Math Remediation for the College Bound: Homework, Sample Tests, and Answer Keys

 Daryao Khatri

R&L Education | 2011 | 144 páginas | rar - pdf | 1,7 Mb

link (password: matav)

Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (S. T. E. M) discipline. Math Remediation for the College Bound fosters mastery of critical math and algebraic concepts and skills essential to all of the S.T.E.M. disciplines and some of the social sciences. This booklet is designed to accompany the main book, Math Remediation for the College-Bound: How Teachers Can Close the Gap, from the Basics through Algebra. With the exception of Chapters 1 and 2, each chapter of the booklet consists of five sections: (1) practice homework, (2) a sample test, (3) the answers to selected and numbered exercises corresponding to their numbering in the book, (4) answers to the practice homework, and (5) answers to sample tests. This pattern begins with Chapter 3 and continues for the remainder of the book.

Contents
Introduction
3 Mental Math
4 Integers and Arithmetic Operations
5 Data, Statistics, and Graphs
6 A Love-Hate Relationship - Facts about Triangles, Intersecting Lines, and Units of Measurement
7 The Two Great Devils-The Negative Sign and the Negative Numbers
8 Change for Currency Notes-Simple Fractions
9 Exponents-Powers of 10
10 Powers of Variabl s and Constants
11 The World of Expressions and Elementary Equations
12 The Algebra Savior-Cross Products
13 Ratio and Proportion
14 just Shopping for the Best Deal
15 How Big? Perimeter, Area, and Volume
16 Slopes and Intercepts on the Algebra Trail
17 Mixed Numerals
18 Polynomials and Thei r Basic Operations
19 Factoring
20 Rati onal, Complex Rational, and Radical Expressions-Becoming an Algebra Guru
About the Authors

Help Your Kids with Math: A visual problem solver for kids and parents

 

Barry Lewis

DK Publishing | 2010 | 258 páginas | rar - pdf | 9,7 Mb

link (password : matav)

Studying math is often a source of great anxiety for children and also proves troublesome for parents helping with their homework.

Using uniquely accessible illustrated stress-free approach, Help Your Kids with Math looks at every aspect of math, from simple sums to simultaneous equations, and explains each facet in easily understandable language so that adults and kids can master the subject together.

In Help Your Kids with Math tricky concepts are explored and examined step-by-step, so that even the most math-phobic individual will be able to approach and solve complex problems with confidence.

Contents
NUMBERS
Introducing numbers ; Addition ; Subtraction ; Multiplication ; Division ; Prime numbers ; Units of measurement ; Positive and negative numbers ; Powers and roots ; Standard form ; Decimals in action; Fractions, Ratio and proportion, Percentages, Converting fractions, decimals, and percentages ; Mental math ; Rounding off ; Using a calculator ; Personal finance ; Business finance
GEOMETRY
What is geometry?; Angles; Straight lines; Symmetry; Coordinates; Vectors; Translations ; Rotations; Reflections; Enlargements; Scale drawings; Bearings; Constructions; Loci ; Triangles; Constructing triangles; Congruent triangles; Area of a triangle; Similar triangles ; Pythagorean Theorem ; Quadrilaterals; Polygons ; Circles ; Circumference and diameter ; Area of a circle ; Angles in a circle; Chords and cyclic quadrilaterals ; Tangents ; Arcs ; Sectors ; Solids ; Volumes ; Surface area 148
TRIGONOMETRY
What is trigonometry? ; Working with trigonometry ; Finding missing sides ; Finding missing angles 
ALGEBRA
What is algebra?; Sequences; Working with expressions; Expanding and factorizing expressions; Quadratic expressions; Formulas; Solving equations; Linear graphs; Simultaneous equations; Factorizing quadratic equations; The quadratic formula; Quadratic graphs ; Inequalities 
STATISTICS
What is statistics? ; Collecting and organizing data ; Bar charts ; Pie charts ; Line graphs;  Averages; Moving Averages ; Measuring spread ; Histograms ; Scatter diagrams 
PROBABILITY
What is probability? , Expectation and reality ; Multiple probability ; Dependent events ; Tree diagrams 
Reference section 232
Glossary 244
Index 252
Acknowledgments 256

Intermediate Algebra

 Alan S. Tussy e R. David Gustafson

 Cengage Learning | 2012 - 5 ª edição | 1046 páginas | pdf | 21 Mb

link 

4.ª ediçâo - 2008

Algebra can be like a foreign language, but INTERMEDIATE ALGEBRA, 5E, gives you the tools and practice you need to fully understand the language of algebra and the "why" behind problem solving. Using Strategy and Why explanations in worked examples and a six-step problem solving strategy, INTERMEDIATE ALGEBRA, 5E, will guide you through an integrated learning process that will expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Feel confident about your skills through additional practice in the text and Enhanced WebAssign. With INTERMEDIATE ALGEBRA, 5E, algebra will make sense because it is not just about the x...it's also about the WHY.

