Beginning and Intermediate Algebra Practice Problems Only
[Pages:177]Beginning and Intermediate Algebra Practice Problems Only
An open source (CC-BY) textbook by Tyler Wallace
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Table of Contents
Chapter 0: Arithmetic 0.1 Integers....................................................5 0.2 Fractions..................................................7 0.3 Order of Operations................................9 0.4 Properties of Algebra.............................10 Chapter 1: Linear Equations 1.1 One-Step Equations...............................12 1.2 Two-Step Equations...............................13 1.3 General Linear Equations......................14 1.4 Solving with Fractions...........................15 1.5 Formulas................................................16 1.6 Absolute Value Equations.....................17 1.7 Variation................................................18 1.8 Appliction: Number and Geometry.......21 1.9 Application: Age....................................24 1.10 Application: Distance..........................27 Chapter 2: Graphing 2.1 Points and Lines....................................31 2.2 Slope......................................................32 2.3 Slope-Intercept Form.............................34 2.4 Point-Slope Form...................................36 2.5 Parallel and Perpendicular Lines...........38
Chapter 3: Inequalities 3.1 Solve and Graph Inequalities................40 3.2 Compound Inequalitites........................42 3.3 Absolute Value Inequalities..................43 Chapter 4: Systems of Equations 4.1 Graphing...............................................44 4.2 Substitution..........................................45 4.3 Addition/Elimination...........................47 4.4 Three Variables.....................................48 4.5 Application: Value................................50 4.6 Application: Mixtures...........................53 Chapter 5: Polynomials 5.1 Exponent Properties.............................56 5.2 Negative Exponents..............................57 5.3 Scientific Notation................................58 5.4 Introduction to Polynomials.................59 5.5 Multiply Polynomials............................61 5.6 Multiply Special Products....................62 5.7 Divide Polynomials...............................63
3
Chapter 6: Factoring 6.1 Greatest Common Factor......................64 6.2 Grouping...............................................65 6.3 Trinomials where a = 1..........................66 6.4 Trinomials where a 1..........................67 6.5 Factoring Special Products...................68 6.6 Factoring Strategy................................69 6.7 Solve by Factoring................................70 Chapter 7: Rational Expressions 7.1 Reduce Rational Expressions................71 7.2 Multiply and Divide..............................72 7.3 Least Common Denominator................73 7.4 Add and Subtract.................................74 7.5 Complex Fractions................................75 7.6 Proportions...........................................77 7.7 Solving Rational Equations...................79 7.8 Application: Dimensional Analysis.......80 Chapter 8: Radicals 8.1 Square Roots.........................................82 8.2 Higher Roots.........................................83 8.3 Adding Radicals....................................84 8.4 Multiply and Divide Radicals...............85 8.5 Rationalize Denominators.....................86 8.6 Rational Exponents..............................88 8.7 Radicals of Mixed Index.......................89 8.8 Complex Numbers................................90
Chapter 9: Quadratics 9.1 Solving with Radicals.............................91 9.2 Solving with Exponents..........................92 9.3 Complete the Square..............................93 9.4 Quadratic Formula.................................94 9.5 Build Quadratics From Roots................95 9.6 Quadratic in Form..................................96 9.7 Application: Rectangles..........................97 9.8 Application: Teamwork..........................98 9.9 Simultaneous Products.........................102 9.10 Application: Distance and Revenue....103 9.11 Graphs of Quadratics.........................105 Chapter 10: Functions 10.1 Function Notation...............................106 10.2 Operations on Functions.....................108 10.3 Inverse Functions................................111 10.4 Exponential Functions........................112 10.5 Logarithmic Functions........................113 10.6 Application: Compound Interest........114 10.7 Trigonometric Functions.....................116 10.8 Inverse Trigonometric Functions.........121
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0.1
Practice - Integers
Evaluate each expression. 1) 1 - 3 3) ( - 6) - ( - 8) 5) ( - 3) - 3 7) 3 - ( - 5) 9) ( - 7) - ( - 5) 11) 3 - ( - 1) 13) 6 - 3 15) ( - 5) + 3 17) 2 - 3 19) ( - 8) - ( - 5) 21) ( - 2) + ( - 5) 23) 5 - ( - 6) 25) ( - 6) + 3 27) 4 - 7 29) ( - 7) + 7 Find each product. 31) (4)( - 1) 33) (10)( - 8) 35) ( - 4)( - 2) 37) ( - 7)(8) 39) (9)( - 4)
2) 4 - ( - 1) 4) ( - 6) + 8 6) ( - 8) - ( - 3) 8) 7 - 7 10) ( - 4) + ( - 1) 12) ( - 1) + ( - 6) 14) ( - 8) + ( - 1) 16) ( - 1) - 8 18) 5 - 7 20) ( - 5) + 7 22) 1 + ( - 1) 24) 8 - ( - 1) 26) ( - 3) + ( - 1) 28) 7 - 3 30) ( - 3) + ( - 5)
41) ( - 5)(2) 43) ( - 5)(4) 45) (4)( - 6) 32) (7)( - 5) 34) ( - 7)( - 2)
5
36) ( - 6)( - 1) 38) (6)( - 1) 40) ( - 9)( - 7)
Find each quotient.
