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This book covers all of the mathconcepts you need to know for theNew SAT, organized in twenty chaptersby subject, so you can focus on areasyou find especially challenging.Important vocabularies, definitions,and formulas are in the beginning ofeach section to teach you as directlyand clearly as possible. Accompanyingexamples and solutions show you howto apply your knowledge.These realistic practice tests give youpractical preparation, helping you getcomfortable with the New SAT exam.Complete answers and explanationshelp you identify weaknesses and attainmaximum benefits out of the practice test.CREATED FOR THENEW SAT EXAM!A set of exercises in each section, andchapter test at the end of each chapter, comewith detailed step-by-step solutions.Acing the New SAT MathUnderstand the BasicConcepts of Algebra I, II,Geometry, Statistics,and Trigonometry. LearnProblem SolvingTechniques.AcingCreatedfor theNew SATExam!3 Full-LengthPractice Tests20 Chapter TestsDefinitions,Theorems, andKey FormulasHundreds ofExamples andExercises 14.00ISBN 978-0-9754753-6-2* SAT is a registered trademark of the College Entrance Examination Board, which isnot affiliated with this booktheNewSATMathPDF

Acing theNew SAT Mathby Thomas HyunGREENHALL PUBLISHINGTHOUSAND OAKS, CA

Copyright 2016 by Greenhall PublishingAll rights reserved. No part of this book may be used or reproduced in anymanner without the written permission of the publisher.This edition published by Greenhall PublishingGreenhall PublishingThousand Oaks, CA 91358http:// greenhallpublishing.comWritten by Thomas HyunCover design by Hespenheide DesignPrinted in the United States of AmericaISBN-10: 0-9754753-6-3ISBN-13: 978-0-9754753-6-2SAT is a registered trademark of the College Entrance Examination Board,which is not affiliated with this book.

CONTENTSTo the StudentsviPart A – Math ReviewI. Heart of AlgebraChapter 1: The Language and Tools of Algebra1-11-21-31-4Variables and ExpressionsExponents and Order of OperationsSimplifying Algebraic ExpressionsRational, Irrational, and DecimalChapter 1 Practice TestAnswers and ExplanationsChapter 2: Solving Linear Equations2-12-22-32-42-5Writing EquationsSolving EquationsSolving Equations with Variables on Both SidesEquations with No Solution and IdentitySolving for a Specific VariableChapter 2 Practice TestAnswers and ExplanationsChapter 3: Functionsand Linear Equations3-13-23-33-43-53-6Relations and FunctionsRate of Change and SlopeSlope-Intercept Form and Point-Slope FormParallel and Perpendicular LinesSolving Systems of Linear EquationsAbsolute Value EquationsChapter 3 Practice TestAnswers and ExplanationsChapter 4: Linear Inequalities and Graphs4-14-24-34-4Solving InequalitiesCompound and Absolute Value InequalitiesGraphing Inequalities in Two VariablesGraphing Systems of InequalitiesChapter 4 Practice TestAnswers and 50525461616365676971

ii ContentsChapter 5: Word Problems in Real-Life Situation5-15-25-35-4Solving Word Problems Using Linear ModelsSolving Word Problems with EquationsSolving Word Problems Using Systems of EquationsSolving Word Problems Using InequalitiesChapter 5 Practice TestAnswers and Explanations77777981838587II. Statistics and Data AnalysisChapter 6: Ratios, Rates, and Proportions6-1 Ratios and Rates6-2 Proportions6-3 Ratios, Rates, and Proportions Word ProblemsChapter 6 Practice TestAnswers and ExplanationsChapter 7: Percents959597991011031097-1 Percent of Change7-2 Percents and Equations7-3 Percent Word Problems109111113Chapter 7 Practice TestAnswers and Explanations115117Chapter 8: Statistics8-18-28-38-48-5Mean, Median, Mode, and RangeStandard DeviationGraphical DisplaysScatter PlotsPopulations, Samples, and Random SelectionChapter 8 Practice TestAnswers and ExplanationsChapter 9: Categorical Data and Probability9-1 Permutations and Combinations9-2 Rules of Probability9-3 Categorical Data and Conditional ProbabilitiesChapter 9 Practice TestAnswers and 5147

iv ContentsChapter 14: Rational Expressions14-114-214-314-4Rational ExpressionsSolving Rational EquationsDirect, Inverse, and Joint VariationSolving Word Problems Using Rational EquationsChapter 14 Practice TestAnswers and ExplanationsChapter 15: Trigonometric Functions15-1 Trigonometric Ratios of Acute Angles15-2 The Radian Measure of an Angle15-3 Trigonometric Functions of General Angles and the Unit CircleChapter 15 Practice TestAnswers and 1IV. GeometryChapter 16: Lines and Angles16-1 Lines, Segments, and Rays16-2 Angles16-3 Parallel and Perpendicular LinesChapter 16 Practice TestAnswers and Explanations to Exercises and Practice TestChapter 17: Triangles17-117-217-317-4Angles of a TrianglesPythagorean Theorem and Special Right TrianglesSimilar Triangles and Proportional PartsArea of a TriangleChapter 17 Practice TestAnswers and ExplanationsChapter 18: Polygons18-1 Parallelograms18-2 Rectangles, Squares, and Trapezoids18-3 Regular PolygonsChapter 18 Practice TestAnswers and 9295295297299301303

Contents vChapter 19: Circles19-119-219-319-419-5Arcs, Angles, and TangentsArc Lengths and Areas of SectorsInscribed AnglesArcs and ChordsEquations of CirclesChapter 19 Practice TestAnswers and ExplanationsChapter 20: Surface Areas and Volumes20-1 Prisms20-2 Cylinders and Spheres20-3 Pyramids and ConesChapter 20 Practice TestAnswers and 3335Part B – Practice TestsPSAT 10 Practice Test341Answers and Explanations360SAT Practice Test 1367Answers and Explanations388SAT Practice Test 2399Answers and Explanations421