Algebra 1

by Benson, John; Dodge, Sara; Dodge, Walter; Hamberg, Charles; Milauskas, George; Rukin, Richard

• ISBN13: 9780812387513
• ISBN10: 0812387511
• Edition: Revised
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: HOUGHTON MIFFLIN SCHOOL

Table of Contents

A Letter to Students	xiv
A Preview of Algebra	2	(48)
Getting Started	4	(4)
Mathematical Excursion: Perfect Numbers	7	(1)
Expressing Numbers	8	(6)
Beginning to Work with Algebraic Expressions	14	(6)
Understanding Equations and Inequalities	20	(5)
Ways to Represent Data	25	(4)
Graphing	29	(5)
Translating Between Words and Symbols	34	(5)
Career Profile: Safe Skies, Happy Landings	38	(1)
Probability	39	(11)
Historical Snapshot: A Professional Mathematician	43	(1)
Chapter Summary	44	(1)
Review Problems	45	(3)
Chapter Test	48	(1)
Puzzles and Challenges	49	(1)
The Rules of Algebra	50	(42)
Algebraic Basics	52	(6)
Historical Snapshot: Child Prodigies	57	(1)
Solving Equations	58	(6)
Properties of Equality	64	(4)
The Substitution and Distributive Properties	68	(6)
Applications of Equation Solving	74	(7)
Career Profile: Looking at the Future	80	(1)
Formal Properties	81	(11)
Chapter Summary	86	(1)
Review Problems	87	(3)
Chapter Test	90	(1)
Puzzles and Challenges	91	(1)
Signed Numbers	92	(56)
The Number Line	94	(7)
Comparing Numbers on the Number Line	101	(7)
Addition of Real Numbers	108	(7)
Career Profile: Tornado Watch	114	(1)
Subtraction of Real Numbers	115	(5)
Multiplication and Division of Real Numbers	120	(6)
Mathematical Excursion: The Golden Ratio	125	(1)
Special Relationships	126	(6)
More Properties of Equality and Operations	132	(6)
Line Graphs, Bar Graphs, and Frequency Polygons	138	(10)
Chapter Summary	142	(1)
Review Problems	143	(3)
Chapter Test	146	(1)
Puzzles and Challenges	147	(1)
Working with Equations	148	(50)
Equations with Variables on Both Sides	150	(6)
Special Equations	156	(8)
Career Profile: Danger! Bridge Ahead	163	(1)
The Distributive Property in Equations	164	(7)
Rate Problems	171	(7)
Equations with Absolute Values or Squared Quantities	178	(7)
Historical Snapshot: Women in Mathematics	184	(1)
More Equations with Absolute Values or Squared Quantities	185	(6)
Survey Projects	191	(7)
Chapter Summary	192	(1)
Review Problems	193	(3)
Chapter Test	196	(1)
Puzzles and Challenges	197	(1)
Working with Inequalities	198	(46)
Solving Inequalities	200	(8)
Using Inequalities	208	(6)
Compound Inequalities	214	(6)
Mathematical Excursion: Boolean Algebra	219	(1)
Absolute Value and Other Inequalities	220	(7)
Properties of Inequality	227	(7)
Career Profile: Prescription for Financial Health	233	(1)
Circle Graphs, Pictographs, and Artistic Graphs	234	(10)
Chapter Summary	238	(1)
Review Problems	239	(3)
Chapter Test	242	(1)
Puzzles and Challenges	243	(1)
Graphing	244	(60)
Tables, Graphs, and Equations	246	(11)
Slope-Intercept Form of an Equation	257	(8)
The Geometry of Slope	265	(8)
Mathematical Excursion: The Geometry of Billiards	272	(1)
Other Forms of Linear Equations	273	(8)
One More Form of a Linear Equation	281	(8)
Career Profile: Where Have All the Sardines Gone?	288	(1)
Nonlinear Graphing	289	(15)
Historical Snapshot: From Salmon Fishing to Card Tricks	297	(1)
Chapter Summary	298	(1)
Review Problems	299	(3)
Chapter Test	302	(1)
Puzzles and Challenges	303	(1)
Formulas and Functions	304	(58)
Working with Formulas	306	(7)
Special Formulas of Geometry	313	(11)
Career Profile: New Solutions to Old Problems	323	(1)
Using the Quadratic Formula	324	(7)
Historical Snapshot: The Mathematics Follies	330	(1)
Literal Equations	331	(6)
Functions and Relations	337	(9)
Function Notation and Graphing	346	(7)
Mathematical Excursion: Mirrors Reveal the Stars	352	(1)
Mean, Mode, and Median	353	(9)
Chapter Summary	356	(1)
Review Problems	357	(3)
Chapter Test	360	(1)
Puzzles and Challenges	361	(1)
Systems of Equations	362	(52)
Solving Systems of Equations by Graphing	364	(10)
Career Profile: The Language of Space Science	373	(1)
More About Linear Systems	374	(8)
Solving Systems of Equations Using the Substitution Method	382	(9)
Mathematical Excursion: Clock Arithmetic	390	(1)
The Multiplication-Addition Algorithm and the Computer	391	(10)
Solving Systems of Inequalities by Graphing	401	(13)
Chapter Summary	408	(1)
Review Problems	409	(3)
Chapter Test	412	(1)
Puzzles and Challenges	413	(1)
Exponents and Radicals	414	(68)
Large Numbers	416	(7)
Multiplication Properties of Exponents	423	(9)
Division Properties of Exponents	432	(7)
Negative and Zero Exponents	439	(7)
Simplifying Radicals	446	(6)
Rationalizing	452	(6)
Career Profile: Marci Laurel, Speech and Language Pathologist	458	(1)
Radical Equations	459	(7)
Other Roots and Fractional Exponents	466	(6)
Historical Snapshot: Wartime Code Broken	471	(1)
Scattergrams	472	(10)
Chapter Summary	476	(1)
Review Problems	477	(3)
Chapter Test	480	(1)
Puzzles and Challenges	481	(1)
Polynomials	482	(60)
Anatomy of a Polynomial	484	(6)
Addition and Subtraction of Polynomials	490	(6)
Mathematical Excursion: Prime Number Generators	495	(1)
Multiplication of Polynomials	496	(5)
Special Multiplications	501	(7)
Historical Snapshot: Srinivasa Ramanujan	507	(1)
Factoring	508	(6)
Factoring Trinomials	514	(8)
Career Profile: Creative Applications of Chemistry	521	(1)
More About Factoring Trinomials	522	(8)
Factoring Special Polynomials	530	(12)
Chapter Summary	536	(1)
Review Problems	537	(3)
Chapter Test	540	(1)
Puzzles and Challenges	541	(1)
Quadratics	542	(56)
Graphing the Parabola	544	(9)
Mathematical Excursion: Euclid's Algorithm	552	(1)
Graphing Other Parabolas	553	(9)
Completing the Square in Quadratic Functions	562	(7)
The Parabola and the Quadratic Equation	569	(12)
Career Profile: Exploring Space Without Leaving Earth	580	(1)
Projectile Motion	581	(7)
Measures of Dispersion	588	(10)
Chapter Summary	592	(1)
Review Problems	593	(3)
Chapter Test	596	(1)
Puzzles and Challenges	597	(1)
Proportion and Rational Equations	598	(102)
Ratio and Proportion	600	(7)
Applications of Proportion	607	(9)
Direct and Inverse Variation	616	(8)
Historical Snapshot: Fractions Within Fractions	623	(1)
Simplifying Rational Expressions	624	(7)
Multiplication and Division of Rational Expressions	631	(7)
Solving Rational Equations	638	(8)
Career Profile: A Habitat Study of Alaskan Birds	645	(1)
Addition and Subtraction of Rational Expressions	646	(6)
Stem-and-Leaf Plots and Box-and-Whisker Plots	652	(11)
Chapter Summary	656	(1)
Review Problems	657	(3)
Chapter Test	660	(1)
Puzzles and Challenges	661	(2)
Table of Squares and Square Roots	663	(1)
Table of Properties	664	(2)
Table of Formulas	666	(1)
GRAPHING CALCULATOR HANDBOOK
Lesson 1 Working with Expressions	667	(4)
Lesson 2 Adding and Subtracting Matrices	671	(3)
Lesson 3 Scalar Multiplication and Matrix Multiplication	674	(2)
Lesson 4 Graphing Inequalities	676	(2)
Lesson 5 Graphing Linear Equations	678	(3)
Lesson 6 Setting the Viewing Window	681	(4)
Lesson 7 Finding Statistical Means	685	(3)
Lesson 8 Solving Systems of Linear Equations	688	(4)
Lesson 9 Finding a Line of Best Fit	692	(4)
Lesson 10 Finding Roots of Quadratic Equations	696	(4)
Selected Answers	700	(41)
Glossary	741	(6)
Index	747	(5)
Credits	752