46)
30 - 10
48)
- 12 -4
50)
30 6
52)
27 3
54)
80 -8
56)
50 5
58)
48 8
60)
54 -6
42) ( - 2)( - 2) 44) ( - 3)( - 9)
47)
- 49 -7
49)
-2 -1
51)
20 10
53)
- 35 -5
55)
-8 -2
57)
- 16 2
59)
60 - 10
6
0.2
Practice - Fractions
Simplify each. Leave your answer as an improper fraction.
1)
42 12
3)
35 25
5)
54 36
7)
45 36
9)
27 18
11)
40 16
13)
63 18
15)
80 60
17)
72 60
19)
36 24
Find each product.
2)
25 20
4)
24 9
6)
30 24
8)
36 27
10)
48 18
12)
48 42
14)
16 12
16)
72 48
18)
126 108
20)
160 140
21)
(9)(
8 9
)
23)
(2)( -
2 9
)
25)
(
-
2)(
13 8
)
27)
(
-
6 5
)(
-
11 8
)
29)
(8)(
1 2
)
31)
(
2 3
)(
3 4
)
33
(2)(
3 2
)
35)
(
1 2
)(
-
7 5
)
Find each quotient.
22)
(-
2)(
-
5 6
)
24)
(-
2)(
1 3
)
26)
(
3 2
)(
1 2
)
28)
(-
3 7
)(
-
11 8
)
30)
(-
2)(
-
9 7
)
32)
(-
17 9
)(
-
3 5
)
34)
(
17 9
)(
-
3 5
)
36)
(
1 2
)(
5 7
)
37)
-
2
?
7 4
7
39)
-1 9
?
-1 2
41)
-3 2
?
13 7
43)
-
1
?
2 3
45)
8 9
?
1 5
47)
-9 7
?
1 5
49)
-2 9
?
-3 2
51)
1 10
?
3 2
38)
- 12 7
?
-9 5
Evaluate each expression.
53)
1 3
+(-
4 3
)
55)
3 7
-
1 7
57)
11 6
+
7 6
59)
3 5
+
5 4
61)
2 5
+
5 4
63)
9 8
+(-
2 7
)
65)
1
+
(
-
1 3
)
67)
(
-
1 2
)
+
3 2
69)
1 5
+
3 4
71)
(
-
5 7
)
-
15 8
73)
6
-
8 7
75)
3 2
-
15 8
77)
(
-
15 8
)
+
5 3
79)
(
-
1)
-
(
-
1 6
)
81)
5 3
-(-
1 3
)
40)
-
2
?
-3 2
42)
5 3
?
7 5
44)
10 9
?
-
6
46)
1 6
?
-5 3
48)
- 13 8
?
- 15 8
50)
-4 5
?
- 13 8
52)
5 3
?
5 3
54)
1 7
+(-
11 7
)
56)
1 3
+
5 3
58)
(-
2)
+
(
-
15 8
)
60)
(7
- 1)
-
2 3
62)
12 7
-
9 7
64)
(-
2)
+
5 6
66)
1 2
-
11 6
68)
11 8
-
1 2
70)
6 5
-
8 5
72)
(-
1 3
)
+
(
-
8 5
)
74)
(-
6)
+
(
-
5 3
)
76)
(-
1)
-
(
-
1 3
)
78)
3 2
+
9 7
80)
(-
1 2
)
-
(-
3 5
)
82)
9 7
-(-
5 3
)
8
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