POST UTME IMS U 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. \( x = 1, y = 1 \)
B. \( x = 1, y = -1 \)
C. \( x = -1, y = 1 \)
D. \( x = -1, y = -1 \)
Question 2
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^4 + 8x^6 + ldots \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 3
Find the value of ( x ) in the equation \( \sin^2 x + \cos^2 x = 1 \).
A. \frac{\pi}{4}
B. \frac{3\pi}{4}
C. \frac{5\pi}{4}
D. \frac{7\pi}{4}
Question 4
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = x + 2 \)
D. \( y = x - 2 \)
Question 5
Find the sum of the first 10 terms of the geometric sequence ( 2, 6, 18, 54, ... ).
A. ( 10494 )
B. ( 10496 )
C. ( 10498 )
D. ( 10500 )
Question 6
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \frac{-1}{2x^{3/2}}
B. \frac{1}{2x^{3/2}}
C. \frac{1}{x^{3/2}}
D. \frac{-1}{x^{3/2}}
Question 7
Find the sum of the first 5 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = \frac{1}{2} \).
A. \frac{31}{16}
B. \frac{63}{32}
C. \frac{127}{64}
D. \frac{255}{128}
Question 8
Find the derivative of $f(x) = \frac{1}{x^2+1}$.
A. -\frac{2x}{\( x^2+1 \)^2}
B. \frac{2x}{\( x^2+1 \)^2}
C. -\frac{2}{\( x^2+1 \)^2}
D. \frac{2}{\( x^2+1 \)^2}
Question 9
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. \( x = -10 \)
B. \( x = 3 \)
C. \( x = -3 \)
D. \( x = 10 \)
Question 10
In the circuit below, if the voltage across the 2 Ω resistor is 12 V, what is the current through the 4 Ω resistor?
A. 1 A
B. 2 A
C. 3 A
D. 4 A
Question 11
Solve the inequality $\frac{x^2-4}{x^2-9} > 0$.
A. \( -3,-2 \) \cup (2,3)
B. \( -3,-2 \) \cup \( 2,\infty \)
C. \( -\infty,-3 \) \cup \( -2,2 \) \cup \( 3,\infty \)
D. \( -\infty,-3 \) \cup \( -2,2 \) \cup \( 3,\infty \)
Question 12
Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2 x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{3}
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( -\frac{5}{4}, \frac{3}{2} \right \)
B. \left\( -\frac{3}{2}, \frac{5}{4} \right \)
C. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{5}{4}, \infty \right \)
D. \left\( -\infty, \frac{5}{4} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
Question 14
Find the derivative of the function ( f(x) = x^2 \sin x ) u\sing the product rule.
A. x^2 \cos x + 2x \sin x
B. x^2 \cos x - 2x \sin x
C. x^2 \sin x + 2x \cos x
D. x^2 \sin x - 2x \cos x
Question 15
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}} )

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