##### Document Text Contents

Page 2

GRE

T

CAT

SUCCESS

2004

Page 220

Once parentheses have been removed, the order of operations is multiplica-

tion and division, then addition and subtraction from left to right.

Example

(215 1 17) { 3 2 [(4 { 9) 4 6] 5 ?

Work inside the parentheses first:

(2) { 3 2 [36 4 6] 5 ?

Then work inside the brackets:

2 { 3 2 [6] 5 ?

Multiply first, then subtract, proceeding from left to right:

6 2 6 5 0

The placement of parentheses and brackets is important. Using the same numbers

as above with the parentheses and brackets placed in different positions can give

many different answers.

Example

215 1 [(17 { 3) 2 (4 { 9)] 4 6 5 ?

Work inside the parentheses first:

215 1 [(51) 2 (36)] 4 6 5 ?

Then work inside the brackets:

215 1 [15] 4 6 5 ?

Since there are no more parentheses or brackets, proceed from left to right,

dividing before adding:

215 1 2

1

2

5 212

1

2

MATHEMATICS REVIEW

213GRE CAT Success www.petersons.com

Page 221

OPERATIONS

When letter symbols and numbers are combined with the operations of arithmetic

(1, 2, {, 4) and with certain other mathematical operations, we have an alge-

braic expression. Algebraic expressions are made up of several parts connected

by a plus or a minus sign; each part is called a term. Terms with the same letter

part are called like terms. Since algebraic expressions represent numbers, they

can be added, subtracted, multiplied, and divided.

When we defined the commutative law of addition in arithmetic by writing a

1 b 5 b 1 a, we meant that a and b could represent any number. The expres-

sion a 1 b 5 b 1 a is an identity because it is true for all numbers. The

expression n 1 5 5 14 is not an identity because it is not true for all numbers; it

becomes true only when the number 9 is substituted for n. Letters used to

represent numbers are called variables. If a number stands alone (the 5 or 14 in

n 1 5 5 14), it is called a constant because its value is constant or unchanging. If

a number appears in front of a variable, it is called a coefficient. Because the letter

x is frequently used to represent a variable, or unknown, the times sign 3, which

can be confused with it in handwriting, is rarely used to express multiplication in

algebra. Other expressions used for multiplication are a dot, parentheses, or

simply writing a number and letter together:

5 { 4 or 5(4) or 5a

Of course, 54 still means fifty-four.

Addition and Subtraction

Only like terms can be combined. Add or subtract the coefficients of like terms,

using the rules for signed numbers.

Example 1

Add x 1 2y 2 2x 1 3y.

x 2 2x 1 2y 1 3y 5 2x 1 5y

Example 2

Perform the subtraction:

230a 2 15b 1 4c

2 (2 5a 1 3b 2 c 1 d)

Change the sign of each term in the subtrahend and then add, using the rules for

signed numbers:

230a 2 15b 1 4c

5a 2 3b 1 c 2 d

225a 2 18b 1 5c 2 d

UNIT 7

214www.petersons.com GRE CAT Success

Page 439

in wording can affect how you approach writing the essay. Read these two sets of

instructions for the personal statement.

1. Please state your reasons for deciding to pursue a graduate degree in the

field you have chosen. Include references to your past study and research in

your chosen field, your plans for study at the university, including problems

and issues you want to address, and your personal goals.

2. The personal statement is an important part of your application. It is your

opportunity to provide information about your background, interests and

aspirations, and how they relate to your proposed academic program. In

your statement, describe your reasons for pursuing graduate study, the

program you hope to follow at the university, and the strengths and

weaknesses of your preparation for graduate study. All personal statements

should be double-spaced and typed, two to three pages.

These instructions cover more or less the same ground, but the second school

asks you to describe the strengths and weaknesses of your preparation for

graduate study, whereas the first school merely asks you to describe your past

study. When writing the essay for the second school, therefore, you must be sure

to address your preparation in greater detail. You will have to both describe and

evaluate your readiness—or lack thereof.

