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1.Mathematical Expressions

2.Percents

Be familiar with the difference of perfect squares. Be comfortable factoring quadratic equa-

See Chapter 4, pp. 6068.

6. Inequalities

Know that the rules for solving inequalities are basically the same as those for solving equa-

tions. Be able to apply the properties of inequalities, to solve inequalities with absolute val

ues,

and to relate solutions of inequalities to graphs.

See Chapter 4, pp. 6870.

7.Rational Expressions

8.Systems

12.Polygons

17.Graphing Inequalities and Absolute Value

McGRAW-HILLs

SAT

SUBJECT TEST

MATH LEVEL 1

THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY,

EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PAR-

CONTENTS

Chapter 1Test Basics / 3

Chapter 2Calculator Tips / 7

Chapter 3Diagnostic Test / 9

Chapter 4Algebra / 39

CONTENTS

Solving by Substitution / 66

Inequalities / 68

Transitive Property of Inequality / 69

Rational Expressions / 71

Simplifying Rational Expressions / 71

Systems / 74

Solving by Substitution / 74

xi

Area Formulas / 116

Chapter 10Data Analysis, Statistics, and Probability / 180

199

Answer Key / 216

Practice Test 2 / 225

Answer Key / 240

Practice Test 3 / 249

Answer Key / 264

Practice Test 4 / 273

Answer Key / 288

Practice Test 5 / 297

Answer Key / 312

Practice Test 6 / 321

Answer Key / 338

PART I

ABOUT THE

SAT MATH

LEVEL 1 TEST

28%

Plane

CHAPTER 1

TEST BASICS

About the Math Level 1 Test

ity to apply concepts, and higher-order thinking. Students are not expected

PART I / ABOUT THE SAT MATH LEVEL 1 TEST

The Level 1 vs. Level 2 Test

5

Level 1 TestLevel 2 Test

3842%4852%

Data Analysis, Statistics, and Probability610%610%

Number and Operations1014%1014%

As shown in the table, the Level 2 test does not directly cover Plane Euclid-

PART I / ABOUT THE SAT MATH LEVEL 1 TEST

How to Use This Book

CHAPTER 2

CALCULATOR TIPS

It is critical to know how and when to use your calculator effectively ...

Squaring a number

usually the {^} buttonusually the {^} button

Taking the square root of a number

Taking the cube root of a number (or, in other words, raising a number to

thepower)

Sine, cosine, and tangent

Sin

Since programmable calculators are allowed on the SAT Math test, some

students may frantically program their calculator with commonly used math

On the Day of the Test

Make sure your calculator works! (Putting new batteries in your calcula-

Bring a backup calculator and extra batteries to the test center.

3

CHAPTER 3

DIAGNOSTIC TEST

1.Algebra

4

4

DIAGNOSTIC TEST

MATH LEVEL 1

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

DIAGNOSTIC TEST

1.A calculator will be needed to answer some of the questions on the test.

:Volume

:

Volume

=

r

4

B

and height

h

Volume

=

Bh

3

3

2

1.(

BB(

CC(

DD(

2.In square

AA(4,

BB(5,

CC(

DD(

EE1, 21, 2

3.If

BB18

CC0

DD27

4.Assuming

x

3

3

)

B

D

D

5.If

BB2

CC6

EE3

6.If

AA9

BB27

CC81

DD243

EE729

7.If 2

AA6

BB1

CC8

DD4

EE2

8.In Figure 2, if

AA55

BB45

CC135

DD90

EE180

9.What is the

AA0, 240, 24

BB0, 60, 6

CC0, 80, 8

DD0, 40, 4

EE0, 20, 2

10.If 2

CC5

DD25

2

2

4

3

2

2

USE THIS SPACE AS SCRATCH PAPER

x

3

t

11.A cone and a cylinder both have a height

AA4

BB12

CC24

DD36

EE48

12.In Figure 3,

AA50

BB130

CC65

DD75

EE25

13.In terms of

3

2

2

3

=

1

2

x

+

1

21

YZ

50

16.If 24

AA2

BB12

CC9

DD6

EE3

17.If three coins are tossed, what is the probability that

18.A circle has a circumference of 16

AA8

BB16

CC332

DD64

EE256

19.If

�2,what values of

20.In Figure 4,

AA40

BB50

CC80

DD100

EE120

5

2

8

4

3

3

USE THIS SPACE AS SCRATCH PAPER

Q

P

R

21.In Table 1,

AA9

22.The slope of

is . If

EE7

23.Mark wears a uniform to school. According to the

AA2

BB6

CC8

DD16

EE32

24.A bike has wheels with radii of 8 inches. How far

4

USE THIS SPACE AS SCRATCH PAPER

(

3

4

n

25.In Figure 5, a circle is inscribed in a square whose

AA36 in

BB27

CC36

DD36

EE9

3

7

3

x

3

3

USE THIS SPACE AS SCRATCH PAPER

a

8

30.The line with the equation

AA0, 30, 3

BB(0,

CC0.46, 2.540.46, 2.54

DD(

EE(6,

31.What is the measure of each interior angle of a regu-

AA180

BB720

CC60

DD120

EE90

35.Which of the following equations does NOT represent

DD4

EE4

36.What is the maximum value of the function

AA4

BB28

CC3

37.What is the

2

n

n

3

n

5

5

5

USE THIS SPACE AS SCRATCH PAPER

39.The cube in Figure 7 has edges of length 5. What is

CC5

40.At the end of 2000, the number of students attending

AA1062

BB1086

CC1110

DD1135

EE1161

41.If

AA1

BB4

DD7

42.The area of the rhombus

AA64

BB32

CC5.7

DD45.3

642

x

+

102

USE THIS SPACE AS SCRATCH PAPER

V

8

23

43.Which of the following is equal to (sec

AAsin

BBcos

CCsec

DDcsc

EEcot

44.If

CC1

45.The statement, If a triangle is equilateral, then it is

I.If a triangle is not scalene, then it is equilateral.

II.If a triangle is not equilateral, then it is scalene.

III.If a triangle is scalene, then it is not equilateral.

AAI only

BBII only

CCIII only

DDI and II only

EEI and III only

46.(2sin

AA18

BB18sin

CC18sin

DD36

EE1

47.If the sides of a right triangle have lengths

1,and

BB15

CC4

DD5

EE12

48.If

BB1

CC0

PART I / ABOUT THE SAT MATH LEVEL 1 TEST

AA

BB

CC

DD

EE

223

2332

3223

+

5

32

+

=

USE THIS SPACE AS SCRATCH PAPER

STOP

25

2. B

10. D

D

You dont need to start multiplying the sec-

ond trinomial by the first. Instead, group

x

and

y

as

a single expression.

(

+

y

+

3)(

x

+

y

3)

=

[(

+

y

+

3][(

+

y

3]

=

(

+

y

3(

+

y

+

3(

+

y

9

=

(

+

y

9

2.

B

Recognize that

is a square, so all four

sides have equal measure. You know

n

=

2 because

there is no change in the

=

coordinate on side

has an

-coordinate of 1

+

2

n,

which equals 1

22

=

5 and a

-coordinate of

2.

B

has coordinates (5,

2).

3.

A

Substitute

a

=

3

3

3

3

9

2

2

2

2

2

x

x

=

5.

B

Solve for

by isolating the variable on one

side of the equation.

Multiply both sides by 2.

x

2

=

3

9

x

4

=

6

18

=

6

18

=

18

x

=

2

6.

E

Cubing is the inverse of cube rooting, so cube

both sides first.

Now square both sides to solve

x.

An alternate way of solving the problem is to rewrite

the given equation using rational exponents:

=

. Raise each side to the sixth power to solve

for

x.

3729

2

1

3

1

6

3

=

729

2

2

3

=

3

3

3

2

12. C

21. C

31. D

41. C

PART I / ABOUT THE SAT MATH LEVEL 1 TEST

C

Since you have two variables and two

+

m

=

10

+

=

5

n

=

1

Since 2

+

m

=

10, you can substitute

n

=

3

4

4

the clock, so there are or 30

=+()=()=12121

2141

121

x

f

=

+

1

21

1

2

12

+

=

+

124

431

2134275

xxxx

+++++

2

�4 2or

216

thenumberofpossibleoutcomesof

etotalnumberofpossibleoutcomes

Q

P

R

90

x

x

4.If a row in the table represented

==

900

18

50

5

5

C

=

x

.

cosine

adjacent

hypotenuse

cos37

cos

((

1002

cos

=

1

3

7

=

yxb

=

B

610

4

yy

xx

=

21

B

A quadratic equation can be thought of as

a

sum of the rootssum of the roots

+

product of the rootsproduct of the roots

=

0

Since the sum of the two roots is

is

1

12

1

12

1

12

c

=

1

4

,all 6 angles are congru-

54

76308222

785

.%

29

PART I / ABOUT THE SAT MATH LEVEL 1 TEST

E

Answer A is in slope-intercept form. Answers

B and C are in point-slope form, and answers D and E

are in a variation on the standard form of the equa-

An alternate way to solve the problem is to substitute

the

x

- and

-coordinates of the two points into the

4

1

8

1

=

x

)

n

333

)

3

3

=

)

8

21

4

A

=

2

x

39.

B

This is a distance problem where you use the

Pythagorean Theorem

HIIKHK

222

552

2550

==

50

52

2

2

=

=

IK

IK

IK

1

4

1

8

8

1

8

xx

x

xx

=

=

=

the two, congruent legs must measure , or .

2

x

y

x

x

y

xy

xy

fx

+

=

+

=

+

=+

=

=

2

3

2

3

2

23

23

If a triangle is equilateral

sec

cos

cos

sin

cot

sin

csc

V

X

8

45

sin

sin.

8455657

E

The volume of the pool is given by

V

=

w

h

V

=

15

12

5

=

900 ft

157

Vrh

157

.ft

PART I / ABOUT THE SAT MATH LEVEL 1 TEST

B

Use the Pythagorean Theorem to solve for

x.

The hypotenuse,

c

(

3)

(

+

1)

(

+

5)

6

+

9

+

x

2

+

1

=

x

10

+

25

2

4

+

10

=

x

10

+

25

x

14

15

=

0

(

15)(

+

1)

=

0

x

=

15

(

=

1 would not result in the measures of sides of a

triangle, since one side would equal zero and one

side would be negative.)

48.

B

Recognize that

y

fect square binomials. Then, factor

x

y

for

x

y.

x

y

x

+

y

(

+

y

y

=

x

+

y

(

+

y

y

(

+

y

=

0

(

+

y

x

y

1]

=

0

(

+

y

=

0 or (

y

=

1

x

=

y

The problem states that

y,

so the only solution to

the problem is (

x

y

=

1.

49.

E

Rationalize the denominator by multiplying

the numerator and denominator by the conjugate of

.

632

3232

1812

3223

11

3223

3232

PART I / ABOUT THE SAT MATH LEVEL 1 TEST

Diagnose Your Strengths and Weaknesses

134567101316193334384849

2922273540Total Number Correct

152129303641Total Number Correct

172332Total Number Correct

374445Total Number Correct

4

SAT Subject Test Approximate Score

4650

750800

4145

700750

3640

640700

2935

590640

2228

510590

Below Average

22

510

35

PART II

MATH REVIEW

CHAPTER 4

ALGEBRA

28%

4.Percents

a.Converting Percents to Decimals

b.Converting Fractions to Percents

c.Percent Problems

5.Exponents

a.Properties of Exponents

b.Common Mistakes with Exponents

c.Rational Exponents

d.Negative Exponents

e.Variables in an Exponent

6.Real Numbers

a.Vocabulary

b.Properties of Real Numbers

i.Properties of Addition

ii.Properties of Multiplication

iii.Distributive Property

iv.Properties of Positive and Negative Numbers

7.Absolute Value

8.Radical Expressions

a.Roots of Real Numbers

b.Simplest Radical Form

c.Rationalizing the Denominator

d.Conjugates

9.Polynomials

a.Vocabulary

b.Adding and Subtracting Polynomials

c.Multiplying Polynomials

d.Factoring

i.Trinomials

ii.Difference of Perfect Squares

iii.Sum and Difference of Cubes

10.Quadratic Equations

a.Factoring

b.Quadratic Formula

c.Solving by Substitution

d.The Discriminant

e.Equations with Radicals

11.Inequalities

a.Transitive Property of Inequality

b.Addition and Multiplication Properties

c.And vs. Or

d.Inequalities with Absolute Value

12.Rational Expressions

a.Simplifying Rational Expressions

b.Multiplying and Dividing Rational Expressions

c.Adding and Subtracting Rational Expressions

d.Solving Equations with Rational Expressions

13.Systems

a.Solving by Substitution

b.Solving by Linear Combination

c.No Solution vs. Infinite Solutions

d.Word Problems with Systems

Evaluating Expressions

arentheses (or other group-

Within a grouping symbol, work from the innermost to the outermost

expression. Evaluate exponents and roots from left to right. Then, perform

2

+

[52

(7

3)].

