POST UTME OSUSTECH 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( 2^x + 2^{-x} = 3 \).
A. x = 1
B. x = -1
C. x = ln(2)
D. x = -ln(2)
Question 2
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. \( int_{0.5}^{1} 2x , dx \)
B. \( int_{0}^{0.5} 2x , dx \)
C. \( int_{0}^{1} 2x , dx \)
D. \( int_{0}^{1} 2x^2 , dx \)
Question 3
Let ( f(x) = \frac{x^2 - 4}{x - 2} ). Find the value of \( lim_{x \to 2} f\( x \ \) ).
A. 1
B. 2
C. 3
D. 4
Question 4
A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, find the probability that a randomly selected score is greater than 90.
A. \( P\( X > 90 \ \) = 0.1587 )
B. \( P\( X > 90 \ \) = 0.8413 )
C. \( P\( X > 90 \ \) = 0.5 )
D. \( P\( X > 90 \ \) = 0.25 )
Question 5
Find the value of \( \log_{10} \( 1000 \ \) ).
A. 3
B. 2
C. 1
D. 0
Question 6
A vector (mathbf{a}) has magnitude 5 and direction \( 30^circ \) counterclockwise from the positive x-axis. Find the vector (mathbf{a} cdot mathbf{b}) if \( mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix} \).
A. ( 11 )
B. ( 13 )
C. ( 15 )
D. ( 17 )
Question 7
A vector ( mathbf{a} ) has magnitude 5 and direction \( 30^circ \) from the positive x-axis. Find the vector ( mathbf{a} ).
A. \( egin{pmatrix} 4 \ 3 \end{pmatrix} \)
B. \( egin{pmatrix} 3 \ 4 \end{pmatrix} \)
C. \( egin{pmatrix} 4 \ -3 \end{pmatrix} \)
D. \( egin{pmatrix} -3 \ 4 \end{pmatrix} \)
Question 8
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x in [0, 2pi] ).
A. \( x = 0, pi, 2pi \)
B. \( x = \frac{pi}{2}, \frac{3pi}{2} \)
C. \( x = 0, \frac{pi}{2}, pi, \frac{3pi}{2}, 2pi \)
D. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)
Question 9
A solid is formed by rotating the region bounded by the curve \( y = x^2 \) and the x-axis about the x-axis. Find the volume of the solid.
A. π/2
B. π
C. 2π
D. 3π
Question 10
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
B. \( x - 3 \)^2 + \( y - 4 \)^2 = 30
C. \( x - 3 \)^2 + \( y - 4 \)^2 = 35
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 40
Question 11
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. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 12
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 13
Find the equation of the circle with center at ((2,3)) and radius 4.
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 32 )
C. \( x-2 \ \)^2 + \( y-3 \)^2 = 64 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 256 )
Question 14
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( -∞,-3 \)∪(1,∞)
B. \( -∞,-3 \)∪\( -3,1 \)
C. \( -∞,-3 \)∪(1,3)
D. \( -∞,3 \)∪(3,∞)
Question 15
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \( V = \frac{8}{15} pi \)
B. \( V = \frac{8}{3} pi \)
C. \( V = \frac{4}{3} pi \)
D. \( V = \frac{16}{5} pi \)

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