5. An absent minded teller switched dollars and cents when cashing a check for Jill. After she spent 5¢ on candy she noticed that she had left twice as much as the original check. For what amount was the check made? (8 points)
6. Nina noticed that every 30 seconds the temperature of a reaction in her lab was decreasing by a fixed number of degrees. Initially, the temperature was 28C and 5 minutes later was -12C. In a second experiment, she noticed that the temperature was initially -57C and was decreasing by 3C each minute. If she started the two reactions at the same time, answer the following:
a) When were the temperatures of the two reactions the same? (5 points)
b) What was the temperature? (3 points)
7. The directions on a juice can say to mix a can of concentrate with 3 cans of water.
a. What is the ratio of water to concentrate? (3 points)
b. How many 6oz. cans of concentrate will be needed to make 72 oz. of juice? (5 points)
8. A school has 1400 students. The ratio of students to teachers is 35:1. If more teachers are hired to make the ratio 20:1, how many teachers were hired? (8 points)
9. An old platform is 33 ft. by 24 ft. What should be cut away so that the ratio of the shorter side to the longer side is 2:3 and as little as possible is removed? (8 points)
10. A tire comes with 
inch of tread. The first 
inch wears off quickly during the first 1000 miles. Then it wears slowly and uniformly. It is worn out when 
inch is left.
a) What is left after 1000 miles? (3 points)
b) A tire has traveled 20, 000 miles and has 
inch left. How much farther will it last before it is worn out? (5 points)
II. CONCEPTS.
1. If you are given that f(x) = 
and g(x) = 4x+2, find the following: (3 points each)
a) g( f(1))
b) f ( g(-2) )
2. Which of the following arrow diagrams are functions? (2 points each)
a)
b)
c)
3. Simplify the following expressions using a single exponent in each case. (3 points each)
a) 
b) 
4. Given the following sets:
A = { 1, 3, 5, 7 }
B = { 1, 2, 3, 4 } ( 2 points each)
a) 
b) 
c) 
5. List all of the subsets of { u, v, w }. (5 points)
6. Shade the Venn Diagram below
to represent 
( 5 points)
7. Identify the shaded portion of the Venn Diagram below using set notation. (5 points)
8. Consider the table below: (2 points each)
*| A | B | C | D
| A | C | D | A | B
| B | D | A | B | C
| C | A | B | C | D
| D | B | C | D | A
| |
a)| 5 x ( 3 x 5 ) = 5 x ( 5 x 3 ) | 1) | Closure +
| 2) | Closure x
| b) | 3 x (5 + 2) = (3 x 5)+(3 x 2) | 3) | Commutativity +
| 4) | Commutativity x
| c) | 32 + (24 + 6) = 32 + (6+24) | 5) | Associativity +
| 6) | Associativity x
| d) | 6 x ( 3 x 7 ) = ( 3 x 7 ) x 6 | 7) | Identity +
| 8) | Identity x
| e) | 6 + ( 5 + 9 ) = ( 6 + 5 ) + 9 | 9) | Distributive Property
| |
12. Do truth tables for each of the following. ( 4 points each)
a)
b) 
13. What is the contra positive of the below statement. ( 4 points)
If it rains it pours.
14. Translate the following into symbols. ( 4 points)
If you go or he stays there will be trouble.
III. COMPUTATION. SHOW YOUR WORK WHENEVER POSSIBLE.
1. Change MMCMLXIXVII to Hindu-Arabic numerals. (3 points)
2. Change 1933 to each of the following systems. (4 points each)
a) Myan
b) Babylonian
c) Egyptian
3) Write in Hindu Arabic numerals each of the following numbers:(4 points each)
a) 
Babylonian
b) 
Babylonian
c) 
Myan
d) 
Myan
4. Change 838 to a base eleven numeral. (4 points)
5. Change 
from Egyptian to a Hindu Arabic number. ( 4 points)
6. Calculate the following by the algorithm of your choice. (Do not convert to base 10) (5 points each)
a) Base 5
b) Base 7
7. Divide 
in base eight. (6 points)
35 x 1 = 35
35 x 2 = 72
35 x 3 = 127
35 x 4 = 164
35 x 5 = 221
35 x 6 = 256
35 x 7 = 313
8. Find the missing values in the lattice multiplication problem shown below. Then find the product. (5 points)
9. Is 3,344,558,822 divisible by: (2 points each)
a) 2?
b) 3?
c) 4?
d) 5?
e) 6?
f) 9?
g) 11?
h) 12?
10. Which is greater, the GCF(800,120) or LCM(6,120)? (4 points)
11. Find the GCF(111547, 104927). (8 points)
12. Find the GCF and LCM of 
and 
. Use the method of your choice. Show your work. (8 points)
13. Determine whether 10447 is a prime or not. Explain your decision. (8 points)
14. Find a fraction between 
and 
. (4 points)
15. Illustrate 1/2 x 2/3 on a unit square model. (4 points)
16. What is the reciprocal of 
? (4 points)
17. Compute by adding the complement. (4 points)
18. 2 is what percent of 104? (4 points)
19. 44 is 110% of what? (4 points)
20. Complete the below table. Fractions do not have to be expressed in lowest terms. Decimals to 4 places. ( 2 points per blank.)
21. Find the character in the 200th decimal place of 
. (6 points)
22. Express 
as a fraction. (5 points)
23. If A and B are negative integers, and C is a positive integer, then determine whether each of the following are positive or negative or indeterminate. (3 points each)
a) A * (-B)
b) (-A) * (B-C)
24. Write 
as a fraction. (5 points)
25. What is the slope of the line 
(3 points)
26. Write the equation of the line through ( 3, 5) with slope -3/2. (5 points)
IV DEFINITIONS. Define each of the following terms. (4 points each)
1. x is a rational number.
2. Associative property of +.
3. Complement of set A or 
or 
.
4. Density property for rational numbers.
V MULTIPLE CHOICE. In each case, circle the letter of the best response. (4 points each)
1. Cindy has an equal number of dimes, nickels, and pennies. If the total value of the coins is $13.44, how many coins does she have?
Which of the following equations is useful in solving the problem?
a) p + 5p + 10d = 1344
b) 1p + 5n + 10d = 1344
c) p + n + d = 13.44
d) None of the above.
2. Which of the following is false?
a) The sum of positive rationals is a positive rational number.
b) The difference of positive rationals is a positive rational number.
c) The product of positive rationals is a positive rational number.
d) The quotient of positive rationals is a positive rational number.
3. Which of these fractions is between 
and 
a) 
b) 
c) 
d) 
4. What do the following numbers have in common?
43 347 1019
a) They are all multiples of 3
b) They are all divisible by 7
c) They have a common factor greater than 10
d) They are all prime
5. Which of the following fractions has a non-terminating decimal representation?
a) 
b) 
c) 
d) None of these.
6. Which statement below justifies the placement of the digit 9 when using the standard multiplication algorithm for the problem below?
a) 9 = 4 x 2 + 1
b) 90 = 5 x 20 - 10
c) 900 = 40 x 20 + 10
d) 900 = 40 x 20 + 100
7. The number 
has 192 divisors altogether. Therefor, x is?
a) 5
b) 5
c) 6
d) 7
8. Which of the following numbers is irrational?
a) 
b) 4.233233233...
c) 7.121231234...
d) None of the above.
9. If the 7 digit number 1, 336, 56_ is to be divisible by 6 then which of the following may be the missing digit?
a) 4
b) 5
c) 6
d) 7
10. Which of the following gives a value for 
?
a) 22/7
b) 3.14159
c) 
d) None of these
11. Which is the equation of this graph?