GREmathPractice.pdf

MATH REVIEW

for

Practicing to Take the

GRE ®

General Test

EDUCATIONAL TESTING SERVICE, ETS, the ETS logos, GRADUATE RECORD EXAMINATIONS,

and GRE are registered trademarks of Educational Testing Service.

MATH REVIEW

The Math Review is designed to familiarize you with the mathematical skills and

concepts likely to be tested on the Graduate Record Examinations General Test.

This material, which is divided into the four basic content areas of arithmetic,

algebra, geometry, and data analysis, includes many definitions and examples

with solutions, and there is a set of exercises (with answers) at the end of each

of these four sections. Note, however, this review is not intended to be compre-

hensive. It is assumed that certain basic concepts are common knowledge to all

examinees. Emphasis is, therefore, placed on the more important skills, concepts,

and definitions, and on those particular areas that are frequently confused or

misunderstood. If any of the topics seem especially unfamiliar, we encourage

you to consult appropriate mathematics texts for a more detailed treatment of

those topics.

TABLE OF CONTENTS

1. ARITHMETIC

1.1 Integers ..................................................................................................... 6

1.2 Fractions ................................................................................................... 7

1.3 Decimals ................................................................................................... 8

1.4 Exponents and Square Roots .................................................................. 10

1.5 Ordering and the Real Number Line ...................................................... 11

1.6 Percent .................................................................................................... 12

1.7 Ratio ....................................................................................................... 13

1.8 Absolute Value ........................................................................................ 13

ARITHMETIC EXERCISES ........................................................................ 14

ANSWERS TO ARITHMETIC EXERCISES .............................................. 17

2. ALGEBRA

2.1 Translating Words into Algebraic Expressions ....................................... 19

2.2 Operations with Algebraic Expressions .................................................. 20

2.3 Rules of Exponents ................................................................................. 21

2.4 Solving Linear Equations ....................................................................... 21

2.5 Solving Quadratic Equations in One Variable ........................................ 23

2.6 Inequalities ............................................................................................. 24

2.7 Applications ............................................................................................ 25

2.8 Coordinate Geometry ............................................................................. 28

ALGEBRA EXERCISES ............................................................................. 31

ANSWERS TO ALGEBRA EXERCISES ................................................... 34

3. GEOMETRY

3.1 Lines and Angles .................................................................................... 36

3.2 Polygons ................................................................................................. 37

3.3 Triangles ................................................................................................. 38

3.4 Quadrilaterals ......................................................................................... 40

3.5 Circles ..................................................................................................... 42

3.6 Three-Dimensional Figures .................................................................... 45

GEOMETRY EXERCISES .......................................................................... 47

ANSWERS TO GEOMETRY EXERCISES ............................................... 50

4. DATA ANALYSIS

4.1 Measures of Central Location ................................................................ 51

4.2 Measures of Dispersion .......................................................................... 51

4.3 Frequency Distributions ......................................................................... 52

4.4 Counting ................................................................................................. 53

4.5 Probability .............................................................................................. 54

4.6 Data Representation and Interpretation .................................................. 55

DATA ANALYSIS EXERCISES .................................................................. 62

ANSWERS TO DATA ANALYSIS EXERCISES ....................................... 69

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