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Introduction to Algebra (The Art of Problem Solving)

by Richard Rusczyk Author

A rigorous and thorough introduction for students in grades 6-9 to algebra topics such as linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and more! Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual contains full solutions to all of the problems, not just answers. This book can serve as a complete Algebra I course, and also includes many concepts covered in Algebra II.

Tags:

algebra

Additional Details

Resource Type: Book
ISBN: 9781934124147
Print Status: In Print
Lessons: 120
Pages: 656
Publisher: AoPS Incorporated
Edition: 2nd Edition
Copyright: 2009
URL: http://www.artofproblemsolving.com/Store/viewit...

Lessons

1 1.1 Numbers (Chapter 1 Follow the Rules)
2 1.2 Order of Operations (Chapter 1 Follow the Rules)
3 1.3 When Does Order Matter? (Chapter 1 Follow the Rules)
4 1.4 Distribution and Factoring (Chapter 1 Follow the Rules)
5 1.5 Equations (Chapter 1 Follow the Rules)
6 1.6 Exponents (Chapter 1 Follow the Rules)
7 1.7 Fractional Exponents (Chapter 1 Follow the Rules)
8 1.8 Radicals (Chapter 1 Follow the Rules)
9 1.9 Summary (Chapter 1 Follow the Rules)
10 2.1 Expressions (Chapter 2 x Marks the Spot)
11 2.2 Arithmetic with Expressions (Chapter 2 x Marks the Spot)
12 2.3 Distribution, Subtraction, and Factoring (Chapter 2 x Marks the Spot)
13 2.4 Fractions (Chapter 2 x Marks the Spot)
14 2.5 Summary (Chapter 2 x Marks the Spot)
15 3.1 Solving Linear Equations I (Chapter 3 One-Variable Linear Equations)
16 3.2 Solving Linear Equations II (Chapter 3 One-Variable Linear Equations)
17 3.3 Word Problems (Chapter 3 One-Variable Linear Equations)
18 3.4* Linear Equations in Disguise (Chapter 3 One-Variable Linear Equations)
19 3.5 Summary (Chapter 3 One-Variable Linear Equations)
20 4.1 Evaluating Multi-Variable Expressions (Chapter 4 More Variables)
21 4.2 Still More Arithmetic (Chapter 4 More Variables)
22 4.3 Distribution and Factoring (Chapter 4 More Variables)
23 4.4 Fractions (Chapter 4 More Variables)
24 4.5 Equations (Chapter 4 More Variables)
25 4.6 Summary (Chapter 4 More Variables)
26 5.1 Introduction to Two-Variable Linear Equations (Chapter 5 Multi-Variable Linear Equations)
27 5.2 Substitution (Chapter 5 Multi-Variable Linear Equations)
28 5.3 Elimination (Chapter 5 Multi-Variable Linear Equations)
29 5.4 Word Problems (Chapter 5 Multi-Variable Linear Equations)
30 5.5 More Linear Equations in Disguise (Chapter 5 Multi-Variable Linear Equations)
31 5.6 More Variables (Chapter 5 Multi-Variable Linear Equations)
32 5.7 Summary (Chapter 5 Multi-Variable Linear Equations)
33 6.1 Basic Ratio Problems (Chapter 6 Ratios and Percents)
34 6.2 More Challenging Ratio Problems (Chapter 6 Ratios and Percents)
35 6.3 Conversion Factors (Chapter 6 Ratios and Percents)
36 6.4 Percent (Chapter 6 Ratios and Percents)
37 6.5 Percentage Problems (Chapter 6 Ratios and Percents)
38 6.6 Summary (Chapter 6 Ratios and Percents)
39 7.1 Direct Proportion (Chapter 7 Proportion)
40 7.2 Inverse Proportion (Chapter 7 Proportion)
41 7.3 Joint Proportion (Chapter 7 Proportion)
42 7.4 Rate Problems (Chapter 7 Proportion)
43 7.5 Summary (Chapter 7 Proportion)
44 8.1 The Number Line and the Cartesian Plane (Chapter 8 Graphing Lines)
45 8.2 Introduction to Graphing Linear Equations (Chapter 8 Graphing Lines)
46 8.3 Using Slope in Problems (Chapter 8 Graphing Lines)
47 8.4 Find the Equation (Chapter 8 Graphing Lines)
48 8.5 Slope and Intercepts (Chapter 8 Graphing Lines)
49 8.6 Comparing Lines (Chapter 8 Graphing Lines)
50 8.7 Summary (Chapter 8 Graphing Lines)
51 9.1 The Basics (Chapter 9 Introduction to Inequalities)
52 9.2 Which Is Greater? (Chapter 9 Introduction to Inequalities)
53 9.3 Linear Inequalites (Chapter 9 Introduction to Inequalities)
54 9.4 Graphing Inequalities (Chapter 9 Introduction to Inequalities)
55 9.5 Optimization (Chapter 9 Introduction to Inequalities)