=

16

2

+

[52

4]

=

16

2

+

13

=

14

+

13

=

27 Answer

Fractions

2

2

PART II / MATH REVIEW

EXAMPLE:

4 and 12 have a common factor of 4. Divide both the numerator and denom-

30

4

+

x

xy

xy

4

+

x

312

x

2

82

3

12

43

fractions.

+

.

You already know that the LCD of 4 and 30 is 60. Rewrite each fraction using

60 as the denominator.

The least common denominator is also used when simplifying complex

fractions. A

is a fraction whose numerator or denominator

contains one or more fractions. Find the LCD of the simple fractions and

Multiply the numerator and the denominator by the LCD of the simple

fractions,

5x.

Answer

11

5

x

xx

.

115

415

302

Answer

30

4

PART II / MATH REVIEW

. This is

known as the Division Rule for Fractions. Of course,

b, c,

and

d

cannot equal

zero, since you cannot divide by zero.

4

3

1

4

=+

implify

Dividethrough

.

byacommonfactorof6.

Answer

311

=

=

Removethecommonfactors

of2and3.

114

517

implify

Divideb

234

567

yacommon

factortosimplify.

Answer

b

c

d

ac

bd

=

.

When is written as the fraction , it is called an

Solve

TheLCDofand

is2

xx

826

Answer

Simplify

Then

242

33

=

Multiplybythereciprocalof

66

Answer

266

262

4

1

4

431

into the original equation results in or 1/5

3into

1. Both answers check,so

Percents

1064

10624

424

Answer

10

1

5

=

710

=+

232

or3

3Answer

olve

710

fraction to a decimal first, and then move the decimal point two places to the

left.

to a decimal first, and then move the decimal point two places to the

right.

6is25%ofwhatnumber?

Think

2625

%of.

and

so26

2625

55

025

Answer

Whenwrittenasapercent,7

iswhatvalu

ee?

Answer

725

0440

Simplify

Answer

.%.

040004

5100005

====

outof100

outo

f100

====

10007510000075

324Think

0)5

1.To multiply two powers with the same base, you

2.To divide two powers with the same base, you

3.To raise a power to a power, you

4.To raise a product to a power, you

532

Whatpercentof12is4?Roundanswertothe

enearesttenth.

Think

412

abc

is%of.

and12

12100

4100

==

333

.%Answer

5.To raise a quotient to a power, you

Watch your negative exponents. The quantity should be put in the

2.3

2

2

1

8

implify

Assume,and

abc

abc

abc

donotequal0.

abc

abc

abc

3223

22

2222

abc

Userules#3and#5.Multiplythe

exponents.

Isolateeachvar

=

iable.

Userule#2.Subtractthee

=

abc

204

xponentsforeachbase.

Answer

=

Simplify

Assumeanddonot

equal0.

Isol

ateeachvariable.

Userule#2

=

3253

.Subtracttheexponentsforeachbase.

6Answer

4

8

4

2

2

=

b

a

b

m

m

=

3.2

4.4

5.2

6.(

ber can be expressed as and results from dividing an integer by another

reads as 4 to the one-half power and equals .

reads as 5 to the two-thirds power and equals or . can

also be represented as .

equals or as long as

81531441

implify81

Answer

327

a

b

b

2

3

3

3

q

51

EXAMPLE:

2

Remember that expressions in simplest form typically do not contain neg-

ative exponents.

.Recognize that 4 and 32 can be written in base 2.

3

implify

Assumeandd

yxy

oonotequal0.

yxy

33

Userule#5.

11

Simplifythenegativeexponents.

yy

Answer

1

2

1

2222

1

16

4

Simplify8

==

2Answer

PART II / MATH REVIEW

{1, 2, 3, ...}

{0, 1, 2, 3, ...}

{...

1, 0, 1, 2, 3, ...}

Numbers that can be expressed as and result

integer., , 0.7, 1.333, ... and 8 are examples

Numbers that cannot be expressed as . In deci-

andare examples of irrational

q

4

3

q

AABB

CCDD1.33333...EE5.020020002...

infinite and nonrepeating, such as answer E. 5.02020202 ... is a repeating

decimal, but 5.020020002 ... is nonrepeating, since the number of zeros

DD1.333333 Answer

PART II / MATH REVIEW

Associative Property of Addition

(

+

b

+

c

=

a

+

(

+

c

(8

+

9)

+

10

=

8

+

(9

+

10)

4.

Identity Property of Addition

Additive IdentityAdditive Identity

There is a unique real number

such that:

a

+

0

=

a

77

+

0

=

77

5.

Property of Opposites

Additive InverseAdditive Inverse

For each real number

there is a real unique number

such that:

a

+

a

=

0

is the

of

a.

It is also called the

of

a.

6

+

6

=

0

Properties of Multiplication

1.

Closure Property of Multiplication

The product

b

results in a unique real number.

3

11 equals the real number 33.

2.

Commutative Property of Multiplication

ab

=

ba

20

5

=

5

20

3.

Associative Property of Multiplication

b

c

=

a

(

c

(8

9)

10

=

8

(9

10)

4.

Identity Property of Multiplication

Multiplicative IdentityMultiplicative Identity

There is a unique real number

such that:

a

1

=

a

77

1

=

77

5.

Property of Reciprocals

Multiplicative InverseMultiplicative Inverse

For each real number

a

except 0except 0

such that:

is the

of

a.

It is also called the

of

a.

Zero has no reciprocal, since

is undefined.

1

6

1

=

0

a

a

1

1

a

and(

)Distribute the 2.

10)Distribute the 5.

A positive number times a positive number equals a positive number.

A positive number times a negative number equals a negative number.

A negative number times a negative number equals a positive number.

To subtract a number, add its opposite.

The sum of the opposites of two numbers is the opposite of their sum.

3and

PART II / MATH REVIEW

It is often used when simplifying rational expressions and factoring, so it

Absolute Value

=

1or

1Recognize when the expression

4or

xxx

=

=

1222

22

57

A radical is a symbol such as where

is not written, it is assumed to equal 2, for example, (read the

has two square roots: and

Example 1:Example 2:

125

x

x

PART II / MATH REVIEW

always a good idea!)

(

(

=

125

When working with radicals, remember the product and quotient prop-

erties:

The Product Property of Radicals

The Quotient Property of Radicals

Be careful not to apply the product and quotient properties to finding the

sum of radicals.

1.Factor all perfect

2.Rationalize the denominators so that no radicals remain in the denomi-

32

3

27

3

272

3

345345

222222

+=+

but

===

b

a

b

n

n

449

93=6

abab

nnn

59

EXAMPLE:

=

Multiplying the denominator by 3 will create a perfect square,

3

is another way of writing

1,

the identity element for multi-

plication.

=

=

Answer

Solving a cube root with a fractional radicand is nearly identical. You must

multiply by a perfect square this time in order to create a perfect cube in the

denominator.

.

Multiplying the denominator by 2

cube, 2

is another way of writing

1,

the identity element for

multiplication.

Answer

3

206

206

60

2

8

2

2

2

2

2

2

2

3

9

3

3

PART II / MATH REVIEW

The denominator is rationalized here, but the numer-

ator is not in simplest radical form.

Answer

mialradical expression.

Polynomials

monomial

is a single term, such as a constant, a variable, or the product of

constants and variables. 7,

x,

5

x

3

xy

polynomial

contains many terms. By definition, a polynomial is the sum of

322

322

1222

12

+

+

.

12

+

+

1931931919193319331936

=+==

ababaaabbabbab

=+=

abab

and.

21532

6018

3206

61

x

3

+

2 is an example of a polynomial containing the

terms x

3

and 2.

Polynomials can be added, subtracted, multiplied, and divided following

the properties of real numbers.

combining like terms.

Like terms

have the same variables raised to the same power. In other words, theyre

terms that differ only by their coefficients.

a

4

a

a

(

4

a

=

3

a

x

and 2

xy

are not like terms.

x

2

+

5 from 3

4.

3

4

(

2

+

5Change the subtraction to

5)Combine like terms.

(

+

4)(

x

6)

The

1))Rewrite (1

1)FOIL

1)Distribute the

2

Examples

+

b

a

2

+

b

+

9)

4

36

+

81

b

a

2

+

b

12)

x

24

+

144

(

+

b

b

=

a

b

+

3

3

=

x

9

63

actor

xxx

++=+

RRecognizethat

and

64)Always factor out the greatest common factor first.

1.Sum of Cubes

2.Difference of Cubes

25) AnswerSince 8

Up to this point, when given a problem such as

x

8

+

9, you would say the

polynomial is unfactorable. In other words, its prime.

x

8

+

9 doesnt fit

any of the three special products, and factoring the trinomial also doesnt

work.

x

8

+

9

=

(

+

?)(

+

?)

What two numbers will multiply to give you 9 and add to give you

first glance, 9 and 1 seem to work resulting in four possibilities:

+

9)(

x

+

1) (

x

9)(

x

1) (

x

+

9)(

x

1) (

x

9)(

x

+

1)

None of the four, however, give you a positive 9 constant and a negative 8

coefficient for

x.

The

Quadratic Formula

can be used to solve a trinomial

65

ax

bx

+

c

=

0.

tion,

ax

bx

+

c

=

0,

bbac

x

8

x

+

9

=

bbac

=()()

88419

11

86436

828

827

x

=()=Simplify.

((

Dividethenumeratorby2.

4Answer

PART II / MATH REVIEW

x

u

u

22

8110

8110

250

===

++=

Let

Let

uxuu

=++=

=

250

tt

+=

370

abc

bbac

===

=()()1514

=()=4114

52556

581

59

2

59

2

14

2

7

59

2

4

2

2

=

+

==

=

=

=

x

x

0or(

16or

discriminant

of a quadratic equation equals

4

the radicand in the

Example 1:

Example 2:

x

xx

+=

+

+==

198

,so

x

x

=

=

11

11

121

2

PART II / MATH REVIEW

EXAMPLE:

multiplying or dividing both sides of an inequality by a negative number

� 8 becomes

x

15 becomes

�

2

olve

Isolatetheradical

++=

+=

460

xx

+=

436

Squarebothsides.

3212

=

Isolatethesecondradical.

Squarebothsidesasec

ondtime.

Answer

11212

211212

olve

Combineliketer

2121012

1210

=

ms.

Isolatetheradicalandsqua

1210

rebothsides.

Answer

12100

69

Transitive Property of Inequality

states that for any real numbers

a, b,

and

c:

If

a

b

and

b

c,

then

a

c.

It makes sense that if 3 4 and 4 5, then 3 5.

equalities.

Multiplication Property of Inequality

If

a

b

and

c

is positive,

ac

bc.

222

If

a

b

and

c

is negative,

ac

�

bc.

If 5 6, then 5(

a

b,

then

a

+

c

b

+

c.

If 40 50, then 40

1 50

1.

x

� 4

+

x.

x

x

{

� 29and

� 5or

2and

6Divide both sides by

376376

313

Rx

Rx

ORx

+

&#x-32;錀

or

Answer

71

Rational numbers are numbers that can be expressed as, a quotient of

quotient of polynomials. are examples

91025

q

+

b

a

2

+

b

b

a

2

+

b

+

b

b

=

a

b

Factor the numerator and denominator. Rec-

and the denominator is the difference

of perfect squares. Now simplify by dividing

3).

Answer

Typically, rational expressions are in simplest form when they do not con-

Multiplication Rule for Fractions

Division Rule for Fractions

bcd

=

.,,0

=

.,0

3

3

x

x

x

+

,

9

23

33

2

x

xx

xx

=

9

2

x

as . Now you

Answer

xyxy

xyxy

xy

2

1

+

+

xy

2

xyxy

2222

implify

=

Multiplybytherecipro

ccalof

Answer

73

EXAMPLE:

and 4

with a denominator of 8

x

Now simplify. Change the subtraction to adding the

opposite of the second term.

x

1)(

x

1) and (

+

1)(

x

1), result-

ing in an LCM of (

x

+

1)(

x

1)

denominator gives you

LCDLCD

Solve

xxx

11

21

11

21

2

xx

x

xx

x

+

2222

++

==

Answer

implify

Recallthat

=

xx

.Theequationthenbecomes

xx

xx

x

x

8

2

8

2

8

2

Answer

8

1

4

2

2

x

implify

0Since this equation is not factorable, use the Qua-

Systems

=+

=

314

322

=

314

322

=

5213

x

yx

=

=

14

2410

+=

bbac

696

646

326Answer

75

+

14 for

in the second equation and solve for

y:

3(

+

14)

2

=

2

+

42

2

=

2

=

44

y

=

4

Substitute 4 for

in either of the original equations in the system to solve

for

x:

x

+

44

=

14

x

+

12

=

14

x

=

2

2, 42, 4

2, 42, 4

the equations.

linear combination

of

the equations. For example:

++=

+=

431

PART II / MATH REVIEW

It is important that one variable cancels out. If this doesnt happen, check

your work for errors or try multiplying by a different number in the first step.

is eliminated, you are able to solve for

=

44

y

=

4

Substitute 4 for

y

in either of the original equations in the system to solve for

3

44

=

2

3

8

=

2

3

=

6

x

=

2

2, 42, 4

This, of course, is the same answer you got by using the substitution

2

+=

+=

+=

3942

322

01144

77

y

in terms of

x,

6218

6218

000

+=

++=

6218

6218

+=

+=

+=

+=

6218

2

2

2

436

836

836

+=+

PART II / MATH REVIEW

351396

33948

02448

++=

351396

79

EXAMPLE:

times as old as her daughter was then. Find the mothers present age.

