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Math 105
Practice Final
(answers in bold)
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, __5___, _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
50
Age
Expected addition years 30
60
23
70
16
80
9
90
2
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. It rained on April 1, 2007.
b. Some houses have white shutters. All houses do not have white shutters.
c. Tennis and soccer are team sports. Either tennis or soccer is not a team sport.
d. If the light is on then the sun has set. The light is on and the sun has not set.
3. (a)
Write MDCLXIV as Hindu-Arabic number.
1664
_
(b) Write .7 as a ratio of two integers. [There is a bar over the 7.]
7/9
(c) What is the base two number 1101111 equal to in our base ten system.
111
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: If you come to a true conclusion, then you use a valid argument.
T F
Inverse: If you do not use a valid argument, then you do not come to a true conclusion
T F
Contrapositive: If you come to a true conclusion, then you use a valid argument.
5. A pollster conducting a telephone poll asked three questions: I will do this problem in class.
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
F
F
T
F
T
F
F
F
T
T
F
T
T
T
p
q
r
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
~q
p~q
F
F
T
T
F
F
T
T
T
T
T
T
F
F
T
T
(p~q) r
T
F
T
F
F
F
T
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'
{p,q,r,s,t,u}
c.
n(A)
b. A ∪ (B ∩ C)
{q,w,u,w,x,y,z}
d. All subsets of {u, t}  , {u}, {t}, {u, t}
5
8. Below is the complete preference table for an election. Use it to answer each part.
Abe
Bob
Cal
1 1 1 1 1 2 2 3 3 3 3
2 3 3 3 3 1 1 1 1 2 2
3 2 2 2 2 3 3 2 2 1 1
a. Who wins with the plurality method. (Explain why.)
Abe
b. Who wins with the Borda Count method. (Show your calculations.)
Abe with 23
c. Who wins if we use the pairwise comparison method? (Explain why.)
3 way tie
d. Who wins if we use the plurality with elimination method? (Explain why.)
Bob
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"
9.
(a) If exercise lowers cholesterol then exercise is healthy.
qr
(b) Exercise lowers cholesterol but does not prevent heart disease.
q~p
(c) Exercise lowers cholesterol if it prevents heart disease.
pq
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.
18%
b. What percent of the respondents watched the news less that 3 times in the past week? 43%
c. How many respondents watched the news 7 or more times in the past week?
2216
11. Write the each of the following in the other two equivalent forms. Round off if necessary.
Fraction
? 135/100 or 27/20
?
Decimal
?
37/100
13/29
?
Percent
135%
1.35
.37
?
37%
.448
?
44.8%
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
23/75
b. 5/12 x 9/10
c. 4/7  6/11
3/8
22/21
d. Find the GCD and LCM of the number 40 and 24.
8
120
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.
pq
pq
Therefore p
b.
Not Valid
Do the truth table for [(pq)  (pq)]p
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.
Invalid
I will do the diagrams in class.
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?
$24,948
b. What is the percent increase of Ann’s Salary from her starting salary to her salary after the second
raise?
13.4%
*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?
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