Contents

1. A REVIEW OF BASIC ALGEBRA.
The Language of Algebra. The Real Numbers. Operations with Real Numbers. Simplifying Algebraic Expressions Using Properties of Real Numbers. Solving Linear Equations Using Properties of Equality. Solving Formulas; Geometry. Using Equations to Solve Problems. More about Problem Solving. Chapter Summary and Review. Chapter Test. Group Project.
2. GRAPHS, EQUATIONS OF LINES, AND FUNCTIONS.
Graphs. Graphing Linear Equations in Two Variables. Rate of Change and the Slope of a Line. Writing Equations of Lines. An Introduction to Functions. Graphs of Functions. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
3. SYSTEMS OF EQUATIONS.
Solving Systems of Equations by Graphing. Solving Systems of Equations Algebraically. Solving Systems of Equation in Three Variables. Solving Systems of Equations Using Matrices. Solving Systems of Equations Using Determinants. Problem Solving Using Systems of Two Equations. Problem Solving Using Systems of Three Equations. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
4. INEQUALITIES.
Solving Linear Inequalities in One Variable. Solving Compound Inequalities. Solving Absolute Value Equations and Inequalities. Linear Inequalities in Two Variables. Systems of Linear Inequalities. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
5. EXPONENTS, POLYNOMIALS, AND POLYNOMIAL FUNCTIONS.
Exponents. Scientific Notation. Polynomials and Polynomial Functions. Multiplying Polynomials. The Greatest Common Factor and Factoring by Grouping. Factoring Trinomials. The Difference of Two Squares; the Sum and Difference of Two Cubes. Summary of Factoring Techniques. Solving Equations by Factoring. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
6. RATIONAL EXPRESSIONS AND EQUATIONS.
Rational Functions and Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. Simplifying Complex Fractions. Dividing Polynomials. Synthetic Division. Solving Rational Equations. Problem Solving Using Rational Equations. Proportion and Variation. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review
7. RADICAL EXPRESSIONS AND EQUATIONS.
Radical Expressions and Radical Functions. Rational Exponents. Simplifying and Combining Radical Expressions. Multiplying and Dividing Radical Expressions. Solving Radical Equations. Geometric Applications of Radicals. Complex Numbers. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
8. QUADRATIC EQUATIONS, FUNCTIONS, AND INEQUALITIES.
The Square Root Property and Completing the Square. The Quadratic Formula. The Discriminant and Equations That Can Be Written in Quadratic Form. Quadratic Functions and Their Graphs. Quadratic and Other Nonlinear Inequalities. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
9. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Algebra and Composition of Functions. Inverse Functions. Exponential Functions. Logarithmic Functions. Base-e Exponential and Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
10. CONIC SECTIONS; MORE GRAPHING.
The Circle and the Parabola. The Ellipse. The Hyperbola. Solving Nonlinear Systems of Equations. Chapter Summary and Review. Chapter Test. Group Project.
11. MISCELLANEOUS TOPICS.
The Binomial Theorem. Arithmetic Sequences and Series. Geometric Sequences and Series. Chapter Summary and Review. Chapter Test. Group Project. Cumulative Review.
Appendix 1: Roots and Powers.
Appendix 2: Answers to Selected Problems.