CHAPTER 5

PLANE GEOMETRY

28%

Undefined Terms

3.Plane

PART II / MATH REVIEW

D

A

B

D

Lines, Segments, Rays

line segment

congruent

segments. For

example, if

=

CD,

then

AB

is congruent to

. In a mathematical expres-

sion, congruency is written as the symbol

,

AB

CD

. Congruency is depicted

as tick marks in diagrams as shown below:

D

PART II / MATH REVIEW

and

Z:

+

YZ

=

XZ.

In other words, the distance from

to

Y

added to the dis-

tance from

to

Z

equals the total distance from

X

to

Z.

This is called the

Segment Addition Postulate.

4

=

JL

36

=

JL

JL

=

2

2

3

4

36

T

Q

R

is equilateral, each side measures 12. Since

RT

is the bisector of

the side

,

point

T

must be the midpoint of the side. The Midpoint Theorem

tells you that

=

QS.

QT

=

12

QT

=

6 Answer

angle

is the union of two noncollinear rays. The rays themselves are called

the

sides,

and the shared endpoint is called the

vertex.

Some textbooks teach

that the union of two collinear rays is called a straight angle. Since this is not

a universal term, it will not appear on the SAT Level 1 test.

2

2

measure of an angle

measure greater than 90

but less than 180

If two lines intersect to form right angles, the lines are said to be

perpen-

dicular.

The symbol for perpendicular is

. The expression

l

l

1 is perpendicular to line 2. In diagrams, perpendicular lines are shown by

C

Z

Y

PART II / MATH REVIEW

tests. Just because an angle appears to be acute or lines appear to be per-

pendicular, dont assume this is true. Look at the given information in the

are two angles whose measures add up to 90

plementary angles may or may not share a side. (If they do share side, they

)

are two angles whose measures add up to 180

.

Similar to complementary angles, supplementary angles may or may not

41

60

less than the measure of the supplement of that angle. What is the measure

AAA complement of an acute angle is acute.

BBA supplement of an obtuse angle is acute.

CCThe supplement of an acute angle is obtuse.

DDThe complement of a right angle is a right angle.

EEThe supplement of a right angle is a right angle.

. Its supplement is 80

,

which is an acute angle. B is true. Answer C states the opposite of B and is

also true. D and E involve right angles. Since 90

+

90

=

180, a right angle and

another right angle are in fact supplementary, so answer E must be true. That

+

0

=

90, and weve

are opposite angles formed by two intersecting lines. Verti-

cal angles are always congruent, as shown by the congruency marks in the

pairs of vertical angles are formed when two lines intersect.

and

CEB.

E

B

C

E

B

C

PART II / MATH REVIEW

linear pair of angles

is formed by two angles that share a common side and

whose noncommon sides form a straight line. By definition, linear pairs of

angles are always adjacent angles and are also always supplementary.

ABC

and

DBE

are right angles and the measure of

is four times the measure of

Find the measure of

A

D

C

B

E

Triangles

A triangle with one obtuse angle

Right

A triangle with one right angle

Equiangular

PART II / MATH REVIEW

Isosceles

Equilateral

Scalene

sum of the measures of the interior angles

in a triangle is always 180

. This

is a useful theorem that is often used when solving problems involving tri-

angles and other polygons. One way to show this concept is to draw a triangle,

20

x

+

100

+

20

=

180, so

=

60

measures of two angles in a triangle, subtract their sum from 180

to find the

measure of the missing angle. A triangle with all angles congruent is called

Each angle of an equiangular triangle measures 60

+

x

+

x

must equal 180

An exterior angle is an angle on the outside of a triangle formed by extend-

ing one of the triangles sides. Each exterior angle of a triangle has two

remote interior

angles

are the two angles inside the triangle that do not share a vertex with

the exterior angle. The

measure of an exterior angle

is equal to the sum of the

measures of its two remote interior angles.

60

x

B

C

CAB

and

ABC

are the remote interior angles for the

exterior angle measuring

. Therefore,

=

60

+

70

=

130

. You can check your

answer by looking the

adjacent interior angle

for

and

are

a linear pair, so

=

50

60

+

70,

which does, in fact, equal 180

The

sum of the measures of the exterior angles of a triangle

is always 360

This sum is found by including

one

exterior angle for each vertex of the tri-

angle, not two. In fact, the sum of the measures of the exterior angles of

any

polygon is 360

y

x

55

80

45

x

+

y

+

z

=

360

tracting the measure of its adjacent interior angle from 180

x

=

125

y

=

135

=

100

125

+

135

+

100

=

360

given

m

=

m

=

45

triangle by its angles and sides.

S

3

3

PART II / MATH REVIEW

EXAMPLE:

angles and sides.

y

x

+

y

=

120. Notice that the triangle is equilat-

eral. By definition, all equilateral triangles are equiangular. Each angle mea-

x

=

60

and

y

=

60

median

of a triangle is a segment extending from one vertex to the mid-

point of the opposite side. Every triangle actually has three medians.

AM

is

a median of

CB

M

altitude

of a triangle is a segment extending from one vertex and is per-

or the line containing the opposite sideor the line containing the opposite side

Every triangle also has three altitudes.

AD

is an altitude of each of the tri-

angles below.

CB

D

C

B

D

angle bisector

of a triangle is a segment that divides an interior angle

of the triangle into two congruent angles and has an endpoint on the oppo-

D

AAAcute

BBObtuse

CCRight

DDEquilateral

given two congruent triangles, if you cut out one and place it over the other,

1.SSSSSS

2.SASSAS

3.ASAASA

4.AASAAS

6

8

8

6

6

8

10

66

AAI and II

BBII and III

CCI and IV

DDIII and IV

EEAll four are congruent.

at least

two sides congruent. By this definition, equi-

lateral triangles are also classified as isosceles. In an isosceles triangle, the

legs,

the remaining side is the

base,

the

vertex

angle

is the angle included by the two congruent sides, and the

base angles

are

the angles having the base as a side.

Isosceles Triangle Theorem

The

Isosceles Triangle Theorem

states that if two sides of a triangle are con-

the base anglesthe base angles

congruent. Given

is isosceles and

AB

=

BC,

then

BCA.

I.40, 40, 80

II.45, 45, 90

III.30, 60, 90

AAI only

BBII only

CCIII only

DDI and II only

EEII and III only

Triangle Inequality Theorem

states that the sum of the lengths of any two

C

�5 8Not true

Pythagorean Theorem

shows a special relationship among the sides of a

PART II / MATH REVIEW

abc

345

51213

72425

81517

Pythagorean Theorem. Take a 3-4-5 right triangle and multiply the sides by

2. 6-8-10 will work in the Pythagorean Theorem. Multiply 3-4-5 by 3 and

13

x

-45

-90

and a 30

-60

-90

, occur often in

5

4

triangles as parts of other figures. The next example illustrates this concept.

-45

-90

triangle is an isosceles right triangle

whose sides are in the following ratios:

45

In other words, the length of the hypotenuse is times longer than the

30

x

x

) is times longer than the length of the shorter leg.

10cm Answer

hypotenuse, inches. The longer leg is times the shorter leg.

2

2

of bigger than the legs. To find the measure of the legs,

. is not in simplest form, though. Now, multiply the numerator and

denominator by to rationalize the denominator.

Parallel Lines

==

Answer

2

l

87

12

43

on the figure below, the angles are as follows:

Corresponding angles.

A pair of nonadjacent angles, one interior and the second exterior, on the

same side of the transversal

Alternate interior angles.

A pair of nonadjacent, interior angles on opposite sides of the transversal

Alternate exterior angles.

A pair of nonadjacent, exterior angles on opposite sides of the transversal

Interior angles on the same side of the transversal.

3 and

6,

4

and

5

Exterior angles on the same side of the transversal.

1 and

8,

2

and

7

When the two lines cut by the transversal are parallel, then corresponding

angles, alternate interior angles, and alternate exterior angles are

congruent.

same side of the transversal are

supplementary.

If two parallel lines are cut

by a transversal and the transversal is perpendicular to one of the parallel

l

l

m

=

2

and

m

=

x,

find the measure of

m

+

m

=

180

2

+

x

=

180

3

=

180

x

=

60

Thus,

m

=

6060

=

120

fore, they are congruent.

=

120

Answer

Polygons

Not Polygons

sides,

and each endpoint is called a

vertex.

The plural of vertex is vertices.The plural of vertex is vertices.

is a segment that connects one

vertex to another, nonconsecutive vertex. (A segment connecting one vertex

to another,

vertex is a side.) Rectangle

ABCD,

for example, has

two diagonals

AC

and

BD

.

PART II / MATH REVIEW

regular polygon

is both equiangular and equilateral. A square is an exam-

ple of a regular polygon.

Number of SidesName of Polygon

2Doesnt exist

3Triangle

4Quadrilateral

5Pentagon

6Hexagon

7Heptagon

8Octagon

9Nonagon

10Decagon

11Hendecagon or undecagon

12Dodecagon

The total number of diagonals can be expressed as , where

the number of sides. A rectangle, for example, has two diagonals: .

An octagon has diagonals.

883

443

=

3

2

AAThe larger the number of sides of a polygon, the greater the sum of its

BBThe sum of the interior angles of a polygon is always a multiple of 180

CCThere is a polygon whose interior angles add up to 900

DDThere is a polygon whose interior angles add up to 800

EEAny interior and exterior angles of a regular polygon are supplementary.

polygon is convex and that there is one exterior angle at each vertex.

The sum of all 6 exterior angles of a hexagon is 360

. A regular hexagon is

equiangular, meaning that each interior angle has the same measure. Each

exterior angle will also have the same measure since it forms a linear pair

6 or 60

.

60

Answer

more than its

adjacent exterior angle. How many sides does the polygon have?

30

360

30

12

n

n

n

=

=

=

properties are named as follows:

QuadrilateralDefinition

AAA pair of opposite sides is parallel and congruent.

BBBoth pairs of opposite angles are congruent.

CCThe diagonals are perpendicular.

DDThe diagonals bisect each other.

EEAll pairs of consecutive angles are supplementary.

1.Both pairs of opposite sides are parallel.

2.Both pairs of opposite sides are congruent.

PART II / MATH REVIEW

have the same shape but different size. A square with sides of

2 cm is

to a square with sides of 4 cm. Both have the same shape, but

is the quotient , where b

ritetheratioinsimplestform.

218

Ifthen

adcb

Let

Crossmultiplytosolvefo

yCD

153

r,resultingin:

cmAnswer

375

b

b

The numerator is the difference of perfect squares, so it can be further fac-

tored to:

Dividing the numerator and denominator by a factor of

x

3 gives you:

AAAny two equilateral triangles are similar.

BBAny two isosceles triangles are similar.

CCAny two congruent polygons are similar.

DDAny two squares are similar.

EEAny two regular pentagons are similar.

1.AAAA

2.SASSAS

Answer

233

3

x

)

PART II / MATH REVIEW

TVU

and

WVX

are vertical angles and are, therefore, congruent. Now, take

a look at the ratio of the lengths of corresponding sides:

By the Side Angle Side theorem, SAS, the two triangles are similar.

Yes,

Answer

AMN

ABC,

find

BC

.

TV

XV

UV

==

==

10

14

5

7

15

21

5

21

15

10

T

X

U

C

B

A

M

4

3

1

3.SSSSSS

AMN

ABC

by the

theorem.

AMN

and

ABC

are both 90

and both triangles share a common angle,

A.

Because the triangles are sim-

ilar, the sides must be proportional.

The

Triangle Proportionality Theorem

actually states that if a line is paral-

lel to one side of a triangle and intersects the other two sides, then the line

divides those sides proportionally. The converse of this theorem is also true.

MN

BC

.

circle

chord

is a segment whose endpoints are on the circle. A chord that passes

through the center of the circle is called the

somustmeasure

44

units.

Answer

PART II / MATH REVIEW

but a counterexample to show that it is false is as shown below:

X

is a secant, the points

X

and

Y

do not lie on the circumference

of the circle.

is not a chord.

E is the correct answer. Answer

tangent

to a circle is a line that intersects a circle at exactly

point and

that lies in the plane of the circle. At the point of tangency, the tangent forms

a 90

angle with the radius. In the figure below, ray

JH

is a tangent and is per-

pendicular to radius

.

H

I

and

JI

in the figure above are called tangent segments.

Tangent seg-

ments

from a given exterior point (in this case, point

J

gruent. The ray from the exterior point

J

through the center

O

of the circle

bisects

the angle formed by the tangent segments.

and

TS

are tangent segments.

SO

=

10,

ST

=

8, and

m

=

53

and

m

T

R

S

=

RS

since both are tangent segments from the same exterior point

S. RS

must also measure 8 units. A tangent segment is perpendicular to the radius

at the point of tangency, making

m

=

90

a right tri-

angle. Use the Pythagorean Theorem to find the length of

OT

.

