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1、MATH REVIEW for Practicing to Take the General Test Published for the Graduate Record Examinations Board by Educational Testing Service Copyright 1994 by Educational Testing Service. All rights reserved. EDUCATIONAL TESTING SERVICE, ETS, The ETS logo, GRADUATE RECORD EXAMINATIONS, and GRE are regist
2、ered trademarks of Educational Testing Service. U T H REVIEW This review is designed to familiarize you with the mathematical skills and concepts likely to be tested on the Graduate Record Examinations General Test. The text includes many examples with solutions, and there is a set of exercises at t
3、he end of each section. The following material, which is divided into the four basic content areas of arithmetic, algebra, geometry, and data analysis, is not intended to be comprehensive. It is assumed that certain basic concepts are common knowledge to all examinees. Emphasis is, therefore, placed
4、 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 CO
5、NTENTS 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 Translatin
6、g Words into Algebraic Expressions 19 . 2.2 Operations with Algebraic Expressions 19 . 2.3 Rules of Exponents 20 . 2.4 Solving Linear Equations 21 . 2.5 Solving Quadratic Equations in One Variable 22 . 2.6 Inequalities 23 . 2.7 Applications 24 . ALGEBRA EXERCISES 27 . ANSWERS TO ALGEBRA EXERCISES 29
7、 3 . GEOMETRY . 3.1 Lines and Angles 31 3.2 Polygons . 32 . 3.3 Triangles 33 3.4 Quadrilaterals . 35 . 3.5 Circles 37 . 3.6 Coordinate Geometry 40 . 3.7 Three-Dimensional Figures 42 . GEOMETRY EXERCISES 44 . ANSWERS TO GEOMETRY EXERCISES 48 4 . DATA ANALYSIS . 4.1 Measures of Central Location 49 . 4
8、.2 Measures of Dispersion 49 . 4.3 Frequency Distributions 50 . 4.4 Counting 51 . 4.5 Probability 52 . 4.6 Data Representation and Interpretation 53 . DATA ANALYSIS EXERCISES 59 . ANSWERS TO DATA ANALYSIS EXERCISES 67 ARITHMETIC 1.1 Integers The set of integers, I, is composed of all the counting nu
9、mbers (i.e., 1,2, 3, . . .), zero, and the negative of each counting number; that is, Therefore, some integers are positive, some are negative, and the integer 0 is neither positive nor negative. Integers that are multiples of 2 are called even integers, namely . . . , - 6, - 4, - 2, 0, 2, 4, 6, . .
10、 . All other integers are called odd integers; therefore, . . . , - 5, - 3, - 1, 1, 3, 5, . . . represents the set of all odd integers. Integers in a sequence, such as 57,58,59, or -14, - 13, - 12, - 11, are called consecutive integers. The rules for performing basic arithmetic operations with integ
11、ers should be familiar to you. Some rules that are occasionally forgotten include: (i) Multiplication by 0 always results in 0; e.g., (0)(15) = 0. (ii) Division by 0 is not defined; e.g., 5 i 0 has no meaning. (iii) Multiplication (or division) of two integers with different signs yields a negative
12、result; e.g., (-7)(8) = -56, and (-12) + (4) = -3. (iv) Multiplication (or division) of two negative integers yields a positive result; e.g., (-5)(-12) = 60, and (-24) + (-3) = 8. The division of one integer by another yields either a zero remainder, sometimes called “dividing evenly,“ or a positive-integer remainder. For ex- ample, 215 divided by 5 yields a zero remainder,
