Barron's SAT Math Workbook - Educational materials

1 DedicationTo Rhona:For the understanding,for the sacrifices,andfor the love Copyright 2016, 2012, 2009, 2005, 2000, and 1996 by Barron s Educational Series, rights part of this publication may be reproduced or distributed in any form or by any means without the written permission of the copyright inquiries should be addressed to:Barron s Educational Series, Wireless BoulevardHauppauge, New York : 978-1-4380-6811-4 Publication date: June, 2016 ContentsPrefaceLEARNING ABOUT SAT MATH1 Know What You re Up AgainstLesson 1-1 Getting Acquainted with the Redesigned SATL esson 1-2 Multiple-Choice QuestionsLesson 1-3 Grid-In Questions2 SAT math StrategiesLesson 2-1 SAT math Strategies You Need to KnowLesson 2-2 Guessing and Calculators on the SATTHE FOUR MATHEMATICS CONTENT AREAS3 Heart of AlgebraLesson 3-1 Some Beginning math FactsLesson 3-2 Solving Linear EquationsLesson 3-3 Equations with More Than One VariableLesson 3-4 Polynomials and Algebraic FractionsLesson 3-5 FactoringLesson 3-6 Quadratic EquationsLesson 3-7 Systems of EquationsLesson 3-8 Algebraic InequalitiesLesson 3-9 Absolute Value Equations and InequalitiesLesson

2 3-10 Graphing in the xy-PlaneLesson 3-11 Graphing Linear SystemsLesson 3-12 Working with Functions4 Problem Solving and Data AnalysisLesson 4-1 Working with PercentLesson 4-2 Ratio and VariationLesson 4-3 Rate ProblemsLesson 4-4 Converting Units of MeasurementLesson 4-5 Linear and Exponential FunctionsLesson 4-6 Graphs and TablesLesson 4-7 Scatterplots and SamplingLesson 4-8 Summarizing Data Using Statistics5 Passport To Advanced MathLesson 5-1 Rational ExponentsLesson 5-2 More Advanced Algebraic MethodsLesson 5-3 Complex NumbersLesson 5-4 Completing The SquareLesson 5-5 The Parabola and Its EquationsLesson 5-6 Reflecting and Translating Function Graphs6 Additional Topics in MathLesson 6-1 Reviewing Basic Geometry FactsLesson 6-2 Area of Plane FiguresLesson 6-3 Circles and Their EquationsLesson 6-4 Solid FiguresLesson 6-5 Basic TrigonometryLesson 6-6 The Unit CircleTAKING PRACTICE TESTSP ractice Test 1 Practice Test 2 How to Evaluate Your Performance on a Practice TestSOLUTIONS FOR TUNE-UP EXERCISES AND PRACTICE TESTSW orked out solutions for Chapters 3 6 Answer Explanations for Practice Test 1 Answer Explanations for Practice Test 2 TPrefacehis new edition of the Barron s SAT math Workbook is based on the redesigned 2016 SAT.

3 It is organized arounda simple, easy-to-follow, and proven four-step study plan:STEP 1. Know what to expect on test 2. Become 3. Review SAT math topics and SAT-type 4. Take practice exams under test 1 KNOW WHAT TO EXPECT ON TEST DAYC hapter 1 gets you familiar with the format of the test, types of math questions, and special directions that will appearon the SAT you will take. This information will save you valuable testing time when you take the SAT. It will also helpbuild your confidence and prevent errors that may arise from not understanding the directions on test 2 BECOME TESTWISEBy paying attention to the test-taking tips and SAT math facts that are strategically placed throughout the book, you willimprove your speed and accuracy, which will lead to higher test scores.

4 Chapter 2 is a critically important chapter thatdiscusses essential SAT math strategies while also introducing some of the newer math topics that are tested by theredesigned 3 REVIEW SAT math TOPICS AND SAT-TYPE QUESTIONSThe SAT test redesigned for 2016 and beyond places greater emphasis on your knowing the topics that matter mostfrom your college preparatory high school mathematics courses. Chapters 3 to 6 serve as a math refresher of themathematics you are expected to know and are organized around the four key SAT math content areas: Heart ofAlgebra, Problem Solving and Data Analysis, Passport to Advanced math , and Additional Topics in math (geometricand trigonometric relationships). These chapters also feature a large number and variety of SAT-type math questionsorganized by lesson topic.

5 The easy-to-follow topic and lesson organization makes this book ideal for either independentstudy or use in a formal SAT preparation class. answers and worked-out solutions are provided for all practiceproblems and sample 4 TAKE PRACTICE EXAMS UNDER TEST CONDITIONSP ractice makes perfect! At the end of the book, you will find two full-length SAT math practice tests with answer keysand detailed explanations of answers . Taking these exams under test conditions will help you better manage your timewhen you take the actual test. It will also help you identify and correct any remaining weak spots in your S. LeffWelcome to Barron s math Workbook for the NEW SAT e-Book version!Please note that depending on what device you are using to view this e-Book on, equations, graphs, tables, andother types of illustrations will look differently than it appears in the print book.

6 Please adjust your e-Book contains hundreds of hyper links that will bring you to helpful resources and allow you to clickbetween questions and ABOUTSAT MATHTKnow What You re Up Against1his chapter introduces you to the test format, question types, and the mathematics topics you need to know for theredesigned 2016 SAT. Compared to prior editions of the SAT, the new SAT Places a greater emphasis on algebra: forming and interpreting linear and exponential models; analyzingscatterplots, and two-way tables. Includes two math test sections: in one section you can use a calculator and in the other section a calculator is notallowed. Does not deduct points for wrong IN THIS CHAPTERL esson 1-1 Getting Acquainted with the Redesigned SATL esson 1-2 Multiple-Choice QuestionsLesson 1-3 Grid-In QuestionsLESSON 1-1 GETTING ACQUAINTED WITH THE REDESIGNED SATOVERVIEWThe March 2016 SAT test date marks the first administration of a redesigned SAT.

7 The mathematics contentof the new version of the test will be more closely aligned to what you studied in your high school mathclasses. The redesigned SAT is a timed exam lasting 3 hours (or 3 hours and 50 minutes with an optionalessay).What Does the SAT Measure?The math sections of the new SAT seek to measure a student s understanding of and ability to apply those mathematicsconcepts and skills that are most closely related to successfully pursuing college study and career Do Colleges Require the SAT?College admissions officers know that the students who apply to their colleges come from a wide variety of highschools that may have different grading systems, curricula, and academic standards. SAT scores make it possible forcolleges to compare the course preparation and the performances of applicants by using a common academic SAT score, together with your high school grades and other information you or your high school may be asked toprovide, helps college admission officers to predict your chances of success in the college courses you will Have the SAT math Sections Changed?

8 Here are five key differences between the math sections of the SAT given before 2016 and the SAT for 2016 andbeyond: There is no penalty for wrong answers . Multiple-choice questions have four (A to D) rather than five (A to E) answer choices. Calculators are permitted on only one of the two math sections. There is less emphasis on arithmetic reasoning and a greater emphasis on algebraic reasoning with more questionsbased on real-life scenarios and math TopicsBeginning with the 2016 SAT, these additional math topics will now be required: Manipulating more complicated algebraic expressions including completing the square within a quadraticexpression. For example, the circle equation x2 + y2 + 4x 10y = 7 can be rewritten in the more convenientcenter-radius form as (x + 2)2 + (y 5)2 = 36 by completing the square for both variables.

9 Performing operations involving the imaginary unit i where i = . Solving more complex equations including quadratic equations with a leading coefficient greater than 1 as well asnonfactorable quadratic equations. Working with trigonometric functions of general angles measured in radians as well as summarizes the major differences between the math sections of the previous and newly redesigned you don t know an answer to an SAT math question, make an educated guess! There is no point penalty for a wrong answeron the redesigned SAT. You get points for the questions you answer correctly but do not lose points for any wrong comparing Old and New SAT MathTest FeatureOld SAT math (before 2016)Redesigned SAT math (2016 and after)Test Time70 minutes80 minutesNumber of sectionsThreeTwo: one 55-minute calculator section and one25-minute no-calculator sectionNumber of questions54 = 44 multiple-choice + 10 grid-in58 = 45 multiple-choice + 13 grid-inCalculatorsAllowed for each math sectionPermitted for longer math section onlyPoint penalty for a wrong answer?

10 YesNoMultiple-choice questions5 answer choices (A to E) 4 answer choices (A to D)Point valueEach question counts as 1 question counts as 1 content Topics from arithmetic, algebra,and geometry Only a few algebra 2 topics Not aligned with college-boundhigh school mathematics curricula Greater focus on three key areas:algebra, problem solving and dataanalysis, and advanced math More algebra 2 and trigonometrytopics, more multistep problems,and more problems with real-worldsettings Stronger connection to college-bound high school mathematicscoursesWhat math Content Groups Are Tested?The new test includes math questions drawn from four major content groups: Heart of Algebra: linear equations and functions Problem Solving and Data Analysis: ratios, proportional relationships, percentages, complex measurements,graphs, data interpretation, and statistical measures Passport to Advanced math : analyzing and working with advanced expressions Additional Topics in math .