POST UTME BOWEN UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( x^3 - 2x^2 - 5x + 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 2
A line passes through the points (2, 3) and (4, 5). Find the equation of the line.
A. y = 1x + 1
B. y = 2x + 1
C. y = 3x + 1
D. y = 4x + 1
Question 3
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 4
A circle has a radius of 4 cm. If a chord of the circle is 6 cm long, what is the angle subt\ended by the chord at the center of the circle?
A. \( \theta = \frac{1}{2} \sin^{-1} \frac{3}{4} \)
B. \( \theta = \frac{1}{2} \sin^{-1} \frac{1}{2} \)
C. \( \theta = \frac{1}{2} \sin^{-1} \frac{3}{5} \)
D. \( \theta = \frac{1}{2} \sin^{-1} \frac{2}{3} \)
Question 5
Solve for ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = \frac{\pi}{4}
B. x = \frac{\pi}{2}
C. x = \frac{3\pi}{4}
D. x = \frac{5\pi}{4}
Question 6
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 7
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. -\frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2x}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 8
Solve the inequality \( \frac{x+2}{x-1} > 0 \) for \( x in \( -infty, infty \ \) ).
A. \( x < -2 \) or \( x > 1 \)
B. \( x < -2 \) or \( x < 1 \)
C. \( x > -2 \) or \( x > 1 \)
D. \( x > -2 \) or \( x < 1 \)
Question 9
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing the method of integration.
A. \( \frac{64}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{16}{3} \)
D. \( \frac{8}{3} \)
Question 10
Determine the sum of the first 5 terms of the geometric series \( 2x + 4x^2 + 8x^3 + \ldots \).
A. 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5
B. 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 + 64x^6
C. 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 + 64x^6 + 128x^7
D. 2x + 4x^2 + 8x^3 + 16x^4 + 32x^5 + 64x^6 + 128x^7 + 256x^8
Question 11
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 12
A particle moves in a straight line with a velocity given by ( v(t) = 2t + 5 ). Find the displacement of the particle from \( t = 0 \) to \( t = 3 \).
A. ( 27 )
B. ( 30 )
C. ( 33 )
D. ( 36 )
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 14
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. \( V = \frac{\pi}{3} \)
B. \( V = \frac{\pi}{2} \)
C. \( V = \frac{\pi}{4} \)
D. \( V = \frac{\pi}{6} \)
Question 15
Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 4) ).
A. 6
B. 12
C. 18
D. 24

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