Barrons math workbook for the new SAT (6th, 2016)

SAT điểm 1500+ This completely revised edition reflects all of the new questions and question types that will appear on the new SAT, scheduled to be administered in Spring 2016. Students will discover: Hundreds of revised math questions with answer explanations Math strategies to help testtakers approach and correctly answer all of the question types on the SAT All questions answered and explained Here is an intensive preparation for the SATs allimportant Math section, and a valuable learning tool for collegebound students who need extra help in math and feel the need to raise their math scores.

Dedication To Rhona: For the understanding, for the sacrifices, and for the love © Copyright 2016, 2012, 2009, 2005, 2000, and 1996 by Barron’s Educational Series, Inc All rights reserved No part of this publication may be reproduced or distributed in any form or by any means without the written permission of the copyright owner All inquiries should be addressed to: Barron’s Educational Series, Inc 250 Wireless Boulevard Hauppauge, New York 11788 www.barronse duc.com eISBN: 978-1-4380-6811-4 Publication date: June, 2016 Contents Preface LEARNING ABOUT SAT MATH Know What You’re Up Against Lesson 1-1 Lesson 1-2 Lesson 1-3 Getting Acquainted with the Redesigned SAT Multiple-Choice Questions Grid-In Questions SAT Math Strategies Lesson 2-1 Lesson 2-2 SAT Math Strategies You Need to Know Guessing and Calculators on the SAT THE FOUR MATHEMATICS CONTENT AREAS Heart of Algebra Lesson 3-1 Lesson 3-2 Lesson 3-3 Lesson 3-4 Lesson 3-5 Lesson 3-6 Lesson 3-7 Lesson 3-8 Lesson 3-9 Lesson 3-10 Lesson 3-11 Lesson 3-12 Some Beginning Math Facts Solving Linear Equations Equations with More Than One Variable Polynomials and Algebraic Fractions Factoring Quadratic Equations Systems of Equations Algebraic Inequalities Absolute Value Equations and Inequalities Graphing in the xy-Plane Graphing Linear Systems Working with Functions Problem Solving and Data Analysis Lesson 4-1 Working with Percent Lesson 4-2 Ratio and Variation Lesson 4-3 Rate Problems Lesson 4-4 Converting Units of Measurement Lesson 4-5 Linear and Exponential Functions Lesson 4-6 Graphs and Tables Lesson 4-7 Scatterplots and Sampling Lesson 4-8 Summarizing Data Using Statistics Passport To Advanced Math Lesson 5-1 Lesson 5-2 Lesson 5-3 Lesson 5-4 Lesson 5-5 Lesson 5-6 Rational Exponents More Advanced Algebraic Methods Complex Numbers Completing The Square The Parabola and Its Equations Reflecting and Translating Function Graphs Additional Topics in Math Lesson 6-1 Lesson 6-2 Lesson 6-3 Lesson 6-4 Lesson 6-5 Lesson 6-6 Reviewing Basic Geometry Facts Area of Plane Figures Circles and Their Equations Solid Figures Basic Trigonometry The Unit Circle TAKING PRACTICE TESTS Practice Test Practice Test How to Evaluate Your Performance on a Practice Test SOLUTIONS FOR TUNE-UP EXERCISES AND PRACTICE TESTS Worked out solutions for Chapters 3–6 Answer Explanations for Practice Test Answer Explanations for Practice Test Preface T his new edition of the Barron’s SAT Math Workbook is based on the redesigned 2016 SAT It is organized around a simple, easy-to-follow, and proven four-step study plan: STEP STEP STEP STEP Know what to expect on test day Become testwise Review SAT Math topics and SAT-type questions Take practice exams under test conditions STEP KNOW WHAT TO EXPECT ON TEST DAY Chapter gets you familiar with the format of the test, types of math questions, and special directions that will appear on the SAT you will take This information will save you valuable testing time when you take the SAT It will also help build your confidence and prevent errors that may arise from not understanding the directions on test day STEP BECOME TESTWISE By paying attention to the test-taking tips and SAT Math facts that are strategically placed throughout the book, you will improve your speed and accuracy, which will lead to higher test scores Chapter is a critically important chapter that discusses essential SAT Math strategies while also introducing some of the newer math topics that are tested by the redesigned SAT STEP REVIEW SAT MATH TOPICS AND SAT-TYPE QUESTIONS The SAT test redesigned for 2016 and beyond places greater emphasis on your knowing the topics that matter most from your college preparatory high school mathematics courses Chapters to serve as a math refresher of the mathematics you are expected to know and are organized around the four key SAT Math content areas: Heart of Algebra, Problem Solving and Data Analysis, Passport to Advanced Math, and Additional Topics in Math (geometric and trigonometric relationships) These chapters also feature a large number and variety of SAT-type math questions organized by lesson topic The easy-to-follow topic and lesson organization makes this book ideal for either independent study or use in a formal SAT preparation class Answers and worked-out solutions are provided for all practice problems and sample tests STEP TAKE PRACTICE EXAMS UNDER TEST CONDITIONS Practice makes perfect! At the end of the book, you will find two full-length SAT Math