Diophantos of Alexandria: A Study in the History of Greek Algebra

Thomas Little Heath

Cambridge, University press | 1985 | 298 páginas

online: ualberta.ca
archive.org
hathitrust.org
forgottenbooks.org

pdf - link (google books)

The Greek mathematician Diophantos of Alexandria lived during the third century CE. Apart from his age (he reached eighty-four), very little else is known about his life. Even the exact form of his name is uncertain, and only a few incomplete manuscripts of his greatest work, Arithmetica, have survived. In this impressive scholarly investigation, first published in 1885, Thomas Little Heath (1861-1940) meticulously presents what can be gleaned from Greek, Latin and Arabic sources, and guides the reader through the algebraist's idiosyncratic style of mathematics, discussing his notation and originality. This was the first thorough survey of Diophantos' work to appear in English. Also reissued in this series are Heath's two-volume History of Greek Mathematics, his treatment of Greek astronomy through the work of Aristarchus of Samos, and his edition in modern notation of the Treatise on Conic Sections by Apollonius of Perga.

Mastering Mathematics - Algebra

Hodder Education | 2014 | 237 páginas | rar - pdf | 9,13 Mb

link (password: matav)

Deliver outstanding lessons that build fluency, problem-solving and mathematical reasoning skills to enable sustained progress at Key Stage 3, in preparation for GCSE. Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics. Mastering Mathematics Student Books and Whiteboard eTextbooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources: - Enable students to identify appropriate remediation or extension steps they need in order to progress, through easy to follow progression charts - Clear explanations of the tools needed for the chapter followed by questions that develop fluency, reasoning and problem-solving in order to ensure transferability of skills - Show band of difficulty for each chapter and links with other areas of maths throughout the books so students know how they are doing and what they need to learn next

Contents
Strand 1 Starting algebra 01
Unit 1 Making and using word formulae 02
Unit 2 Using letters 10
Unit 3 Combining variables 19
Unit 4 Working with formulae 26
Unit 5 Setting up and solving simple equations 35
Unit 6 Using brackets 47
Unit 7 Working with more complex equations 56
Unit 8 Solving equations with brackets 64
Unit 9 Simplifying harder expressions 71
Unit 10 Using complex formulae 78
Strand 2 Sequences 89
Unit 1 What is a sequence? 90
Unit 2 Generating sequences 100
Unit 3 Linear sequences 106
Unit 4 Special sequences 118
Unit 5 Quadratic sequences 126
Strand 3 Functions and graphs 133
Unit 1 Real-life graphs 134
Unit 2 Plotting graphs of linear functions 154
Unit 3 The equation of a straight line 164
Unit 4 Plotting quadratic and cubic graphs 178
Strand 4 Algebraic methods 187
Unit 1 Trial and improvement 188
Unit 2 Linear inequalities 196
Unit 3 Solve pairs of equations by substitution 206
Unit 4 Solve simultaneous equations using elimination 212
Unit 5 Using graphs to solve simultaneous equations

Mathematical Connections: A Companion for Teachers

(Classroom Resource Material) 

Al Cuoco

The Mathematical Association of America | 2005 | 261 páginas | pdf | 6,3 Mb

link
link1

This book is about some of the topics that form the foundations for high school mathematics. It focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics, topics that have fallen out of fashion and that deserve to be resurrected While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self-study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book.

Contents
1. Difference tables and polynomial fits. Doing it with sums
Doing it with differences
Finding a formula: combinatorial polynomials
Making it formal: the [delta] operator
Going the other way: polynomials to tables
Conversions
From Newton to Lagrange
Agreeing to disagree
2. Form and function: the algebra of polynomials. Polynomials
The basic theorems
Coefficients and values
Up a level
Transformations
Coefficients and zeros.
3. Complex numbers, complex maps, and trigonometry. Complex numbers
The complex plane
The geometry behind multiplying
Trigonometric identities
Complex maps
Julia sets and the Mandelbrot set.
4. Combinations and locks. Combinatorial proofs and identities
The simplex lock
Some approaches to the simplex lock problem
Connections to the Mahler basis.
5. Sums of powers. Summatory polynomials
Bernoulli's method.

A Historian Looks Back: The Calculus as Algebra and Selected Writings

(Spectrum)

Judith V. Grabiner

 Mathematical Association of America |  2010 |304 páginas | rar - pdf | 1,7 Mb

link (password: matav)

Judith Grabiner, the author of A Historian Looks Back, has long been interested in investigating what mathematicians actually do, and how mathematics actually has developed. She addresses the results of her investigations not principally to other historians, but to mathematicians and teachers of mathematics. This book brings together much of what she has had to say to this audience.

The centerpiece of the book is The Calculus as Algebra: J.-L. Lagrange, 1736-1813. The book describes the achievements, setbacks, and influence of Lagrange s pioneering attempt to reduce the calculus to algebra. Nine additional articles round out the book describing the history of the derivative; the origin of delta-epsilon proofs; Descartes and problem solving; the contrast between the calculus of Newton and Maclaurin, and that of Lagrange; Maclaurin s way of doing mathematics and science and his surprisingly important influence; some widely held myths about the history of mathematics; Lagrange s attempt to prove Euclid s parallel postulate; and the central role that mathematics has played throughout the history of western civilization.

The development of mathematics cannot be programmed or predicted. Still, seeing how ideas have been formed over time and what the difficulties were can help teachers find new ways to explain mathematics. Appreciating its cultural background can humanize mathematics for students. And famous mathematicians struggles and successes should interest -- and perhaps inspire -- researchers. Readers will see not only what the mathematical past was like, but also how important parts of the mathematical present came to be.

Contents

Introduction .. . . xi

Part I. The Calculus as Algebra .. . . .1

Preface to the Garland Edition .. .3

Acknowledgement. . . .7

Introduction . . . . .9

1. The Development of Lagrange’s Ideas on the Calculus: 1754–1797 .. . 17

2. The Algebraic Background of the Theory of Analytic Functions . . . 37

3. The Contents of the Fonctions Analytiques . . . 63

4. From Proof-Technique to Definition: The Pre-History of Delta-Epsilon Methods . . 81

Conclusion .  . . .101

Appendix . .103

Bibliography .. . .105

Part II. Selected Writings  . .125

1. The Mathematician, the Historian, and the History of Mathematics . . . .127

2. Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus∗ . . . 135

3. The Changing Concept of Change: The Derivative from Fermat to Weierstrass† . . 147

4. The Centrality of Mathematics in the History of Western Thought† . . . 163

5. Descartes and Problem-Solving† . . . .175

6. The Calculus as Algebra, the Calculus as Geometry: Lagrange, Maclaurin, and Their Legacy . .191

7. Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions∗ . . 209

8. Newton, Maclaurin, and the Authority of Mathematics∗ .. .229

9. Why Should Historical Truth Matter to Mathematicians? Dispelling Myths while PromotinMaths . . .243

10. Why Did Lagrange “Prove” the Parallel Postulate?∗ .  . 257

Index .. . 275

About the Author .  . .287

Prospective Mathematics Teachers’ Knowledge of Algebra A Comparative Study in China and the United States of America

Rongjin Huang

Springer Spektrum | 2014 | 196 páginas | rar - pdf |1,76 Mb

link (password: matav)

Rongjin Huang examines teachers’ knowledge of algebra for teaching, with a particular focus on teaching the concept of function and quadratic relations in China and the United States. 376 Chinese and 115 U.S.A. prospective middle and high school mathematics teachers participated in this survey. Based on an extensive quantitative and qualitative data analysis the author comes to the following conclusions: The Chinese participants demonstrate a stronger knowledge of algebra for teaching and their structure of knowledge of algebra for teaching is much more interconnected. They show flexibility in choosing appropriate perspectives of the function concept and in selecting multiple representations. Finally, the number of college mathematics and mathematics education courses taken impacts the teachers’ knowledge of algebra for teaching.

Contents

·        Knowledge Needed for Teaching

·        Mathematics Teacher Education in China and the U.S.A.

·        Instrumentation, Data Collection, and Data Analysis

·        Comparison of Knowledge of Algebra for Teaching (KAT) between China and the U.S.A.

·        Relationship among Different Components of KAT

·        Comparison of KTCF between China and the U.S.A.

Target Groups

·        Researchers, academics, and scholars of mathematics and didactics

·        Teachers

Algebra for College Students

Jerome E. Kaufmann e Karen L. Schwitters

Cengage Learning | 2010 - 9ª edição | 831 páginas | rar - pdf | 9,7 Mb

link (password: matav)

Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics courses. Algebraic ideas are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism. The open and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad range of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. The text's resource package--anchored by Enhanced WebAssign, an online homework management tool--saves instructors time while also providing additional help and skill-building practice for students outside of class.

