POST UTME OSUSTECH 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm and upper base radius 2cm.
A. 24π
B. 48π
C. 96π
D. 192π
Question 2
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 3
A number is 5 more than the square of a number. If the number is 11, find the original number.
A. 4
B. 6
C. 8
D. 10
Question 4
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the lowest score is 40, find the highest score.
A. 85
B. 90
C. 95
D. 100
Question 5
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 6
Determine the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. \( 2\( 3^{10}-1 \ \)/\( 3-1 \) )
B. \( 2\( 3^{10}+1 \ \)/\( 3+1 \) )
C. \( 2\( 3^{10}-1 \ \)/\( 3+1 \) )
D. \( 2\( 3^{10}+1 \ \)/\( 3-1 \) )
Question 7
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. \( V = \frac{16}{5} pi \)
Question 8
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 9
Find the value of x in the equation \( \frac{1}{x} + \frac{1}{2x} = \frac{3}{4x} \).
A. 4
B. 2
C. 1
D. 0.5
Question 10
Solve for x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^x \).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 11
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for ( x in mathbb{R} ).
A. \( -infty, -2 \ \) cup (2, infty) )
B. \( -infty, -2 \ \) cup \( -2, 2 \) cup (2, infty) )
C. \( -infty, -2 \ \) cup (2, infty) )
D. \( -infty, -2 \ \) cup \( -2, 2 \) )
Question 12
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{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 13
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 14
A curve is defined by the equation \( y = x^2 - 4x + 3 \). Find the x-coordinate of the vertex of the curve.
A. 2
B. 3
C. 4
D. 5
Question 15
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 )

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: