© Scarborough
Math 365
Exam 2
Fall 2011
Scarborough
Fall 2011
Math 365-502
Exam II
1
NEATLY PRINT NAME: ______________________________________
STUDENT ID: __________________________
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.
Old mathematicians never die; they just lose some of their functions.
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Exam II
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(10 pts: 1 pt for each TF) On problems 1 through 10, circle either “True” or “False.”
1. True or False: Multiplication of whole numbers has the closure, commutative, associative, and unique
identity properties.
2. True or False: a  b has two distinct additive inverses: a  b and   a  b 
3. True or False: For a set of subsets of a nonempty set, “is a subset of” is reflexive and symmetric, but not
transitive.
4. True or False: For any numbers a, b, and c, if ac = bc, then a = b.
5. True or False: x  0
6. True or False: Mental math is the process of producing an approximate answer to a computation without
external computational aids.
7. True or False:  x  3 x  2 x  2 x for x  0 .
8. True or False: The relation “lives within 5 kilometers of” is an equivalence relation.
9. True or False: “Since 3800  5400  3896  5421  3900  5500 , then the sum 3896  5421 is between
9200 and 9400” is an example of computational estimation.
10. True or False: 16 x3  4 x2  4 x 1   4 x  1  4 x2 1 is fully factored over the integers.
11. (4 pts) Simplify fully: 14  110  12  2  3 

5  8 
  2  42 
12. (6 pts) Write each of these in algebraic form.
a. The difference of a number n times twice itself and 9: __________________________
b. For every 100 students (S), there are 9 computers (C): __________________________
13. (4 pts) a. Use the block illustration to model 3  2  4  3  2  3  4 .
b. What whole number property is this illustrating? _____________________________________
14. (4 pts) Use the number line model (with fish) to calculate  5  8 .
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15. (4 pts) If f  x  
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x2
Math 365-502
Exam II
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and g  x   4  x , find and simplify  f g  x  .
5-point Bonus: In interval notation, what is the domain of f g ? _____________________________
16. (4 pts) Use the array model with intersections to model and to answer the following problem: “What is
the area of a 5 inch by 7 inch picture?”
17. (5 pts) Use partial products to calculate ETtwelve  35twelve .
18. (4 pts) Use the dealing out set model to calculate 20  4 .
19. (6 pts) In a sequence the first three figures composed of unit square tiles are given. Let S  n  be the
function giving the total number of unit square tiles in the nth figure. Find the formula for S  n  in terms
of n.
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20. (6 pts) Use the charged field model to calculate the following.
a.
b.

35

42
21. (3 pts) Use mental math to calculate 56 – 38. Clearly indicate your „mental‟ steps.
22. (4 pts) What property justifies each of the following?
a.
3 10  6 1   4 10  2 1  3 10  6 1    4 10   2 1
b.
3 10  6 1   4 10  2 1  3 10  6 1   4 10  2 1


23. (5 pts) Use the distributive property of multiplication over addition of integers to show 1a  a  0 ;
justify each step. Hint: a  1a .
24. (3 pts) Use the definition of less than to prove  2  3 .
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25. (7 pts) How many grams of 25% red dye should be added to a 60% red dye powder to obtain 35 grams
of 40% red dye powder?
a. Define your variable.
b. Set up ONE equation.
c. Solve the equation.
d. Answer the question. Remember the units.
26. (4 pts) Prove  a  b   ab .
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27. (7 pts) If n is a whole number such that n  0 , prove that 0  n  0 .
28. (5 pts) Use repeated subtraction to calculate 10011two  11two . If there is a remainder, express your
answer using the division algorithm form.
29. (5 pts) For integers x and y, prove if x < y, then –x > –y. Assume: If x < y and n is any integer, then
x + n < y + n.