Preview GRE Math Workbook, 11th Edition by Kaplan Publishing (2018) Preview GRE Math Workbook, 11th Edition by Kaplan Publishing (2018) Preview GRE Math Workbook, 11th Edition by Kaplan Publishing (2018) Preview GRE Math Workbook, 11th Edition by Kaplan Publishing (2018) Preview GRE Math Workbook, 11th Edition by Kaplan Publishing (2018)
GRE® MATH WORKBOOK ELEVENTH EDITION Table of Contents GRE Math Workbook Cover Title Page Copyright Acknowledgments How to Use This Book Related Titles Part One: Getting Started Chapter 1: Introduction to GRE Math Understanding the GRE Quantitative Reasoning Sections MST Mechanics Question Types Quantitative Comparison Problem Solving Data Interpretation Part Two: Quantitative Reasoning Chapter 2: Quantitative Comparison Quantitative Comparison Quantitative Comparison Questions Quantitative Comparison Practice Set Quantitative Comparison Practice Set: Answer Key Quantitative Comparison Practice Set: Answers and Explanations Chapter 3: Problem Solving Problem Solving Questions (Single Answer) Problem Solving (All-That-Apply) Problem Solving Questions (Numeric Entry) Problem Solving Practice Set Problem Solving Practice Set: Answer Key Problem Solving Practice Set: Answers and Explanations Chapter 4: Data Interpretation Data Interpretation Questions (One Answer) Data Interpretation Questions (All-That-Apply) Data Interpretation Questions (Numeric Entry) Data Interpretation Practice Set Data Interpretation Practice Set: Answer Key Data Interpretation Practice Set: Answers and Explanations Chapter 5: Quantitative Reasoning Practice Quantitative Reasoning Practice Set Quantitative Reasoning Practice Set Answer Key Quantitative Reasoning Practice Set Answers and Explanations Quantitative Reasoning Practice Set Diagnostic Tool Quantitative Reasoning Practice Set Quantitative Reasoning Practice Set Answer Key Quantitative Reasoning Practice Set Answers and Explanations Quantitative Reasoning Practice Set Diagnostic Tool Quantitative Reasoning Practice Set Quantitative Reasoning Practice Set Answer Key Quantitative Reasoning Practice Set Answers and Explanations Quantitative Reasoning Practice Set Diagnostic Tool Quantitative Reasoning Practice Set Quantitative Reasoning Practice Set Answer Key Quantitative Reasoning Practice Set Answers and Explanations Quantitative Reasoning Practice Set Diagnostic Tool Quantitative Reasoning Practice Set Quantitative Reasoning Practice Set Answer Key Quantitative Reasoning Practice Set Answers and Explanations Quantitative Reasoning Practice Set Diagnostic Tool Quantitative Reasoning Practice Set Quantitative Reasoning Practice Set Answer KeyQuantitative Reasoning Practice Set Answer Key Quantitative Reasoning Practice Set Answers and Explanations Quantitative Reasoning Practice Set Diagnostic Tool Part Three: Math Content Review Chapter 6: Arithmetic Arithmetic Real Numbers Number Operations Number Operations Exercises Number Operations Exercises Answer Key Number Properties Number Properties Exercises Number Properties Exercises Answer Key Averages (Arithmetic Means) Averages (Arithmetic Means) Exercises Averages (Arithmetic Means) Exercises Answer Key Ratios Ratios Exercises Ratios Exercises Answer Key Percents Percents Exercises Percents Exercises Answer Key Powers and Roots Powers and Roots Exercises Powers and Roots Exercises Answer Key Chapter 7: Algebra Understanding Algebra Operations with Algebraic Expressions Operations with Algebraic Expressions Exercises Operations with Algebraic Expressions Exercises Answer Key Rules of Exponents Rules of Exponents Exercises Rules of Exponents Exercises Answer Key Solving Linear Equations Solving Linear Equations Exercises Solving Linear Equations Exercises Answer Key Quadratic Equations Quadratic Equations Exercises Quadratic Equations Exercises Answer Key Solving Inequalities Solving Inequalities Exercises Solving Inequalities Exercises Answer Key Translation into Algebra Translation into Algebra Exercises Translation into Algebra Exercises Answer Key Functions Functions Exercises Functions Exercises Answer Key Coordinate Geometry Coordinate Geometry Exercises Coordinate Geometry Exercises Answer Key Graphs of Functions Graphs of Functions Exercises Graphs of Functions Exercises Answer Key Chapter 8: Geometry Understanding Geometry Lines and Angles Lines and Angles Exercises Lines and Angles Exercises Answer Key Triangles and Pythagorean Theorem Triangles and Pythagorean Theorem Exercises Triangles and Pythagorean Theorem Exercises Answer Key Polygons Polygons Exercises Polygons Exercises Answer Key Circles Circles Exercises Circles Exercises Answer Key Multiple Figures Multiple Figures Exercises Multiple Figures Exercises Answer Key Three-Dimensional Figures (Uniform Solids) Three-Dimensional Figures (Uniform Solids) Exercises Three-Dimensional Figures (Uniform Solids) Exercises Answer Key Chapter 9: Data Interpretation Understanding Data Analysis Counting Methods Counting Methods Exercises Counting Methods Exercises Answer Key Descriptive Statistics Descriptive Statistics Exercises Descriptive Statistics Exercises Answer Key Data Graphs and Tables Data Graphs and Tables Exercises Data Graphs and Tables Exercises Answer Key Probability Probability Exercises Probability Exercises Answer Key Part Four: Advanced Math Practice Chapter 10: High-Difficulty Question Sets Introduction to High-Difficulty Question Sets Advanced Math Questions Practice Set Advanced Math Questions Practice Set Answer Key Advanced Math Questions Practice Set Answers and Explanations Advanced Math Questions Practice Set Advanced Math Questions Practice Set Answer Key Advanced Math Questions