Intermediate Algebra An Integrated Approach, Preliminary Edition

by Aufmann, Richard N.; Lockwood, Joanne

• ISBN13: 9780395888315
• ISBN10: 039588831X
• Edition: 1st
• Format: Paperback
• Copyright: 1999-12-14
• Publisher: Brooks Cole

Summary

This worktext for students in Intermediate Algebra or Algebra II is designed specifically to support instructors seeking a cohesive approach to presenting integrated math topics. Throughout the text, the authors weave together themes of logic, geometry, number sense, probability, and trigonometry at increasing levels of sophistication, enabling students to see mathematics as a unified subject.

Table of Contents

Fundamental Concepts	1	(102)
Problem Solving	3	(14)
Problem Solving	3	(3)
Inductive Reasoning	6	(1)
Deductive Reasoning	7	(8)
Exploration The Game of Sprouts	15	(2)
Sets	17	(18)
Sets of Numbers	17	(3)
Union and Intersection of Sets	20	(2)
Interval Notation	22	(1)
Subsets and Venn Diagrams	23	(3)
The Complement of a Set	26	(8)
Exploration Examining a Set of Positive Integers	34	(1)
Principles of Logic	35	(16)
Statements	35	(1)
The Logical Operators and and or	35	(3)
Negations	38	(2)
The Conditional	40	(2)
Euler Diagrams	42	(7)
Exploration Logic Gates	49	(2)
Analyzing Real Number Data	51	(16)
Organizing Data into Frequency Tables and Histograms	51	(3)
Range, Mean, Median, and Mode	54	(2)
Standard Deviation	56	(10)
Exploration Analyzing SAT Scores	66	(1)
Algebraic Expressions	67	(12)
Evaluating Expressions	67	(2)
Simplifying Variable Expressions	69	(4)
Scientific Notation	73	(5)
Exploration Examining Algebraic Expressions	78	(1)
Sequences and Series	79	(10)
Sequences	79	(2)
Series	81	(6)
Exploration Recursive Sequences	87	(2)
Introduction to Probability	89	(14)
The Counting Principle	89	(1)
Probability	90	(4)
Exploration Empirical Probability	94	(1)
Chapter Summary	95	(4)
Chapter Review Exercises	99	(4)
The Rectangular Coordinate System	103	(76)
Introduction to Rectangular Coordinates	105	(16)
Graphing Points on a Rectangular Coordinate System	105	(3)
Pythagorean Theorem	108	(1)
The Distance Formula	109	(1)
The Midpoint Formula	110	(10)
Exploration Medians of a Triangle	120	(1)
Geometric Transformations	121	(14)
Translating Geometric Figures	121	(1)
Dilation	122	(2)
Reflections and Symmetry	124	(10)
Exploration Symmetry with Respect to a Diagonal Line	134	(1)
Reading and Drawing Graphs	135	(12)
Reading Graphs	135	(1)
Drawing Graphs from Equations	135	(4)
Applications	139	(7)
Exploration Translations of Graphs	146	(1)
Relations and Functions	147	(14)
Evaluating Functions	147	(4)
Domain and Range	151	(1)
Graphs of Functions	152	(8)
Exploration Functions of More than One Variable	160	(1)
Properties of Functions	161	(18)
Intercepts	161	(1)
1-1 Functions	162	(1)
Increasing and Decreasing Functions	163	(9)
Exploration Turning Points of a Graph	172	(1)
Chapter Summary	173	(2)
Chapter Review Exercises	175	(2)
Cumulative Review Exercises	177	(2)
First-Degree Equations and Inequalities	179	(62)
Solving First-Degree Equations	181	(12)
Solving First-Degree Equations	181	(3)
Solving Equations Using the Addition and Multiplication Properties	184	(1)
Equations Containing Parentheses	185	(1)
Applications to Uniform Motion	186	(6)
Exploration Modular Equations	192	(1)
Applications of First-Degree Equations	193	(8)
Percent Mixture Problems	193	(2)
Value Mixture Problems	195	(5)
Exploration Gold Alloys	200	(1)
Applications to Geometry	201	(14)
Angles	201	(1)
Intersecting Lines	202	(3)
Angles of a Triangle	205	(1)
Angles and Circles	206	(2)
Similar Triangles	208	(6)
Exploration Fractals	214	(1)
Inequalities in One Variable	215	(10)
Addition and Multiplication Properties of Inequalities	215	(2)
Compound Inequalities	217	(2)
Application Problems	219	(5)
Exploration Inequalities and Logic	224	(1)
Absolute-Value Equations and Inequalities	225	(16)
Absolute-Value Equations	225	(1)
Absolute-Value Inequalities	226	(2)
Application Problems	228	(6)