ST

OT

OS

OT

10

100

64

=

36

OT

=

6

SO

bisects

RST.

Since you know two angles in

OTS,

the third angle,

OST,

equals 180

(90

+

53)

=

37

.

RSO

and

OST

are congruent, so

m

RSO

=

37

.

OT

=

6,

RS

=

8, and

=

35

Answer

1.Semicircle.

ABC

ABC

PART II / MATH REVIEW

equals the measure of its central angle. Thus, the measure of

equals the measure of

ABC

B

O

C

I

H

O

G

m,m

are inscribed angles, so they measure half of their intercepted .

is inscribed in a circle. Each of the following statements is

true EXCEPT:

AA

m

=

60

BB

m

minor

=

m

minor .

CC

m

major

=

m

major .

DD

AC

and

AB

are equidistant from the center of the circle.

EE

m

=

60

It is helpful to draw a diagram to visualize the given information.

BCA

CAB

C

minor , since

An alternative way of solving the problem is to realize that , , and

measure or 120

is the distance around a circle. It is calculated using one of the

following formulas:

C

=

2

r

or

C

=

d

where

r

=

the length of the radius and

=

7

C

d

3

formula.

the ratio of the two circles circumferences is 3:1, find the circumference of the

arc length

is a fraction of the circumference of a circle. Arc length is mea-

360

1

2

=

x

r

=

2

2

3

1

8

3

1

38

28

4

+

)

+

)

=+

=

r

r

r

r

rr

The measure of is 60

central angle. The length of is therefore:

x

r

r

r

=

360

2

33

220

360

2

33

11

18

2

33

11

9

rr

339

27inches

Thediameteris227

((

or54inches.Answer

=()6036023166ftAnswer

A

O

3 ft

PART II / MATH REVIEW

is the measure of the region enclosed by a figure. Every polygon has a

unique area, and congruent polygons have equal areas. Area is measured in

square units,

bhb

r

=

360

AasnorAap

Abbh

bhorAdd

=

4

legleg

Abh

sector

is a part of a circle

that resembles a slice of the circle. Its edges are two radii and an arc.

cm.

Since

C

=

2

90

O

B

includes the shaded region. The area of the sector is as follows:

The problem is asking only for the area of the shaded region, not the area of

the entire sector. Subtract the area of the right triangle

AOB

from the area

of the sector. Note that the right triangle is an isosceles right triangle whose

Area of the sector

Area of the triangle

1212

3672

cmAnswer

A

A

=

=

90

360

12

1

4

144

36

cm

PART II / MATH REVIEW

EXAMPLE:

966

mAnswer

bhAdd

A

675

225inAnswer

ratio of the length of a part of one polygon to the length of the corresponding

scale factor.

Take a look at two equilateral

triangles. All equilateral triangles are similar because they have congruent cor-

being given a

2

reaoftriangle2

163

reaoftriangle1

PART II / MATH REVIEW

EXAMPLE:

WZ

tangle and the missing piece is a right trapezoid. The trapezoid missing base

(3

+

5), or 4 cm. To solve, find the area of the rectangle and

subtract the area of the trapezoid.

is a square of area 36 cm

bbh

A

A

=+

126

432

727

mAnswer

3

6

2

35

2

CHAPTER 6

SOLID GEOMETRY

28%

Plane

Right circular cone with circumference of base Lateral Area

Volume

=

r

4

B

and height

h:

Volume

=

Bh

3

3

2

3

Vocabulary for Polyhedra

PART II / MATH REVIEW

Base

of a pyramid or conefor a conefor a cone(

pyramid) face that does not contain the common vertex

Lateral faces.

ss(

the lateral faces are always parallelograms).

Altitude.

The segment perpendicular to the plane of both bases (for a

prism or cylinder); the perpendicular segment joining the vertex to the

for a pyramid or conefor a pyramid or cone

Height

(

Slant height

(

vertex

Base

Base

Height

Lateral

face

such as cones, cylinders, and spheres, have curved faces. Solids with curved

faces are not polyhedra, however, since they are not created by connecting

prism

is a polyhedron consisting of two congruent, parallel bases connected

by lateral faces shaped like parallelograms. Prisms are classified by their

V

=

Bh

where

B

=

the area of the base and

h

=

the height.

In the case of a rectangular prism, the area of the base is the product of

its length and width,

Substituting

for

B

results in

V

=

The vol-

ume of a cube with edge

s

is therefore

=

Bh

=

(

=

s

in

cubic units,

w

Lateral Surface Area

Volume

S

=

2

+

2

+

2

S

=

2

+

2

V

=

s

s

PART II / MATH REVIEW

P

8

4

. First find the length of the diagonal

cylinder

is similar to a prism with circular bases. Right circular cylinders

are the most commonly used cylinders on the Level 1 test. They consist of two

congruent, parallel, circular bases joined by an

axis

that is perpendicular to

each. The axis of a right circular cylinder is also its

altitude.

Distance

=++==

88414412

222

Distance

=++

222

824

64216

12816144

=+=

44

Answer

222

12882

Base

altitudealtitude

Lateral surface

PART II / MATH REVIEW

for any prism and can be written as:

V

=

Bh

where

B

=

the area of the base and

h

=

the height.

In the case of a right circular cylinder, the area of the base is

tuting

B

results in

V

=

r

WXYZ

360

around

side

XY

___

.

Lateral Surface Area

Volume

S

=

2

2

S

=

2

V

=

r

5

W

Y

2 cm

Z

ing the rectangle. Picture rectangle

WXYZ

rotating fully around the axis

___

.

A right circular cylinder is created whose height is 5 cm (the length

XY

___

) and

whose radius is 2 cm. (You may think of this cylinder as being on its side,

Using

r

=

2 cm and

=

5 cm, its volume is

V

=

22

V

=

20

cm

face area and whose height is 10 inches.

=

10, and the radius that you just found,

r

=

2,

pyramid

consists of one base and triangular lateral faces that connect at a

common vertex. Like prisms, pyramids are classified by their base: Rectan-

gular pyramids have a base shaped like a rectangle, triangular pyramids have

Base

V

=

Bh

where

B

=

the area of the base and

h

=

the height.

3

Lateral Surface Area

Volume

=

+

BS

=

=

Bh

B

=

area of the base

=

slant height

P

=

3

2

9 cm,

cone

consists of one circular base and a lateral surface that comes to a

common vertex. Right circular cones are the most commonly used cones

on the Level 1 test. They consist of a circular base connected to a vertex by

axis

perpendicular to the base. The axis of a right circular cone is also

its

altitude.

123cmAnswer

VBh

439

3

43cm

s

A

=

=

2

4

43

4

3

3

Base

altitudealtitude

Slant

height

any pyramid and can be written as:

where

B

=

the area of the base and

h

=

the height.

In the case of a right circular cone, the area of the base is

r

B

results in

V

=

r

Remember that the volume formula for a right circular cone,

V

=

r

and the lateral surface area formula,

S

=

c

, are listed in the reference

inform

ation of the Level 1 test. You dont need to memorize these!

2

3

3

VBh

and the slant height,

to use the formula for lateral surface area.

Lateral Surface Area

Volume

=

c

+

r

=

c

V

=

r

=

slant height

c

=

circumference of the base

3

2

2

PART II / MATH REVIEW

8

6

100

=

10

Now you have enough information to solve for the lateral area.

S

=

c

S

=

(12

S

=

60

cm

volume. If the cone has a height of 18 inches, find the height of the cylinder.

3

2

2

sphere

Volume

S

=

4

=

r

3

V

=

r

area formula,

=

4

r

test. Again, you dont need to memorize these!

3

3

3

3

PART II / MATH REVIEW

fore, you have enough information to write an equation for the volume of the

Now substitute

r

=

Volume Ratio of Similar Figures

233

3

:.

3

288

3

4

288

216

216

6

3

3

3

3

r

r

r

r

r

=

=

=

=

CHAPTER 7

COORDINATE GEOMETRY

28%

Plane

6.Equations of Lines

a.Horizontal and Vertical Lines

b.Standard Form

c.Point-Slope Form

d.Slope-Intercept Form

Plotting Points

x

II

IV

III

ordered pair

(

simply graph the location of its

x

and

y

coordinates. The

x

point is also referred to as the

abscissa,

while the

y

-coordinate is also referred

to as the

A

C

123456789101112

121110987654321

B

A

D

x

121

122

3

120

=

1

2

3

0, 0, (2,

midpoint

of a segment with endpoints (

y

y

Finding the midpoint of a line segment can also be thought of as finding

the

average

of the

and

y

AB

___

given the endpoints

distance

xxyy

80

+=

+=

and

118

,Answer

++

,Ans

swer

xxyy

1212

3

7532

1232

Answer

=

=+==

212533991832

2222

=+==

=

55243169255

2222

2222

2270497

123456789101112

121110987654321

B

A

D

x

PART II / MATH REVIEW

BC

___

is the base of the parallelogram and the height is the length of the

perpendicular from vertex

to side

BC

___

. Notice that there is no change in the

y

-coordinate in the segment

BC

___

, so the distance from

B

to

C

can be found sim-

ply by using absolute value.

BC

=

2

1

=

The height is

1

1

=

The area of the parallelogram is therefore

=

bh

=

22

=

6

6 units

is the measure of the steepness of a line. The slope of a line containing

the points (

y

y

Horizontal lines have no change in

so the slope of a horizontal line is zero:

Vertical lines have no change in

Since you cannot divide by zero, verti-

cal lines have an undefined slope.

A line having

rises from left to right, and a line having

neg-

ative slope

falls from left to right.

changein

undefined

changein

slope

rise

run

changein

changein

===

21

x

123456789101112

121110987654321

y

123456789101112

121110987654321

Negative slope

S

from

R.

Order

does

ator and the denominator. We could have found the slope by subtracting the

R

from

S

Slope of Parallel and Perpendicular Lines

are equations whose graphs are straight lines. Equations

containing two variables

x

and

y

raised to the first power are linear. By defi-

nition, linear equations have a constant slope.

Answer

3

yy

xx

m

=

=

=

21

30

5

3

Answer

PART II / MATH REVIEW

The following equations are linear:

Point-Slope Form

Standard Form

y

=

mx

+

by

y

m

x

Ax

+

By

=

C

ceeding paragraphs.

Horizontal lines are written in the form

y

=

a,

where

a

is any constant. Verti-

cal lines are in the form

x

=

a,

where, again,

a

is any constant.

y

=

7 and

=

5.

The graph of the two lines clearly shows their intersection.

321

+=+=

standard form

of the equation of a line is:

Ax

+

By

=

C

(where

A

and

B

are both

0)

The

slope

of a line in standard form is

.

B

B

0

123456789101112

121110987654321

point-slope form

of a line containing the point (

x

y

m

is

y

y

m

x

A

B

Start by finding the slope:

Now, choose one of the two points and substitute its

and

y

-coordinates into

x

y

is , the line intersects the

-axis at the point .

1

2

,

1

2

010

631

+=

Answer

A

B

PART II / MATH REVIEW

EXAMPLE:

=

5

1?

Recall that parallel lines have the same slope. Answers B, C, D, and E can quick-

ly be eliminated, since their slopes do not equal 5, the

x

coefficient of the given

line. Answer A is the only equation in which

m

=

5, so A is the correct answer.

The correct answer is A. Answer

Using

m

=

3, you can write the equation of the line as:

y

=

3

+

b

=

=+

EE

xy

-coordinate plane. The

Level 1 test includes questions on some curved graphs; however, they mainly

involve circles and parabolas. Circle questions involve manipulating the stan-

=+

4

3

4

=

40

03

4

3

PART II / MATH REVIEW

123456789101112

121110987654321

Parabolas

4

2

4

5

5

y

y = x

4

2

4

5

5

PART II / MATH REVIEW

y

=

ax

bx

+

c

is

a parabola. The standard form of a parabola is

y

k

=

a

h

The graph opens upward when

a

� 0 and opens downward when

a

0. The

greater

a

, the more narrow the graph becomes. Parabolas in this form have

4

2

4

5

5

y

x = y

4

2

4

5

5

y

x = y

b

a

=

2

PART II / MATH REVIEW

=

123456789101112

121110987654321

y

4.Graph the parabola on your calculator to see where the vertex is.

when . The value is a maximum when

yaxbxc

fxxx

=++

,meaningthatand

bb

Solveforwhentoget

Graphing Absolute Value

=

123456789101112

121110987654321

y

123456789101112

121110987654321

123456789101112

121110987654321

y

y

x

+ 5|

y

=

x

+

5

. When

=

PART II / MATH REVIEW

y

x

+

5

. The graph is sim-

ilar to the graph of

=

x

+

5

with a dotted line at

y

=

x

+

5

. As with any

123456789101112

121110987654321

y

y

x

+ 5|

CHAPTER 8

TRIGONOMETRY

28%

Plane

PART II / MATH REVIEW

true when focusing on one acute angle in a right triangle. Take

ABC,

for

example:

Opposit

C

A.AB

sine

opposite

hypotenuse

cosine

==

jjacent

hypotenuse

tangent

opposite

jjacent

Z

10 cm

XY

,

the side opposite

sine

opposite

hypotenuse

sin35

40

h

tan40

4540

45083910

3776

tan

Tangent

opposite

adjacent

PART II / MATH REVIEW

sin28

=

=

x

x

1528

704

(sin)

Opposit

C

A.AC

A.AB

cosecant

sin

hypotenuse

opposite

===

eecant

cos

hypotenuse

adjacent

cot

===

angent

tan

adjacent

opposite

===

Ladder

15 ft

x

28

tan

sin

cos

cot

cos

sin

3

6

3

measures 6 and the leg adjacent to

measures

3. Write an equation for the secant of

\r

cos

\r+

\r

cos

sin

cos

cossin

sin

sin

sin

==

csc

Answer

sec

hypotenuse

adjacent

Answer

PART II / MATH REVIEW

cofunctions.

