5
MATHEMATICS TEST (RESCALED)
PRACTICE BOOK
Linear algebra: matrix algebra, systems of linear
equations, vector spaces, linear transformations, char-
acteristic polynomials, eigenvalues and eigenvectors
Abstract algebra and number theory: elementary
topics from group theory, the theory of rings and
modules, field theory, and number theory
Additional Topics
— 25%
Introductory real analysis: sequences and series of
numbers and functions, continuity, differentiability
and integrability, elementary topology of ޒ and ޒ
n
Discrete mathematics: logic, set theory, combina-
torics, graph theory, and algorithms
Other topics: general topology, geometry, complex
variables, probability and statistics, and numerical
analysis
The above descriptions of topics covered in the test
should not be considered exhaustive; it is necessary to
understand many other related concepts. Prospective
test takers should be aware that questions requiring no
more than a good precalculus background may be quite
challenging; some of these questions turn out to be
among the most difficult questions on the test. In
general, the questions are intended not only to test
recall of information, but also to assess the test taker’s
understanding of fundamental concepts and the ability
to apply these concepts in various situations.
Preparing for a Subject Test
GRE Subject Test questions are designed to measure
skills and knowledge gained over a long period of time.
Although you might increase your scores to some extent
through preparation a few weeks or months before you
take the test, last minute cramming is unlikely to be of
further help. The following information may be helpful.
Ⅲ A general review of your college courses is
probably the best preparation for the test. How-
ever, the test covers a broad range of subject
matter, and no one is expected to be familiar
with the content of every question.
Ⅲ Use this practice book to become familiar with
the types of questions in the GRE Mathematics
Test (Rescaled), paying special attention to the
directions. If you thoroughly understand the
directions before you take the test, you will
have more time during the test to focus on
the questions themselves.
Test-Taking Strategies
The questions in the practice test in this book illus-
trate the types of multiple-choice questions in the test.
When you take the test, you will mark your answers on
a separate machine-scorable answer sheet. Total testing
time is two hours and fifty minutes; there are no
separately timed sections. Following are some general
test-taking strategies you may want to consider.
Ⅲ Read the test directions carefully, and work as
rapidly as you can without being careless. For
each question, choose the best answer from the
available options.
Ⅲ All questions are of equal value; do not waste
time pondering individual questions you find
extremely difficult or unfamiliar.
Ⅲ You may want to work through the test quite
rapidly, first answering only the questions about
which you feel confident, then going back and
answering questions that require more thought,
and concluding with the most difficult questions
if there is time.
Ⅲ If you decide to change an answer, make sure
you completely erase it and fill in the oval
corresponding to your desired answer.
Ⅲ Questions for which you mark no answer or more
than one answer are not counted in scoring.
Ⅲ As a correction for haphazard guessing, one-
fourth of the number of questions you answer
incorrectly is subtracted from the number of
questions you answer correctly. It is improbable
that mere guessing will improve your score
significantly; it may even lower your score.
If, however, you are not certain of the correct
answer but have some knowledge of the question
and are able to eliminate one or more of the
answer choices, your chance of getting the right
answer is improved, and it may be to your advan-
tage to answer the question.
6
MATHEMATICS TEST (RESCALED)
PRACTICE BOOK
Ⅲ Record all answers on your answer sheet.
Answers recorded in your test book will not
be counted.
Ⅲ Do not wait until the last five minutes of a
testing session to record answers on your
answer sheet.
What Your Scores Mean
Your raw score — that is, the number of questions you
answered correctly minus one-fourth of the number
you answered incorrectly
— is converted to the scaled
score that is reported. This conversion ensures that a
scaled score reported for any edition of a Subject Test
is comparable to the same scaled score earned on any
other edition of the same test. Thus, equal scaled
scores on a particular Subject Test indicate essentially
equal levels of performance regardless of the test
edition taken. Test scores should be compared only
with other scores on the same Subject Test. (For
example, a 680 on the Computer Science Test is not
equivalent to a 680 on the Mathematics Test.)
Note that the Mathematics Test has been rescaled
effective October 2001 and renamed “Mathematics
Test (Rescaled).” Scores earned on the Mathematics
Test (Rescaled) after October 2001 should not be
compared to Mathematics Test scores earned before
October 2001. Additional information about the
rescaled test is available on the GRE Web site and will
also be included in the score interpretive leaflet that
will accompany score reports.
Before taking the test, you may find it useful to
know approximately what raw scores would be
required to obtain a certain scaled score. Several
factors influence the conversion of your raw score
to your scaled score, such as the difficulty of the test
edition and the number of test questions included in
the computation of your raw score. Based on recent
editions of the Mathematics Test, the following table
gives the range of raw scores associated with selected
scaled scores for three different test editions that have
been rescaled. (Note that when the number of scored
questions for a given test is greater than the range of
possible scaled scores, it is likely that two or more raw
scores will convert to the same scaled score.) The
three test editions in the table that follows were
selected to reflect varying degrees of difficulty. Examin-
ees should note that future test editions may be some-
what more or less difficult than the test editions
illustrated in the table.
Range of Raw Scores* Needed
to Earn Selected Scaled Scores on
Three Mathematics Test (Rescaled)
Editions That Differ in Difficulty
Raw Scores
Scaled Score Form A Form B Form C
900 66 62 60 – 61
800 55 51 49
700 43 40 38
600 30 29 28
Number of Questions Used to Compute Raw Score
66 66 65
*Raw Score = Number of correct answers minus one-fourth the
number of incorrect answers, rounded to the nearest integer.
For a particular test edition, there are many ways to
earn the same raw score. For example, on the edition
listed above as “Form A,” a raw score of 30 would earn
a scaled score of 600. Below are a few of the possible
ways in which a scaled score of 600 could be earned on
that edition.
Examples of Ways to Earn
a Scaled Score of 600 on the
Edition Labeled As “Form A”
Number of
Questions
Questions Questions Questions Used to
Raw Answered Answered Not Compute
Score Correctly Incorrectly Answered Raw Score
30 30 0 36 66
30 33 14 19 66
30 37 27 2 66
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MATHEMATICS TEST (RESCALED)
PRACTICE BOOK
PRACTICE TEST
To become familiar with how the administration will be conducted at the test center, first remove the
answer sheet (pages 59 and 60). Then go to the back cover of the test book (page 54) and follow the
instructions for completing the identification areas of the answer sheet. When you are ready to begin the
test, note the time and begin marking your answers on the answer sheet.
9
10
MATHEMATICS TEST (RESCALED)
Time—170 minutes
66 Questions
Directions: Each of the questions or incomplete statements below is followed by five suggested answers or
completions. In each case, select the one that is the best of the choices offered and then mark the corresponding
space on the answer sheet.
Computation and scratchwork may be done in this examination book.
Note: In this examination:
(1) All logarithms with an unspecified base are natural logarithms (that is, with base e).
(2) The set of all real numbers x such that a ≤ x ≤ b is denoted by [a, b].
(3) The symbols ޚ, ޑ, ޒ, and ރ denote the sets of integers, rational numbers, real numbers, and
complex numbers, respectively.
11
SCRATCHWORK
12
13
SCRATCHWORK
14
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