Exploration Graphing in Restricted Domains	234	(1)
Chapter Summary	235	(2)
Chapter Review Exercises	237	(2)
Cumulative Review Exercises	239	(2)
Linear Functions	241	(48)
Properties of Linear Functions	243	(14)
Intercepts	243	(2)
Slope of a Line	245	(3)
Equations of the Form Ax + By = C	248	(8)
Exploration Slopes of Perpendicular Lines	256	(1)
Finding Linear Models	257	(14)
Finding Linear Models	257	(3)
Regression Lines	260	(1)
Parallel and Perpendicular Lines	261	(9)
Exploration Linear Parametric Equations	270	(1)
Arithmetic Sequences as Linear Functions	271	(8)
Finding the nth Term of an Arithmetic Sequence	271	(2)
Sum of an Arithmetic Series	273	(1)
Applications	274	(4)
Exploration Recursive Sequences	278	(1)
Linear Inequalities in Two Variables	279	(10)
Solution Sets to Inequalities in Two Variables	279	(3)
Exploration Constraints	282	(1)
Chapter Summary	283	(1)
Chapter Review Exercises	284	(3)
Cumulative Review Exercises	287	(2)
Systems of Linear Equations and Inequalities	289	(60)
Solving Linear Systems of Equations in Two Variables	291	(14)
Solving Systems of Equations by Graphing	291	(2)
Solving Systems of Equations by the Substitution Method	293	(1)
Applications	294	(2)
Solving Systems of Two Linear Equations by the Addition Method	296	(2)
Rate-of-Wind and Rate-of-Current Problems	298	(6)
Exploration Ill-Conditioned Systems of Equations	304	(1)
Introduction to Matrices	305	(14)
Operations on Matrices	305	(12)
Exploration Stochastic Matrices	317	(2)
Solving Systems of Linear Equations Using Matrices	319	(14)
Solving Systems of Three Linear Equations in Three Variables Using the Addition Method	319	(2)
Solving Systems of Equations Using Matrices	321	(3)
Determinants	324	(1)
Applications Using Matrices	325	(7)
Exploration Properties of Matrix Multiplication	332	(1)
Systems of Linear Inequalities and Linear Programming	333	(16)
Graph the Solution Set of a System of Linear Inequalities	333	(1)
Linear Programming	334	(8)
Exploration Cryptography	342	(1)
Chapter Summary	343	(2)
Chapter Review Exercises	345	(2)
Cumulative Review Exercises	347	(2)
Radical Expressions and Rational Exponents	349	(88)
Rational Exponents and Radical Expressions	351	(10)
Expressions with Rational Exponents	351	(3)
Exponential Expressions and Radical Expressions	354	(6)
Exploration Developing Rules for Rational Exponents	360	(1)
Simplifying Radical Expressions	361	(8)
Simplify Radical Expressions that Are Roots of Perfect Powers	361	(2)
Decimal Approximations of Radical Expressions	363	(1)
Radical Expressions in Simplest Form	364	(4)
Exploration Mathematical Models of Data	368	(1)
Operations on Radical Expressions	369	(8)
Add and Subtract Radical Expressions	369	(1)
Multiply Radical Expressions	370	(2)
Divide Radical Expressions	372	(4)
Exploration Comparing Radical Expressions with Polynomial Expressions	376	(1)
Solving Radical Equations	377	(8)
Solving Equations Containing Radical Expressions	377	(7)
Exploration Hydroplaning	384	(1)
Radical Functions	385	(10)
Graphs of Radical Functions	385	(9)
Exploration Translations of Graphs of Radical Functions	394	(1)
Right Triangle Trigonometry	395	(20)
Geometry of a Right Triangle	395	(2)
Trigonometric Functions of an Acute Angle	397	(4)
Inverse Trigonometric Functions	401	(1)
Solving Right Triangles	402	(2)
Angles of Elevation and Depression	404	(1)
Bearing	405	(9)
Exploration Trigonometric Identities	414	(1)
Complex Numbers	415	(22)
Simplify Complex Numbers	415	(2)
The Complex Plane	417	(1)
Add and Subtract Complex Numbers	418	(1)
Multiply Complex Numbers	419	(2)
Divide Complex Numbers	421	(7)
Exploration Powers of i	428
Graphs of Complex Numbers	421	(8)
Chapter Summary	429	(2)
Chapter Review Exercises	431	(4)
Cumulative Review Exercises	435	(2)
Quadratic Equations	437	(74)
Solving Equations by Factoring	439	(16)
Quadratic Equations	439	(1)
Factoring	440	(4)
Solve Equations by Factoring	444	(3)
Write a Quadratic Equation Given Its Solutions	447	(7)
Exploration Solutions of a Quadratic Equation and Zeros of a Quadratic Function	454	(1)
