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.
2. The cost of producing x units of a product is given by:

   

   The product sells for $45 per unit.

   • Find the break-even point.
   • What revenue will the company receive if it sells just the number of units from the part above?
   • Find the profit function, P(x).
   • Find the average cost per unit to produce 100 units.
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 no further deposits. If the account pays 12% interest compounded quarterly, how much will be in the account when the man retires at age 65?
4. Use the method of matrix inverses to solve the system of equations

   

5. Sketch the graph of f(x)=|3x-12|. Identify and include any intercepts in your sketch.
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. That is, if you believe that the first expression is (or is not) a function, explain how you came to this conclusion. Do the same for the second expression.
8. Use the elimination method to solve the following system:

   

9. Consider the supply and demand curves in the sketch below:
   
   • At what price are 20 items supplied?
   • Find the equilibrium demand and the equilibrium price.
   • Are the supply and demand curves linear, quadratic, exponential, logarithmic, or none of these? (graph)
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 in equal payments at the end of each quarter for years at an interest rate of 6% compounded quarterly. Find the amount of each payment.
11. Consider the function .
    • What is the domain of f(x).
    • Find any intercepts and asymptotes.
    • Sketch the graph of f(x), including the intercepts and asymptotes in your sketch.
12. If , , and .
    Find .
13. Using the Gauss-Jordan method, solve the system of equations:

    

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

    

    where t is time in hours since the patient was admitted, and y is the blood count.

    • What was the patient's minimum blood count, and when did it occur?
    • When the patient's blood count reached 3225, the patient was discharged. When did this occur?
    • Is the given equation linear, quadratic, exponential, logarithmic, or none of these?
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!
16. Let

    
    

    • Give the dimensions of each matrix, and identify any square, column, or row matrices.
    • Find the following if possible:
      • CA
      • E-2D
      • BA
      • CB

        
        

        
        

        
        

    Formulas
    • Future value for simple interest:

      

    • Future value for compound interest:

      

    • Future value of an ordinary annuity:

      

    • Future value of an annuity due:

      

    • Present value of an annuity:

      

    • Amortizing a loan:

      

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Tue Aug 12 21:45:49 MDT 1997

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