Practice Set Answers and Explanations Advanced Math Questions Practice Set Advanced Math Questions Practice Set Answer Key Advanced Math Questions Practice Set Answers and Explanations Advanced Math Questions Practice Set Advanced Math Questions Practice Set Answer Key Advanced Math Questions Practice Set Answers and Explanations Part Five: GRE Resources Appendix: Math Reference GRE® is a registered trademark of the Educational Testing Service, which neither sponsors nor endorses this product This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service If legal advice or other expert assistance is required, the services of a competent professional should be sought © 2019 Kaplan, Inc Published by Kaplan Publishing, a division of Kaplan, Inc 750 Third Avenue New York, NY 10017 ISBN: 978-1-5062-3528-8 10 9 8 7 6 5 4 3 2 1 All rights reserved under International and Pan-American Copyright Conventions By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this eBook on screen No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of the publisher Acknowledgments Special thanks to the team that made this book possible: Arthur Ahn, Matthew Belinkie, Shannon Berning, Lauren T Bernstein, Kim Bowers, Gerard Cortinez, Elisa Davis, Lola Disparte, Boris Dvorkin, John Evans, Paula Fleming, Darcy Galane, Joanna Graham, Adam Grey, Allison Harm, Jack Hayes, Adam Hinz, Gar Hong, Sunny Hwang, Cinzia Iacono, Avi Lidgi, Kate Lopaze, Keith Lubeley, TJ Mancini, Jennifer Moore, Jason Moss, Walt Niedner, Robert Reiss, S Ross, Derek Rusnak, Emily Sachar, Stephanie Schrauth, Sheryl Stebbins, Glen Stohr, Sascha Strelka, Gene Suhir, Martha Torres, Liza Weale, Lee A Weiss, and many others who have contributed materials and advice over the years How to Use This Book Kaplan has prepared students to take standardized tests for more than 75 years Our team of teachers and researchers knows more about preparation for the GRE than anyone else, and you’ll find Kaplan’s accumulated knowledge and experience throughout this book The GRE is a standardized test, so every test covers the same content in roughly the same way This is good news for you; it means that the best way to prepare is to focus on the sort of questions you are likely to see on Test Day The main focus of this book is on strategic reviews, exercises, and practice sets with explanations that will help you brush up on any math skills you may have forgotten There is a lot of math to absorb, and it’s hard to it all at once Instead, plan out a study schedule and work through this book over the course of several weeks GETTING STARTED In Part of this book, “Getting Started,” we’ll provide you with background information on the Quantitative Reasoning section of the test, what it covers, and how it’s organized QUANTITATIVE REASONING SECTION The Quantitative Reasoning section of the GRE contains three main question types: Quantitative Comparison, Problem Solving, and Data Interpretation Part of this book covers these types with strategies and sample questions Your focus here should be to familiarize yourself with the question types so you won’t be trying to figure out how to approach them on Test Day And practice, practice, practice! MATH CONTENT REVIEW Once you have the big picture, focus on the content Part of this book, “Math Content Review,” gives you a complete tour of the math that you will see on Test Day The material in the math content review is divided into particular subjects Each subject begins with a review, followed by practice exercises organized by level of difficulty This structure makes it easy for you to pinpoint the math concepts you need to review and quickly get your skills up to speed We suggest that you read the content review that introduces a section and then try some of the exercises After checking your answers to those exercises, decide whether you need to spend more time with the content review before completing the sets of exercises Keep track of your progress as you proceed with the content review Not only will this build your skills, it will increase your confidence leading up to Test Day If you find that you would like access to more of Kaplan’s practice tests and quizzes, as well as in-depth instruction on the question types and strategies, look into the variety of course options available at kaptest.com/GRE If you have questions about what you’re studying, ask our expert GRE faculty on our Facebook page: www.facebook.com/KaplanGradPrep Thanks for choosing Kaplan We wish you the best of luck on your journey to graduate school For more GRE® prep, Kaplan offers a range of print and digital products, available in stores and online, including: Kaplan GRE® Prep Plus with Practice Tests and 500-Question Qbank Kaplan GRE® Prep with Practice Tests GRE® Verbal Workbook Kaplan GRE® Vocabulary Flashcards To learn more about Kaplan’s comprehensive prep courses for the GRE®, please visit kaptest.com/GRE Part One GETTING STARTED Chapter Introduction to GRE Math Understanding the GRE Quantitative Reasoning Sections The Quantitative Reasoning sections of the GRE test your ability to reason quantitatively—to read a math problem, understand what it is asking, and solve it The basic math disciplines covered on the GRE are arithmetic, algebra, geometry, and data interpretation In this way, the GRE has topics similar to those covered on the SAT There is no trigonometry or calculus on the GRE The aim of the test is to provide an accurate indication of your ability to use your knowledge of the fundamental topics and apply reasoning skills to the various question types The goal is to make the test a true indicator of your ability to