FE Practice Test 1

Consider the movement of the particle in the x-y plane. The locations are x=12\sin{t} and y=15\cos{t} , where x- and y-coordinates are the locations of the particles after t seconds. Which of the following equations represents the path of the particle?

The equation defined as 16x^2-32x-9y^2-90y=353 is:

Consider the shown right-triangle ABC:

What is the approximate value of cot⁡ A?

A line has a slope of 3 and passes through the point (2, 4). Determine the approximate distance between this point on the line and the y-intercept point.

What is the equation of a circle with center (-5, 7) and passing through the point (4, 7)?

If the fourth and sixth terms of a geometric progression are 125/2 , and 3125/8 , respectively, then find the first term of the sequence.

Find the approximate length of the resultant of the following vectors.

5\mathbf{i}-3\mathbf{j}+6\mathbf{k}
4\mathbf{i}+10\mathbf{j}-4\mathbf{k}
-6\mathbf{i}-8\mathbf{j}+7\mathbf{k}

Find the inverse of matrix A.

\mathbf{A}=\left[\begin{matrix}2&6\\5&7\\\end{matrix}\right]

Find the product of the complex numbers 5 – 4j and 9 – 4j.

Find the subtraction of the vector -10 + 9j from the vector 9 + 19j.

Which of the following is NOT a correct derivative?

Which of the following is the approximate area bounded by the curves y=x^2-6x+8 and y=4x-x^2 ?

If the vector field is F=x\mathbf{i}-y\mathbf{j} , where i and j are unit vectors, then

I.      div\vec{F} = 0
II.    curl\vec{F} = 0
III.  div\vec{F} ≠ 0
IV.  curl\vec{F} ≠ 0

A baker estimates that if she sells her freshly baked bread now, she will obtain 210 loaves, which she can sell at $5.00 per loaf. However, she estimates that her production will increase by an additional 20 loaves of bread for each day that she delays selling, but the price will drop at a rate of $0.10 per loaf per day. In addition, she will experience a spoilage rate of approximately 5 loaves for each day she delays. In order to maximize her revenue, how many days should she wait before selling the bread?

Consider the given parametric equations:

x=t-9t^3
y=t^4-2t^3+3t^2+4

Find \frac{dy}{dx} .

What is the general solution for the differential equation \frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=0 ?

What is the solution of the differential equation \frac{dy}{dx}-\frac{1}{x}y+sec\left(\frac{y}{x}\right)=0 .

Consider a sequence of numbers that follows a unique pattern such that each term is the sum of the two preceding terms.

If f(1) = 10 and f(2) = 4.5, what is the value of f(5)?

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

5, 6, 6, 7, 9, 9, 10, 10, 13, 16, 19, 20, 22, 23

Which value is closest to the mean?

A box contains 200 chits, each with a unique number from 1 to 200 written on it. One chit is drawn from the box. What is the probability that the number on the drawn chit will be even or greater than 120?