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MATH 154 PRACTICE MIDTERM III

Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Do all your work and give all your answers on you own sheet of paper.  Show your work.  

Printable Key

Problem 1 (20 Points)  Solve the following system of nonlinear equations:

        x2 + y2  =  25

        3x + 5y  =  15

  Solution

Problem 2

A. (8 Points)  Find the first four terms of the sequence whose general term is given. Then find the 100th term. 

        an  =  n - 1/n

  Solution

B. (8 Points)  Expand and simplify

       

  Solution

C. (8 Points)  Write the series in summation notation

        1       2       3       4
            +       +       +       + ...
        2       3        4       5                       

Solution

 

Problem 3 

A)     (11 Points)  Find the indicated unknown

        8, 13, 18, 23, ..., 88            n  =  ?

Solution

B)    (11 Points)  Find the sum of the given series

       

Solution

Problem 4 

A. (11 Points)  Find the indicated unknown

        a1  =  5,   a5  =  0.008        r  =  ?

Solution

B. (11 Points)  A rubber ball is dropped on a hard surface and bounces to a height of 200 ft.  On each rebound it bounces 95% as high as on the previous bounce.  How high does the ball bounce on the 20th bounce?

Solution

 

Problem 5 

A. (11 Points)  Find the sum of the infinite series if it exists.

              1       1         1       
       1+       +        +         + ...
              3       9         27                 

Solution      

B. (11 Points)  Write the repeating decimal as the ratio of two integers.

        0.18   

Solution

Problem 6  (20 Points)

Expand the binomial using the binomial theorem

        (3m - 2)5

Solution 

Problem 7  (20 Points)

One muffin, two pies, and three cakes cost $23.  One Muffin, three pies , and two cakes cost $21.  One muffin, four pies, and five cakes cost $39.  Find the cost of each.

Solution