Algebra Structure and Method Book 1

by Brown, Richard G.

• ISBN13: 9780395461402
• ISBN10: 0395461405
• Format: Hardcover
• Copyright: 1989-04-01
• Publisher: MCDOUG-LITTELL

Table of Contents

Introduction to Algebra
Variables and Equations
Variables	1	(5)
Grouping Symbols	6	(4)
Equations	10	(4)
Applications and Problem Solving
Translating Words into Symbols	14	(5)
Translating Sentences into Equations	19	(4)
Translating Problems into Equations	23	(4)
A Problem Solving Plan	27	(4)
Numbers on a Line
Number Lines	31	(5)
Opposites and Absolute Values	36	(9)
Working with Real Numbers
Additon and Subtraction
Basic Assumptions	45	(4)
Addition on a Number Line	49	(5)
Rules for Addition	54	(5)
Subtracting Real Numbers	59	(6)
Multiplication
The Distributive Property	65	(5)
Rules for Multiplication	70	(5)
Problem Solving: Consecutive Integers	75	(4)
Division
The Reciprocal of a Real Number	79	(4)
Dividing Real Numbers	83	(12)
Solving Equations and Problems
Transforming Equations
Transforming Equations: Addition and Subtraction	95	(7)
Transforming Equations: Multiplication and Division	102	(5)
Using Several Transformations	107	(5)
Solving Problems
Using Equations to Solve Problems	112	(4)
Equations with the Variable on Both Sides	116	(5)
Extending Your Problem Solving Skills
Problem Solving: Using Charts	121	(5)
Cost, Income, and Value Problems	126	(4)
Proof in Algebra	130	(11)
Polynomials
Addition and Subtraction
Exponents	141	(5)
Adding and Subtracting Polynomials	146	(6)
Multiplication
Multiplying Monomials	152	(3)
Powers of Monomials	155	(3)
Multiplying Polynomials by Monomials	158	(3)
Multiplying Polynomials	161	(4)
Problem Solving
Transforming Formulas	165	(2)
Rate-Time-Distance Problems	167	(5)
Area Problems	172	(3)
Problems without Solutions	175	(10)
Factoring Polynomials
Quotients and Factoring
Factoring Integers	185	(4)
Dividing Monomials	189	(5)
Monomial Factors of Polynomials	194	(6)
Products and Factors
Multiplying Binomials Mentally	200	(4)
Differences of Two Squares	204	(4)
Squares of Binomials	208	(5)
Factoring Patterns
Factoring Pattern for x2 + bx + c, c positive	213	(4)
Factoring Pattern for x2 + bx + c, c negative	217	(3)
Factoring Pattern for ax2 + bx + c	220	(4)
General Factoring and its Application
Factoring by Grouping	224	(3)
Using Several Methods of Factoring	227	(3)
Solving Equations by Factoring	230	(4)
Using Factoring to Solve Problems	234	(13)
Fractions
Algebraic Fractions
Simplifying Fractions	247	(4)
Multiplying Fractions	251	(4)
Dividing Fractions	255	(4)
Adding and Subtracting Fractions
Least Common Denominators	259	(5)
Adding and Subtracting Fractions	264	(6)
Polynomial Division
Mixed Expressions	270	(4)
Polynomial Long Division	274	(13)
Applying Fractions
Ratio and Proportion
Ratios	287	(6)
Proportions	293	(5)
Fractional Equations
Equations with Fractional Coefficients	298	(6)
Fractional Equations	304	(5)
Percent Problems
Percents	309	(6)
Percent Problems	315	(6)
Mixture and Work Problems
Mixture Problems	321	(5)
Work Problems	326	(5)
Problems Involving Exponents
Negative Exponents	331	(5)
Scientific Notation	336	(13)
Introduction to Functions
Using Two Variables
Equations in Two Variables	349	(4)
Points, Lines, and Their Graphs	353	(7)
Linear Equations
Slope of a Line	360	(6)
The Slope-Intercept Form of a Linear Equation	366	(5)
Determining an Equation of a Line	371	(3)
Functions
Functions Defined by Tables and Graphs	374	(5)
Functions Defined by Equations	379	(4)
Linear and Quadratic Functions	383	(8)
Variation
Direct Variation	391	(6)
Inverse Variation	397	(16)
Systems of Linear Equations
Solving Systems of Linear Equations
The Graphing Method	413	(4)
The Substitution Method	417	(4)
Solving Problems with Two Variables	421	(5)
The Addition-or-Subtraction Method	426	(4)
Multiplication with the Addition-or-Subtraction Method	430	(8)
Application
Wind and Water Current Problems	438	(6)
Puzzle Problems	444	(13)
Inequalities
Inequalities in One Variable
Order of Real Numbers	457	(5)
Solving Inequalities	462	(7)
Solving Problems Involving Inequalities	469	(9)
Combining Open Sentences
Solving Combined Inequalities	478	(4)
Absolute Value in Open Sentences	482	(4)
Absolute Values of Products in Open Sentences	486	(4)
Inequalities in Two Variables
Graphing Linear Inequalities	490	(5)
Systems of Linear Inequalities	495	(12)
Rational and Irrational Numbers
Rational Numbers
Properties of Rational Numbers	507	(5)
Decimal Forms of Rational Numbers	512	(5)
Rational Square Roots	517	(4)
Irrational Numbers
Irrational Square Roots	521	(4)
Square Roots of Variable Expressions	525	(4)
The Pythagorean Theorem	529	(8)
Radical Expressions
Multiplying, Dividing, and Simplifying Radicals	537	(3)
Adding and Subtracting Radicals	540	(4)
Multiplication of Binomials Containing Radicals	544	(3)
Simple Radical Equations	547	(14)
Quadratic Functions
Quadratic Equations
Quadratic Equations with Perfect Squares	561	(3)
Completing the Square	564	(3)
The Quadratic Formula	567	(5)
Graphs of Quadratic Equations: The Discriminant	572	(4)
Using Quadratic Equations
Methods of Solution	576	(3)
Solving Problems Involving Quadratic Equations	579	(5)
Variation
Direct and Inverse Variation Involving Squares	584	(4)
Joint and Combined Variation	588	(12)
Looking Ahead
Probability
Sample Spaces and Events	600	(3)
Probability	603	(3)
Statistics
Frequency Distributions	606	(5)
Presenting Statistical Data	611	(5)
Geometry
Points, Lines, and Angles	616	(3)
Pairs of Angles	619	(2)
Triangles	621	(3)
Similar Triangles	624	(3)
Trigonometry
Trigonometric Ratios	627	(3)
Values of Trigonometric Ratios	630	(3)
Problem Solving Using Trigonometry	633	(6)
Extra Practice: Skills	639	(26)
Problem Solving	665	(16)
Tables	681	(4)
Appendix: Preparing for College Entrance Exams	685	(4)
Glossary of Properties	689	(2)
Glossary of Terms	691	(10)
Index	701	(10)
Acknowledgments	711