Intermediate Algebra Through Applications

by Akst, Geoffrey; Bragg, Sadie

• ISBN13: 9780201312249
• ISBN10: 0201312247
• Edition: 1st
• Format: Paperback
• Copyright: 2005-01-01
• Publisher: Addison Wesley

Summary

Throughout this text, motivating real-world applications, examples, and exercises demonstrate how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format, pairing each example with a corresponding practice exercise, encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section. Mindstretchers incorporate related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and historical connections. To show how mathematics has evolved over the centuries, in many cultures, and throughout the world, each chapter features a compelling Cultural Note that investigates and illustrates the origins of mathematical concepts. Diverse topics include art, music, the evolution of digit notation, and the ancient practice of using a scale to find an unknown weight.

Table of Contents

1 Algebra Basics	1	(102)
1.1 Introduction to Real Numbers	3	(16)
1.2 Operations with Real Numbers	19	(16)
1.3 Properties of Real Numbers	35	(15)
1.4 Laws of Exponents and Scientific Notation	50	(23)
1.5 Algebraic Expressions: Translating, Evaluating, and Simplifying	73	(30)
2 Linear Equations and Inequalities	103	(88)
2.1 Solving Linear Equations	105	(25)
2.2 Solving Literal Equations and Formulas	130	(8)
2.3 Solving Linear Inequalities	138	(16)
2.4 Solving Compound Inequalities	154	(12)
2.5 Solving Absolute Value Equations and Inequalities	166	(25)
3 Graphs, Linear Equations and Inequalities, and Functions	191	(130)
3.1 The Rectangular Coordinate System	196	(13)
3.2 Slope	209	(21)
3.3 Graphing Linear Equations	230	(18)
3.4 More on Graphing Linear Equations	248	(18)
3.5 Graphing Linear Inequalities	266	(13)
3.6 Introduction to Functions	279	(42)
4 Systems of Linear Equations and Inequalities	321	(82)
4.1 Solving Systems of Linear Equations by Graphing	324	(16)
4.2 Solving Systems of Linear Equations Algebraically by Substitution or Elimination	340	(13)
4.3 Solving Systems of Linear Equations in Three Variables	353	(14)
4.4 Solving Systems of Linear Equations by Using Matrices	367	(12)
4.5 Solving Systems of Linear Inequalities	379	(24)
5 Polynomials	403	(90)
5.1 Addition and Subtraction of Polynomials	405	(13)
5.2 Multiplication of Polynomials	418	(14)
5.3 Division of Polynomials	432	(9)
5.4 The Greatest Common Factor and Factoring by Grouping	441	(8)
5.5 Factoring Trinomials	449	(11)
5.6 Special Factoring	460	(11)
5.7 Solving Quadratic Equations by Factoring	471	(22)
6 Rational Expressions and Equations	493	(80)
6.1 Multiplication and Division of Rational Expressions	495	(15)
6.2 Addition and Subtraction of Rational Expressions	510	(14)
6.3 Complex Rational Expressions	524	(9)
6.4 Solving Rational Equations	533	(16)
6.5 Variation	549	(24)
7 Radical Expressions and Equations	573	(86)
7.1 Radical Expressions and Rational Exponents	576	(15)
7.2 Simplifying Radical Expressions	591	(10)
7.3 Addition and Subtraction of Radical Expressions	601	(8)
7.4 Multiplication and Division of Radical Expressions	609	(14)
7.5 Solving Radical Equations	623	(11)
7.6 Complex Numbers	634	(25)
8 Quadratic Equations, Functions, and Inequalities	659	(86)
8.1 Solving Quadratic Equations by Completing the Square	662	(13)
8.2 Solving Quadratic Equations by Using the Quadratic Formula	675	(11)
8.3 More on Quadratic Equations	686	(11)
8.4 Graphing Quadratic Functions	697	(23)
8.5 Solving Quadratic and Rational Inequalities	720	(25)
9 Exponential and Logarithmic Functions	745	(92)
9.1 The Algebra of Functions	748	(21)
9.2 Exponential Functions	769	(14)
9.3 Logarithmic Functions	783	(13)
9.4 Properties of Logarithms	796	(10)
9.5 Common Logarithms, Natural Logarithms, and Change of Base	806	(7)
9.6 Solving Exponential and Logarithmic Equations	813	(24)
10 Conic Sections	837	(76)
10.1 Introduction to Conics; The Parabola	841	(14)
10.2 The Circle	855	(12)
10.3 The Ellipse and the Hyperbola	867	(13)
10.4 Solving Nonlinear Systems of Equations	880	(8)
10.5 Solving Nonlinear Inequalities and Nonlinear Systems of Inequalities	888	(25)
Appendixes	913
Table of Symbols	913	(2)
Introduction to Graphing Calculators	915	(2)
Determinants and Cramer's Rule	917	(7)
Synthetic Division	924
Glossary	G-1
Index	I-1
Index of Applications	I-9
Video Index	I-13
Answers (Student Edition)	A-1