(c) Scarborough Fall 2015 Math 365-505 Exam I 1
Math 365 NEATLY PRINT NAME : _______________________________
Exam 1 STUDENT ID : ______________________
Fall 2015 DATE : ____________________________
"On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work."
________________________________
Signature of student
My signature in this blank allows my instructor to pass back my graded exam in class or allows me to pick up my graded exam in class on the day the exams are returned. If I do not sign the blank or if I am absent from class on the day the exams are returned, I know I must show my Texas A&M student ID during my instructor’s office hours to pick up my exam.
Signature of student ____________________________________________
You are authorized to use a pencil, eraser, and your own TAMU student ID; use of anything else is a violation of the Aggie Honor Code.
Note: It is a violation of the Aggie Honor Code to continue writing on the exam after time is called and in doing so will result in a zero for this exam and will be reported to the Aggie Honor Council.
ALL CELL PHONES MUST BE TURNED OFF AND PLACED AT THE FRONT OF THE ROOM! It is academic dishonesty to have any electronic devices, including cell phones, on your person during this exam.
Having an electronic device on your person can result in a zero on this exam and an F* for this course.
“There are only 10 types of people in the world — those who understand binary, and those who don't.”

(c) Scarborough Fall 2015 Math 365-505 Exam I 2
(8 pts: 1 pt for each TF) On problems 1 through 8, circle either “True” or “False.”
1.
True or False: The Egyptian and the Roman numeration systems have the additive property.
2.
True or False:

is a subset of every set.
3.
True or False: ‘You are happy’ is a statement.
4.
True or False: The Babylonians were believed to have had first a symbol for zero.
5.
True or False: Place value assigns a value of a digit depending upon its placement in a numeral.
6.
True or False: The Tally numeration system had a one-on-one correspondence between the marks and the items being counted.
7.
True or False: The whole numbers are an example of an infinite set.
8.
True or False: ‘Write an equation’ is part of ‘understanding the problem’ in Polya’s Four-Step
Problem Solving Process.
9.
(2 pts) Give a counterexample to the statement, “Bobcats are the largest member of the cat family.”
10.
(3 pts) Negate the statement, “Some stars are shining and zero is a positive number.”
11.
(4 pts) Write the number 119 in Roman numerals.
12.
(4 pts) Whole numbers are not closed under what operations (that we have studied)? Give example(s) to support your answer(s).
13.
(4 pts) Write 377 in Mayan.
______________________________________

(c) Scarborough Fall 2015 Math 365-505 Exam I 3
14.
Consider the sequence 3, 3, 6, 9, 15, 24, 39, …. a.
(2 pts) What are the next two terms?
___________ ___________ b.
(4 pts) What is the n th
term?
15.
(2 pts) What justifies (4

10 + 5

10) + (2

1+ 3

1) = (4 + 5)

10 + (2 + 3)

1?
16.
Let A
 
, ,

and B
  
, such that the universal set U A B . a.
(2 pts) Use roster notation to indicate the set A

B . b.
(2 pts) List all subsets of set B . c.
(2 pts) List all elements in A B . d.
(2 pts) Calculate


B

.
17.
(2 pts) Use an array model using intersections to illustrate 2 4 and give its product.

(c) Scarborough Fall 2015 Math 365-505 Exam I 4
Exam grade:________________
18.
(3 pts) Use short division to compute 852 6

.
19.
(5 pts) Complete the following truth table. p q ~ p ~ p
 q

~ p
 q
  q
20.
(3 pts) Use lattice multiplication to calculate 83 nine

56 nine
.
21.
(3 pts) Use the set model to illustrate and find the sum 3 + 1.

(c) Scarborough Fall 2015 Math 365-505 Exam I 5
22.
(2 pts) Give a Venn diagram illustrating A

B .
23.
(6 pts) Find the difference, as well as model with Base-Three Blocks: 201 three
– 112 three
.
24.
(4 pts) Shade

A

C


B in the Venn diagram.

(c) Scarborough Fall 2015 Math 365-505 Exam I 6
25.
(4 pts) Use repeated subtraction to calculate 1314 six

54 six
.
26.
(5 pts) Convert 12T eleven
to base eight.

(c) Scarborough Fall 2015 Math 365-505 Exam I 7
27.
(8 pts) Find the sum of the first 20 terms of an arithmetic sequence in which the sixth term is 73 and the
17 th
term is 194.
28.
(4 pts) A student says that 1 is the identity for division, because if a is a whole number, then a 1 a .
How do you respond?

(c) Scarborough Fall 2015 Math 365-505 Exam I 8
29.
(6 pts) Give the n th
term of a nontrivial geometric sequence and then give its first four terms.
__________ __________ __________ _________
30.
(4 pts) Prove 0 0 is undefined in the whole numbers.
5-point Bonus : Give an example of a tautology and prove it is a tautology.