Focus on Advanced Algebra

by Dossey

• ISBN13: 9780201869804
• ISBN10: 0201869802
• Format: Hardcover
• Copyright: 1998-01-01
• Publisher: Addison-Wesley
• More Book Details
• Purchase Benefits

Table of Contents

Getting Started: What Do You Think?	xiii
Working Together	xiv
Solving Problems	xvi
Making Connections	xviii
Mathematical Models	2	(72)
Graphical Models	5	(26)
Data and Scatter Plots	6	(7)
Patterns and Relationships	13	(8)
Functions	21	(6)
Making Connections	27	(4)
Experimental Probability and Simulation	31	(18)
Theoretical and Experimental Probability	32	(6)
Simulation	38	(8)
Making Connections	46	(3)
Matrices	49	(25)
Matrices and Data Handling	50	(8)
Multiplying Matrices	58	(8)
Making Connections	66	(4)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	70	(2)
Assessment (Test, Performance Task)	72	(2)
Linear Functions, Equations, and Inequalities	74	(82)
Linear Functions and Equations	77	(26)
Direct Variation and Linear Functions	78	(8)
Solving Equations	86	(6)
Analyzing Equations of Lines	92	(8)
Making Connections	100	(3)
Fitting Linear Functions to Data	103	(24)
Using Equations of Trend Lines	104	(5)
The Median-Median Line of Fit	109	(8)
Fitting Lines Using Technology	117	(5)
Making Connections	122	(5)
Linear Inequalities	127	(29)
One-Variable Inequalities	128	(7)
Inequalities and Absolute Value	135	(7)
Linear Inequalities with Two Variables	142	(7)
Making Connections	149	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	152	(2)
Assessment (Test, Performance Task)	154	(2)
Solving Systems of Linear Equations and Inequalities	156	(72)
Systems of Linear Equations	159	(38)
Solving Systems of Equations Graphically	160	(8)
Solving Systems of Equations Symbolically	168	(9)
Solving Systems Using Matrices	177	(9)
Systems with Three Variables	186	(8)
Making Connections	194	(3)
Systems of Linear Inequalities	197	(31)
Systems of Inequalities	198	(6)
Linear Programming Constraints	204	(8)
Solving Linear Programming Problems	212	(9)
Making Connections	221	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	224	(2)
Assessment (Test, Performance Task)	226	(2)
Patterns and Structure in Algebra	228	(76)
Analyzing Arithmetic Growth	231	(18)
Arithmetic Sequences	232	(7)
Arithmetic Series	239	(6)
Making Connections	245	(4)
Analyzing Geometric Growth	249	(22)
Geometric Sequences	250	(6)
Geometric Series	256	(6)
Investigating the Concept of a Limit	262	(6)
Making Connections	268	(3)
Algebraic Structure and Fractal Geometry	271	(33)
Real Numbers and Field Properties	272	(6)
Rational and Irrational Numbers	278	(8)
Imaginary and Complex Numbers	286	(5)
Graphing Complex Numbers	291	(6)
Making Connections	297	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	300	(3)
Assessment (Test, Performance Task)	303	(1)
Quadratic Functions and Relations	304	(114)
Quadratic Functions	307	(32)
Investigating Quadratic Functions	308	(8)
Sketching Parabolas: f(x) = ax2	316	(7)
Translations: f(x) = a(x-h)2 + k	323	(7)
Completing the Square	330	(6)
Making Connections	336	(3)
Solving Quadratic Equations	339	(32)
Solving Quadratic Equations Graphically	340	(8)
Solving Quadratic Equations by Factoring	348	(6)
Using the Quadratic Formula	354	(7)
Classifying Solutions	361	(7)
Making Connections	368	(3)
Conic Sections	371	(28)
Circles	372	(8)
Ellipses	380	(8)
Hyperbolas	388	(8)
Making Connections	396	(3)
Quadratic Systems	399	(19)
Quadratic-Linear Systems	400	(5)
Quadratic-Quadratic Systems	405	(5)
Making Connections	410	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	413	(3)
Assessment (Test, Performance Task)	416	(2)
Counting and Arranging Discrete Objects	418	(38)
Counting Objects and Permutations	421	(16)
Methods of Counting	422	(6)
Arrangements and Permutations	428	(6)
Making Connections	434	(3)
Combinations and the Binomial Theorem	437	(19)
Combinations	438	(5)
The Binomial Theorem	443	(5)
Making Connections	448	(4)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	452	(2)
Assessment (Test, Performance Task)	454	(2)
Investigating Roots and Powers	456	(82)
Variation and Integral Exponent Powers	459	(26)
Inverse, Combined, and Joint Variation	460	(7)
Positive Integer Exponents	467	(7)
