Math For Social Sciences. Practice Exam


1.
Find an equation for the line through the point (-2,5), which is perpendicular to the line 3y-x+2=0.



Answer: The equation is y=-3x-1.


2.
The cost of producing x-units of a product is given by: C(x)=20x+100. The product sells for $45 per unit.
3.
A 45-year old man puts $1,500 in a retirement account at the end of the each quarter until he reaches the age of 60 and makes not further deposits. If the account pays 12% interest compounded quarterly, how much will be in the account when the man retires at age 65?



Answer: The amount of money at the end will be about $441,739.


4.
Use the method of matrix inverses to solve the system of equations.

\begin{eqnarray*}3x+y&=&-3\\
-4x+2y&=&1
\end{eqnarray*}




Answer: $\displaystyle x=-\frac{7}{10} $, $\displaystyle y=-\frac{9}{10} $.


5.
Sketch the graph of f(x)=|3x-12|. Identify and include any intercepts in your sketch.



Answer:

The x-intercept is 4, and the y-intercept is 12.


6.
Solve each of the following for x:
7.
Which of the following (if any) represent y as a function of x? Explain your answers to 7a and 7b. That is, if you believe that 7a is (or is not) a function, explain how you came to this conclusion. do the same for 7b.



Answer: The first equation represents a function, because its graph passes the vertical line test.
The second equation is not a function, because for many values of x in the domain, there will be two different values for y in the range, one positive and the other negative. This violates the definition of a function.


8.
Use the elimination method to solve the following system:

\begin{displaymath}\begin{array}{rrrrrrr}
x&+&y&-&4z&=&0\\
2x&+&y&-&3z&=&2
\end{array}.\end{displaymath}



Answer: (Since there are only two equations and three unknowns, the solutions will be parametrized in terms of one variable)

All solutions are given by (x, 8-5x, 2-x), where x is arbitrary. There are other parametrizations.


9.
Consider the supply and demand curves in the sketch below:
10.
A small resort must add a swimming pool to compete with a new resort built nearby. The pool will cost $28,000. The resort borrows the money and agrees to repay it with equal payments at the end of each quarter for $\displaystyle 6\frac{1}{2} $ years at an interest rate of 6% compounded quarterly. Find the amount of each payment.



Answer: The amount of each payment is $1,308.49.


11.
Consider the function $\displaystyle f(x)=3^{x}-1 $.
12.
Using the Gauss-Jordan method, solve the system of equations:

\begin{displaymath}\begin{array}{rrrrrrr}
x&-&2y&+&4z&=&6\\
x&+&y&+&13z&=&6\\
-2x&+&6y&-&z&=&-10
\end{array}.\end{displaymath}



Answer: $x=-14,\,y=-6,\,z=2$.


14.
A patient was admitted to a hospital with a declining white blood cell count, described by the equation:

y=t2-30t+2225

where t is time in hours since the patient was admitted, and y is the blood count.
15.
The Waputi Indians make woven blankets, rugs, and skirts. Each blanket requires 24 hrs for spinning the yarn, 4 hrs for dying the yarn, and 15 hrs for weaving. Rugs require 30 hrs for spinning, 5 hrs for dying, and 18 hrs for weaving. Skirts require 12 hrs for spinning, 3 hrs for dying, and 9 hrs for weaving. There are 306 hours available for spinning, 59 hrs for dying, and 201 hrs for weaving. Set up a system of equations which could be used to determine the number of blankets, rugs, and skirts made. Do not solve



Answer: Let a= the number of blankets, b= the number of rugs and let c= the number of skirts. The system of equations is:

\begin{displaymath}\begin{array}{rrrrrrr}
24a&+&30b&+&12c&=&306\\
4a&+&5b&+&3c&=&59\\
15a&+&18b&+&9c&=&201
\end{array}.\end{displaymath}

16.
Let $\displaystyle A=\left[\begin{array}{rr}
5&0\\
-1&3\\
4&7
\end{array}\right] $ $\displaystyle B=\left[\begin{array}{r}
6\\
1\\
0
\end{array}\right] $ $\displaystyle C=[\begin{array}{rrr}
1&3&-4\end{array}] $ $\displaystyle D=\left[\begin{array}{rr}
-1&4\\
3&7
\end{array}\right] $



$\displaystyle E=\left[\begin{array}{rr}
2&5\\
1&6
\end{array}\right] $

Formulas


If you would like to go back to the original menu, click on Menu.


June 2, 1998

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour