Sample Exam II
I. PROBLEM SOLVING.
1. 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)
II DEFINITIONS.
Define each of the following terms. (4 points each)
1. x is a prime number.
2. Associative property of +.
3. a divides b or a|b.
III MULTIPLE CHOICE.
In each case, circle the letter of the best response. (4 points each)
1. What do the following numbers have in common? 357 819 1001
a) They are all multiples of three b) They are all prime numbers
c) They are all divisible by seven d) They have a common factor greater than 10
2. What is the LCM of 
and
?
a) 
b) 
c) 
d) 
3. What is the GCF of 
and 
?
a) 
b) 
c) 
d) 
4. In base twelve.
a) T + E = 19 is not a basic fact.
b) 17 - T = 9 is not a basic fact.
c) 6 + 6 = 10 is not a basic fact.
d) They all are basic facts.
5. The following subtraction problem takes place in base "a". What is "a"?
a) nine
b) ten
c) eleven
d) twelve
6. The number 
has 168 divisors altogether. Therefor, x is?
a) 4
b) 5
c) 6
d) 7
7. 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
8. If x is a positive integer, then
a) -x is positive
b) -(-x) = -x
c) |-x| = x
d) None of the above
9. If A and C are integers, then
a) A + C is an integer
b) A - C is an integer
c) A ƒ C is an integer
d) All of the above
10. | -x | is which?
a) x
b) - x
c) x if 0 > x
-x if 
d) -x if 0 > x
x if
IV. CONCEPTS.
1. Solve? (2 points each)
a) 
b) 
2. If A and B are negative integers, and C is a positive integer, then determine whether each of the following are positive or negative. (3 points each)
a) (-A) * (-B)
b) A * (B-C)
c) A * C
d) (C-B) * (C-A)
3. In base five the next four numbers after 132(five) are: (4 points)
4. Complete the addition facts table below for base seven. (10 points)
5. Give the largest 5 digit number in base seven. (4 points)
6. What is wrong with 5345(five)? (4 points)
V. COMPUTATION. SHOW YOUR WORK WHENEVER POSSIBLE.
1. Calculate the following by the algorithm of your choice. (Do not convert to base 10) (6 points each)
a) Base 5
b) Base 7
c) Base Twelve
2. 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
3. Find the missing values in the lattice multiplication problem shown below. Then find the product. (6 points)
4. 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?
5. Which is greater, the GCF(800,120) or LCM(6,120)? (4 points)
6. Find the GCF(111547, 104927). (6 points)
7. Find the GCF and LCM of 90 and 468. Use the method of your choice. Show your work. (6 points)
8. Determine whether 10447 is a prime or not. Explain your decision. (6 points)
9. Change each of the following to base ten. ( 6 points each)
a) 
b)
c) 
10. Change each of the following to the given base.. (6 points each)
a) 4631 to base five
b) 1324 to base eight
11. Compute by adding the complement. (4 points)
