Math 105                    Practice Final                           Name ____________________________

Do your work on this paper.  You may add additional sheets.  Harder questions are marked with *.

1. a. Identify a pattern in the list of numbers. Then use this pattern to find the next three numbers.

              2,  1, 3,  1, 1,  4, 1, 1, 1, _____,  _____ , _____

   b. The following table relates the female expected addition life span in years. Find a pattern and fill in the rest of the table

Age 	50     60      70      80     90   	
Expected addition years	30     23      16 	

2.  Write down a negation of each of the following statements without putting something like “it is not true that” in front of the statement.  

      a..   It did not rain on April 1, 2007.    

      b.   Some houses have white shutters.   

      c.   Tennis and soccer are team sports.

      d.    If the light is on then the sun has set.

3. (a)    Write  MDCLXIV  as Hindu-Arabic number.

                      _
   (b)   Write .7  as a ratio of two integers.  [There is a bar over the 7.]

   (c)   What is the base two number 1101111 equal to in our base ten system.

4.   Given the following statement, write its converse, inverse and contrapositive and circle the appropriate True or False for each.

      T    F       If you use a valid argument, then you come to a true conclusion.

      T    F       Converse:  ____________________________________________________

      T    F        Inverse:    ____________________________________________________

      T    F       Contrapositive:  ________________________________________________

5.  A pollster conducting a telephone poll asked three questions:
	1. Are you a registered voter?
             2. Do you currently have any children in grades kindergarten through 12th grade?
	3. Would you support a tax increase to build a new school?

Label the circles in the Venn diagram above to allow you to describe how people answered the three questions, and then do the following: 

a.  Write the letter x in the region of the diagram that identifies all registered voters polled who 
       have children in school and who do not support a tax increase.
b.  Write the letter y in the region of the diagram that identifies people who are not registered to vote, who 
       do not have children in school, and who support a tax increase.
c.  Write the letter z in the region of the diagram that identifies all registered voters polled who have 
       children in school, and who support a tax increase

6.  Fill in the following truth tables.

  p 	  q	 ~p	q~p    	
				
  T	  T	 		
  T	  F	    		
  F	  T	    		
  F	  F	 		
                                   
p	q	r	~q	 p~q	(p~q) r	
						
T	T	T				
T	T	F				
T	F	T				
T	F	F				
F	T	T				
F	T	F				
F	F	T				
F	F	F				

7. Let U = {p, q, r, s, t, u, v, w, x, y, z}
	A = {q, s, u, w, x}
	B = {q, s, y, z}
	C = {v, w, x, y, z}.  List the elements in the set.
        Find   the  following:

    a.    C'     ___________________                   b.   A ∪ (B ∩ C)           _______________________

    c.    n(A)   _________________                      d.   All subsets of  {u, t}   _________________________ 

8. Below is the complete preference table for an election.  Use it to answer each part. 

    Abe     1   1   1   1   1  2   2   3  3   3   3
    Bob     2   3   3   3   3  1   1   1  1   2   2
    Cal      3   2   2   2   2  3   3   2  2   1   1

a.   Who wins with the plurality method.  (Explain why.)

b.  Who wins with the Borda Count method.  (Show your calculations.)

c.   Who wins if we use the pairwise comparison method? (Explain why.)

 d.   Who wins if we use the plurality with elimination method? (Explain why.)

9.	Write the followng in symbolic form using p, q, r, ~, , , , , where p, q, and r represent the following statements.
	         p = "Exercise prevents heart disease."
	         q = "Exercise lowers cholesterol"
	         r = "Exercise is healthy"
	  
	(a)  If exercise lowers cholesterol then exercise is healthy.

	(b)  Exercise lowers cholesterol but does not prevent heart disease.

	(c)   Exercise lowers cholesterol if it prevents heart disease.

10.  The circle graph shows the number of times a group of survey respondents watched the news in the past week. Use the chart to answer the questions.  There were 44,322 respondents.

  a.  What percent of the respondents watched the news 5-6 times in the past week.  ____________

  b.  What percent of the respondents watched the news less that 3 times in the past week?  __________

  c.  How many respondents watched the news 7 or more times in the past week?   _____________

11.   Write the each of the following in the other two equivalent forms. Round off if necessary.   

Fraction	Decimal	Percent	
?	?	             135%	
?	             .37	?	
13/29	?	?	

12.  Perform the following fraction calculations (without a calculator) and reduce your answer to
     simplest form. Show your steps and indicate the answers clearly.  [ 1/2  means  1 over 2 ]

a.   7/15  -   4/25

b.   5/12  x  9/10

c.   4/7    6/11

d.   Find the GCD and LCM of the number 40 and 24.

13. a.   Is the following argument valid?  Explain your answer using a truth table.

                  If there is lightning then there is thunder.  
                  There is lightning or there is thunder.
               There is lightning.

  b.	Use Euler diagrams to determine the validity of the following argument.
	
	          All first year students take a writing course 
                        All seniors take a capstone course
                        Joan is a senior 
	      Joan is not a taking a writing course.

14.  a. Ann took a job making $22,000 a year.  She was promised a 5% raise after one year and then an 8% raise after the second year.  What would her salary be after the second raise?

 

   b.  What is the percent increase of Ann’s Salary from her starting salary to her salary after the second raise?

*15.  Adam always plants his cherry trees in rectangular arrays so that the length is always twice the width, like those illustrated.  This year he planted 30 more trees in his rectangular orchard.  If the orchard is still twice as long as it is wide, how many cherry trees are there in the orchard this year?