DON’T WRITE TOO MUCH OR TOO LITTLE

The second thing you should keep in mind as you begin your draft is the length of

the essay. Often, the length is specified; for example, the second school’s instruc-

tions above indicate that the statement should be two to three double-spaced pages.

What should you do if length is not specified, as it is not in the first set of instruc-

tions above? Then write one to two typed pages. An essay that is shorter than one

page does not allow room for you to develop your ideas. And an essay that is longer

than two pages becomes a chore for the admissions committee to read.

Finally, when you write your first draft, do not waste space by repeating

information that the admissions committee can get from other parts of your

application, like your transcript or résumé. Use the essay to provide them with

new information or to highlight particular accomplishments.

REVIEW THE FIRST DRAFT

Once you have drafted your essay, read the question again. Has your draft

answered the question fully? If the essay is incomplete, go back and fill in the

missing material. Then ask people for feedback. Although your spouse and friends

may be helpful, you may get more valuable suggestions from faculty members

who know you and who also know what a personal essay should be like. Ask

whether you’ve included things you should leave out or should add things you’ve

forgotten. Is the tone right? Have you achieved the right balance between

boasting and being too modest? Are there any problems with organization, clarity,

grammar, or spelling?

APPENDIX D

432www.petersons.com GRE CAT Success

Page 440

Felecia Bartow, an M.S.W. candidate at Washington University in St. Louis,

gave her drafts to several people. “It helped to have a couple of people (from

different disciplines) read various drafts of my essays in order to give me feedback

on the clarity and conciseness of my writing.” Jim Lipuma, a Ph.D. candidate in

environmental science at the New Jersey Institute of Technology, recommends,

“Proofreading goes without saying, but always read it to yourself, have someone

else read it, and then read it aloud to someone. This will show all the problems,

highlight the areas that need work, and allow for any weaknesses to be exposed.”

PREPARE THE FINAL DRAFT

Once you’ve revised the essay and are satisfied with your final draft, ask someone

with a sharp eye to proofread it for you. The final draft should be absolutely free

of grammar and spelling errors, so do not rely on grammar- or spell-checks to find

all of the errors. Once you are done, be sure to keep backup files as well as a

hard copy. Although you won’t be able to use the whole essay for all your

applications, you may be able to use parts of it. If you do work this way, be

absolutely sure when you submit the final essays that you have not made any

careless editing mistakes. “If you’re applying to multiple schools, make sure that

you don’t have any ‘cut and paste’ errors in your application,” warns Neill Kipp, a

Ph.D. candidate in computer science at Virginia Tech. “If you apply to Florida

State in one letter and the University of Florida in another but forget to change

every occurrence of the university name, then count on being the semester-long

laughingstock of the admissions office.”

Finally, if you are submitting the statement on separate sheets of paper rather

than on the application form itself, put your name, social security number, and

the question on the essay, and type “see attached essay” on the application form.

MAKE IT YOURS

If after reading this appendix you are still daunted by the prospect of writing your

personal statement, just put the whole task aside for a few days. You will find that

the ideas, suggestions, and excerpts you’ve just read will trigger some mental

activity and that soon you will have some ideas of your own to jot down.

Also remember that it’s not necessary to have an exotic background or a

dramatic event to recount in order to write a good essay and gain admission to a

program. Admissions committees are looking for diversity—in gender, race,

ethnicity, nationality, and socioeconomic status, to name some obvious character-

istics. But they are also looking for people with diverse life experiences to add

richness to their student body. Your background, which may seem perfectly

ordinary to you, nevertheless has unique and relevant elements that can be assets

to the program you choose. Your task is to identify and build upon these ele-

ments to persuade the admissions committee that you should be selected.

