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:  Solve the following equations

A.   x³ - 2x² + x = 0

B.    4x² = 15 - 4x

Problem 4:  The pressure p in pounds per square foot of a wind is directly proportional to the square of the velocity v of he wind.  If a 10-mi/hr wind produces a pressure of 0.3 lb/ft², what pressure will a 100-mi/hr wind produce?  

Problem 5  Solve each inequality.

A.  | 2x - 4 | + 3 > 7

B.  | 3x - 8 | + 5  < 4

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

                             r
        S  =  1  +            
                         m

Problem 8  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 9  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 10  Simplify

                          x
           3 -                          
                        x + 1
                                          
             x            1
                    +                      
             6            4

Problem 11  The south facing part of a small roof is to be constructed so that its length is four feet more than the vertical distance from the ceiling to its top.  Find the length of the roof if the horizontal length of the roof is 8 feet.

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