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Math 152B Practice Midterm 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 4   Simplify the expression.  Assume all variables represent positive real number.

   Solution

Problem 5    Multiply and Simplify

   Solution

Problem 6  Rationalize the denominator

             5
                       
          4 -

     Solution

Problem 7   Simplify

   Solution

Problem 8 

Write down the quadratic formula

  Solution

Problem 9

Use the discriminant to determine the nature of the roots of the following quadratics.

A.     2x² + 3x + 4  =  0

  Solution

B.    3x² + x - 4  =  0 

  Solution

Problem 10  

Solve the equation by using the factoring or root method.

A) 10x²  =  13x + 3 

            Solution

B)   2x² - 15 = 11

  Solution

Problem 11 

Solve the following by completing the square

   5x² - 20x - 21  =  0

Solution

Problem 12

Solve the following by any method

A)   6x² + 5x - 4  =  0 

    Solution

B)    2x³ - 18x  =  0 

    Solution

Problem 13 

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?

    Solution

Problem 14

Factor

        4x² -12x + 9

Solution

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).

Solution

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