FE Practice Test 2

What is the approximate total surface area of a 14-meter-high right cylinder with a base diameter of 10 meters?

If the area of the sector is 50π cm^2 and the central angle is 110°, then what is the approximate radius of the circle?

Consider the illustration below:

What are the lengths x and y, respectively?

Which of the following expressions is equivalent to cos⁡2θ?

If the equation of the circle is x^2-4x+y^2-6y-12=0 , what is the center of the circle?

What is the nearest numerical value for the following expression, using logarithmic identities?

\log_5{\frac{5}{3}}+\log_5{10}-\log_5{\frac{2}{3}}

Consider the following system of linear equations:

6x + 5y + 8z = 10
4x + 7y + 6z = 8
2x – 3y – 5z = 12

Consider the matrix A and matrix B as follows:

If the determinant of the matrix A is -724, then what is the determinant of matrix B?

Consider the following vectors:

\mathbf{A}=2\mathbf{i}-\mathbf{j}+3\mathbf{k}
\mathbf{B}=2\mathbf{i}+\mathbf{k}

Which of the following statements is true?

Find the resultant of the vectors A = 5i + 7j – 3k and B = 10i + 14j – 6k.

What is the derivative, \frac{dy}{dx} , of the expression xy-e^x\cos{\left(5y\right)=0} ?

What are the minimum and maximum values, respectively, of the equation f\left(x\right)=x^3-9x^2+24x+5 in the interval [1, 6]?

Which of the following illustrations represents the vector field, \mathbf{F}\left(x,y\right)=y\mathbf{i}-x\mathbf{j} ?

Find the following indefinite integral.

\int{\frac{x^{3/2}-x+10}{\sqrt x}dx}

Find the following limit.

\lim_{x\rightarrow 9} \left(\frac{x^2-81}{x-9}\right)

What are the values of k so that y=e^{kx} is a solution of the differential equation?

\frac{d^2y}{dx^2}-\frac{dy}{dx}-12y=0

What is the solution to the differential equation?

y^\prime=y^\frac{1}{2}, y\left(0\right)=0

Consider a study which gives the results for a total sample size of 14 as follows:

4, 6, 7, 10, 10, 13, 13, 15

If the mean of the sample is 9.75, then which value is closest to the standard deviation?

A box contained a certain number of pens and had 20% defective pens. Twelve pens are chosen randomly from this box. What is the probability that exactly eight of the chosen items are defective?

If A and B are two events such that P\left(A\right)=\frac{1}{3} , P\left(B\right)=\frac{1}{4} , and P\left(A\cap B\right)=\frac{1}{7} , then which of the following statements is true?