Notice that in

and

are complementary. The acute

angles of any right triangle are actually complementary, since the sum of all

40

C

ortan 50

5

5

5

sin

opposite

hypotenuse

PART II / MATH REVIEW

73.7

53.1353.13

106.3

angles, 106.3

is the correct answer.

106.3

Answer

Special Right Triangles

xxx

32.

2

tan

==

3687

tan.

tan

tan.

.13

V

1

1

sin

sin

==

==

22

cos

cos

==

==

==

==

==

tan

tan

sin

sin

cos

cos

tan

=

=

==

33

==

tan

1

2

30

60

W

Y

PART II / MATH REVIEW

12(sin

+

cos

=

11

=

12 Answer

sin

sin

Recall that sin

sin

(1

+

sin

sin

=

1

sin

+

1

sin

cos

Answer

CHAPTER 9

FUNCTIONS

1.Functional Notation

2.Functions vs. Relations

a.Graphing Functions

3.Composition of Functions

a.Identity, Zero, and Constant Functions

28%

Plane

7.Rational Functions

8.Higher-Degree Polynomial Functions

9.Exponential Functions

Functional Notation

165

EXAMPLE:

D

0

1

R

0

IV.

AAI and II

BBII and III

CCIII and IV

DDI only

EEII and IV

x

.

PART II / MATH REVIEW

x

and

x

x

10 Answer

f

=

2

5, find

3).

Replace

x

in the original function with the expression

x

3.

f

3)

=

2(

3)

5

f

3)

=

2

6

5

f

3)

=

2

11 Answer

3

xx

+

3

xx

+

x

ated with this graph? It is useful to know that V-shaped graphs are asso-

y

=

x

1

. The domain is

167

where

y

is negative.

D

=

{all real numbers}, R

=

{

0} Answer

Functions vs. Relations

+

+

x

x

PART II / MATH REVIEW

x

y

4 is not a function. Answer

An equation that is not a function is called a relation. By definition, a

relation

x

y

x

x

AA{(

BB{(

CC{(

DD{(

EE{(

169

xy

find the coordinates of points for which the function is true. Start with the

Composition of Functions

2

3

2

3

3

3

PART II / MATH REVIEW

identity function

is the function for which

y

=

x. f

x

)

=

x.

Its graph is a

diagonal line passing through the origin whose slope is 1.

The

zero function

is the function that assigns 0 to every

x. f

x

)

=

0. Its graph

is the horizontal line in which

=

0, otherwise known as the

x

A

constant function

is any function that assigns a constant value

c

to every

x. f

(

=

c.

Its graph is a horizontal line,

=

c,

whose

y

(0,

c

x

I.

x

II.

x

III.

AAI only

BBII only

CCIII only

DDI and II

EEII and III

The maximum value is or

)

21

b

a

2

16

=++=

++

91816

3

8

4

3

8

3

3

8

1

=

+

+

8

=

)

b

a

2

3

24

3

8

b

a

2

PART II / MATH REVIEW

w

=

15,

l

=

30

15

=

The Roots of a Quadratic Function

173

a

0

+

(

=

0

Inverse Functions

This means that if every horizontal line intersects the

, does, however,

+

4

2

+

4

2

+

4

2

x

x

+

1

x

+

3

2

PART II / MATH REVIEW

and

f

1

over the line

=

x.

4

2

4

5

5

y

f

f

(

f

=

and

f

f,

what is

f

=

y

=

x

=

3

=

y

+

6

3

6

=

y

f

3

6

f

=

3(

6

=

9 Answer

f

=

4

1, then what is

Interchange the

x

and

y

values in the function

=

4

1 and solve for

y.

y

=

4

1

x

=

4

1

x

+

1

=

4

f

Answer

+

1

4

+

6

3

+

6

3

+

6

3

+

6

3

175

EXAMPLE:

g

=

x

y

=

x

=

y

y

rational function

i.e., fractionali.e., fractional

variable and can be written as

f

=

. Unlike the linear and quadratic

functions that have been discussed thus far in this chapter, rational functions

are not necessarily continuous. They contain a break in the graph at the point

f

has

vertical asymptotes

at the zeros of the denominator

f

=

.

x

2

9

x

2

9

xx

2

4

xx

2

4

qx

==

Higher-Degree Polynomial Functions

1.They are continuous.

2.They have rounded curves.

3.If

4.If

5.If

6.If

x

2

177

PART II / MATH REVIEW

f

=

d

+

r

where

d

q

Applying this algorithm to the last example results in:

f

=

(

2)(2

5

3)

You can further factor 2

x

5

Exponential Functions

2

4

5

5

y

2

5

5

y

y

-intercept of 1 and a horizontal asymptote at

y

=

0.

The graph of

=

a

=

a

3

x

179

==

(3

3

3

f

f

=

2

g

=

3

3

x

CHAPTER 10

DATA ANALYSIS, STATISTICS,

AND PROBABILITY

28%

Plane

1.Counting Problems

2.Probability

3.Mean, Median, Mode

181

Fundamental Counting Principle

states that if one action can be done in

a

ways, and for each of these a second action can be done in

b

ways, the num-

ber of ways the two actions can be done in order is

a

b.

For example, if an automobile manufacturer produces 4 different models

of cars and each one is available in 5 different colors, there are

20 different combinations of car model and color can be created.

Mutually exclusive

events are events that cannot occur at the same time.

For example, when you roll a die, you either roll a 1, 2, 3, 4, 5, or 6. 1, 2, 3, 4,

64372

schedules

55530

4520

PART II / MATH REVIEW

Now, try the previous example assuming that you can leave questions blank.

The number of true/false questions doesnt change, but now you have 3 pos-

34224

=

222222222222222232768

==

that logic, there are 3 possible students to choose for the third desk, 2 for the

5

4

3

2

1

=

120

Notice that 5

4

3

2

1

=

5!. You can use a

to solve problems in

which order matters. A

permutation

is an ordered arrangement of elements.

The number or permutations of

n

objects is

permutations in this problem.

12

1

4

)

theprobabilityis

thenumberofpossibleou

utcomes

thetotalnumberofpossibleoutcom

ees

Answer

thenumberofpossibleoutcomesofE

etotalnumberof

ossibleoutcomes

PART II / MATH REVIEW

probability of choosing the second piece of yellow chalk is

Notice that in the previous problem the first piece of chalk is

not replaced

before the second is drawn. This decreases the total number of outcomes to

11 when the second piece of chalk is selected.

bility that the event

occur from 1.

The probability of not passing this weeks math test is 1

70%

=

30%.

The probability of not passing this weeks English test is 1

80%

=

20%.

Notice that these are

meaning that passing the math test

is not dependent on how you do on the English test and vice versa. Multiply

They are

Mean

Mode

The mean is calculated by finding the sum of all the terms and dividing

by the total number of terms. After the data is ordered, the median is simply

the middle value of an odd number of terms or the average of the two

14, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18

Theansweristherefore

Answer

1.MeanCalculate the mean by finding the sum of all the ages and divid-

2.MedianThe sixth term of 11 total terms is the middle number.

3.Mode17 occurs 4 times in the given data.

2

5

+

=

6578818290

480396

+++++

1415151616161717171718

++++++++++

.18

PART II / MATH REVIEW

AAThe interval 8089 contains the most scores.

BBThe median score is in the interval 7079.

CC9 students scored 70 or above.

DD13 students took the test.

EEOne student got 100 percent.

1

5060708090100

days in question. Adding up the frequencies results in:

2

+

5

+

6

+

6

+

5

+

3

+

2

+

1

=

30 days

June actually has 30 days, so this number makes sense. Now find the sum of

the 30 given temperatures and divide by 30.

5926056166266356436526

1859

6197

degreesAnswer

TemperatureFrequency

2

5

6

6

5

3

2

66

1

CHAPTER 11

NUMBER AND OPERA

TIONS

28%

Plane

1.Invented Operations

2.In Terms Of Problems

3.Sequences

, and represent. When

=

2

PART II / MATH REVIEW

n

equals 216. You know that 6

6 and 6

36.

You may or may not know off the top of your head what 6

6

6

=

36

6

=

On a graphing calculator, type 6 ^ 3.On a graphing calculator, type 6 ^ 3.

n

=

3 Answer

In Terms Of Problems

sequence

cdabcxdx

cdabxcd

cdab

+=+

Answer

+=+

369

xyxy

xyx

=+

+=+

=+

Answer

1, 4, 9, 16, 25, ...

, ...

1, 4, 7, 10, 13, ... 3

2, ...

, ... .

n

aa

PART II / MATH REVIEW

EXAMPLE:

where

===

=++++++

12345200

10020120100

20100

,Answer

=++++++++++++++

24681012141618202224262830

SS

230

1516

))

240Answer

193

,,,

arrra

=

=

44

Answer

aar

aar

==

and

28

2

aar

Answer

and

===

,,,,,

where

PART II / MATH REVIEW

ments, converses, inverses, and contrapositives. A

conditional statement

is an

if-then statement that may or may not be true. Some examples of conditional

If two lines are perpendicular, then they intersect at a 90

angle.

Answer

a

r

S

=

=

1

1

7

10

10

195

tive is also true. When the given conditional statement is false, the contra-

positive is also false. This means that the contrapositive is

logically equivalent

to the conditional statement, and because of this, logic questions on the Level

General FormExample

, then it True

is obtuse, then it False

Inverse

If not

then not

If

does not measure 100

is not obtuse, then itTrue

General FormExample

supplementary, then theyFalse

If two angles are right angles,True

If two angles are notTrue

If two angles are not right False

AAI only

BBII only

CCIII only

DDI and II only

EEI, II, and III

Number Theory

a

197

AnswerIn Words

ExampleEven or Odd?

oddodd4

10Even

even22

6Even

oddif it is an integerif it is an integer

odd raised to an even power3

even raised to an odd power2

667

3

4

=

a

is positive and

b

is negative, which of the following must be negative?

AA

a

+

b

BB

a

+

b

CC

a

b

DD

ab

EE

a

b

Answers B and D are always positive because of the absolute value. Answers

result in a negative value. In answer E,

a

is positive

and

b

is negative. The product of a positive number and a negative number

is always negative.

The correct answer is E.

PART III

SIX PRACTICE

TESTS

PRACTICE TEST 1

PRACTICE TEST 1

MATH LEVEL 1

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

PRACTICE TEST 1

11A calculator will be needed to answer some of the questions on the test.

:Volume

Volume

=

4

B

and height

h

Volume

=

3

Bh

3

r

2

c

3

rh

1.If

AA3

BB4

CC7

BBsin 3

CCsin 9

DD1

EEsec 3

3.A fax machine sends

BB25

DD25

4.It is possible to have a triangle with all of the fol-

x

4

1

4

n

25

sincos

6.In Figure 1,

__

DD180

EE180

7.What is the slope of the line parallel to the line seg-

AA4

EE0

8.In Figure 2,

AA10.5

BB6.7

CC24.8

DD5.8

EE0.49

9.If

BB8

DD8

EE8

10.If

AA9

BB2

CC7

DD5

EE9

11.If

AA0

CC0

EE3

4

21

x

+

)

8

7

4

1

4

4

USE THIS SPACE AS SCRATCH PAPER

W

a

b

c

C

12.What is the area of the base of a triangular pyramid

AA5.5 cm

BB11 cm

CC8 cm

DD16.5 cm

EE22 cm

13.Which of the following is the

ab

ab

ab

+

=

5

2

15

7

17.The cost of 2 candy bars and 4 sodas is $6.00. If the

AA$1.10

BB$2.70

CC$1.35

DD$0.80

EE$1.60

18.If each exterior angle of a regular polygon measures

AA1,260

BB10

CC18

DD9

EE8

19.John spends 25 percent of his monthly salary on rent

AA$6,720

BB$2,240

CC$840

DD$560

EE$2,420

20.The cube root of twice a number,

AA0.422

BB0.211

CC0.909

DD0.454

EE0.563

21.A cube with an edge of 3 cm has the same volume as

AA1.86 cm

BB6.45 cm

CC2.25 cm

DD1.29 cm

EE11.46 cm

4

USE THIS SPACE AS SCRATCH PAPER

23.If log

24.If a circle has a radius of 5 and is tangent to both the

DD(

EE(

x

x

150

29.If the distance from

AA11

DD8

EE6

30.In Figure 4,

AA50

BB142

CC25

DD26

EE168

31.What is the maximum value of

32.The diagonal of a square is 12. What is the length of

BB14.1

CC8.5

DD6.9

EE17

33.In Figure 5, what is the length of

AA3

BB5

CC4

DD9

EE8

3

4

3

2

4

2

USE THIS SPACE AS SCRATCH PAPER

X

W

Z

n

m

142

50

5

18

3

3

N

O

Q

34.When

AA2

BB2

DD2

EE2

35.If

36.If

AA13

BB8

CC7

DD5

EE2

37.If

AAII only

BBIII only

CCI and III only

DDII and III only

EEI, II, and III

38.In Figure 6,

4

JI

K

39.Which of the following is NOT a true statement?

