GRE Mathematics Test

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  • Edition: 5th
  • Format: Paperback
  • Copyright: 5/19/2010
  • Publisher: Research & Education Assn
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If You're Serious About Your Career,Use the Most Comprehensive GRE Guide on the Market Today! REA's NEW GRE Mathematics Test Prep Gets You into Grad School! Higher GRE scores mean better options! Scoring well on the GRE Mathematics Subject Test doesn't just help you get into grad school, it helps move your career forward. So it's worth every minute of your valuable time to be knowledgeable, confident, and prepared to do your best. REA's new test prep will get you ready for the GRE and on your way to grad school! Designed for students and professionals looking to advance their careers, this fifth edition of our popular test prep contains everything you need to succeed. Focused chapter reviews cover all the information tested on the GRE Mathematics exam. Each review chaptercontains all the formulas, definitions, and information you need to master the material and achieve an excellent GRE score. The book includes six full-length practice tests based on the most recent GRE Mathematics exam. Each test contains every type of question that can be expected on the GRE so you can "practice for real" and boost your confidence before taking the exam. Our detailed explanations of answers help you identify your strengths and weaknesses. We don't just say which answers are right we also explain why the other answer choices are incorrect so you'll be prepared on test day! Our exclusive Pro Study Plan helps you maximize your valuable study timewhile learning effective test-taking strategies and timesaving tips from the pros. As an added bonus, up-to-the-minute GRE test information and updates are available at: www.rea.com/GRE If you're serious about your career and are ready to take on the GRE Mathematics Subject Test get the most comprehensive guide on the market today!

Table of Contents

About This Bookp. ix
About the Testp. ix
Scoring Your Practice Testsp. x
Pro Study Planp. xiii
Algebra Review
Polynomials and Equationsp. 3
Inequalitiesp. 9
Linear Algebrap. 13
Abstract (Modern) Algebrap. 23
Calculus Review
Functionsp. 45
Coordinate Geometryp. 50
Trigonometric Functionsp. 62
Limitsp. 67
Derivativesp. 71
Application of Derivativesp. 79
Integralsp. 86
Sequences and Seriesp. 92
Differential Equationsp. 98
Miscellaneous Topics
Probability and Statisticsp. 117
Combinational Analysisp. 146
Numerical Analysisp. 152
Real Variablesp. 182
Complex Variablesp. 186
Set Theoryp. 216
Topologyp. 243
Logicp. 262
Algorithmic Processesp. 280
Practice Test I
Answer Sheet Form Ip. 3
Test Ip. 5
Answer Keyp. 30
Detailed Explanations of Answersp. 31
Practice Test II
Answer Sheet Form IIp. 67
Test IIp. 69
Answer Keyp. 93
Detailed Explanations of Answersp. 94
Practice Test III
Answer Sheet Form IIIp. 117
Test IIIp. 119
Answer Keyp. 143
Detailed Explanations of Answersp. 144
Practice Test IV
Answer Sheet Form IVp. 179
Test IVp. 181
Answer Keyp. 206
Detailed Explanations of Answersp. 207
Practice Test V
Answer Sheet Form Vp. 227
Test Vp. 229
Answer Keyp. 254
Detailed Explanations of Answersp. 255
Practice Test VI
Answer Sheet Form VIp. 285
Test VIp. 287
Answer Keyp. 315
Detailed Explanations of Answersp. 316
Answer Sheetsp. 335
Table of Contents provided by Ingram. All Rights Reserved.



This book provides an intensive, complete review of all the math
essentials you need to know to master the GRE Mathematics Subject Test.
It is our intention to provide practice that is somewhat more demanding
than the test itself, so that you can be confident come Test Day. Our goal
is to help the student reach a high level of math competence.
Inside this book you’ll find six full-length REA practice tests based on the format
of the most recently administered GRE test, but even more challenging.
Like the GRE test itself, each of our model tests lasts two hours and 50
minutes. Each one includes every type of question you can expect to
encounter on the actual exam. We also give you an answer key complete
with detailed explanations that spell out how the correct answers were
arrived at. By completing all six practice exams and studying the
explanations that follow, you can discover your strengths and weaknesses
and become well prepared for the actual exam.

To help you brush up on the subject matter, the book also features
281 pages of topical reviews, summarizing the essentials of the various
topics covered on the GRE Mathematics test. Again, our approach is to
cover all the ground necessary to fully frame the test. Our reviews are
designed to work as an at-a-glance overview of the many topics the test
covers. Should you require more detailed coverage, you’ll want to consult
a textbook whose contents parallel the topical coverage of the GRE.


The GRE Mathematics Test is offered three times a year by Educational
Testing Service, under the direction of the Graduate Record
Examinations Board. Applicants for graduate school submit GRE test
results together with other undergraduate records as part of a highly
competitive admission process.

The questions on the test are composed by a committee of specialists
who are selected from various undergraduate and graduate faculties
across the U.S. This test consists of 66 multiple-choice questions. Some
questions are grouped together under a particular diagram and/or graph.

Emphasis is placed on these areas:

I. Calculus (50%)
Material learned in the usual sequence of elementary
calculus courses—differential and integral calculus of one and
of several variables—includes calculus-based applications and
connections with coordinate geometry, trigonometry, differential
equations, and other branches of mathematics.

II. Algebra (25%)
A. Elementary algebra: basic algebraic techniques
and manipulations acquired in high school and used throughout
B. Linear algebra: matrix algebra, systems of linear
equations, vector spaces, linear transformations, characteristic
polynomials, eigenvalues and eigenvectors
C. Abstract algebra and number theory: elementary
topics from group theory; the theory of rings and modules, field
theory, and number theory

III. Additional Topics (25%)
A. Introductory real analysis: sequences and series of
numbers and functions, continuity, differentiability and intergrability,
elementary topology of R and Rn
B. Discrete mathematics: logic, set theory, combinatorics,
graph theory, and algorithms
C. Other topics: general topology, geometry, complex
variables, probability and statistics, and numerical analysis

This list is by no means all-embracing. (You may, for example,
face questions asking you to find the correct mathematical model to
represent a “real-life” situation.) The test requires more than simple
recall: It gauges both your understanding of fundamental concepts and
your ability to apply these concepts in specific situations. Because of
the wide gamut of coursework in undergraduate mathematics, not all
the material that you may have studied will be presented on the exam.
Rather, the questions are based on the courses of study most commonly
offered in an undergraduate mathematics curriculum.

Each correct answer receives one “raw score” point, each incorrect answer
deducts one-quarter of a point, and any omissions are not counted.
Your scaled score is what is sent on to the colleges, and your estimated
percentile rank shows how you stack up against other students who have
taken the exam in a recent three-year period.

While taking REA’s practice tests, it is critical to observe the same
conditions that you will find during the actual test administration:

• Work in a quiet place, free from distractions and interruptions.
• Do not use any reference materials, calculators, or slide rules
since these items cannot be used during the test.
• Work straight through each test. There are no breaks during the
actual exam.
• Time yourself accurately, if possible with a wristwatch, stopwatch
or clock alarm. Looking up to check the time will act as a
distraction (watches with alarms or flashing lights are not permitted at
the testing center).
• Since incorrect answers are each penalized one-quarter of a point,
and unanswered questions are not counted, it is not generally a good
idea to guess. However, if you are able to eliminate one or more of the
answers, guessing may be to your advantage statistically (that is, your
odds of choosing the correct answer will improve).

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