/2
C. x = π
D. x = 2π

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