POST UTME FUTO 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector ( mathbf{a} ) has a magnitude of 5 and makes an angle of 60° with the positive x-axis. Find the unit vector in the direction of ( mathbf{a} ).
A. \begin{pmatrix} 0.5 \ 0.866 \end{pmatrix}
B. \begin{pmatrix} 0.866 \ 0.5 \end{pmatrix}
C. \begin{pmatrix} 0.5 \ -0.866 \end{pmatrix}
D. \begin{pmatrix} -0.866 \ 0.5 \end{pmatrix}
Question 2
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the chain rule.
A. 6x + 2
B. 6x^2 + 2x
C. 6x^2 + 4x
D. 6x^2 - 2x
Question 3
Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 \) about the x-axis, from \( x = 0 \) to \( x = 2 \).
A. 4π
B. 8π
C. 16π
D. 32π
Question 4
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 expected value of X.
A. \( \frac{1}{2} \)
B. \( \frac{3}{4} \)
C. \( \frac{5}{6} \)
D. \( \frac{7}{8} \)
Question 5
A binary operation $\ast$ is defined as $a \ast b = a^2 + b^2$. Find the value of $2 \ast 3$.
A. 13
B. 25
C. 37
D. 49
Question 6
Find the mean and s\tandard deviation of the data set: { 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 }.
A. \( \text{mean} = 10, \text{std dev} = 4 \)
B. \( \text{mean} = 12, \text{std dev} = 6 \)
C. \( \text{mean} = 14, \text{std dev} = 8 \)
D. \( \text{mean} = 16, \text{std dev} = 10 \)
Question 7
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. 0.9544
B. 0.9772
C. 0.9987
D. 0.9999
Question 8
Find the derivative of the function ( f(x) = \sin^2(x) ).
A. ( f'(x) = 2\sin\( x)\cos(x \) )
B. ( f'(x) = \sin(x) )
C. ( f'(x) = \cos(x) )
D. ( f'(x) = 2\cos(x) )
Question 9
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 5 \ \)^2 + \( y - 3 \)^2 = 25 )
D. \( x - 3 \ \)^2 + \( y - 5 \)^2 = 25 )
Question 10
Solve the inequality: \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \text{ or } x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \text{ or } x > \frac{3}{2} \)
C. \( x < -\frac{3}{2} \text{ or } x < \frac{1}{2} \)
D. \( x > -\frac{3}{2} \text{ or } x < \frac{1}{2} \)
Question 11
If ( f(x) = \frac{x^2 - 4}{x - 2} ), find \( f\( -2 \ \) ).
A. \( f\( -2 \ \) = \frac{\( -2 \)^2 - 4}{-2 - 2} \)
B. \( f\( -2 \ \) = \frac{\( -2 \)^2 + 4}{-2 - 2} \)
C. \( f\( -2 \ \) = \frac{\( -2 \)^2 - 4}{-2 + 2} \)
D. \( f\( -2 \ \) = \frac{\( -2 \)^2 + 4}{-2 + 2} \)
Question 12
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. 1/6
B. 1/12
C. 1/24
D. 1/36
Question 13
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \( \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix} \ \)
B. \( \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 1 \end{bmatrix} \ \)
C. \( \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix} \ \)
D. \( \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 3 \end{bmatrix} \ \)
Question 14
Solve the inequality \( 2^x > 3^x \) for ( x ).
A. \( x < 0 \)
B. \( x > 0 \)
C. \( x < 1 \)
D. \( x > 1 \)
Question 15
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 2 \)

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: