Addison-Wesley : Algebra

by Smith, Stanley A.

• ISBN13: 9780201812480
• ISBN10: 0201812487
• Edition: Student
• Format: Hardcover
• Copyright: 1994-01-01
• Publisher: PRENTICE HALL SCHOOL GROUP

Table of Contents

Introduction to Algebra
Ready for Introduction to Algebra?	2	(2)
Symbols and Expressions	4	(5)
Calculator: Order of Operations	7	(2)
The Commutative and Identity Properties	9	(6)
Exponential Notation	15	(4)
Calculator: Evaluating Expressions Involving Exponents	17	(2)
The Associative Properties	19	(5)
Calculator: Evaluating Expressions	20	(4)
The Distributive Property of Multiplication over Addition	24	(5)
Explore	24	(4)
Writing to Learn	28	(1)
Problem Solving: Writing Expressions	29	(4)
Historical Note	32	(1)
Solving Equations: An Introduction	33	(5)
Explore	33	(5)
Problem Solving: Strategies Draw a Diagram	38	(2)
Using Formulas	40	(4)
Problem for Programmers	43	(1)
Problem Solving: Strategies Guess, Check, Revise	44	(10)
Summary and Review	47	(3)
Test	50	(2)
Integers and Rational Numbers
Ready for Integers and Rational Numbers?	52	(2)
Integers and the Number Line	54	(5)
Connections: Geometry	58	(1)
Rational Numbers	59	(4)
Addition of Rational Numbers	63	(8)
Subtraction of Rational Numbers	71	(6)
Calculator: Adding and Subtracting Rational Numbers	73	(3)
Historical Note	76	(1)
Multiplication of Rational Numbers	77	(4)
Explore	77	(3)
Subsets of the Rational Numbers	80	(1)
Division of Rational Numbers	81	(8)
Problem for Programmers	86	(1)
Bonus Topic: Terminating and Repeating Decimals	86	(1)
Problem Solving: Application Moment Problems	87	(2)
Using the Distributive Property	89	(4)
Inverse of a Sum and Simplifying	93	(5)
Problem Solving: Strategies Write an Equation	98	(4)
Number Properties and Proofs	102	(12)
Summary and Review	107	(3)
Test	110	(2)
Equations
Ready for Equations?	112	(2)
The Addition Property of Equality	114	(5)
Explore	114	(5)
The Multiplication Property of Equality	119	(6)
Using the Properties Together	125	(5)
Connections: Geometry	129	(1)
Problem Solving: Expressions and Equations	130	(6)
Problem for Programmers	135	(1)
More on Solving Equations	136	(3)
Clearing an Equation of Fractions or Decimals	139	(3)
Formulas	142	(3)
Solving Equations Involving Absolute Value	145	(3)
Looking for Errors	147	(1)
Problem Solving: Proportions	148	(4)
Problem Solving: Using Percent	152	(6)
Math History	152	(2)
Calculator: Percents	154	(4)
Problem Solving: More Expressions and Equations	158	(5)
Problem Solving: Strategies Make an Organized List	163	(9)
Summary and Review	165	(3)
Test	168	(2)
Inequalities
Ready for Inequalities?	170	(2)
Inequalities and Their Graphs	172	(3)
The Addition Property of Inequalities	175	(5)
Connections: Geometry	179	(1)
The Multiplication Property of Inequalities	180	(3)
Using the Properties Together	183	(4)
Biographical Note: George Polya	186	(1)
Problem Solving: Using Inequalities	187	(7)
Problem for Programmers	191	(1)
Connections: Discrete Math If-Then Statements	192	(1)
Problem Solving: Application Reading Graphs	193	(1)
Problem Solving: Strategies Use Logical Reasoning	194	(10)
Summary and Review	196	(1)
Test	197	(1)
Cumulative Review	198	(4)
Exponents and Polynomials
Ready for Exponents and Polynomials?	202	(2)
Exponents	204	(5)
More with Exponents	209	(5)
Calculator: Evaluating Expressions	209	(4)
Suppose	213	(1)
Multiplying and Dividing Monomials	214	(3)
Scientific Notation	217	(4)
Calculator: Calculating with Scientific Notation	219	(2)
Polynomials	221	(5)
More on Polynomials	226	(5)
Calculator: Evaluating Polynomials	228	(3)
Addition of Polynomials	231	(5)
Problem for Programmers	235	(1)
Subtraction of Polynomials	236	(4)
Multiplication of Monomials and Binomials	240	(5)
Looking for Errors	244	(1)
Multiplying Binomials: Special Products	245	(4)
Writing to Learn	248	(1)
Multiplying Polynomials	249	(5)
Problem Solving: Application Formulas in Health Care	253	(1)
Problem Solving: Strategies Make a Table, Look for a Pattern	254	(8)
Summary and Review	256	(3)
Test	259	(1)
Polynomials and Factoring
Ready for Polynomials and Factoring?	260	(2)
Factoring Polynomials	262	(4)
Explore	262	(3)
Connections: Geometry	265	(1)
Differences of Two Squares	266	(4)
Trinomial Squares	270	(3)
Factoring x2 + bx + c	273	(5)
Suppose	277	(1)
Factoring ax2 + bx + c	278	(3)
Writing to Learn	280	(1)
Factoring by Grouping	281	(2)
Factoring: A General Strategy	283	(3)
Connections: Discrete Math Binomial Expansion	285	(1)
Solving Equations by Factoring	286	(5)
Problem for Programmers	290	(1)
Problem Solving: Using Equations	291	(13)
Biographical Note: Thomas Harriot	296	(1)
Problem Solving: College Entrance Exams Factoring	297	(2)
Summary and Review	299	(2)
Test	301	(1)
Graphs and Linear Equations
Ready for Graphs and Linear Equations?	302	(2)
Graphing Ordered Pairs	304	(5)
Math History	304	(5)
Graphing Equations	309	(4)
Linear Equations and Their Graphs	313	(5)
Explore	313	(4)
Spatial Relations	317	(1)
Slope	318	(5)
Writing to Learn	322	(1)
Equations and Slope	323	(5)
Explore	323	(4)
Suppose	327	(1)
Finding the Equation of a Line	328	(5)
Problem Solving: Fitting Equations to Data	333	(5)
Parallel and Perpendicular Lines	338	(4)
Explore	338	(3)
Problem for Programmers	341	(1)
Proofs	342	(2)
Problem Solving: Strategies Simplify the Problem	344	(14)
Problem Solving: Application Compound Interest	346	(1)
Summary and Review	347	(3)
Test	350	(1)
Cumulative Review	351	(5)
Systems of Equations
Ready for Systems of Equations?	356	(2)
Solving Systems of Equations by Graphing	358	(4)
Explore	358	(4)
The Substitution Method	362	(5)
Problem for Programmers	366	(1)
The Addition Method	367	(6)
Problem Solving: Using Systems of Equations	373	(7)
Problem Solving: Motion Problems	380	(7)
Looking for Errors	386	(1)
Problem Solving: Digit and Coin Problems	387	(13)
Problem Solving: College Entrance Exams Systems of Equations	392	(2)
Problem Solving: Application Sales Taxes	394	(1)
Summary and Review	395	(2)
Test	397	(1)
Inequalities and Absolute Value
Ready for Inequalities and Absolute Value?	398	(2)
Sets, Intersections, and Unions	400	(5)
Suppose	404	(1)
Compound Sentences	405	(6)
Connections: Discrete Math Truth Tables	410	(1)
Equations and Absolute Value	411	(2)
Inequalities and Absolute Value	413	(4)
Explore	413	(3)
Problem for Programmers	416	(1)
Inequalities in Two Variables	417	(4)
Writing to Learn	420	(1)
Graphing Systems of Linear Inequalities	421	(11)
Problem Solving: College Entrance Exams Quantitative Comparisons	425	(2)
Summary and Review	427	(2)
Test	429	(1)
Rational Expressions and Equations
Ready for Rational Expressions and Equations?	430	(2)
Simplifying Rational Expressions	432	(4)
Explore	432	(3)
Looking for Errors	435	(1)
Multiplying Rational Expressions	436	(3)
Dividing Rational Expressions	439	(3)
Addition and Subtraction: Like Denominators	442	(3)
Addition and Subtraction: Unlike Denominators	445	(6)
Connections: Geometry	450	(1)
Solving Rational Equations	451	(4)
Problem Solving: Using Rational Equations	455	(5)
Problem for Programmers	459	(1)
Problem Solving: Mixture Problems	460	(5)
Suppose	464	(1)
Dividing Polynomials	465	(4)
The Rule of False Position	468	(1)
Complex Rational Expressions	469	(3)
Biographical Note: Mary Somerville	471	(1)
Proofs	472	(3)
Problem Solving: Strategies Work Backward	475	(7)
Summary and Review	477	(2)
Test	479	(1)
Radical Expressions and Equations
Ready for Radical Expressions and Equations?	480	(2)
Real Numbers	482	(5)
Calculator: Square Roots	484	(2)
The Density Property	486	(1)
Radical Expressions	487	(4)
Math History	487	(1)
Calculator: Evaluating Radical Expressions	488	(2)
Connections: Geometry	490	(1)
Simplifying Radical Expressions	491	(4)
Explore	491	(3)
Bonus Topic: Cube Roots	494	(1)
Multiplying Radical Expressions	495	(3)
Bonus Topic: Approximating Square Roots	497	(1)
Dividing and Simplifying	498	(6)
Explore	498	(5)
Bonus Topic: Rational Exponents	503	(1)
Calculator: Finding Roots	503	(1)
Addition and Subtraction	504	(5)
Problem Solving: Application Injury Severity Score	507	(2)
The Pythagorean Theorem	509	(5)
Calculator: Finding Missing Lengths	510	(2)
Problem for Programmers	512	(1)
Bonus Topic: The Distance Formula	513	(1)
Problem Solving: Using the Pythagorean Theorem	514	(5)
Writing to Learn	518	(1)
Equations with Radicals	519	(17)
Problem Solving: College Entrance Exams Odd and Even Problems	523	(2)
Summary and Review	525	(3)
Test	528	(1)
Cumulative Review	529	(5)
Relations and Functions
Ready for Relations and Functions?	534	(2)
Relations and Functions?	536	(6)
Calculator: Evaluating Functions	539	(2)
Writing to Learn	541	(1)
Functions and Graphs	542	(5)
Explore	542	(3)
Problem for Programmers	545	(1)
Biographical Note: Leonard Euler	545	(1)
Bonus Topic: Exploring Absolute Value Functions	546	(1)
Problem Solving: Linear Functions	547	(5)
Connections: Discrete Math Interval Graphs	550	(2)
Quadratic Functions	552	(5)
Explore	552	(4)
Connections: Geometry	556	(1)
Direct Variation	557	(4)
Inverse Variation	561	(4)
Spatial Relations	564	(1)
Joint and Combined Variation	565	(11)
Problem Solving: Situational Problem Solving Starting a Business	570	(1)
Summary and Review	571	(2)
Test	573	(1)
Quadratic Equations
Ready for Quadratic Equations?	574	(2)
Introduction to Quadratic Equations	576	(4)
More Solving Quadratic Equations	580	(6)
Connections: Geometry	585	(1)
Solving by Completing the Square	586	(3)
The Quadratic Formula	589	(6)
Calculator: Approximating Solutions of Quadratic Equations	592	(3)
Solving Rational Equations	595	(3)
Problem for Programmers	597	(1)
Solving Radical Equations	598	(4)
Looking for Errors	601	(1)
Problem Solving: Quadratic Equations	602	(12)
Problem Solving: Applications Annual Percentage Rate	607	(1)
Problem Solving: Situational Problem Solving Designing a School Picnic	608	(1)
Summary and Review	609	(2)
Test	611	(1)
Trigonometry
Ready for Trigonometry?	612	(2)
Similar Right Triangles	614	(5)
Trigonometric Ratios	619	(6)
Calculator Investigation	624	(1)
Trigonometric Values	625	(3)
Calculator: Finding Trigonometric Values	625	(1)
Calculator: Finding Angles	626	(2)
Problem Solving: Right Triangle Problems	628	(12)
Problem for Programmers	632	(1)
Problem Solving: Application Surveying	633	(1)
Problem Solving: Situational Problem Solving Designing a Park	634	(1)
Summary and Review	635	(2)
Test	637	(1)
Introduction to Probability and Statistics
Ready for Introduction to Probability and Statistics?	638	(2)
Probability	640	(4)
Math History	640	(3)
Probability: It's a Small World	643	(1)
More on Probability	644	(5)
Experimental Probability and Simulation	649	(4)
Statistics: Organizing Data	653	(4)
Graphs of Data	657	(4)
Measures of Central Tendency	661	(4)
Problem for Programmers	664	(1)
Scatter Plots and Data Relationships	665	(19)
Problem Solving: Application Weather Vane Plot	669	(2)
Problem Solving: College Entrance Exams Averages	671	(2)
Summary and Review	673	(2)
Test	675	(2)
Cumulative Review	677	(7)
Appendix
Mixed Practice	684	(30)
Computer Exploration	714	(10)
TI-81 Investigations	724	(16)
Milestones in Mathematics	740	(4)
Tables	744	(5)
Table 1 Squares and Square Roots	745	(1)
Table 2 Values of Trigonometric Functions	746	(1)
Table 3 Geometric Formulas	747	(1)
Table 4 Symbols	748	(1)
Glossary	749	(8)
Selected Answers	757	(38)
Index	795