Name                                    

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) 

Sketch the graphs of the given functions:

A.      (10 Points)      x2
                               + 4y2 = 1
                        9            

Solution

B.   (10 Points)   x2 + y2 + 2x - 4y - 4  =  0    

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)

Find the equation of conic with the graph shown below:

 

   

Solution