CONTENTS
1 Basic Concepts and Properties 1
1.1 Sets, Real Numbers, and Numerical Expressions 2
1.2 Operations with Real Numbers 10
1.3 Properties of Real Numbers and the Use of Exponents 20
1.4 Algebraic Expressions 27
Chapter 1 Summary 36
Chapter 1 Review Problem Set 38
Chapter 1 Test 40
2 Equations, Inequalities, and Problem Solving 41
2.1 Solving First-Degree Equations 42
2.2 Equations Involving Fractional Forms 49
2.3 Equations Involving Decimals and Problem Solving 57
2.4 Formulas 64
2.5 Inequalities 74
2.6 More on Inequalities and Problem Solving 81
2.7 Equations and Inequalities Involving Absolute Value 90
Chapter 2 Summary 97
Chapter 2 Review Problem Set 101
Chapter 2 Test 104
Chapters 1– 2 Cumulative Review Problem Set 105
3 Polynomials 107
3.1 Polynomials: Sums and Differences 108
3.2 Products and Quotients of Monomials 114
3.3 Multiplying Polynomials 119
3.4 Factoring: Greatest Common Factor and Common Binomial Factor 127
3.5 Factoring: Difference of Two Squares and Sum or Difference of Two Cubes 135
3.6 Factoring Trinomials 141
3.7 Equations and Problem Solving 149
Chapter 3 Summary 155
Chapter 3 Review Problem Set 158
Chapter 3 Test 161
4 Rational Expressions 163
4.1 Simplifying Rational Expressions 164
4.2 Multiplying and Dividing Rational Expressions 169
4.3 Adding and Subtracting Rational Expressions 175
4.4 More on Rational Expressions and Complex Fractions 182
4.5 Dividing Polynomials 190
4.6 Fractional Equations 196
4.7 More Fractional Equations and Applications 202
Chapter 4 Summary 211
Chapter 4 Review Problem Set 216
Chapter 4 Test 218
Chapters 1– 4 Cumulative Review Problem Set 219
5 Exponents and Radicals 221
5.1 Using Integers as Exponents 222
5.2 Roots and Radicals 229
5.3 Combining Radicals and Simplifying Radicals That Contain Variables 238
5.4 Products and Quotients Involving Radicals 243
5.5 Equations Involving Radicals 249
5.6 Merging Exponents and Roots 254
5.7 Scientific Notation 259
Chapter 5 Summary 265
Chapter 5 Review Problem Set 269
Chapter 5 Test 271
6 Quadratic Equations and Inequalities 273
6.1 Complex Numbers 274
6.2 Quadratic Equations 281
6.3 Completing the Square 289
6.4 Quadratic Formula 293
6.5 More Quadratic Equations and Applications 300
6.6 Quadratic and Other Nonlinear Inequalities 308
Chapter 6 Summary 314
Chapter 6 Review Problem Set 318
Chapter 6 Test 320
Chapters 1– 6 Cumulative Review Problem Set 321
7 Linear Equations and Inequalities in Two Variables 323
7.1 Rectangular Coordinate System and Linear Equations 324
7.2 Linear Inequalities in Two Variables 337
7.3 Distance and Slope 342
7.4 Determining the Equation of a Line 353
7.5 Graphing Nonlinear Equations 363
Chapter 7 Summary 371
Chapter 7 Review Problem Set 376
Chapter 7 Test 379
8 Functions 381
8.1 Concept of a Function 382
8.2 Linear Functions and Applications 391
8.3 Quadratic Functions 398
8.4 More Quadratic Functions and Applications 407
8.5 Transformations of Some Basic Curves 416
8.6 Combining Functions 425
8.7 Direct and Inverse Variation 432
Chapter 8 Summary 440
Chapter 8 Review Problem Set 447
Chapter 8 Test 449
Chapters 1– 8 Cumulative Review Problem Set 450
9 Polynomial and Rational Functions 453
9.1 Synthetic Division 454
9.2 Remainder and Factor Theorems 458
9.3 Polynomial Equations 463
9.4 Graphing Polynomial Functions 473
9.5 Graphing Rational Functions 483
9.6 More on Graphing Rational Functions 492
Chapter 9 Summary 499
Chapter 9 Review Problem Set 503
Chapter 9 Test 504
10 Exponential and Logarithmic Functions 505
10.1 Exponents and Exponential Functions 506
10.2 Applications of Exponential Functions 513
10.3 Inverse Functions 524
10.4 Logarithms 534
10.5 Logarithmic Functions 542
10.6 Exponential Equations, Logarithmic Equations, and Problem Solving 549
Chapter 10 Summary 559
Chapter 10 Review Problem Set 565
Chapter 10 Test 567
Chapters 1– 10 Cumulative Review Problem Set 568
11 Systems of Equations 571
11.1 Systems of Two Linear Equations in Two Variables 572
11.2 Systems of Three Linear Equations in Three Variables 582
11.3 Matrix Approach to Solving Linear Systems 589
11.4 Determinants 598
11.5 Cramer’s Rule 607
11.6 Partial Fractions (Optional) 613
Chapter 11 Summary 619
Chapter 11 Review Problem Set 623
Chapter 11 Test 625
12 Algebra of Matrices 627
12.1 Algebra of 2 2 Matrices 628
12.2 Multiplicative Inverses 634
12.3 m n Matrices 640
12.4 Systems of Linear Inequalities: Linear Programming 649
Chapter 12 Summary 658
Chapter 12 Review Problem Set 662
Chapter 12 Test 664
Chapters 1 – 12 Cumulative Review Problem Set 665
13 Conic Sections 669
13.1 Circles 670
13.2 Parabolas 676
13.3 Ellipses 684
13.4 Hyperbolas 693
13.5 Systems Involving Nonlinear Equations 702
Chapter 13 Summary 709
Chapter 13 Review Problem Set 714
Chapter 13 Test 715
14 Sequences and Mathematical Induction 717
14.1 Arithmetic Sequences 718
14.2 Geometric Sequences 725
14.3 Another Look at Problem Solving 733
14.4 Mathematical Induction 738
Chapter 14 Summary 744
Chapter 14 Review Problem Set 746
Chapter 14 Test 748
Appendix A Prime Numbers and Operations with Fractions 749
Appendix B Binomial Theorem 757
Answers to Odd-Numbered Problems and All Chapter Review, Chapter Test, Cumulative Review, and Appendix A Problems 761
Index I-1