practice tests with answer keys and detailed explanations of answers Taking these exams under test conditions will help you better manage your time when you take the actual test It will also help you identify and correct any remaining weak spots in your test preparation Lawrence S Leff Welcome 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, and other types of illustrations will look differently than it appears in the print book Please adjust your device accordingly This e-Book contains hundreds of hyper links that will bring you to helpful resources and allow you to click between questions and answers LEARNING ABOUT SAT MATH Know What You’re Up Against T his chapter introduces you to the test format, question types, and the mathematics topics you need to know for the redesigned 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; analyzing scatterplots, 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 not allowed ■ Does not deduct points for wrong answers LESSONS IN THIS CHAPTER Lesson 1-1 Getting Acquainted with the Redesigned SAT Lesson 1-2 Multiple-Choice Questions Lesson 1-3 Grid-In Questions 24 (A) Simplify the given function by factoring the numerator: 25 (C) Find the weighted average by calculating the sum of the products of the number of weeks of vacation and the number of people who receive the vacation, and then dividing the sum of the products by 25: 26 (D) If p(x) is a polynomial function and p(−1) = 3, then when x is divided by x − (−1) or, equivalently, x + 1, the remainder is 27 (A) A system of linear equations has no solution if the graphs of the lines are parallel Two lines are parallel when they have the same slope ■ If hy − 8x = 5, then ■ ■ Find the value of h that makes the system of equations have no solution by setting the slopes equal: 28 (B) Five troy ounces is equivalent to The volume is closest to cubic centimeters grams Since density is mass divided by volume, V: 29 (B) To have an increase in the confidence level for survey results, the sample size should be as large as possible and the standard deviation should be as small as possible A larger sample size will result in a data set that more completely mirrors the population, and if the standard deviation is low, the surveyor can be confident that there will not be great variation among the survey results 30 (A) It is given that the vertex of a parabola is (−4, k) so its equation is y = a(x + 4)2 + k Since it is also given that the parabola contains the points (0, 12) and (−3, 7), the coordinates of these points must satisfy the parabola equation ■ For (0, 12): ■ For (−3, 7): ■ Solve the two equations simultaneously for k From the second equation, a = − k Substitute − k for a in the first equation: 31 (28/3) Find the slope of each line ■ Since perpendicular lines have slopes that are negative reciprocals: 32 (405) Rate of change in depth in feet per second is Since 1.5 minutes is equivalent to 90 seconds, 1.5 minutes after his initial descent the diver will be below sea level 33 (3.2) Since |−3| = 3, rewrite the inequality as < 4x − < 10 Adding to each member of the inequality gives 12 < 4x < 13 Dividing each member of the inequality by makes or, equivalently, < x < 3.25 Hence, x can be any number between and 3.25, such as 3.2 34 (1,215) Assume that the ratio of the tagged animals drawn to its sample size is approximately the same If x represents the total number of fish of interest in the lake, then 35 (47) The volume of the rectangular container is 10 × 15 × 20 = 3,000 cubic inches The volume of the cylinder is πr2 h = π(2)2 (5) = 20π To find the maximum number of full cylindrical cups of water that can be placed into the container with no overflow, divide the volume of the rectangular container by the volume of the cylindrical cup and round the answer down: so, the maximum number of full cups of water without overflowing is 47 36 (42) The area of an equilateral triangle with side s is Hence, Since the pendant has sides each of which has a length of centimeters, the distance around the pendant is × = 42 centimeters 37–38 It is given that the function h(t) = −4.9t2 + 88.2t describes the height of a projectile, in meters, after t seconds have elapsed 37 (18) The projectile will hit the ground when h(t) = 0: 37–38 It is given that the function h(t) = −4.9t2 + 88.2t describes the height of a projectile, in meters, after t seconds have elapsed 38 (397) To find the maximum height, write the parabola equation in vertex form: The y-coordinate of the vertex, to the nearest meter, is 397 ... essential SAT Math strategies while also introducing some of the newer math topics that are tested by the redesigned SAT STEP REVIEW SAT MATH TOPICS AND SAT- TYPE QUESTIONS The SAT test redesigned for. .. GETTING ACQUAINTED WITH THE REDESIGNED SAT OVERVIEW The March 2016 SAT test date marks the first administration of a redesigned SAT The mathematics content of the new version of the test will be more... success in the college courses you will take How Have the SAT Math Sections Changed? Here are five key differences between the math sections of the SAT given before 2016 and the SAT for 2016 and