Download 1 - Sumner

Name
Period
[1] Tell if the numbers shown are rational or irrational.
Consider these numbers:
7.54365436…
13
0.38
3.
0
2
0.344344434444…
a.) Write each of the numbers in the list above in the correct box:
Rational Numbers
Irrational Numbers
b.) Circle one of the numbers you said was rational. Explain how you decided that the
number was rational.
c.) Circle one of the numbers you said was irrational. Explain how you decided that the
number was irrational.
Compare the given numbers by inserting , >, or = to make a true statement.
[2]
13
3.0
[3] 7
3
4
 88
[4] Select True or False to indicate whether each comparison is true or false. Justify your
answer by showing your thinking.
True
False
Justify
[5] Locate the following numbers on a number line.

27

4
25
100
 4.25
[6] Sally and Johnny were asked to estimate 29 to the nearest integer. Sally said it was
closer to 5, while Johnny said it was closer to 6. Who is correct? Explain why you picked
your answer.
[7] What are all the possible values of y that make the statement true? Explain your answer.
y 
25
[8] Put the following numbers in order from least to greatest.
7
8
 36
0.81
11
12.9

6.1
[9] Give an example of an irrational number that would fall between 6 and 7. Justify your
answer.
Solve each equation. Show your supporting work.
[10] y³ = 64
[11] m² = 49
[12] The value of a cube is 1000 cm³. What is the length of an edge?
[13] A gift box in the shape of a cube has a volume of 216 cm³. What is the area of the base
of the box?
[14] The length of each side of a cube is x centimeters. If x is an integer, why can’t the
volume of the cube equal 15 cm³? Support your answer.
[15] If x is a positive integer, is
1
greater than, less than, or equivalent to
X2
3
1
? Show
X3
your work.
Simplify (write in exponential form):
*reminder: make all negative exponents positive
3
16.)
53  54  5
19.)
79
713
22.)
 6 w5  3w8 


7
 2w

25.) Explain why
17.)
20.)
4 xy 3  6 x 5 y 2 
  7 3 5 


4
x0  1
23.)
4 4
   
9 9
18.)
2
4
 
9
21.)  2x y 
4
3
3
2
6
4

2 5
24.)
9 8 
2 6
1
93
26.) Place the following expressions into the appropriate column:
a.)
62 y 4
36x y
b.)
x6
63 x 2 y 5
Equivalent to 6 x 4 y
6
4
c.)
62 y 4 x 6
d.)
Not Equivalent to:
62 x 2 y 4
63 x 2 y 5
6 x4 y
27.) Alexa says that the product of 25 and 34 is 69. Is she correct? Explain.
8
28.) Write 16 as a power with a base of 4.
29.) Which expression is equivalent to
a.)
2410
b.)
2425
30.)Which expression is equivalent to
a.)
7
b.)
45  65 ?
c.)
 72 
825  3
d.)
85  35
5
7 6
74
c.)
713
d.)
716
31.) Select all of the expressions that have a value between 0 and 1.
4
a.)
87  812
b.)
7
7 3
c.)
1
 
3
2
1
 
3
 5 
 5  10
6
9
d.)