Intermediate Algebra with P.O.W.E.R. Learning

 Sherri Messersmith, Lawrence Perez e Robert Feldman

McGraw-Hill Science/Engineering/Math | 2013 | 1029 páginas | rar - pdf | 34,4 Mb

link (password: matav)

"After having written five developmental algebra textbooks, I decided to team up with Larry Perez from Saddleback College in California to write a paperback series beginning with Basic College Math or arithmetic. We know, first-hand, that teaching developmental mathematics is about so much more than the math. Today, many of our students are also in developmental reading and/or writing courses, so they don't read well. Many students are poor note-takers, do not know how to read/use a textbook, have poor study skills, and have never learned time-management skills. Instructors know that a major reason for high failure rates in developmental math courses is due to the fact that many of our students do not know how to be college students. They don't want to fail, they just don't know how to succeed! Larry and I have adapted what we do in the classroom to try to address the non-math needs of our students. But, we wondered, how can we do this in a textbook? Enter P.O.W.E.R.. P.O.W.E.R. is a five-step process to promote learning and critical thinking. Each step in the process--Prepare, Organize, Work, Evaluate, and Rethink--provides students with a proven framework that will help them achieve academic success. P.O.W.E.R. maximizes the success of students by using a research-based "best practices" approach. It is a scientifically-based framework promoting student success, with each step in the process based on empirical research findings related to students' academic performance in a college environment"--