AA3

BB2

DD2

40.A jar contains 4 red, 1 green, and 3 yellow marbles. If

41.If , then what is the domain of the

AAAll

BBAll

CCAll

DDAll

EEAll real numbers

42.The width of a rectangular prism is doubled, its

AA2

BB4

CC16

DD6

EE3

43.If cos

AA0.623

BB1.29

CC0.793

DD38

EE0.783

2

3

or

x

2

(

x

=

49

56

4

28

1

)

648

USE THIS SPACE AS SCRATCH PAPER

44.The probability that Claire passes chemistry is 0.75,

AA0.22

BB0.66

CC0.13

DD0.25

EE0.03

45.A comedian has rehearsed 10 different jokes. During

AA10

BB252

CC42

DD84

EE126

46.What is the maximum value of the function

AA3

BB2

CC5

DD1

EE6

47.If

BBAll real numbers except

EEAll real numbers

48.Assuming each factor has only real coefficients,

2333

xxx

2633

xxx

x

USE THIS SPACE AS SCRATCH PAPER

215

49.If

sequence 1, 0, 1, 4, 9, ... is which of the following?

CC(

DD(

DD2

62

3

x

x

)

23

3

x

x

+

3

x

x

)

++

=

62

3

69

9

2

x

xx

x

STOP

C

Since

XY

____

WZ

____

,

and

are alternate

interior angles and are, therefore congruent.

YXZ

=

a. b

is an exterior angle to the triangle containing

the angles

a

and

c,

so

b

equals the sum of the two

remote interior angles.

b

=

a

+

c

c

=

b

a

7.

A

The slope of the line segment is

Any line parallel to the segment must have the same

slope, so 4 is the correct answer.

8.

D

12

=

=

44

02

8

4

PART III / SIX PRACTICE TESTS

2. D

10. E

B

Substitute

b

=

3

5 into the equation for

a

=

2(3

5)

10

a

=

6

10

10

a

=

6

20

20

=

5

a

=

4

2.

D

It will take minutes to

create a triangle.

xxx

===

n

sincos

9911

+==

12. D

21. A

31. C

41. D

-coordinate is positive).

+

sides

abab

output of 2

=

15

7

883

1

3

16

=

)

3

1928921

xxx

+=+=+

4

gxx

4

PART III / SIX PRACTICE TESTS

B

8

8

16

=

0

8

x

2)

=

0

8

+

2)(

x

1)

=

0

8

=

0 or (

+

2)

=

0 or (

1)

=

0

x

=

0 or

x

=

2 or

x

=

1

{

27.

C

The measure of the exterior angle of a trian-

gle equals the sum of the two remote interior angles.

150

=

x

+

x

20

170

=

2

x

=

85

The measure of

=

85

20

=

65

28.

B

The base of the triangle measures

1

5

=

6 units and the height measures

8

1

=

7 units. The

area of the triangle is

29.

B

Use the distance formula to solve for

x.

x

=

5 is the only valid answer given in

the problem.

dxxyy

+

16210

))

==

810

1810

11006436

=

==

==

166

or1

Abh

units

6721

B

Since 25 percent of Johns monthly salary is

Volume

27075

644318

64431

8186

.cm

207504219

02109

025075420

01875420

01875

224

00

angles in both triangles measure .

2610

216

2

.units

b

a

x

f

=

=

=

+

2

3

21

3

2

3

3

3

3

=+

==

JI

K

6

6

60

30

3

AA3

BB2

222

231

64648

=+=

333363104

The sequence: 1, 0, 1, 4, 9, ... is equivalent

, ... . Since

, ... , so the

++

=

62

3

69

9

9

6

2

2

2

x

xx

x

x

x

++

233

xx

218

233

233

xxx

33

(

x

x

=

=

1

(

x

x

==

1

40.

B

There are eight marbles in the jar. The prob-

ability of choosing the first yellow marble is

. The

probability that your second marble will also be yellow

is

. The probability that both will be yellow is

therefore

41.

D

42.

E

The volume of the original prism was

V

=

w

h

The volume of the new prism is

V

=

2

3

h

=

3

w

h

=

3

43.

E

cos

=

38

x

=

38.

cos (

+

0.5)

0.5)

=

38.538.5

44.

A

The probability that Claire does NOT pass

chemistry is

1

0.75

=

0.25

The probability that she does NOT pass chemistry

and she does pass history is then

0.880.88

=

0.22

45.

B

The order that he performs the jokes does

105

678910

1234

((

7292

mustbepositiveorequaltozero.

x

or

==

7

8

PART III / SIX PRACTICE TESTS

Diagnose Your Strengths and Weaknesses

(_____________________________)

135111516171920263637394850Total Number Correct

71314242529Total Number Correct

93134354147Total Number Correct

404445Total Number Correct

102349Total Number Correct

4

223

SAT Subject test Approximate Score

4650

750800

4145

700750

3640

640700

2935

590640

2228

510590

Below Average

22

510

PRACTICE TEST 2

PRACTICE TEST 2

MATH LEVEL 1

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

PRACTICE TEST 2

11A calculator will be needed to answer some of the questions on the test.

:Volume

Volume

=

r

4

B

and height

h

Volume

=

Bh

3

3

2

3

1.The cost to rent a DVD is $4.50 for the first five days,

AA4.50

BB4.50

CC7

DD4.50

EE4.50

2.If

3.What are all values of

4

6

3

2

3

2

2

2

PART III / SIX PRACTICE TESTS

6.If 4

BB1

EE4

7.If the fourth root of the square of a number is 2, then

AA2

BB4

CC8

DD16

EE32

8.If a line is perpendicular to the line 2

DD3

9.If

AA8

BB0

CC10

DD4

10.If

AAThey are the same.

BBThey are the line

CCThey are the same except when

DDThey are the same except when

EEThey do not share any points.

11.(2

AA2

BB2

CC2

DD2

EE2

x

4

2

3

3

231

12.If the lines

AA45

BB90

CC180

DD360

2

2

a

\r

232

PART III / SIX PRACTICE TESTS

17.If 2

0 has as one of its solutions, what

BB8

EE6

18.Assuming you are factoring over the real numbers,

1

41

x

+

4

x

+

41

x

2

x

2

x

2

USE THIS SPACE AS SCRATCH PAPER

3

60

60

10

x

E

D

A

B

C

PRACTICE TEST 2

233

22.If the triangle in Figure 3 is reflected across the

AA(

BB1, 11, 1

CC(

DD1, 01, 0

EE(0,

23.What is the measure of each exterior angle of a reg-

AA90

BB60

CC120

DD108

EE72

24.The triangle in Figure 4 has sides measuring 3, 4, and

AA45

BB30

CC60

DD36.9

EE53.1

123456789101112

121110987654321

C

A

3

4

234

PART III / SIX PRACTICE TESTS

27.(cos

AA1

CC0

DD2

28.If the equation of a circle is

AA12

DD0

x

+

1

2

USE THIS SPACE AS SCRATCH PAPER

E

D

GH

I

J

K

L

235

32.Assuming both

AA10

BB6

CC5

DD4

EE3

33.If

AA17

BB15

CC16

DD16

EE16

34.What is the equation of the graph in Figure 6?

35.What is the range of the function

BB2

36.If

BB10

DD9

1

2

0

y

1

1

y

1

USE THIS SPACE AS SCRATCH PAPER

123456789101112

121110987654321

PART III / SIX PRACTICE TESTS

2

n

m

USE THIS SPACE AS SCRATCH PAPER

237

42.What is the area of the quadrilateral in Figure 7?

AA80

BB70

CC140

DD60

EE105

BB2

CC2(

DD2(

EE2

44.What is the lateral surface area of a right circular

AA36 cm

BB18 cm

CC18

DD36

EE72

45.If the measure of one angle of a rhombus is 120

b

If

then

xxx

7

6

15

20

PART III / SIX PRACTICE TESTS

47.In Figure 8,

AA25

BB50

CC10

DD80

EE40

48.All of the following statements are true EXCEPT

AAAll circles are similar.

BBAll squares are similar.

CCAll cubes are similar.

DDAll spheres are similar.

EEAll cones are similar.

49.Given the parallelogram

AA34

BB44

CC102

DD30

EE40

50.An equilateral triangle with sides of length 12 is

BB144

CC108

DD192

EE48

363

1443

363

363

T

50

x

D

C

x

239

STOP

E

3

4

1

2

2

=

=

==

1622

4

2. D

10. C

B

Since

d

� 5, the cost is $4.50 for the first

5 days and $2.50 for the remaining

5 days. The

cost is 4.50

2.50(

5).

2.

D

3.

C

x

�3 9

x

�3 (3

x

+

x

x

�3

3)(

x

+

3)

x

3

+

(

3)(

x

+

�3) 0

(

3)[1

+

(

+

�3)] 0

(

3)(

x

+

�4) 0

x

x

� 3

4.

C

dxxyy

=

=+=

5360

10010

x

x

=

2

3

3

2

3

3

2

1

2

2

so

12. C

21. D

PART III / SIX PRACTICE TESTS

241

A

18.

B

x

16 is the difference of perfect squares. It

can be factored as (

4)(

x

4), but

4 is also the

difference of perfect squares and can be further fac-

tored to

(

2)(

x

+

2)(

x

4)

19.

C

8(10

+

x

=

110

80

+

8

=

110

8

=

30

x

=

3.75

20.

A

83

10

10

+

+

Substituteintotheequationtoget

++=

tan

tan

\r==

oppos

adjacent

117

x

4

3338

2316

5040

++=

pointsand .

2

=

111

i

2

+

b

x

454323

231

023

023

function to solve for the angle whose tangent is .

12or23unit

tan

369

4

5

72

=

fxx

fxx

,andsolvefor.

xy

x

fx

=

+

=

21

4

243

w

=

4, then 8

=

h

h

=

2.

=

32, so

=

8.

V

=

=

422

=

64 cm

D

Since

x

4,

x,

and

x

+

4 are the first three terms

Abbh

1520435270

+

+=

1

57

1

the range, graph

=

sin 2

x

on your calculator and

check the

values under Table.

36.

E

f

(

+

2

=

(

2(

+

2[(

2(

=

4

+

2(

2)

=

+

2(

=

18

37.

D

816

1

2

2

1

2

.

n

m

m

n

=

2

PART III / SIX PRACTICE TESTS

Oppo-

site angles of a parallelogram are congruent, so you

know

m

=

3

=

3434

=

102

50.

E

Since the triangle is equilateral its area is

simply

===

363.

One way to solve for the length of the diagonal

mTRU

180130

25

22343

23.

LateralArea

LateralArear

()()

312

120

60

30

4

48363

3

PART III / SIX PRACTICE TESTS

Diagnose Your Strengths and Weaknesses

123679111317184143

102129313436Total Number Correct

Statistics,

163237Total Number Correct

33384046Total Number Correct

Number of incorrect answersNumber of incorrect answers

Your raw score

___________________________

__________________________________________________________

=

________________

247

SAT Subject test Approximate Score

4650

750800

4145

700750

3640

640700

2935

590640

2228

510590

Below Average

22

510

PRACTICE TEST 3

PRACTICE TEST 3

MATH LEVEL 1

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

PRACTICE TEST 3

11A calculator will be needed to answer some of the questions on the test.

:Volume

Volume

=

4

B

and height

h

Volume

=

3

Bh

3

r

2

c

3

1.If a car travels 300 miles in 6 hours, then assuming

AA5 hours

BB6 hours

CC7 hours

DD7 hours, 12 minutes

EE7 hours, 20 minutes

2.A number

AA23.04

BB0.8

CC0.64

DD4.64

3.If

BB19

CC32

DD11

EE43

4.What is the midpoint of the segment with endpoints

DD(

5.What is percent of 6?

