Math 105               Practice Exam 1 with answers      Name ____________________________

Do your work on this paper.  You may add additional sheets.  Harder questions are marked with *.
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1.   For each of the following, decide if the reasoning is deductive or inductive.

     a. John had $20.  For 30 days in a row Mary gave John $1.  Therefore, John has $50.     DEDUCTIVE

      b. Jane’s first three children were girls.  If she has another, it will be a girl.   INDUCTIVE   

2. Identify a pattern in each list of numbers. Then use this pattern to find the next numbers.

                0, 1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0,      0,4

3.  Look at the following sums and make a conjecture. Use it to fill in the blank.

                       1 + 3    =  2x2
                 1 + 3 + 5   =   3x3
           1 + 3 + 5 + 7   =   4x4 

       Conjecture:  

  1 + 3 + 5 +        . . .       + 31   =   16 x 16

4.  a. Find the range estimate for the sum of 2171 and  5389.

                           7000-9000

     b. Find the sum in part (a) by  rounding  to the nearest 100.

                            7600   

     c.  You plan to share the cost of high speed internet with your three other roommates.  If the monthly charge is $39 for the connection, estimate how much you will spend on it for 1 year.  

                             $120

5. An island has no currency but instead has the following exchange rate.

                  50 bananas = 20 coconuts
                 30 coconuts = 20 fish
                        100 fish = 1 hammock

   How many bananas equal 1 hammock?     375

6. The line graph shows the pollution rate for a certain lake from 1948 to 2002. Use the graph to answer the questions.

a.  About what year was the pollution rate lowest?    1948    

b.  Approximately what was the highest rate of pollutants during this time period?   3%

c. Strong anti-pollution legislation was passed and its effect started to be seen five years later?   About what year do you think it was passed?    1970 or 1971

7. 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.

a.   What percent of people watched the news at least one time?   98%

b.   What percent of people watched the news 4 times or fewer?  77%

c.   If there were 44,222 respondents, about how may watched the news 1-2 times?  18,131

8. Describe a universal set U that includes all elements in the given sets. 
      A = {English, French, Spanish}     B = {Chemistry, Biology, Physics, Economics} 

            Any set that contains the seven elements in A or B

9.  Write the following set in set-builder notation.  {5,7, 9, 11,  . . .  } 

                 several correct answers     for example    {x  x is an odd natural number larger than 3}

10.  Answer True for False to each of the following:

      a.  __F___      { 5,  7,  9} ⊂  {9,  5,  7}     
    
      b. __T__      {a,b,d}⊈ {d,a,c, 4}

     c. __F__       A∩ = A    (in general)

      d  __F_         17   {2, 4, 6, 8,  . . . , 32}

     e. __T_          (AB)' = A' ∩ B'

11. List all the subsets of the set {s,t,u}.
 
        , {s},{t},{u},{s,t},{s,u},{t,u}, {s,t,u}

12.  A pizza can have cheese, sausage, pepperoni, onions, peppers, broccoli, and olives. 
         a.  How many different types of pizza’s can be made? 
                                   128

         b. People in some religions do not eat cheese and meat together.  How many types of pizza can such 
             a person eat?
                                     80

13. Let U = {q, r, s, t, u, v, w, x, y, z}
	A = {q, s, u, w, y}
	B = {q, s, y, z}
	C = {v, w, x, y, z}.  

List the elements in the following sets.
       
          a.  B'      {r,t,u,v,w,x}                                                        b.    A ∩ (B ∪ C).      {q,s,w,y}

14. a. Complete the formula for the cardinal number of the union of two sets        

                  n (A ∪ B) =   n(A) + n(B) – n(A∩B)

       b. Set A contains 20 elements, set B contains 8 elements, and their union has 23 elements.  How many elements are in their intersection?     5

15.  Given the following  Venn diagram find the following:
 
     a.  A  B      {11,12,13,14,15,16,17}            b.  A' ∩ B     {12,15,16,}                                    c.  n(A')    5   

16. Using the Venn diagram below find what regions represent the following sets:

         a.   D ∩ E         II,V                                                         b.  F∪E'    I,IV,V,VI,VII,VIII

17.  1)  A pollster asked 80 people the following questions:
	1. Are you a registered voter?
             2. Do you currently have any children in K-12?
	3. Would you support a tax increase to build a new school? 

Label the Venn diagram and use the information below to fill in the diagram and answer the questions.

Using the regions I-VIII as in the previous problem  

I 18, II 6, III 9,IV 5,V 14,VI 8,VII 10,VIII 10

	43 were registered voters
             20 were both registered voters and had children in k-12
             14 were registered, had children in k-12, and supported the tax increase
             10 supported the tax increase but were not registered and did not have children in k-12
             37 had children in k-12  
               5 supported the tax increase and were registered to vote but had no children in k-12
               8 had children in k-12 and supported the tax increase, but were not registered voters
    
     How many had children in k-12 but were not registered and did not support the tax increase?    9

     How many answered no to all three questions?   10

*18 .  (From the Mathematics Teacher )  Explain how you got your answers.

          i.   A sixty page newspaper, which consists of only one section, has the sheet with page 7 missing.  What other pages are missing? (Ask me if you are not sure how a newspaper is constructed.)

                         pages    8, 53, 54

         ii. In how many ways can you make change for a dollar using nickels, dimes, and quarters?
                                 
                                                        28