Let's Review: Integrated Algebra

Let's Review: Integrated Algebra

by Lawrence S. Leff M.S.


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Reflecting the latest New York State curriculum change, this brand-new addition to Barron’s Let’s Review series covers all topics prescribed by the New York State Board of Regents for the new Integrated Algebra Regents exam, which replaces the Math A Regents exam. This book stresses rapid learning, using many step-by-step demonstration examples, helpful diagrams, enlightening “Math Fact” summaries, and graphing calculator approaches. Fourteen chapters review the following topics: sets, operations, and algebraic language; linear equations and formulas; problem solving and technology; ratios, rates, and proportions; polynomials and factoring; rational expressions and equations; radicals and right triangles; area and volume; linear equations and graphing; functions, graphs, and models; systems of linear equations and inequalities; quadratic and exponential functions; statistics and visual representations of data; and counting and probability of compound events. Exercise sections within each chapter feature a large sampling of Regents-type multiple-choice and extended response questions, with answers at the back of the book. Students will find this book helpful when they need additional explanation and practice on a troublesome topic, or when they want to review specific topics before taking a classroom test or the Regents exam. Teachers will value it as a lesson-planning aid, and as a source of classroom exercises, homework problems, and test questions.

Product Details

ISBN-13: 9780764135910
Publisher: Barron's Educational Series, Incorporated
Publication date: 09/01/2007
Series: Let's Review Series
Pages: 528
Product dimensions: 6.00(w) x 9.00(h) x (d)
Age Range: 14 - 17 Years

Table of Contents

Preface     vii
Sets, Operations, and Algebraic Language     1
Numbers, Variables, and Symbols     1
Classifying Real Numbers     6
Learning More About Sets     8
Operations with Signed Numbers     12
Properties of Real Numbers     16
Exponents and Scientific Notation     21
Order of Operations     27
Translating Between English and Algebra     30
Linear Equations and Inequalities     34
Solving One-Step Equations     34
Solving Multistep Equations     38
Solving Equations with Like Terms     42
Algebraic Modeling     49
Literal Equations and Formulas     56
One-Variable Linear Inequalities     62
Problem Solving and Technology     68
Problem Solving Strategies     68
Using a Graphing Calculator     79
Comparing Mathematical Models     87
Ratios, Rates, and Proportions     94
Ratios and Rates     94
Proportions     99
Solving Motion Problems     104
Solving Percent Problems     109
Probability Ratios     120
Polynomial Arithmetic andFactoring     128
Combining Polynomials     128
Multiplying and Dividing Polynomials     131
Factoring Polynomials     137
Multiplying and Factoring Special Binomial Pairs     140
Factoring Quadratic Trinomials     143
Solving Quadratic Equations by Factoring     148
Solving Word Problems with Quadratic Equations     153
Rational Expressions and Equations     159
Simplifying Rational Expressions     159
Multiplying and Dividing Rational Expressions     163
Combining Rational Expressions     166
Rational Equations and Inequalities     170
Radicals and Right Triangles     173
Square and Cube Roots     173
Operations with Radicals     177
Combining Radicals     183
The Pythagorean Theorem     186
Similar Triangles and Trigonometry     196
Proportions in Similar Triangles     196
Trigonometric Ratios     201
Solving Problems Using Trigonometry     210
Area and Volume     217
Areas of Parallelograms and Triangles     217
Area of a Trapezoid     226
Circumference and Area of a Circle      231
Areas of Overlapping Figures     235
Surface Area and Volume     242
Graphing and Writing Equations of Lines     249
Slope of a Line     249
Slope-Intercept Form of a Linear Equation     258
Slopes of Parallel Lines     266
Graphing Linear Equations     271
Direct Variation     276
Point-Slope Form of a Linear Equation     279
Functions, Graphs, and Models     282
Function Concepts     282
Function Graphs as Models     289
The Absolute Value Function     296
Creating a Scatter Plot     299
Finding a Line of Best Fit     302
Systems of Linear Equations and Inequalities     311
Solving Linear Systems Graphically     311
Solving Linear Systems By Substitution     318
Solving Linear Systems By Combining Equations     325
Graphing Systems of Linear Inequalities     331
Quadratic and Exponential Functions     338
Graphing a Quadratic Function     338
Solving Quadratic Equations Graphically     349
Solving a Linear-Quadratic System     357
Exponential Growth and Decay     361
Statistics and Visual Representations of Data     371
Measures of Central Tendency     371
Percentiles and Quartiles     380
Histograms and Stem-and-Leaf Plots     384
Cumulative Frequency Histograms     394
Counting and Probability of Compound Events     403
Venn Diagrams and Counting     403
Counting Using Permutations     408
Probability of Compound Events     416
Probability Formulas     421
Answers and Solution Hints to Practice Exercises     432
Glossary of Integrated Algebra Terms     456
Learning About the Integrated Algebra Regents Examination     465
Sample Regents Examinations with Answers     469
Index     483

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