AA3

BB0.06

CC0.03

DD12

EE0.003

2

7,

1,

1

1

2

,

1,

6.What are the

AA3, 03, 0

BB0, 30, 3

CC(0,

DD(

EE(

7.All of the following are equivalent to the equation of

CC(

DD2

8.What are all the values of

9.If

AA27

BB3

DD9

EE5.2

10.What is the slope of the line containing the points

AA7

BB0

CCUndefined

6

1

1

2

=+

1

1

USE THIS SPACE AS SCRATCH PAPER

11.The triangle in Figure 1 has sides measuring 6, 8, and

AA53.1

BB36.9

CC60

DD30

EE45

12.How many total diagonals can be drawn from all of

AA13

BB12

CC180

DD90

EE77

AA0

14.(

AA(

EE(

15.In Figure 2,

AA140

BB70

CC110

DD40

EE35

143

743

743

23

8

6

\r

x

16.If

____

____

____

17.What is the measure of

AA18

BB72

CC90

DD108

EE162

18.If the sides of a cube are doubled, then its volume is

AA2

BB3

CC4

DD8

EE16

19.In Figure 4, the length of

AA3

BB4

CC5.3

DD12

EE21.3

20.What is the length of the altitude of

AA5.6

BB10

CC4.6

DD6

EE6.6

4

y

12

35

21.All of the following statements are true regarding the

AAIt is concave up.

BBIts vertex is the origin.

CCIts directrix is the line

DDIt does not represent a function.

10

1010

1010or

?

4

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26.If the sum of two numbers is 40, then what is their

AA391

BB396

CC400

DD399

EE420

DD24

28.Mark received a 92 percent and a 78 percent on the

AA80%

BB82%

CC84%

DD85%

EE86%

345

2

13

5

13

i

12

5

12

i

Ifthen

5

,

USE THIS SPACE AS SCRATCH PAPER

31.How many degrees does the hour hand of a clock

AA30

BB10

CC6

DD15

EE7.5

32.(6sin

AA1

CC18

EE18sin

33.Figure 6 is the graph of which of the following?

34.What is the minimum value of the function

AA0

BB1

DD2

EE4

35.In

CC24

DD12

EE8

USE THIS SPACE AS SCRATCH PAPER

123456789101112

121110987654321

y

A

B

36.If

37.In rectangle

AA3

CC5.2

DD3.9

EE7.8

38.Solve

AA32

BB35

CC19

DD67

EE29

39.Assuming each dimension must be an integer, how

AA2

BB3

CC4

DD5

EE6

40.What is the range of the function

AAAll real numbers

EEAll real numbers except

41.How many points may be contained in the intersec-

I.0 points

II.1 point

III.2 points

IV.3 points

AAIII only

BBII or III only

CCIII or IV only

DDI, II, or III only

EEI, II, III, or IV

38

5

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42.How many different chords can be drawn from 8 dis-

AA48

BB7

CC8

DD16

EE28

43.Assuming

44.If 4

131

+

1313

4499

+++=

2

a

+

1

a

1

a

1

a

+

1

+

1

USE THIS SPACE AS SCRATCH PAPER

263

4,

9

4,

3520

=

25

4

5

2

21

4

4

3

USE THIS SPACE AS SCRATCH PAPER

STOP

C

a

=

% of 6

a

=

66

a

=

0.03

6.

E

4

1

2

or

PART III / SIX PRACTICE TESTS

2. D

10. C

D

2.

D

n

4

=

0.64

n

=

4.64

3.

B

f

=

(

2(

6(

1

=

16

+

16

12

1

=

19

4.

A

Themidpointisgivenby

xxyy

1212

The-coordinateis

The

yy

-coordinateis

408

6360

.hours

7.2hoursise

uivalentto7hoursand12minutes.

12. D

21. D

and are the critical points. Test

x

10

10

8

Let

YZx

XYZ

163

==

124

Recall that is the total number of

4433

743

=

)

)

1512

)

2

10

Slope

undefined

PART III / SIX PRACTICE TESTS

C

103

and

345

345

222

9278

2510

i

i

ii

ii

ii

22

2410

=

i

i

i

==

2

40

21

20

31.

B

155939

1559

.cm

33393

43312

60

E

Answer A equals 1 and Answer B is less than

1, so both can be eliminated. Since C and E have the

same denominator and

a

a

+

1, C will always be less

than E. It can also be eliminated as a possible answer

into answers D

and E to compare the expressions.

Answer E will always result in a greater value.

44.

C

Since the expressions represent the terms

3

3

3

3

4499

4191

2131

+++

=+++

xx

If

a

=

7

6

5

8

6

10

9

11

9

,

,

267

B

39.

C

The volume of a rectangular prism is given

by the formula

=

w

h,

so you need to find

three

integers whose product is 18. There are four

possibilities:

1

1

18

1

2

9

1

3

6

2

3

3

40.

D

Notice that as

x

increases without bound, the

value of

(

=

6

=+=

3232

32335

tuting both solutions into the original equation. is

9

9

3520

325

325

912425

xxx

=

+=

=++

=

,so

44

PART III / SIX PRACTICE TESTS

Diagnose Your Strengths and Weaknesses

1258131426384546484950

3922343640Total Number Correct

Statistics,

242842Total Number Correct

2527434447Total Number Correct

Number of incorrect answersNumber of incorrect answers

Your raw score

___________________________

__________________________________________________________

=

________________

271

SAT Subject test Approximate Score

4650

750800

4145

700750

3640

640700

2935

590640

2228

510590

Below Average

22

510

PRACTICE TEST 4

PRACTICE TEST 4

MATH LEVEL 1

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

PRACTICE TEST 4

11A calculator will be needed to answer some of the questions on the test.

:Volume

Volume

=

4

B

and height

h

Volume

=

3

Bh

3

r

2

c

3

rh

277

1.If 3

BB18

CC14

DD21

EE63

CC16

DD12

EE17

3.9sin

AA1

CC9

EE0

4.If the supplement of twice an angle is 124

AA60

BB30

CC56

DD28

EE27

5.Two times a number

50

3

Ifthen

3

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PART III / SIX PRACTICE TESTS

7.Valerie drives 10 miles due east, then drives 20 miles

AA24 miles

BB22.4 miles

CC25 miles

DD35 miles

EE20.6 miles

8.The measures of the angles of a quadrilateral are

AA33

BB32

CC161

DD166

EE168

9.How many sides does a regular polygon have if each

AA6

BB7

CC8

DD9

EE10

10.What is the solution to the system below?

5

2

,

3

5

6

,

5

2

,

3

2

,

3

2

,

5

2

25

xy

xy

+=

=

!

!

USE THIS SPACE AS SCRATCH PAPER

279

11.Which of the following is NOT an irrational number?

DD1.666 ...

!

!

11

15

1

2

,

11,

5

11

6

,

11,

!

!

1

5

11

6

,

2

USE THIS SPACE AS SCRATCH PAPER

PART III / SIX PRACTICE TESTS

16.Each of the following is equivalent to

17.In

AA4

DD8

EE5

18.A local newspaper company prints 520 pages of the

AA2,600 pages

BB86.7 pages

CC5,200 pages

DD10,400 pages

EE1,300 pages

19.When

AA0

BB1

CC2

DD3

2012

2

)

2222

USE THIS SPACE AS SCRATCH PAPER

B

4

281

21.What is the radius of the circle represented by the

AA2

BB4

CC1

DD3

EE16

x

a

y

b

USE THIS SPACE AS SCRATCH PAPER

3

55

4

4

F

E

D

PART III / SIX PRACTICE TESTS

27.All of the following are properties of a parallelogram

AAThe diagonals are perpendicular.

BBOpposite sides are congruent.

CCConsecutive angles are supplementary.

DDA diagonal forms two congruent triangles.

EEThe diagonals bisect each other.

x

=

2

1134

34

10

13 cm

283

31.What is the maximum value of

BB4

CC1

32.In circle

AA50

BB40

CC100

DD30

EE45

33.A rectangular prism has a length of 15 cm, a width of

AA1:9

BB3:1

CC9:1

DD27:1

EE81:1

34.If

DD4

EE3

35.What is the domain of the function

AAAll real numbers.

BBAll real numbers except 0.

CCAll real numbers except 6.

DDAll real numbers except

EEAll real numbers greater than or equal to

36.If three numbers

AA3

BB17

EE9

x

x

)

+

6

T

U

S

100

284

PART III / SIX PRACTICE TESTS

37.Given the three points

38.In Figure 6,

AA75

BB80

CC155

DD165

EE105

39.In Figure 7,

2

334

4

3

5

USE THIS SPACE AS SCRATCH PAPER

Z

W

X

C

D

10

285

41.What is the length of the edge of a cube having the

AA22.7 cm

BB4.8 cm

CC136 cm

DD5.8 cm

EE11.7 cm

42.What are the

CC0

EENone

43.The number of tails showing when a pair of coins

AA0

BB0.5

CC1

DD1.5

EE2

44.Christines average score on the first three math tests

AA87%

BB85%

CC86.8%

DD88%

EE85.5%

45.The diagonals of a rhombus measure 24 and

AA45.2

BB150

CC145

DD120

EE134.8

5

USE THIS SPACE AS SCRATCH PAPER

PART III / SIX PRACTICE TESTS

46.Eighteen students took an 8-question quiz. The graph

AA5.3

BB5

CC4

DD6

EE5.5

47.If

AA7

BB1

CC8

DD6

EE15

48.(2

AA8

BB8

CC(2

DD8

EE2

49.If (

AA(

BB(

CC(

DD(

EE(

0.012345678

287

STOP

==

2

212

=

2. A

10. B

D

Tripling both sides of the equation 3

=

7

results in 9

=

77

=

21.

2.

A

3.

C

9sin

+

9cos

=

9(sin

+

cos

=

11

=

9

4.

D

350

12. A

21. A

31. B

41. B

PART III / SIX PRACTICE TESTS

nonrepeating. 1.666 ... is not irrational, since it is a

..

enuse is a factor of larger than 4. is the

20122523

+=+

201232

==

=

+

2263

1681

979

=

3

2

425

5010

+=

=

d

20

5

5

10 miles

d

C

x

+

2

+

7

+

3

+

5

+

1

=

360

11

+

8

=

360

11

=

352

x

=

32

3232

+

1

=

161

9.

D

1802

The equation represents an

7757512

+=+=

1

1

1

1

b

b

+=

=

=

a

y

b

==

18.

C

=

055

h

h

=

20(tan 42

20

291

x

=

1,

y

=

4, and when

x

=

3,

y

=

12. The

+=

++=

234

(100)

or 27:1.

2

=

)

21

a

2

123456789101112

121110987654321

PART III / SIX PRACTICE TESTS

B

Since

a

+

b

+

9

=

6

+

(2

b

+

b

=

6 and 2

b

=

26781

s

3

89

267

=

0122110201

+++++++++

ab

ab

+=

+==

3015

b6,so1

x

B

C

C

VZX

and

ZXY

are alternate interior angles

and are, therefore, congruent.

m

VZX

=

75

.

Since

m

ZYX

=

25

and

m

VZX

=

75

, the

remaining angle in

ZYX

must measure 180

(75

+

25)

=

80

m

=

75

+

80

=

155

39.

B

10

ThetangentofCABis

opposite

adja

CAB

ccent

CAB

3

5

293

C

(

+

g

=

f

+

22

=

22

+

1

+

22

22

+

1

=

7

+

1

=

8

48.

B

The binomial expansion of (

+

y

3

+

3

y

Substitute

x

=

2

and

y

=

y

45.2

67.467.4

134.8

.

Since the problem asks for the greater of the two

is the correct answer.

46.

B

tan

tan.

tan

tan

226

==

674

295

Diagnose Your Strengths and Weaknesses

(_____________________________)

13152124293442Total Number Correct

232531354749Total Number Correct

434446Total Number Correct

22040Total Number Correct

151011121416181926364850Total Number Correct

4

PART III / SIX PRACTICE TESTS

SAT Subject test Approximate Score

4650

750800

4145

700750

3640

640700

2935

590640

2228

510590

Below Average

22

510

PRACTICE TEST 5

PRACTICE TEST 5

MATH LEVEL 1

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

PRACTICE TEST 5

11A calculator will be needed to answer some of the questions on the test.

:Volume

Volume

=

4

B

and height

h

Volume

=

3

Bh

3

r

2

c

3

rh

1.If

AA8

CC4

DD2

CC11

3.If 4

BB20

DD4

EE21

4.percent of 50 percent of 1,000 is

BB5

CC0.25

DD25

EE250

5.What is the least positive integer divisible by 2, 6,

AA108

BB54

CC18

DD324

EE162

2

12

12

4

If

then

=

1

?

