© Scarborough Spring 2011 Math 365-502 Exam III 1
Math 365
Exam 3
NEATLY PRINT NAME : ______________________________________
STUDENT ID : __________________________
Spring 2011
Scarborough
DATE : _________________________
"On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work."
________________________________
Signature of student
Academic Integrity Task Force, 2004 http://www.tamu.edu/aggiehonor/FinalTaskForceReport.pdf
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 ____________________________________________
Write all solutions in the space provided as full credit will not be given without complete, correct accompanying work, even if the final answer is correct. Use techniques taught in class to solve; do not use brute force (do not use “list by exhaustion” unless that is the only way to solve the problem). Fully simplify all your answers, and give exact answers unless otherwise stated. Make sure that you indicate your answer clearly by circling your response.
MATH JOKE: How do they prove that all odd integers higher than 2 are prime?
Mathematician : 3 is a prime, 5 is a prime, 7 is a prime, and by induction - every odd integer higher than 2 is a prime.
Physicist : 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime,...
Programmer : 3 is a prime, 5 is a prime, 7 is a prime, 7 is a prime, 7 is a prime,...
Salesperson : 3 is a prime, 5 is a prime, 7 is a prime, 9 -- we'll do for you the best we can,...
Computer Software Salesperson : 3 is prime, 5 is prime, 7 is prime, 9 will be prime in the next release,...
Biologist : 3 is a prime, 5 is a prime, 7 is a prime, 9 -- results have not arrived yet,...
Lawyer : 3 is a prime, 5 is a prime, 7 is a prime, 9 -- there is not enough evidence to prove that it is not a prime,...
Accountant : 3 is prime, 5 is prime, 7 is prime, 9 is prime, deducing 10% tax and 5% other obligations.
Statistician : Let's try several randomly chosen numbers: 17 is a prime, 23 is a prime, 11 is a prime...
Professor : 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.
Computational linguist : 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime,...
Psychologist : 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries to suppress it,...
-http://www.workjoke.com/mathematicians-jokes.html

© Scarborough Spring 2011 Math 365-502 Exam III 2
(10 pts: 1 pt for each TF) On problems 1 through 10, circle either “True” or “False.” a
1.
True or False: If a , b , and c are integers and b > 0, then b c
> b
iff a > c .
2.
True or False: If | then a is a factor or divisor of b , and b is a multiple of a .
3.
True or False:
2

7

5
5 16 11
4.
True or False: The number zero is neither even nor odd.
5.
True or False: Each composite number can be written as a product of primes in one, and only one, way except for the order of the prime factors in the product.
6.
True or False: 4 | 0
7.
True or False: Any positive integer with exactly two distinct divisors is a prime number.
8.
True or False: If 7 | a and 7 | b , then 7 |
 a b

.
9.
True or False: The irrational numbers are closed under addition and multiplication.
10.
True or False:

4
5
6
means
5
6
.
Short Answer #11 – 21 (11 pts – 1 pt each): No work is needed for full credit.
11.
_________________________ What is the smallest composite number greater than 50?
12.
______________________ Give an example of two 2-digit composite numbers that are relatively prime.
13.
_________________________ What is the greatest prime needed to test whether or not 293 is prime?
14.
_________________________ Give an example of a fraction that is not a rational number.
15.
_________________________ Convert 583.21
to scientific notation.
16.
_________________________ Give an example of an improper fraction that is a rational number.
17.
__________________________________ Write 8.765 in expanded fraction form (fractional meaning).
18.
_________________________ Give an example of a mixed number between 4 and 5.
19.
_________________________ Convert

3 into a standard numeral.
20.
_________________________ What is the multiplicative inverse of 3
5
6
?
21.
_____________________________________________ Using rational numbers, give an example of the
Fundamental Law of Fractions.

© Scarborough Spring 2011 Math 365-502 Exam III 3
22.
(8 pts) On the left side of the given grid, use the rectangle method to illustrate and find all the positive divisors of 12. On the right side of the grid, use the colored-rod method to illustrate and find the common positive divisors of 4 and 6.
POSITIVE DIVISORS OF 12 | COMMON DIVISORS OF 4 AND 6
_________________________ are the positive divisors of 12.
_________________________ are the common positive divisors of 4 and 6.
23.
(4 pts) How many positive divisors does
 
9
495 have?
24.
(7 pts) Use the Euclidean algorithm and theorem to find the lcm (130, 39).

© Scarborough Spring 2011 Math 365-502 Exam III 4
25.
(5 pts) Use division by primes to find the lcm (18, 15, 50).
26.
(3 pts) If a < 13 , what is the largest value of a , such that a is rounded to the nearest tenth.
27.
(5 pts) Model and calculate the product:
2 3
.
28.
(5 pts) Using base-ten blocks, with a flat representing one, model and calculate 1.56 + 0.78.
29.
(5 pts) Write in simplest form
18 x z

2 y z
4 yz

12 xz
.

© Scarborough Spring 2011 Math 365-502 Exam III 5
30.
(5 pts) Model and calculate the quotient:
3

1
4 3
.
14
31.
(4 pts) Write
175
as a terminating decimal, if possible, using the methods discussed in class (not using long division). If it is not possible, explain why.
32.
(7 pts) Correctly and properly write the number 3.456 in words.
33.
(5 pts)



3 x

4
2 xy

6


 2


© Scarborough Spring 2011 Math 365-502 Exam III 6
34.
(5 pts) Convert 1.012
to a ratio of integers.
25
2 4 x y
35.
(6 pts)
3 
27
3 12 a c

36.
(5 pts) Prove a c ad b d bc c
where 0 d

.