WRITING A GOOD PERSONAL ESSAY

433GRE CAT Success www.petersons.com

GRE

T

CAT

SUCCESS

2004

Page 220

Once parentheses have been removed, the order of operations is multiplica-

tion and division, then addition and subtraction from left to right.

Example

(215 1 17) { 3 2 [(4 { 9) 4 6] 5 ?

Work inside the parentheses first:

(2) { 3 2 [36 4 6] 5 ?

Then work inside the brackets:

2 { 3 2 [6] 5 ?

Multiply first, then subtract, proceeding from left to right:

6 2 6 5 0

The placement of parentheses and brackets is important. Using the same numbers

as above with the parentheses and brackets placed in different positions can give

many different answers.

Example

215 1 [(17 { 3) 2 (4 { 9)] 4 6 5 ?

Work inside the parentheses first:

215 1 [(51) 2 (36)] 4 6 5 ?

Then work inside the brackets:

215 1 [15] 4 6 5 ?

Since there are no more parentheses or brackets, proceed from left to right,

dividing before adding:

215 1 2

1

2

5 212

1

2

MATHEMATICS REVIEW

213GRE CAT Success www.petersons.com

Page 221

OPERATIONS

When letter symbols and numbers are combined with the operations of arithmetic

(1, 2, {, 4) and with certain other mathematical operations, we have an alge-

braic expression. Algebraic expressions are made up of several parts connected

by a plus or a minus sign; each part is called a term. Terms with the same letter

part are called like terms. Since algebraic expressions represent numbers, they

can be added, subtracted, multiplied, and divided.

When we defined the commutative law of addition in arithmetic by writing a

1 b 5 b 1 a, we meant that a and b could represent any number. The expres-

sion a 1 b 5 b 1 a is an identity because it is true for all numbers. The

expression n 1 5 5 14 is not an identity because it is not true for all numbers; it

becomes true only when the number 9 is substituted for n. Letters used to

represent numbers are called variables. If a number stands alone (the 5 or 14 in

n 1 5 5 14), it is called a constant because its value is constant or unchanging. If

a number appears in front of a variable, it is called a coefficient. Because the letter

x is frequently used to represent a variable, or unknown, the times sign 3, which

can be confused with it in handwriting, is rarely used to express multiplication in

algebra. Other expressions used for multiplication are a dot, parentheses, or

simply writing a number and letter together:

5 { 4 or 5(4) or 5a

Of course, 54 still means fifty-four.

Addition and Subtraction

Only like terms can be combined. Add or subtract the coefficients of like terms,

using the rules for signed numbers.

Example 1

Add x 1 2y 2 2x 1 3y.

x 2 2x 1 2y 1 3y 5 2x 1 5y

Example 2

Perform the subtraction:

230a 2 15b 1 4c

2 (2 5a 1 3b 2 c 1 d)

Change the sign of each term in the subtrahend and then add, using the rules for

signed numbers:

230a 2 15b 1 4c

5a 2 3b 1 c 2 d

225a 2 18b 1 5c 2 d

UNIT 7

214www.petersons.com GRE CAT Success

Page 439

in wording can affect how you approach writing the essay. Read these two sets of

instructions for the personal statement.

1. Please state your reasons for deciding to pursue a graduate degree in the

field you have chosen. Include references to your past study and research in

your chosen field, your plans for study at the university, including problems

and issues you want to address, and your personal goals.

2. The personal statement is an important part of your application. It is your

opportunity to provide information about your background, interests and

aspirations, and how they relate to your proposed academic program. In

your statement, describe your reasons for pursuing graduate study, the

program you hope to follow at the university, and the strengths and

weaknesses of your preparation for graduate study. All personal statements

should be double-spaced and typed, two to three pages.

These instructions cover more or less the same ground, but the second school

asks you to describe the strengths and weaknesses of your preparation for

graduate study, whereas the first school merely asks you to describe your past

study. When writing the essay for the second school, therefore, you must be sure

to address your preparation in greater detail. You will have to both describe and

evaluate your readiness—or lack thereof.

