POST UTME AFE BABALOLA UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + \cdots \).
A. 31x^5 + 30x^4 + 29x^3 + 28x^2 + 27x
B. 31x^5 + 30x^4 + 29x^3 + 28x^2 + 27
C. 31x^5 + 30x^4 + 29x^3 + 28x^2 + 27x + 26
D. 31x^5 + 30x^4 + 29x^3 + 28x^2 + 27x + 26x^2
Question 2
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
B. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
C. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
D. ( f'(x) = \frac{\( x^2 - 4 \)\( 2x + 2 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2} )
Question 3
A set of 5 points is defined by the equation \( x-2 \ \)^2 + \( y-3 \)^2 = 4 ). Find the dis\tance between the points ( (1, 2) ) and ( (3, 4) ).
A. √2
B. √5
C. √10
D. √15
Question 4
If f(x) = 2x^2 + 3x - 1 and g(x) = x^2 - 2x + 1, find the derivative of f(g(x))
A. \( 4x - 3 \)\( x^2 - 2x + 1 \)
B. 4x^3 - 6x^2 + 3x - 1
C. 2x^2 + 3x - 1
D. x^2 - 2x + 1
Question 5
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. 2 < x < 4
B. x > 4
C. x < 2
D. x = 4
Question 6
Find the surface area of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. 64\pi/5
B. 128\pi/5
C. 256\pi/5
D. 512\pi/5
Question 7
Find the value of \( \sin\( 2x \ \) ) given that \( \sin\( x \ \) = \frac{1}{2} ) and \( \cos\( x \ \) = \frac{\sqrt{3}}{2} ).
A. \( \frac{\sqrt{3}}{2} \)
B. \( \frac{1}{2} \)
C. \( \frac{\sqrt{3}}{2} \)
D. \( \frac{1}{2} \)
Question 8
Solve for x in the equation \( \sqrt[3]{x^2} = 4 \).
A. 64
B. 16
C. 256
D. 1024
Question 9
Find the equation of the circle with center ( (1, 2) ) and radius 3.
A. \( x - 1 \)^2 + \( y - 2 \)^2 = 9
B. \( x + 1 \)^2 + \( y - 2 \)^2 = 9
C. \( x - 1 \)^2 + \( y + 2 \)^2 = 9
D. \( x + 1 \)^2 + \( y + 2 \)^2 = 9
Question 10
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
B. \( x > \frac{3}{2} \) or \( x < -\frac{5}{4} \)
C. \( x > -\frac{5}{4} \) and \( x < \frac{3}{2} \)
D. \( x < -\frac{5}{4} \) and \( x > \frac{3}{2} \)
Question 11
Find the sum of the first 10 terms of the arithmetic series 2x + 3x^2 + 4x^3 + ...
A. 1040x^10
B. 1050x^10
C. 1060x^10
D. 1070x^10
Question 12
A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the probability that X is greater than 2.
A. 1/2
B. 1/4
C. 1/8
D. 3/4
Question 13
Find the value of \( \cos\( 2x \ \) ) given that \( \sin\( x \ \) = \frac{1}{2} ) and \( \cos\( x \ \) = \frac{\sqrt{3}}{2} ).
A. \( -\frac{1}{2} \)
B. \( \frac{1}{2} \)
C. \( \frac{\sqrt{3}}{2} \)
D. \( -\frac{\sqrt{3}}{2} \)
Question 14
A right circular cone has a height of 12 cm and a base radius of 6 cm. Find the volume of the cone.
A. 288\pi
B. 288\pi/3
C. 288\pi/2
D. 288\pi/5
Question 15
Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \) u\sing matrices.
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 0 \)
C. \( x = 0, y = 2 \)
D. \( x = 1, y = 2 \)

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