USE THIS SPACE AS SCRATCH PAPER

6.If the area of a square is 100 cm

3289

2

=+

E

A

B

C

11.In Figure 2, if the length of

is , what is the length of

EE3

12.What are three consecutive even integers whose sum

AA12, 14, 16

BB16, 18, 20

CC13, 15, 17

DD15, 16, 17

EE14, 16, 18

AA4

CC8

DD0

EE2

14.If

DD1

4

2

1

2

Ifandthen

=

7

7

9

5

7

y

=

4

3

x

+

4

1

x

+

4

3

x

+

4

1

x

+

16.How many diagonals can be drawn from one vertex

AA15

BB16

CC17

DD18

EE170

17.Which of the following lines is perpendicular to the

18.If the point (

2

4

2

=

=+

1

3

n

2

3

22.2

AA2

BB(2

CC2

DD2

EE2

23.In the triangle shown in Figure 4, what is the value

24.Which one of the following is a counterexample to

AAIf two angles are complementary, then they

BBIf two angles are right angles, then they are

CCIf two angles are not supplementary, then they

DDIf two angles are supplementary, then one could

EEIf two angles are not right angles, then they

25.What is the domain of the function

26.What is the maximum value of the function

CC2

EEInfinity

3

2

2

3

2

x

x

1

36

USE THIS SPACE AS SCRATCH PAPER

9

c

CC0

DD2

28.What is the volume of a sphere whose surface area is

CC160

EE520 units

29.What is the circumference of a circle whose area is

AA16

BB8

CC8

DD128

EE16

30.Which of the following is the solution of

31.Which of the following is the equation of a circle

AA(

BB(

CC(

DD(

EE(

3

2

5

2

or

�

3

2

5

or

5

2

5

x

units

units

cubicunitsorunits

n

Ifandthen,for

nab

=

32.An equation of the line parallel to 8

16

64

4

56

8

=

4

5

2

=+

4

5

USE THIS SPACE AS SCRATCH PAPER

G

F

C

B

E

A

D

BB20

DD8

EE16

39.The operation

AA1

BB2

CC3

40.How many common tangents can be drawn to the

AA0

BB1

CC2

DD3

EE4

2

2

142

1222

If

then

fxxxff

3

3

9

3

If

then

222

()

PART III / SIX PRACTICE TESTS

24

7

24

25

20

If

then

sin,tan

1

1

x

1

x

+

+

1

1

x

3

3

2

g

x

3

1

USE THIS SPACE AS SCRATCH PAPER

W

12

3

311

243

123

6

6

2424

USE THIS SPACE AS SCRATCH PAPER

X

STOP

A

5.

B

Take the prime factorization of each of the

three numbers.

2 is prime.

6

=

33

27

=

3

equals 2(3

=

2727

=

54.

501000

1000

%%,

ofof

==

2. D

10. C

B

2.

D

3.

B

4

3(5

x

=

2(

+

5)

1

4

15

+

3

=

2

+

10

1

3

11

=

2

+

9

x

=

9

+

11

=

20

8

1

41

418

238

211

28

When

==

=

1

2

4

1

2

,.

12. E

21. D

E

3

3

Since

xyyy

+=+==

Since

so

=

5

7

+=

+=

DEDFEF

DExx

DEx

=++

3289

319

313

=+

11

=+

=

=

The-intercep

ptis

The graph of the function has asymp-

the domain is restricted to the interval , the

maximum value of the function occurs when .

Thevolumeis,therefore,

125

500

3

.

n

n

n

n

nn

n

n

n

n

=

+

=

++

=

11

11

2

2

4

4

3

1

1

2

2

=

1

3

2

x

x

1

PART III / SIX PRACTICE TESTS

A

If (

The remainder is zero.

4 is the constant term. 7 is the

coefficient of the first-degree term, and 2 is the coef-

2

7

4

23.

C

The triangle is a 30

special right tri-

angle. Since the side opposite the 60

angle measures

9, the side opposite the 30

angle measures:

The side opposite the 90

angle,

c,

is, therefore,

or units.

233

3

93

3

33

==

whereistheareaofthebaseand

BhB

hh

t

heheight.

=

2

2

=

+

=

+=+=

110212

2

Since

fxxx

+=+=

44628

ff

881222

+=+

4

315

E

A

=

r

r

=

8

The circumference of a circle is given by the formula

C

=

2

so

C

=

2

=

16

30.

A

31.

D

The general equation of a circle is

(

h

(

k

r

is the length of the radius. The equation of a circle

(

1)

(

7)

3

+

1)

(

7)

9

32.

E

Write the equation of the line 8

x

2

y

=

5 in

+==

=+

285

5

2

yx

yx

241

1241

325

=

=

=

B

321

131

B

5454

270 points in their first 5 games and the girls team

5959

42.

B

Rotating the rectangle creates a cylinder of

radius 3 and height 12. The volume of the cylinder is

V

=

r

=

(3

=

108

43.

E

,

i

1,

i

i,

and

i

1. If

is raised

to an exponent that is a multiple of 4, the expression

simplifies to 1. All of the expressions simplify to 1,

i

1

(

i

1

i

1

i

1

i

i

1

+

1

=

2

=

1

270354

567

.points

C

The sum of the interior angles of a polygon is

given by the expression 180(

2) where

=

the

number of sides of the polygon.

49.

C

Start by multiplying both sides by the LCD:

How to solve for

may not be immediately obvious.

One way to solve for

is to substitute

so the

h

term cancels out.

1

=

h

+

4)

+

k

2)

1

=

k

50.

C

Each angle of a regular hexagon measures

120

XO

1

6

2424

142

hxkx

1802

1575

1803601575

225360

n

sides

acute angles of the triangle would, therefore, be .

25

b

7

25

the other leg.

7

b

25

=

24

46.

D

Kate chooses one course out of the five for

her first-period class. She chooses one course out of

5

4

3

2

1

=

120

47.

A

3333

339327

3333273381

3

3

3

33

Thesixthtermis,therefore,33

tan

opposite

adjacent

X

4

2

angle measures 2 units. The

regular hexagon can be broken into 12 right triangles

that are congruent to the one shown in the diagram.

319

Diagnose Your Strengths and Weaknesses

12345101213142227303749

81718203132Total Number Correct

1525263844Total Number Correct

334146Total Number Correct

9394347Total Number Correct

Number of incorrect answersNumber of incorrect answers

Your raw score

___________________________

__________________________________________________________

=

________________

4

PART III / SIX PRACTICE TEST

SAT Subject test Approximate Score

4650

750800

4145

700750

3640

640700

2935

590640

2228

510590

Below Average

22

510

PRACTICE TEST 6

PRACTICE TEST 6

MATH LEVEL 1

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

PRACTICE TEST 6

11A calculator will be needed to answer some of the questions on the test.

:Volume

Volume

=

4

B

and height

h

Volume

=

3

Bh

3

r

2

c

3

rh

BB1

AA4

BB1

3.Which of the following equations has the same solu-

BB3

AA4

CC4

DD4

EE4

5.A cell phone company charges $30 a month for a

AA30

BB30

CC30

DD30

EE30.40

2

3

2

=

6

2

6

4

then

6

7

then

PART III / SIX PRACTICE TESTS

BB5

7.If two similar octagons have a scale factor of 3:5,

AA3:5

CC9:25

DD27:125

EE6:10

8.What is the ratio of the circumference of a circle to

AA2:

CC1:

DD2

EE2:

9.Kelli has taken a job with a starting salary of $35,000.

AA$11,900

BB$37,800

CC$40,600

DD$43,400

EE$46,200

AA2

CC8

Ifand

xyyn

:

7

7

7

If

then

873

==

327

11.In

AA8

BB14

CC11

DD10

EE12

12.If the measure of each exterior angle of a regular

AA18

BB9

CC27

DD22

EE36

13.The ratio of the measures of the angles of a quadri-

AA30

BB150

CC154

DD120

EE144

14.If

AA5

BB11

CC6

DD4

EE10

15.Which of the following is the graph of 2

x

PART III / SIX PRACTICE TESTS

x

x

x

x

329

16.If the point (

AA4

BB3

17.(

AA(

BB(

CC(

BB0.618

CC0.786

DD0.222

EE0.733

19.0, 03, 711, 011, 0

AA(8,

BB14, 714, 7

CC7, 87, 8

DD(3,

EE8, 78, 7

20.A point

AA(

BB(

DD(5,

EE(

AA20

BB1,024

CC64

DD128

EE512

If

then

823

317

InFigure1,

.sin

5

USE THIS SPACE AS SCRATCH PAPER

S

11

\r

330

PART III / SIX PRACTICE TESTS

22.What is the area of the triangle in Figure 2?

DD64

EE32

23.If 4

AA2

BB3

CC4

DD5

EE16

24.For

25.Which of the following is the equation of a line that

DD5

26.If 2 percent of a 12-gallon solution is sodium, how

AA1.79

BB1.02

CC8

DD5

EE0.51

27.The product of the roots of a quadratic equation is

=+

9

=

5

9

2

=+

1

9

23

323

643

PRACTICE TEST 6

331

28.If

AA6

BB5

CC16

DD4

EE8

29.(1

AA1

BBcos

CC1

DDcos

EE1

30.If 25

0 has as a double root,

AA4

CC5

EE1

31.If

DD2

32.Which of the following equations has roots of 4 and

AA2

BB2

CC2

DD2

EE4(2

33.What is the area of the quadrilateral in Figure 3?

DD16 units

EE8 units

units

82units

22units

1

2

25

USE THIS SPACE AS SCRATCH PAPER

PART III / SIX PRACTICE TESTS

34.The volume of a cube is

AA2

16

V

8

V

4

V

2

V

USE THIS SPACE AS SCRATCH PAPER

x

x

x

x

333

36.In Figure 5, which of the following must be true?

II.cos

III.tan

AAI only

BBII only

CCII and III only

DDI and II only

EEI, II, and III

37.What is the lateral area of the right circular cone

AA50

BB75

EE100

253

1253

cot

x

x

4

5

x

y

10

5

PART III / SIX PRACTICE TESTS

38.If

AA4

BB2

CC2

AA35

BB36

CC37

DD35

EE36

41.What is the volume of the right triangular prism in

AA200 cm

CC100 cm

42.tan

AA2cos

BBcos

CCcsc

DDsec

EE1

43.The French Club consists of 10 members and is hold-

1002

3

cm

1002cm

Ifthen

=

166

2

If

and

then

fxxfgxxgx

5

5

PART III / SIX PRACTICE TESTS

2

pq

903

363

543

723

1083

12 cm

K

337

4

If

then

fnf

100

90

10

5

90

9

10

USE THIS SPACE AS SCRATCH PAPER

STOP

10

+

21

=

0, can

be factored as:

(

7)(

x

3)

=

0

Its solutions are also

=

3 or

x

=

7.

4.

E

x

2

+

1

(

8

1)

= 5

x

2

+

1

x

8

1

= 4

9

2

+

2

5.

B

Since $30 is the initial cost and $0.40 is

charged for (

300) additional minutes, the cor-

rect expression is:

30

+

0.40(

m

300)

6.

B

873

873

8727

735

=

x

x

x

x

xx

5

PART III / SIX PRACTICE TESTS

2or

41

2

5

+

=

7

6

+

=

x

x

12. A

21. B

31. D

41. C

339

C

11

317

tan

tan.

38157

381577

+=

2232

315

sides

==

2

2

2

r

rr

r

=

:

or

PART III / SIX PRACTICE TESTS

E

8, 78, 7

zoid as shown:

23.

B

4

36

9

(36

9)

4

=

3

24.

D

Multiply both sides of the equation by the LCD, 36

x

4

x

36

3

36

x

12

25.

C

In order for two lines to never intersect, they

must be parallel. Parallel lines have the same slope, so

051

.gallons

5

9

2

x

=+

5

1

9

==

1223

222

222

123456789101112

121110987654321

the second quadrant and at a distance of from

its legs measure 8 and units. Its area is

==

883

643323

21024

4050

1625

341

C

Recall that a quadratic equation can be

thought of as:

a

[

x

sum of the rootssum of the roots

x

+

product of the rootsproduct of the roots

=

0. Substitute the sum

4 and the product

=

2

5

2

5

0

2

5

An equation with roots of 4 and has fac-

Thefirststatementistruebecause

adj

cot

aacent

opposite

Thesecondstatementisal

sotrue,since

cosandsin

Thet

hhirdstatementisnottrue,since

tan

andtan

AnswerDisthecorrectchoi

cce.

2

1

units

Theareaofthesquareunits

2222428squareunits.

)

=

4

1

2

0

1

.

1

ures5 cm

and the hypotenuse measures cm, the

ansincos

sin

cos

cos

\r\r\r

sin

cos

cos

cos

sincos

cos

sec

\r=

Theareaofthetriangleis

Thevolumeofthesolidis,therefore,

VBH

8100cm

The lateral area of a cone equals , where

Since

==

1111

gxxfgxfxxx

4442

,so

xx

=

x

x

==

2510

10050

c

343

A

Consecutive angles in a parallelogram are sup-

plementary so

KLM

=

180

120

=

60

333

Theareaofsector

Thearea

MNO

369

MNO

6618.

10

2

9

2

10

1

5

==

7

9

2

9

=

.

p

p

2

2

2

12

6

K

60

angle, the height of the parallelogram is

. Its area is

46.

C

Start by arranging the test scores in order of

lowest to highest:

60, 67, 74, 78, 81, 83, 83, 86, 88, 90, 92, 95, 100

The median of the data is 83. To find the interquartile

Lowerquartile

Upperquartile

7478

909

22

7615

Theinterquartilerangeis91.

18631083

12345691014172123242630

345

Diagnose Your Strengths and Weaknesses

151619202544Total Number Correct

27283235383950Total Number Correct

434648Total Number Correct

314047Total Number Correct

4

PART III / SIX PRACTICE TESTS

SAT Subject test Approximate Score

4650

750800

4145

700750

3640

640700

2935

590640

2228

510590

Below Average

22

510