Algebra I
Chapter 1 Review Sheet
Name:
I. Vocabulary
Define each of the following words using your own words or by showing an example.
1. Domain – all of the x-coordinates of a relation
2. Range – all of the y-coordinates of a relation
3. Function – a special relation in which the x cannot repeat (every x can only have 1 y)
4. Relation – a bunch of ordered pairs that make a graph
5. Natural Numbers – counting numbers
6. Whole Numbers – natural numbers and 0
7. Integers – all of the whole numbers and their opposites
8. Rational Numbers – any number that can be expressed as a fraction (repeating or terminating decimals)
9. Irrational Numbers – any number than cannot be turned into a fraction
II. Properties
Write in your own words what each property means. Then, show an example of how each property is
used.
10. Commutative Property CHANGE THE ORDER OF THE NUMBERS
x+3=3+x
OR
7(x – y) = (x – y) ∙ 7
11. Associative Property CHANGE WHAT THE PARENTHESES ARE AROUND (order doesn’t change)
x + (7 + y) = (x + 7) + y
12. Distributive Property GIVE WHATEVER IS ON THE OUTSIDE TO EVERYTHING ON THE INSIDE
8(x – 3) = 8x – 24
13. Reflexive Property TWO SIDES OF AN EQUATION ARE IDENTICAL
3x + 7 = 3x + 7
14. Symmetric Property IF/THEN…SWAP SIDES OF THE EQUAL SIGN WITH THE PROBLEM
If 3 = 2x + 8, then 2x + 8 = 3
15. Transitive Property IF/AND/THEN
If 3x = 9, and 9 = x + 7, then 3x = x + 7
16. Additive Inverse Property Any number plus its opposite is 0.
5 + (–5) = 0
17. Multiplicative Inverse Any number times its reciprocal is always 1.
5 ∙ (1/5) = 1
18. Additive Identity Any number plus 0 is that number.
x+0=x
19. Multiplicative Identity Any number times 1 is that same number.
y∙1=y
20. Multiplicative Property of Zero Any number times 0 is always 0.
xyz ∙ 0 = 0
21. Substitution Plug in a number for something that it is equivalent to.
4(9 – 3) = 4(6)
III. Review Problems
Write an algebraic expression that represents each verbal expression.
22. a number to the fifth power
23. Five times a number squared
x5
5x2
24. the sum of a number and twenty-one
x + 21
25. Eight subtracted from twice a number
2x – 8
26. A frog can jump twenty times the length of its body. If a frog’s body length is b, write an algebraic
expression to describe the length the frog could jump.
20b
Evaluate each expression using the order of operations.
27. 4  3  5(6  3)
2
6( 4 3  2 2 )
28.
93
42 ∙ 3 – 5(9)
=
6(64  4)
93
16 ∙ 3 – 5(9)
=
6(68)
12
48 – 45
=
408
12
3
= 34
29.
6ty
if t = 4, x = 3 and y = 2
x
6(4)( 2)
=
3
=
30. 8( x  y)2  3t if x = 3, y = 2, and t = 4
= 8(3 – 2)2 + 3(4)
48
3
= 8(1)2 + 3(4)
= 16
= 8(1) + 3(4)
= 8 + 12
= 20
31. Alan ran twice as many miles on Tuesday as he did on Monday and five more miles on Wednesday than he
did on Monday. Write and evaluate an expression to find the total number of miles he ran if he ran 5 miles on
Monday.
Monday = 5
Tuesday = 2(5)
Wednesday = 5 + 5
5 + 2(5) + (5 + 5)
5 + 2(5) + 10
5 + 10 + 10
25 miles
Fill in the blank with the property used to evaluate each expression.
1
3(4  4) 2  (4)
(7  7)(5)  3  1
32.)
33.)
4
1
3(1) 2  (4) Substitution
(0)(5)  3  1 Subsitution
4
1
3(1)  ( 4) Multiplicative Identity (1 ∙ 1 = 1)
Mult. Prop. Of Zero
0  3 1
4
1
3  ( 4) Multiplicative Identity
Mult. Identity
03
4
3  1 Multiplicative Inverse (reciprocals)
2
3
Additive Identity
Substitution
34. Emilia promised her brother one half of the cookies that she made. If she did not make any cookies,
determine how many she owes her brother and identify the property represented.
(1/2) of 0 = 0
Multiplicative Property of Zero
Rewrite each expression using the Distributive Property.
35.) 8(15 – 6)
36.) 4(x + 1)
8(15) – 8(6)
4x + 4
120 – 48
37.) –3(2x – 8)
–6x + 24
38. Simplify the following expression: 3(2 + 3x) + 21x
6 + 9x + 21x (Distributive Property)
6 + 30 x
(Added Like Terms…be careful, x’s + x’s = x’s, NOT x2’s!!
39. What number BEST classifies
7
?
15
40. What number BEST classifies
Rational Number
45 ?
Irrational Number
41. Belinda’s square bedroom is 10
41
feet long. The area of Jarrod’s bedroom is 115 square feet. Whose
50
bedroom is larger? Explain.
 41  41 
Area of Belinda’s room = 10 10 
 50  50 
 541  541 
=


 50  50 
=
292681
square feet, which is 117.0724 square feet (divided in calc.)
2500
Since 117.0724 > 115, Belinda’s bedroom must be larger.
Use the following graph to answer questions 42–43.
Score on Math Test
100
B
80
D
60
A
E
40
F
C
20
0
0
1
2
3
4
5
6
Hours of Study
42. Name the ordered pair at point A and explain what it represents.
(2, 60) means this person studied 2 hours and made a 60 on the math test.
43. Is the relation given a function? Why or why not?
Yes, the relation is a function because x does not repeat (my two x’s only have one y)
44. Identify the graph that represents the altitude of an airplane taking off, flying for a while, and then landing.
A.)
B.)
Altitude
C.)
Altitude
Time
Altitude
Time
Time