John Diehl-McGraw-Hill’s SAT Subject Test_ Math Level 1, 2 E (2009)


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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
USE THIS SPACE AS SCRATCH PAPER
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
USE THIS SPACE AS SCRATCH PAPER
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
USE THIS SPACE AS SCRATCH PAPER
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

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