Properties of Exponents and Powers	474	(7)
Making Connections	481	(4)
Roots, Radicals, and Rational Exponents	485	(28)
Rational Exponents	486	(6)
Real-Number Exponents and Modeling	492	(6)
Solving Radical Equations	498	(5)
Other Radical Equations	503	(6)
Making Connections	509	(4)
Combining Functions	513	(25)
Operations with Functions	514	(6)
Composite Functions	520	(5)
Inverse Relations and Functions	525	(6)
Making Connections	531	(4)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	535	(2)
Assessment (Test, Performance Task)	537	(1)
Polynomials and Polynomial Functions	538	(78)
Polynomial Functions and Their Graphs	541	(24)
Graphing Polynomial Functions	542	(6)
Maximums and Minimums	548	(7)
Zeros of a Function	555	(6)
Making Connections	561	(4)
The Fundamental Theorem of Algebra	565	(20)
Solving Polynomial Equations by Graphing	566	(4)
Factors and Roots of Polynomials	570	(7)
The Fundamental Theorem	577	(5)
Making Connections	582	(3)
Rational Expressions and Functions	585	(31)
Rational Expressions	586	(6)
Adding and Subtracting Rational Expressions	592	(6)
Rational Functions	598	(5)
Solving Rational Equations	603	(5)
Making Connections	608	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	611	(3)
Assessment (Test, Performance Task)	614	(2)
Exponential and Logarithmic Functions	616	(60)
Exponential Patterns and Graphs	619	(30)
Exploring Exponential Functions	620	(7)
Exponential Growth and Decay	627	(7)
Modeling Exponential Growth and Decay	634	(6)
The Number e	640	(6)
Making Connections	646	(3)
Logarithmic Functions	649	(27)
Defining Logarithmic Functions	650	(7)
Solving Exponential Equations	657	(6)
Properties of Logarithms	663	(7)
Making Connections	670	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	673	(1)
Assessment (Test, Performance Task)	674	(2)
Trigonometry	676	(76)
Trigonometric Ratios	679	(30)
Triangle Trigonometry	680	(8)
Radian Measure and Special Angles	688	(5)
Arc Length and Sector Area	693	(7)
Extended Trigonometric Values	700	(6)
Making Connections	706	(3)
Laws of Cosines and Sines	709	(20)
Law of Cosines	710	(7)
Law of Sines and Triangle Areas	717	(8)
Making Connections	725	(4)
Trigonometric Functions	729	(23)
Period and Amplitude	730	(8)
Trigonometric Translations	738	(6)
Making Connections	744	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	747	(3)
Assessment (Test, Performance Task)	750	(2)
Advanced Techniques for Chance and Data	752	(48)
Compound Events	755	(24)
The Probability of A or B	756	(6)
Independent and Dependent Events	762	(7)
Conditional Probability	769	(6)
Making Connections	775	(4)
Sampling Methods	779	(21)
Biased and Unbiased Sampling	780	(7)
The Normal Distribution	787	(7)
Making Connections	794	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	797	(2)
Assessment (Test, Performance Task)	799	(1)
Discrete Mathematics and Models	800	(106)
Graph Theory	803	(26)
Euler's Formula and Graphs	804	(6)
Paths and Circuits	810	(7)
Optimization and Trees	817	(7)
Making Connections	824	(5)
Recursion	829	(21)
Recursive Sequences	830	(6)
Probability Matrices	836	(7)
Making Connections	843	(3)
Review (Key Terms, Concepts and Applications, Concepts and Connections, Self-Evaluation)	846	(2)
Assessment (Test, Performance Task)	848	(2)
REFERENCE CENTER
Enrichment
Calculating Inverse Matrices	850	(2)
Solving Systems Using Augmented Matrices	852	(1)
Synthetic Division	853	(1)
Complex Rational Expressions	854	(1)
Trigonometric Inverse Functions	855	(1)
Trigonometric Inverse Relations and Equations	856	(2)
Trigonometric Properties and Identities	858	(2)
Measures of Central Tendency	860	(1)
Standard Deviation	861	(1)
Z-Scores	862	(2)
Hypothesis Testing of Means	864	(2)
Residuals and Linear Regression	866	(2)
Choosing a Mathematical Model	868	(2)
Inequalities from Polynomial, Square Root, and Rational Equations	870	(2)
Inequalities from Exponential and Logarithmic Equations	872	(2)
Spiral Review	874	(24)
Measurement Conversion Factors	898	(1)
Symbols	899	(1)
Random Numbers	900	(1)
Standard Normal Distribution	901	(1)
Geometric Formulas	902	(1)
Algebraic Properties	903	(1)
Algebraic Formulas	904	(2)
Glossary	906	(14)
Selected Answers	920	(32)
Credits	952	(2)
Index	954