56 9.6 Summary (Chapter 9 Introduction to Inequalities)
57 10.1 Getting Started With Quadratics (Chapter 10 Quadratic Equations---Part 1)
58 10.2 Factoring Quadratics I (Chapter 10 Quadratic Equations---Part 1)
59 10.3 Factoring Quadratics II (Chapter 10 Quadratic Equations---Part 1)
60 10.4 Sums and Products of Roots of a Quadratic (Chapter 10 Quadratic Equations---Part 1)
61 10.5* Extensions and Applications (Chapter 10 Quadratic Equations---Part 1)
62 10.6 Summary (Chapter 10 Quadratic Equations---Part 1)
63 11.1 Squares of Binomials (Chapter 11 Special Factorizations)
64 11.2 Difference of Squares (Chapter 11 Special Factorizations)
65 11.3 Sum and Difference of Cubes (Chapter 11 Special Factorizations)
66 11.4 Rationalizing Denominators (Chapter 11 Special Factorizations)
67 11.5 Simon's Favorite Factoring Trick (Chapter 11 Special Factorizations)
68 11.6 Summary (Chapter 11 Special Factorizations)
69 12.1 Numbers, Numbers, and More Numbers! (Chapter 12 Complex Numbers)
70 12.2 Imaginary Numbers (Chapter 12 Complex Numbers)
71 12.3 Complex Numbers (Chapter 12 Complex Numbers)
72 12.4 Summary (Chapter 12 Complex Numbers)
73 13.1 Squares of Binomials Revisited (Chapter 13 Quadratic Equations---Part 2)
74 13.2 Completing the Square (Chapter 13 Quadratic Equations---Part 2)
75 13.3 The Quadratic Formula (Chapter 13 Quadratic Equations---Part 2)
76 13.4* Applications and Extensions (Chapter 13 Quadratic Equations---Part 2)
77 13.5 Summary (Chapter 13 Quadratic Equations---Part 2)
78 14.1 Parabolas (Chapter 14 Graphing Quadratics)
79 14.2 Circles (Chapter 14 Graphing Quadratics)
80 14.3 Summary (Chapter 14 Graphing Quadratics)
81 15.1 Quadratic Inequalities (Chapter 15 More Inequalities)
82 15.2 Beyond Quadratics (Chapter 15 More Inequalities)
83 15.3 The Trivial Inequality (Chapter 15 More Inequalities)
84 15.4* Quadratic Optimization (Chapter 15 More Inequalities)
85 15.5 Summary (Chapter 15 More Inequalities)
86 16.1 The Machine (Chapter 16 Functions)
87 16.2 Combining Functions (Chapter 16 Functions)
88 16.3 Composition (Chapter 16 Functions)
89 16.4 Inverse Functions (Chapter 16 Functions)
90 16.5 Problem Solving with Functions (Chapter 16 Functions)
91 16.6 Operations (Chapter 16 Functions)
92 16.7 Summary (Chapter 16 Functions)
93 17.1 Basics (Chapter 17 Graphing Functions)
94 17.2 Transformations (Chapter 17 Graphing Functions)
95 17.3 Inverse Functions Revisited (Chapter 17 Graphing Functions)
96 17.4 Summary (Chapter 17 Graphing Functions)
97 18.1 Addition and Subtraction (Chapter 18 Polynomials)
98 18.2 Multiplication (Chapter 18 Polynomials)
99 18.3 Summary (Chapter 18 Polynomials)
100 19.1 Exponential Functions (Chapter 19 Exponents and Logarithms)
101 19.2 Show Me the Money (Chapter 19 Exponents and Logarithms)
102 19.3 Interest-ing Problems (Chapter 19 Exponents and Logarithms)
103 19.4 What is a Logarithm? (Chapter 19 Exponents and Logarithms)
104 19.5 Summary (Chapter 19 Exponents and Logarithms)
105 20.1 Radicals (Chapters 20 Special Functions)
106 20.2 Absolute Value (Chapters 20 Special Functions)
107 20.3 Floor and Ceiling (Chapters 20 Special Functions)
108 20.4 Rational Functions (Chapters 20 Special Functions)
109 20.5 Piecewise Defined Functions (Chapters 20 Special Functions)
110 20.6 Summary (Chapters 20 Special Functions)
111 21.1 Arithmetic Sequences (Chapter 21 Sequences & Series)
112 21.2 Arithmetic Series (Chapter 21 Sequences & Series)
113 21.3 Geometric Sequences (Chapter 21 Sequences & Series)
114 21.4 Geometric Series (Chapter 21 Sequences & Series)
115 21.5* Telescoping (Chapter 21 Sequences & Series)
116 21.6 Summary (Chapter 21 Sequences & Series)
117 22.1 Raising Equations to Powers (Chapter 22 Special Manipulations)
118 22.2 Self-similarity (Chapter 22 Special Manipulations)
119 22.3 Symmetry (Chapter 22 Special Manipulations)
120 22.4 Summary (Chapter 22 Special Manipulations)

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