152B Practice Exam I
Please do all of the following problems.  Credit earned will be based on the steps that you show that lead to the final solution.  Good Luck

Key

Problem 1:  Factor the expression completely:

    A.   x4 - 9x2

    B.   x2 + 3x -54

    C.  6x2 + 11x - 10

    D.  128xyz3 + 54x4y

    E.   3st + 18t - 6u -su

Problem 2  Use the method of elimination to solve the system.  Then graph the system to check your solution.

     A.  -3x + 2y  =  6
            9x - 6y  =  36 

     B.  5x + 3y  =  15
           3x - 2y  =  28

 

Problem 3  Use the method of substitution to solve the system.  Then graph the system to check your solution.

     A.  7x + y  =  3
          4x + 3y  =  -8

     B.  y = 3x - 2
          6x - 2y  =  4 

Problem 4  Last year, you inherited $30,000 from a distant relative.  You took the money and invested some of it in a bank account that paid 2% interest and invested the rest in stocks that increased 6%.  The total earnings on the invested money was $900.  How much money was invested in the bank account and how much was invested in the stock market?  Show the equations that you set up and how you either used substitution or elimination to solve the system.

 

Problem 5  You own a non-profit theater that has 2,000 seats.  In order to break on even Saturday's concert you must collect a total of $24,000 from the ticket sales.  You have decided to partition the theater's seats into "premium seats" which you will sell for $30 per seat and "general admission" seats which you will sell for $10 per seat.  If you are certain the tickets will sell out, how many seats should you sell as "premium seats"?  Show the equations that you set up and how you either used substitution or elimination to solve the system.


Extra Credit:  Write down one thing that your instructor can do to make the class better.  (Any constructive remark will be worth full credit)