DON’T WRITE TOO MUCH OR TOO LITTLE

The second thing you should keep in mind as you begin your draft is the length of

the essay. Often, the length is specified; for example, the second school’s instruc-

tions above indicate that the statement should be two to three double-spaced pages.

What should you do if length is not specified, as it is not in the first set of instruc-

tions above? Then write one to two typed pages. An essay that is shorter than one

page does not allow room for you to develop your ideas. And an essay that is longer

than two pages becomes a chore for the admissions committee to read.

Finally, when you write your first draft, do not waste space by repeating

information that the admissions committee can get from other parts of your

application, like your transcript or résumé. Use the essay to provide them with

new information or to highlight particular accomplishments.

REVIEW THE FIRST DRAFT

Once you have drafted your essay, read the question again. Has your draft

answered the question fully? If the essay is incomplete, go back and fill in the

missing material. Then ask people for feedback. Although your spouse and friends

may be helpful, you may get more valuable suggestions from faculty members

who know you and who also know what a personal essay should be like. Ask

whether you’ve included things you should leave out or should add things you’ve

forgotten. Is the tone right? Have you achieved the right balance between

boasting and being too modest? Are there any problems with organization, clarity,

grammar, or spelling?

APPENDIX D

432www.petersons.com GRE CAT Success

Page 440

Felecia Bartow, an M.S.W. candidate at Washington University in St. Louis,

gave her drafts to several people. “It helped to have a couple of people (from

different disciplines) read various drafts of my essays in order to give me feedback

on the clarity and conciseness of my writing.” Jim Lipuma, a Ph.D. candidate in

environmental science at the New Jersey Institute of Technology, recommends,

“Proofreading goes without saying, but always read it to yourself, have someone

else read it, and then read it aloud to someone. This will show all the problems,

highlight the areas that need work, and allow for any weaknesses to be exposed.”

PREPARE THE FINAL DRAFT

Once you’ve revised the essay and are satisfied with your final draft, ask someone

with a sharp eye to proofread it for you. The final draft should be absolutely free

of grammar and spelling errors, so do not rely on grammar- or spell-checks to find

all of the errors. Once you are done, be sure to keep backup files as well as a

hard copy. Although you won’t be able to use the whole essay for all your

applications, you may be able to use parts of it. If you do work this way, be

absolutely sure when you submit the final essays that you have not made any

careless editing mistakes. “If you’re applying to multiple schools, make sure that

you don’t have any ‘cut and paste’ errors in your application,” warns Neill Kipp, a

Ph.D. candidate in computer science at Virginia Tech. “If you apply to Florida

State in one letter and the University of Florida in another but forget to change

every occurrence of the university name, then count on being the semester-long

laughingstock of the admissions office.”

Finally, if you are submitting the statement on separate sheets of paper rather

than on the application form itself, put your name, social security number, and

the question on the essay, and type “see attached essay” on the application form.

MAKE IT YOURS

If after reading this appendix you are still daunted by the prospect of writing your

personal statement, just put the whole task aside for a few days. You will find that

the ideas, suggestions, and excerpts you’ve just read will trigger some mental

activity and that soon you will have some ideas of your own to jot down.

Also remember that it’s not necessary to have an exotic background or a

dramatic event to recount in order to write a good essay and gain admission to a

program. Admissions committees are looking for diversity—in gender, race,

ethnicity, nationality, and socioeconomic status, to name some obvious character-

istics. But they are also looking for people with diverse life experiences to add

richness to their student body. Your background, which may seem perfectly

ordinary to you, nevertheless has unique and relevant elements that can be assets

to the program you choose. Your task is to identify and build upon these ele-

ments to persuade the admissions committee that you should be selected.

WRITING A GOOD PERSONAL ESSAY

433GRE CAT Success www.petersons.com