apply given information, think logically, and draw conclusions These are skills you will need at the graduate level of study The GRE contains two math sections, each having 20 questions The allotted time for each section is 35 minutes To perform well on the Quantitative Reasoning sections, you want to perform the fundamental math skills efficiently and apply your reasoning skills at the same time to answer as many questions correctly as possible The various question types will be explained in detail in part of this book The foundations of arithmetic, algebra, geometry, and data interpretation will be reviewed in part of this book In every chapter, there will be plenty of opportunities to practice and check your answers MST Mechanics The GRE is a multi-stage test (MST) While working within a section of the test during the time allotted, you are allowed to skip questions and return to them as long as time remains for the section The test is computerbased with built-in capabilities such as the “Mark” button to indicate a question you want to examine later (within the time allowed for that section) and the “Review” button to see your progress on the entire set of questions in a section, an optional time display, and an on-screen calculator As you prepare for Test Day, always consider how you plan to manage your time for each section and how these computer capabilities can help you On the GRE, every question has the same value So you not want to waste time dwelling on one question while you may be able to answer several others correctly This is one way the Mark and Review buttons can assist you in managing your time You can turn the time display on or off as you wish Some test takers will find it helpful; others will find it annoying The availability of an on-screen calculator is something you will want to consider as you practice for the test Questions in the Quantitative Reasoning sections are not designed to be calculator-intensive If you find yourself doing a long calculation to answer a question, you may be missing the reasoning aspect completely That means most questions on the GRE are written to be answered without a calculator You will want to reserve the calculator for an isolated calculation or a quick check of an answer, but not use it as your main resource for the questions To help you plan for the best use of the on-screen calculator, an image of it is shown below Notice that it is a simple, four-function calculator with a square root key and change of sign key As you review mathematical foundations and practice answering the various question types in this workbook, use your own calculator strategically This will lead you to rely on your critical thinking skills Question Types A Quantitative Reasoning section with 20 questions will be composed of three question types: Quantitative Comparison Problem Solving Data Interpretation Each question type will require you to draw upon your ability to combine your knowledge of mathematical concepts with your reasoning skills in a particular way However, the question types are not distributed evenly within a section The chart below shows how many questions you can expect of each type, as well as the average amount of time you should spend on each question type Number of Quantitative Problem Data Comparison Solving Interpretation Approx 7–8 Approx 9–10 Approx 1.5 minutes 1.5–2 minutes minutes Questions Time per Question Quantitative Comparison A Quantitative Comparison question will not ask you to identify a particular value as the answer, but it will ask you to make a comparison between two quantities and identify a relationship between them The four answer choices for a Quantitative Comparison are always the same—same wording, same order Because the answer choices are consistent, you will become familiar with them quickly and be able to concentrate on the comparison at hand The Kaplan Method for answering Quantitative Comparison questions and strategies to help solve them efficiently can be found in chapter Problem Solving A Problem Solving question may appear as a math problem, or it may appear as a word problem dealing with a real-world situation These questions deal with percents, ratios, and other proportions; linear and quadratic equations; basic probability and statistics; and two- and three-dimensional geometry The Kaplan Method for answering Problem Solving questions and strategies to help solve them efficiently can be found in chapter Data Interpretation Questions that require you to interpret data will be based on information located in graphs or tables You will see a set of three or four questions based on each data presentation Frequently, you will have to use information from more than one data source to answer a question Data Interpretation questions need to be answered thoughtfully, only after you have taken time to analyze the contents of each graph or table of data The Kaplan Method for answering Data Interpretation questions and strategies to help solve them efficiently can be found in chapter ... For more GRE? ? prep, Kaplan offers a range of print and digital products, available in stores and online, including: Kaplan GRE? ? Prep Plus with Practice Tests and 500-Question Qbank Kaplan GRE? ? Prep... with Practice Tests GRE? ? Verbal Workbook Kaplan GRE? ? Vocabulary Flashcards To learn more about Kaplan? ??s comprehensive prep courses for the GRE? ?, please visit kaptest.com /GRE Part One GETTING... required, the services of a competent professional should be sought © 2019 Kaplan, Inc Published by Kaplan Publishing, a division of Kaplan, Inc 750 Third Avenue New York, NY 10017 ISBN: 978-1-5062-3528-8