Name
Date
Class
California Standards Preparation for AF1.3 and AF1.4
LESSON
Review for Mastery
1-2
Exponents
The exponent tells you how many times to multiply the base
by itself.
exponent
34
base
• To find 34, multiply the base (3) times itself 4 times.
To multiply, say to
yourself:
3 times 3 is 9
9 times 3 is 27
27 times 3 is 81
34 3 • 3 • 3 • 3 81
Find each value.
1. 43 •
•
64
2. 15 •
•
•
•
3. 52
4. 23
5. 33
6. 62
7. 82
8. 41
9. 53
10. 24
• You can write 64 using an exponent with the base 8.
8 • 8 64
So, 64 82.
Think: How many times
must you multiply 8
times itself to get a
product of 64?
Write each number using an exponent and the given base.
11. 216, base 6: and 36 • 6 so, 216 .
12. 16, base 4
13. 8, base 2
14. 9, base 3
15. 81, base 9
16. 27, base 3
17. 49, base 7
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2
Holt Mathematics
California Standards Preparation for AF1.3 and AF1.4
California Standards Preparation for AF2.0
LESSON
Review for Mastery
LESSON
Review for Mastery
1-1
Numbers and Patterns
1-2
Exponents
To identify a number pattern, ask:
What can I do to each number to
get the number that comes next?
2
6
The exponent tells you how many times to multiply the base
by itself.
The pattern is to add 4 to get the next
number. Use the pattern to get the
next three numbers.
10
18
14
22
exponent
34
base
• To find 34, multiply the base (3) times itself 4 times.
26
To multiply, say to
yourself:
3 times 3 is 9
9 times 3 is 27
27 times 3 is 81
34 3 • 3 • 3 • 3 81
2+4=6
6 + 4 = 10
and
236
but
6 3 ≠ 10
10 + 4 = 14
14 + 4 = 18
18 + 4 = 22
22 + 4 = 26
Find each value.
Identify the pattern. Use the pattern to find the next three
numbers.
19 , 16 , 13 , ...
1. 28, 25, 22,
Subtract
3
3
22 2. 6, 24, 42, 60,
18
Add
to get the next number.
19
60 18
78 , 96 , 114 , ...
to get the next number.
3
16
78
18
96
16
3
13
96
18
114
36 , 44 , 52 , ...
4. 3, 6, 12, 24,
•
4
•
4
64
1
•
1
•
1
•
3. 52
1
•
8. 41
36
9. 53
64
4
10. 24
125
16
• You can write 64 using an exponent with the base 8.
8 • 8 64
So, 64 82.
Think: How many times
must you multiply 8
times itself to get a
product of 64?
The pattern is to shade the next square
in a clockwise direction. Use the pattern
to get the next three figures.
To identify a geometric pattern, ask:
How can I change each figure to get the
next figure?
6. 62
27
Multiply by 2 to get the next number.
to get the next number.
1
5. 33
8
7. 82
48 , 96 , 192 , ...
1
4. 23
25
Add 8
4
2. 15 78
19
3. 4, 12, 20, 28,
1. 43 Write each number using an exponent and the given base.
Draw the next three figures in each pattern.
11. 216, base 6: 5.
36 • 6
12. 16, base 4
1
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32
16. 27, base 3
92
17. 49, base 7
33
72
2
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Holt Mathematics
California Standards AF1.3
California Standards AF1.3, AF1.4
LESSON
Review for Mastery
LESSON
Review for Mastery
1-3
Order of Operations
1-4
Properties of Numbers
You can use the Commutative Property, the Associative Property, and
the Distributive Property with mental math to simplify expressions.
To help you remember the order of operations use the phrase
“Please Excuse My Dear Aunt Sally.”
16 47 14 47 16 14
P: first, parentheses (if any)
E: second, exponents (if any)
M and D: then, multiplication and division, in order from left to right
A and S: finally, addition and subtraction, in order from left to right
8•3•53•8•5
Commutative Property
47 (16 14)
Associative Property
3 • (8 • 5)
47 40
Mental math
3 • 40
87
Mental math
120
9(28) 9(20 8)
Evaluate.
Parentheses
Exponents
9(28) 9(30 – 2)
39 (9 4) 5 22
(9 • 20) (9 • 8)
Distributive Property
(9 • 30) (9 • 2)
39 13 5 22
180 72
Mental math
270 – 18
39 13 5 4
252
Mental math
252
Multiply and divide from left to right
354
Add and subtract from left to right
844
Simplify each expression. Tell what properties you used.
45
1. (45 39) 25 (39 Simplify each expression.
1. 12 • 4 2
48
2
46
4. 8 20 4
13
7. 1 4 • 9 6 7
0
10. 4 • 5 8 2 7
17
2. 15 3 • 5
3. 15 • 3 5
5
45
•5
25
39 (
5
3
9
9. (18 6) 3
1
11. 2 • 3 8 22
4
25
(
8
8. 18 (6 3)
4
2. 25 • 7 • 4 25 •
6. 32 6 • 4 52
100
700
(5 •
1
3
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•
50
90
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8
10
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1
25
)
Commutative
Property
Associative
Property
Commutative
Property
Associative
Property
70
•
7
4
)•
7
7
•
3. 5(18) 5 • (10 12. 8(7 6) 23
) 25
109
9
5. 5 2 • 6 4 1
45
39 Distributive
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.
14. 9, base 3
23
15. 81, base 9
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63
so, 216 13. 8, base 2
42
6.
6•6•6
and 36 • 6 4. 6(29) 6 • (30 )
) (5 •
8
(6 •
)
40
180
174
30
Distributive
Property
4
1
)
) (6 •
1
)
6
Property
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Holt Mathematics