Math 152B Practice Exam II

Please do all of the following problems.  All work and all answers must be done on your own paper.  Credit earned will be based on the steps that you show that lead to the final solution.  Good Luck!

   Key 

Problem 1   Find the root:

           

Problem 2   Simplify the expression.  Leave your answer in exponential form with only positive exponents.

        

Problem 3  Multiply and Simplify  

         

Problem 4   Simplify the expression.  Assume all variables represent positive real number.

          

Problem 5    Multiply and Simplify

        

Problem 6  Rationalize the denominator

              5
                       
          4 -

 

Problem 7   Simplify        

        

Problem 8 

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

  1.  -3x + 2y = 6
      9x - 6y  =  36


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

 

  Problem 9

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

  1. 7x + y  =  3
    4x + 3y  =  -8

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

 

  Problem 10   Solve       

         

Problem 11  Solve each inequality.

A.  | 2x - 4 | + 3 > 7

 

B.  | 3x - 8 | + 5  < 4

 

C.  3| x - 5| <  9

 

Problem 12  Solve the equation

        x - 3       x - 6
                 -               =  0
       x + 1       x + 5

 

Problem 13  Solve the following for m

                             r
        S  =  1  +            
                         m

Problem 14  Steve can paint his house in 10 hours working by himself.  Working together, Anne and Steve can paint the house in just 6 hours.  How long would it take Anne to paint the house by herself?

 

Problem 15  Derek bicycled 36 miles to get to Echo Summit and back and Nick bicycled 60 miles to get to Carson Pass and back.  Nick rode 3 miles per hour faster than Derek, and his trip took an hour longer than Derek's.  What is the fastest speed that Derek could have been traveling?  (You must set up the equations, that is, no guessing).

Problem 16  Simplify

                          x
           3 -                          
                        x + 1
                                          
             x            1
                    +                      
             6            4

 

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