Contents

Chapter 1: Real Numbers

Section 1.1 Set of Numbers

Section 1.2 Operations on Real Numbers

Section 1.3 Order of Operations

Section 1.4 Algebraic Expressions and Properties of Real Numbers

Chapter Summary

Chapter Review

Chapter Test

Chapter 2: Linear Equations in One Variable

Section 2.1 Linear Equations in One Variable

Section 2.2 Formulas and Percent 

Section 2.3 Applications of Linear Equations

Section 2.4 Applications Involving Percents

Section 2.5 More Applications of Linear Equations

Chapter Summary

Chapter Review

Chapter TestCumulative 

Review for Chapters 1 and 2

Chapter 3: Linear Inequalities and Absolute Value

Section 3.1 Linear Inequalities in One Variable

Section 3.2 Compound Inequalities in One Variable

Section 3.3 Absolute Value Equations and Inequalities

Chapter SummaryChapter Review

Chapter TestCumulative 

Review for Chapters 1 – 3 

Chapter 4: Linear Equations in Two Variables

Section 4.1 Introduction to Linear Equations in Two Variables

Section 4.2 Slope of a Line and Slope-Intercept Form

Section 4.3 Writing an Equation of a Line

Section 4.4 Linear and Compound Linear Inequalities in Two Variables

Section 4.5 Introduction to Functions

Chapter SummaryChapter Review

Chapter TestCumulative

Review for Chapters 1 – 4 

Chapter 5: Solving Systems of Linear Equations

Section 5.1 Solving Systems of Linear Equations in Two Variables

Section 5.2 Solving Systems of Linear Equations in Three Variables

Section 5.3 Application of Systems of Linear Equations

Section 5.4 Solving Systems of Linear Equations Using Matrices

Chapter Summary

Chapter Review

Chapter Test

Cumulative Review for Chapters 1 – 5 

Chapter 6: Polynomials and Polynomial Functions

Section 6.1 The Rules of Exponents

Section 6.2 More on Exponents and Scientific Notation

Section 6.3 Addition and Subtraction of Polynomials and Polynomial Functions 

Section 6.4 Multiplication of Polynomials and Polynomial Functions

Section 6.5 Division of Polynomials and Polynomial Functions

Chapter SummaryChapter Review

Chapter Test

Cumulative Review for Chapters 1 – 6 

Chapter 7: Factoring Polynomials

Section 7.1 The Greatest Common Factor and Factoring by Grouping

Section 7.2 Factoring Trinomials 

Section 7.3 Special Factoring TechniquesPutting It All Together

Section 7.4 Solving Quadratic Equations by Factoring and Applications

Chapter Summary

Chapter Review

Chapter Test

Cumulative Review for Chapters 1 – 7 

Chapter 8: Rational Expressions, Equations, and Functions

Section 8.1 Simplifying, Multiplying, and Dividing Rational Expressions and Functions

Section 8.2 Adding and Subtracting Rational Expressions

Section 8.3 Simplifying Complex Fractions

Section 8.4 Solving Rational EquationsPutting It All Together

Section 8.5 Application of Rational Equations

Section 8.6 VariationChapter SummaryChapter Review

Chapter Test

Cumulative Review for Chapters 1 – 8 

Chapter 9: Radicals and Rational Exponents

Section 9.1 Radical Expressions and Functions

Section 9.2 Rational Exponents

Section 9.3 Simplifying Expressions Containing Square Roots 

Section 9.4 Simplifying Expressions Containing Higher Roots

Section 9.5 Adding, Subtracting, and Multiplying Radicals

Section 9.6 Dividing RadicalsPutting It All Together

Section 9.7 Solving Radical Equations

Section 9.8 Complex Numbers

Chapter Summary

Chapter Review

Chapter TestCumulative Review for Chapters 1 – 9

Chapter 10: Quadratic Equations and Functions

Section 10.1 The Square Root Property and Completing the Square

Section 10.2 The Quadratic FormulaPutting It All TogetherSection 10.3 Equations in Quadratic Form

Section 10.4 Formulas and Applications

Section 10.5 Quadratic Functions and their Graphs

Section 10.6 Application of Quadratic Functions and Graphing Other Parabolas

Section 10.7 Quadratic and Rational Inequalities

Chapter Summary

Chapter ReviewChapter Test

Cumulative Review for Chapters 1 – 10 

Chapter 11: Exponential and Logarithmic Functions

Section 11.1 Inverse Functions

Section 11.2 Exponential Functions

Section 11.3 Logarithmic Functions

Section 11.4 Properties of Logarithms

Section 11.5 Common and Natural Logarithms and Change of Base

Section 11.6 Solving Exponential and Logarithmic Equations

Chapter Summary

Chapter ReviewChapter Test

Cumulative Review for Chapters 1 – 11 

Chapter 12: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Section 12.1 Graphs of Other Useful Functions 

Section 12.2 The Circle

Section 12.3 The Ellipse

Section 12.4 The HyperbolaPutting It All Together

Section 12.5 Nonlinear Systems of Equations

Sections 12.6 Second-Degree Inequalities and System of Inequalities

Chapter Summary

Chapter Review

Chapter TestCumulative Review for Chapters 1 – 12 

Appendix

Section A Review of Fractions

Section B Geometry Review

Section C Synthetic Division and the Remainder Theorem

Section D Determinants and Cramer’s Rule