POST UTME CRAWFORD UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \frac{x^2 - 4}{x^2 + 4} > 0.
A. \( -\infty, -2 \) \cup \( -2, 2 \) \cup \( 2, \infty \)
B. \( -\infty, -2 \) \cup \( 2, \infty \)
C. \( -2, 2 \)
D. \( -\infty, 2 \) \cup \( 2, \infty \)
Question 2
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. \frac{x}{\( x^2 + 1 \)^{3/2}}
C. \frac{1}{\( x^2 + 1 \)^{3/2}}
D. \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 3
Solve the equation \( 2 \sin^2 x + 3 \sin x - 2 = 0 \).
A. \( \sin x = -1 \) or \( \sin x = \frac{2}{3} \)
B. \( \sin x = 1 \) or \( \sin x = -\frac{2}{3} \)
C. \( \sin x = -\frac{1}{2} \) or \( \sin x = \frac{2}{3} \)
D. \( \sin x = \frac{1}{2} \) or \( \sin x = -\frac{2}{3} \)
Question 4
Solve the inequality \( |x - 2| geq 3 \).
A. \( x leq -1 \) or ( x geq 5 )
B. ( x leq 1 ) or ( x geq 5 )
C. \( x leq -1 \) or ( x geq 4 )
D. ( x leq 0 ) or ( x geq 4 )
Question 5
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10
B. 100
C. 1000
D. 10000
Question 6
Solve for ( x ) in the equation \( 2x - 5 = 3x + 2 \).
A. -7
B. -5
C. 1
D. 3
Question 7
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi
B. 64\pi
C. 80\pi
D. 96\pi
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 9
Find the derivative of the function (f(x) = \frac{1}{x^2 + 1}).
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 10
Determine the value of x in the equation \( \sin^2 x + \cos^2 x = 1 \) if \( \sin x = \frac{3}{5} \).
A. \( \frac{\sqrt{16}}{5} \)
B. \( \frac{\sqrt{9}}{5} \)
C. \( \frac{\sqrt{25}}{5} \)
D. \( \frac{\sqrt{36}}{5} \)
Question 11
Solve for x in the equation \( 2^x + 2^x = 2^{x+1} \).
A. x = 1
B. x = 2
C. x = 3
D. x = 4
Question 12
Find the area under the curve y = 2x^2 from x = 0 to x = 2.
A. 8
B. 16
C. 24
D. 32
Question 13
Find the area of the triangle with vertices (A(1, 2)), (B(3, 4)), and (C(2, 1)).
A. ( 5 )
B. ( 10 )
C. ( 15 )
D. ( 20 )
Question 14
Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).
A. 10^4
B. 10^8
C. 10^12
D. 10^16
Question 15
A circle has a radius of 5 cm. Find the area of the circle.
A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi

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