POST UTME BOWEN UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
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 4
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 5
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 6
Find the derivative of the function ( f(x) = \sin^2(x) ) u\sing the chain rule.
A. ( f'(x) = 2\sin\( x)\cos(x \) )
B. ( f'(x) = \sin(x) + \cos(x) )
C. ( f'(x) = 2\sin^2(x) )
D. ( f'(x) = \cos^2(x) )
Question 7
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 8
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 9
Solve the equation \( x^3 - 2x^2 - 5x + 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 10
A polynomial function is defined as ( p(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( p(2) ).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 11
Solve for x in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)
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
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
Question 14
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
Question 15
A solid cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.
A. ( 800pi ) cm³
B. ( 1000pi ) cm³
C. ( 1200pi ) cm³
D. ( 1600pi ) cm³

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