Solving Equations by Taking Square Roots and by Completing the Square	455	(12)
Solve Equations by Taking Square Roots	455	(2)
Solve Equations by Completing the Square	457	(9)
Exploration Construction Materials	466	(1)
Solving Equations by Using the Quadratic Formula	467	(12)
Solve Equations by Using the Quadratic Formula	467	(5)
Solve Equations Graphically	472	(6)
Exploration The Effect of the Discriminant on Solutions of Quadratic Equations and x-Intercepts of Parabolas	478	(1)
Equations that Are Quadratic in Form	479	(10)
Solve Equations that Are Quadratic in Form	479	(9)
Exploration Solutions of Higher-Degree Equations	488	(1)
Quadratic Functions	489	(22)
Properties of Quadratic Functions	489	(2)
Intercepts of Quadratic Functions	491	(3)
The Minimum or Maximum of a Quadratic Function	494	(8)
Exploration Alternate Form of the Equation of a Parabola	502	(1)
Chapter Summary	503	(2)
Chapter Review Exercises	505	(2)
Cumulative Review Exercises	507	(4)
Exponential and Logarithmic Functions	511	(90)
Exponential Functions	513	(14)
Evaluate Exponential Functions	513	(2)
Graphs of Exponential Functions	515	(2)
Applications of Exponential Functions	517	(8)
Exploration Finding Exponential Models	525	(2)
Geometric Sequences as Exponential Functions	527	(14)
Geometric Sequences	527	(2)
Geometric Series	529	(5)
Application to Probability	534	(6)
Exploration One of Zeno's Paradoxes	540	(1)
A Legendary Geometric Series	540	(1)
Formulating a Proof	540	(1)
Composition of Functions and Inverse Functions	541	(12)
Composition of Functions	541	(2)
Inverse Functions	543	(9)
Exploration The Intersection of the Graphs of Inverse Functions	552	(1)
Graphing Inverses Using Geometry	552	(1)
Logarithmic Functions	553	(12)
Logarithmic Functions	553	(3)
Graphs of Logarithmic Functions	556	(1)
Applications of Logarithmic Functions	557	(6)
Exploration Earthquakes	563	(2)
Properties of Logarithms	565	(12)
Properties of Logarithms	565	(4)
The Change of Base Formula	569	(7)
Exploration The Properties of Logarithms	576	(1)
Exponential and Logarithmic Equations	577	(24)
Solve Exponential and Logarithmic Equations	577	(7)
Standard Normal Distribution	584	(10)
Exploration Earth's Carrying Capacity	594	(1)
Chapter Summary	595	(2)
Chapter Review Exercises	597	(2)
Cumulative Review Exercises	599	(2)
Rational Expressions	601	(98)
Introduction to Rational Expressions	603	(10)
Rational Functions	603	(3)
Simplify Rational Expressions	606	(6)
Exploration Sets of Functions	612	(1)
Operations on Rational Expressions	613	(12)
Multiply Rational Expressions	613	(1)
Divide Rational Expressions	614	(1)
Add and Substract Rational Expressions	615	(2)
Complex Fractions	617	(7)
Exploration Patterns in Mathematics	624	(1)
An Alternative Method of Simplifying a Complex Fraction	624	(1)
Division of Polynomials	625	(10)
Divide Polynomials	625	(2)
Synthetic Division	627	(1)
The Remainder Theorem	628	(6)
Exploration Patterns in Mathematics	634	(1)
The Factor Theorem	634	(1)
Rational Equations	635	(14)
Solve Rational Equations	635	(2)
Work Problems	637	(2)
Uniform Motion Problems	639	(9)
Exploration Golden Rectangles	648	(1)
Applications to Clock Movements	648	(1)
The Law of Sines and Law of Cosines	649	(12)
The Law of Sines	649	(5)
The Law of Cosines	654	(6)
Exploration Applications to Geometry	660	(1)
Binomial Theorem	661	(12)
Expanding Binomials	661	(1)
Factorials	662	(2)
The Binomial Expansion Formula	664	(1)
The rth term in a Binomial Expansion	665	(1)
The Binomial Probability Theorem	665	(7)
Exploration Permutations and Combinations	672	(1)
Conic Sections	673	(26)
The Parabola	673	(3)
The Circle	676	(2)
The Ellipse	678	(2)
The Hyperbola	680	(8)
Exploration The Focus of a Parabola	688	(1)
Chapter Summary	689	(4)
Chapter Review Exercises	693	(2)
Cumulative Review Exercises	695	(4)
Appendix Guidelines for Using Graphing Calculators	699
Solutions to You-Try-Its	1	(1)
Answers to Odd-Numbered Exercises	1	(1)
Index