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 LCD for the given rational expressions and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

A.     10u                7
                       ,                                        
         39v              26u2v

B.        3x             5 + x
                        ,                                      
         x2 - 5x         5 - x

 

Problem 2:  Perform the indicated operations and express your answer in simplest form.

 

A       2x2 - x - 1     x2 - 6x + 8
                           .                         
         x2 - 5x + 4    2x2 - 3x -2

B       x2 + 2 xy + y2            y + x
                                                       
            x2 - x - 2                  x - 2

C.       x2 - x - 5                   1 - 2x
                                +                                 
         x2 +3x + 2            (x + 1)(x + 2)

D.            9                       6
                              -                       
         q2 - q - 2             q2 - 1

 

 

Problem 3

 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 4

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 5  Solve the equation

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

 

Problem 6  Solve the following for m

                             r
        S  =  1  +        
                         m

Problem 7  Perla can paint her house in 10 hours working by herself.  Working together, Bill and Perla can paint the house in just 6 hours.  How long would it take Bill to paint the house by himself?

 

Problem 8  Jason bicycled 36 miles to get to Echo Summit and back and Emma bicycled 60 miles to get to Carson Pass and back.  Emma rode 3 miles per hour faster than Jason, and her trip took an hour longer than Jason's.  What is the fastest speed that Jason could have been traveling?  (You must set up the equations, that is, no guessing).

 

Problem 9  Simplify the complex fraction.  Reduce the answer to lowest terms

        1          5
              -         
       2x         x
                            
        3   -   1/x2

 

Problem 10  Statewide the ratio of student enrolled in beginning algebra who pass to those who do not pass is 3 to 4.5.  If a beginning algebra class had 24 students pass, how many would you expect not to have passed?

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