POST UTME OAU 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...
A. 124
B. 126
C. 128
D. 130
Question 2
Solve the inequality $|x-2|>3$.
A. \( -\infty,-1)\cup\( 5,\infty \ \)
B. \( -\infty,1)\cup\( 5,\infty \ \)
C. \( -\infty,1)\cup\( 2,5 \ \)
D. \( -\infty,5)\cup\( 2,\infty \ \)
Question 3
Find the value of $\frac{d}{dx}\left\( \frac{1}{x^2}\right \)$.
A. -\frac{2}{x^3}
B. \frac{2}{x^3}
C. -\frac{1}{x^3}
D. \frac{1}{x^3}
Question 4
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. \( \frac{pi}{4} \)
B. \( \frac{3pi}{4} \)
C. \( \frac{5pi}{4} \)
D. \( \frac{7pi}{4} \)
Question 5
Solve the system of equations \( egin{cases} x + y = 2 \ x - y = 1 \end{cases} \).
A. x = 1, y = 1
B. x = 1, y = 2
C. x = 2, y = 1
D. x = 2, y = 2
Question 6
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 7
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
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 8
Find the value of $\frac{d}{dx}\left\( \frac{x^2}{x^2+1}\right \)$.
A. \frac{2x}{\( x^2+1 \)^2}
B. -\frac{2x}{\( x^2+1 \)^2}
C. \frac{2x^3}{\( x^2+1 \)^2}
D. -\frac{2x^3}{\( x^2+1 \)^2}
Question 9
Find the derivative of ( f(x) = x^3 - 2x^2 + 3x - 1 ) u\sing the power rule.
A. ( f'(x) = 3x^2 - 4x + 3 )
B. ( f'(x) = x^2 - 2x + 3 )
C. ( f'(x) = 3x^2 - 4x - 3 )
D. ( f'(x) = x^2 - 2x - 3 )
Question 10
Determine the sum of the infinite geometric series ∫_{n=1}^{infty} \frac{1}{2^{n-1}}
A. 1
B. 2
C. 3
D. 4
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x < -1 \) or \( x > \frac{3}{2} \)
Question 12
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in \( -infty, -2 \ \) cup \( -2, infty \) ).
A. \( -2, -1 \) ∪ (1, ∞)
B. \( -∞, -2 \) ∪ (2, ∞)
C. \( -∞, -2 \) ∪ \( -2, 1 \)
D. \( -∞, -1 \) ∪ (1, ∞)
Question 13
Find the equation of the circle with center \( -2,3 \) and radius 4.
A. \( x+2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-2 \ \)^2 + \( y+3 \)^2 = 16 )
C. \( x+2 \ \)^2 + \( y+3 \)^2 = 16 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x > \frac{3}{2} \)
C. \( x < -\frac{1}{2} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 15
Determine the value of x in the equation \frac{x}{x+1} = \frac{2}{3}
A. \frac{2}{5}
B. \frac{3}{5}
C. \frac{4}{5}
D. \frac{5}{6}

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