Test 1 Review

Test #1 Review
The test this week will have questions from Assignments 0.1 through 0.7. You are responsible
for this content whether or not you were in this class at the time. These questions will be very
similar to the questions below. Review solutions are posted on Canvas, but they will not be
available after 7:00am on Wednesday for A-Day and 7:00am on Thursday for B-Day.
1. Set
12
7, ,0,3, , 10,4.5, 100 .
5
A
 
   
 
 
Identify all of the elements of set A that
are (a) rational numbers and (b) natural
numbers.
2. Evaluate the expression if x = –3, y = –4,
and z = 1:
 
2
2 5
2
x z
x y


3. Identify the property illustrated. Let a, b,
and c represent any real numbers.
a.    
a b c b c a
  
b.
2 2
1
7 7
 
c.
3 1 3 1
8 5 8 5
b b
   
  
   
   
d.  
4 4 0
a a
  
e.
1 1
5 5 5
2 2
a a
 
    
 
 
4. Simplify the expression  
3
3 2
4a b c
5. Simplify the following:
   
4 2 4 2
2 2 3 7 3 2
x xy y x xy y
    
6. Multiply the following:
  
3 2 4 7
x x
 
7. Simplify the following:
a.    
2 4 2 4
r s r s
   
  
  
b.
4 3 2
2
2 2 11 6
3
y y y y
y
  

8. Factor out the greatest common factor:
5 2 2 2 4 3 3 3
6 3 24
x y z x y z x y z
 
9. Factor completely:
a. 2
4 12
b b
 
b. 2
5 8 4
n n
 
c. 4 2
6 11 10
x x
 
10. Perform the indicated operations.
a.
2 2
2 2
2 11 15 6
6 8 2 8
x x x x
x x x x
   

   
b. 2 2
4 1
6 8 5 14
x x
x x x x
 

   
c.
2 2
y x
x y
y x
x y



11. Evaluate
2/3
27
125

 

 
 
12. Simplify. Write your answer with only
positive exponents. Assume that all
variables represent positive real numbers.
10
2/5 3/4 1/5
1/2 1/4
a b c
a c
 
 
 
 
13. Simplify. Assume that all variables
represent positive real numbers.
a) 3 5 3
16r s
b) 14 18 5
84a b c
14. Perform the indicated operation,
rationalize the denominator, and simplify.
1 1
3 27


Test 1 Review

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