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Date: _________________
Directions: Please show all of your work. You may not use a calculator for #’s 1 – 20.
ALGEBRA 1B SKILLS REVIEW
Order of Operations
Evaluate the expression.
___________1.)
___________2.) 5  16  2  3
6  32
___________4.)  4  1  5   42
___________3.) 2  12  2  1
___________5.)

1
9  3  18
3
___________7.) 2.5  0.52  5
___________9.)


___________6.) 10  52  2  6
___________8.)
53  2
13  4
18  4 2  1
___________10.)
1  6 8
2
7  4  3 15
2
1
Variable Expressions
Evaluate the expression when a = 10, b = 9, c = 4 and d = -5
___________12.) 4c  7.8
___________11.) 2a  3
___________13.)
27
8
b
___________14.) a 4  9c
___________15.) a 2  18b  c
___________16.) bc  12.3
___________17.) 3a  2b  6c
___________18.)
___________19.)
 (d )
a
abc
c2  b  3
___________20.) ab  3  c  d 
3
Combining Like Terms
11
Evaluate the expression.
___________21.)  6k  7 k
___________22.) 12 y  8  12
___________23.) 3xy  8 z  7 xy  3z
___________24.) a  b  c  2c
___________25.) 3a  2b  6c
___________26.)  6 x 2  9 x 2
___________27.)  6w 12  3w  2 x 2 ___________28.) 3x 2  4 x  8  7 x 2
Distributive Property
Use the distributive property to rewrite the expression without parentheses.
___________29.)  7x  3
___________30.) 54 x  6 y 
___________31.) 8  3 y 3 y
___________32.)  7 x  7
___________33.)  5n  36  7n
___________34.)  2n  9  10n
11
___________35.) 10  59n  9
___________36.)  310b  10  5b  2
Comparing Numbers
Write the real numbers from least to greatest.
1
, 1.75, 23
6
_____________________________37.)
8,  4.1,  9,
_____________________________38.)
10,  6 , 9, 3 ,  11, 0, 3
_____________________________39.)
 , 3.7,  18, 1 ,
2
3
1 11
,  22 , 2.65
3 8
Identify the number that is given. Circle ALL that apply.
40.) Define the following:
a) Natural (or Counting) Numbers:
b) Whole Numbers:
c) Integers:
d) Rational Numbers:
e) Irrational Numbers:
f) Real Numbers:
41.) Identify the following numbers as rational, irrational, real, whole, integer, or
natural. Please write all that apply.
a)
1.417
b)

11
c)
25
𝟏
d)
e)
𝟐
𝟑
2
f) 3.666666 ....
Properties
State each property being demonstrated. Each property from the word bank will be used.
Commutative Property of Addition
Associative Property of Addition
Commutative Property of Multiplication
Identity Property of Addition
Associative Property of Multiplication
Identity Property of Multiplication
Zero Product Property
42. 3𝑏(1) = 3𝑏
_________________________________________
43. 10 + 𝑑 + 5 = 10 + 5 + 𝑑
__________________________________________
44. – 3(4𝑥) = (−3 ∗ 4)𝑥
__________________________________________
45. – 2 + (1 + 𝑥) = (−2 + 1) + 𝑥
__________________________________________
46. 5𝑎 + 0 = 5𝑎
__________________________________________
47. (6)(𝑦)(15) = (6)(15)(𝑦)
__________________________________________
48. (4𝑤 − 3) ∗ 0 = 0
__________________________________________
Formulas
Solve for the indicated variable.
49)
P  2l  2w Solve for l .
51) C 
50)
5
( F  32) Solve for F.
9
I  Pr t
Solve for r.
52) 9  y  1.5 x
11
Solve for y.
53) 1  7 y  5 x  2
Solve for y.
Solving Linear Equations
Solve each equation.
54) a  (6)  22
55)
14  r  3
x
 2
10
57)
 6a  3
56)
3
x  7  17
58)
5
59) 4( x  4)  8
60)
x  6x  4  10x  44
61)  6  2( x  6)  36
62)
5  4x  12  29  x
63) 4 x  2(2 x  3)
Linear Inequalities
11
Solve and graph each inequality.
64) 3 y  8
65)
 16  4z
66) 4 y  16  4
67)
4x  5  6x  2x  18
2
x  1  11
68)
3
y3
 8
69)
2
70)  9 x  4(4 x  3)  33
11
ANSWER KEY
26)
 15x 2
quotient of two
integers
9
27) 2 x  9w  12
2) 11
3) 9
4) 4) -16
5) 27
28)  4 x  4 x  8
1)
2
2
29)
 7 x  21
30) 20 x  30 y
6) 10
7) 0.125
2
31) 24 y  9 y
8) 3
32)
 7x  7
33)
16n  18
34)
8n  9
11) 23
35)
 45n  55
12) 8.2
36)
 25b  20
250
9)
29
10) 27
13) 11
41) a) real, rational
b) real, irrational,
1
6
37)  9,4.1, ,1.75,8,23
14) 10,036
15) -58
19) 
1
200
2
3
39)
43) Commutative Property
of Addition
44) Associative Property of
Multiplication
40) a) 1,2,3,4,5….
20) 230
k
22)
12 y  20
23)
 4 xy  11z
24)
a  b  3c
25)
3a  2b  6c
e) real, irrational
42) Identity Property of
Multiplication
b) 0,1,2,3,4,5,…
21)
d) real, rational
38)  11,0, 3 ,3 , 6 ,9,10
1 11
 18,1 , ,2.65,  ,3.7,  22
3 8
18) 36
c) real, rational,
integer whole number,
natural number
f) real, rational
16) 48.3
17) 24
f) The set of
numbers
consisting of the
positive
numbers,
negative
numbers, and
zero. (rational
and irrational
numbers)
c) Whole numbers
and their
opposites (…-3,2,-1,0,1,2,3,…)
d) A number that
can be written
as the quotient
of two integers
e) A number that
cannot be
written as the
11
45) Associative Property of
Addition
46) Identity Property of
Addition
47) Commutative Property
of Multiplication
48) Zero Product Property
49) l 
P  2w
2
50) r 
I
Pr
9
C  32
5
51) F 
52) y  1.5 x  9
53) y 
5x  3
7
54)
a  16
55)
r  11
56)
x  20
57)
a2
58)
x  40
59)
x  6
60) x  
8
3
61) x  21
62)
x  4
63) No Solution
For #64-70, check student
graphs.
64) y 
65)
8
3
z  4
66) y  3
67) x 
13
4
68) x  18
69) y  19
70)
x  3
11