3. The figure above shows a rectangle intersected
by a line. If b = 2a, then d + e + g + h =
(A) 120
(B) 240
(C) 300
(D) 320
(E) 360
4. For all real numbers x where x ≥ 1, let
. What is the value of f (100)?
(A) 3
(B) 9
(C) 10
(D) 27
(E) 100
5. If 3
k+ m
= 243 and 2
m
= 8, then what is the value
of 2
k
?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
fx x
()
=−1
a° b°

c° d°
e° f°
g° h°
600 MCGRAW-HILL’S SAT
5 5 555 5
GO ON TO THE NEXT PAGE
6. If b varies inversely as the square of c, and if
b = 8 when c = 3, then what could be the value
of c when b = 2?
(A) 2
(B) 5
(C) 6
(D) 25
(E) 36
7. In a certain soccer league, each of the five
teams plays every other team in the league
exactly three times each season. How many
games are played in total in one season?
(A) 15
(B) 24
(C) 30
(D) 60
(E) 120
8. Pump A, working alone, can fill a tank in
3 hours, and pump B can fill the same tank in
2 hours. If the tank is empty to start and pump
A is switched on for one hour, after which
pump B is also switched on and the two work
together, how many minutes will pump B have
been working by the time the pool is filled?

(A) 48
(B) 50
(C) 54
(D) 60
(E) 64
CHAPTER 16 / PRACTICE TEST I 601
5 5 555 5
GO ON TO THE NEXT PAGE
• Mark no more than one circle in any column.
• Because the answer sheet will be machine-scored,
you will receive credit only if the circles are filled
in correctly.
• Although not required, it is suggested that you write
your answer in the boxes at the top of the columns to
help you fill in the circles accurately.
• Some problems may have more than one correct
answer. In such cases, grid only one answer.
• No question has a negative answer.
• Mixed numbers such as 3 must be gridded as
3.5 or 7/2. (If is gridded, it will be
interpreted as , not 3 .)
1
2
31
2
31 2/
1
2
• Decimal Answers: If you obtain a decimal answer
with more digits than the grid can accommodate, it

may be either rounded or truncated, but it must fill
the entire grid. For example, if you obtain an answer
such as 0.6666 , you should record your result as
.666 or .667. A less accurate value such as .66 or
.67 will be scored as incorrect.
Acceptable ways to grid
2
/
3
are:
. . . .
201 102
0
2
3
4
5
1
0
2
3
4
5
1
0
2
3
4
5
1

2
3
4
5
1
. . . .
0
2
3
4
5
1
0
2
3
4
5
1
0
2
3
4
1
2
3
4
5
1
Answer: 201
Either position is correct.

Note: You may start your answers
in any column, space permitting.
Columns not needed should be left
blank.
. . . .
7/12
0
2
3
4
5
6
7
8
9
1
0
2
3
4
5
6
7
8
9
1
0
2
3
4

5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
Grid in
result.
Fraction
line
Write answer
in boxes.
Answer:
7
12
. . . .
2.5
0
2
3
4

5
6
7
8
9
1
0
2
3
4
5
6
7
8
9
1
0
2
3
4
5
6
7
8
9
1
2
3
4
5

6
7
8
9
1
Decimal
point
Answer: 2.5
. . . .
2/3
0
2
3
4
5
6
1
0
2
3
4
5
6
1
0
2
3
4
5
6

1
2
3
4
5
6
1
. . . .
66
.
6
0
2
3
4
5
6
1
0
2
3
4
5
6
7
1
0
2
3
4

5
6
1
2
3
4
5
6
1
. . . .
66
.
7
0
2
3
4
5
6
7
1
0
2
3
4
5
6
7
1
0

2
3
4
5
6
7
8
1
2
3
4
5
6
7
1
Directions: For student-produced response questions 9–18, use the grids at the bottom of the answer
sheet page on which you have answered questions 1–8.
Each of the remaining ten questions requires you to solve the problem and enter your answer by mark-
ing the circles in the special grid, as shown in the examples below. You may use any available space for
scratchwork.
602 MCGRAW-HILL’S SAT
5 5 555 5
9. If four times a certain number is decreased by
5, the result is 25. What is the number?
10. For every integer m greater than 1, let «m» be
defined as the sum of the integers from 1 to
m, inclusive. For instance,
«4» = 1 + 2 + 3 + 4 = 10.
What is the value of «7» − «5»?
11. If the circumference of the circle above is 10π,

then what is the value of a
2
+ b
2
?
A, B, C, D
12. How many different three-letter arrangements of
the letters above are possible if no letter may
be repeated? (An arrangement like ABC is dis-
tinct from an arrangement like BCA.)
13. If 96,878 × x
2
= 10,200, then
14. Every term in a certain sequence is one less
than three times the previous term. If the
fourth term of this sequence is 95, what is the
first term of the sequence?
10 200
5 96 878
2
,
,x ×
=
a
b
P
15. If , what is the value of ?
16. Admission to a museum is $10 for each adult
and $5 for each child. If a group of 30 people
pays a total of $175 in admission, how many

adults are in the group?
17. The perimeter of the isosceles triangle above is
24. If the ratio of a to b is 2 to 3, what is the
value of b?
Note: Figure not drawn to scale.
18. In the figure above, AB = 6, BC = 6, and CD = 2.
What is AD?
A
B
C
D
E
a
bb
4 − b
472+=b .
STOP
If you finish before time is called, you may
check your work on this section only. Do not
turn to any other section of the test.
CHAPTER 16 / PRACTICE TEST I 603
1. The strange signal detected by the radio tele-
scope, rather than being taken as evidence of a
new cosmological phenomenon, was instead
treated as merely of the equipment itself.
(A) a malfunction
(B) a bulwark
(C) an anthology
(D) a mutation
(E) a transfer

6 6 666 6
SECTION 6
Time—25 minutes
24 questions
Turn to Section 6 of your answer sheet to answer the questions in this section.
Directions: For each question in this section, select the best answer from among the choices given and
fill in the corresponding circle on the answer sheet.
GO ON TO THE NEXT PAGE
2. The long-standing divisions among the indige-
nous ethnic groups in the region have created
an problem that may never be solved
without international intervention.
(A) impotent
(B) intractable
(C) evanescent
(D) irate
(E) insipid
3. The ease with which the army’s defenses were
breached surprised the opposing general, who
expected resistance to be far more than
it was.
(A) ephemeral
(B) compatible
(C) egregious
(D) tolerable
(E) imposing
4. Although dependence on electronic devices
has in recent years, the increased effi-
ciency of common appliances has the de-
mand on the power grid.

(A) abated . . decreased
(B) surged . . attenuated
(C) increased . . compromised
(D) diminished . . reduced
(E) flourished . . elevated
Each sentence below has one or two blanks,
each blank indicating that something has been
omitted. Beneath the sentence are five words
or sets of words labeled A through E. Choose
the word or set of words that, when inserted
in the sentence, best
fits the meaning of the
sentence as a whole.
EXAMPLE:
Rather than accepting the theory unquestion-
ingly, Deborah regarded it with

.
(A) mirth
(B) sadness
(C) responsibility
(D) ignorance
(E) skepticism
A
C D
B
604 MCGRAW-HILL’S SAT
6 6 666 6
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5. Although persecution at the hands of

landowners vanquished the will of many, it
the dreams of revolution among the
hardier insurgents.
(A) despotic . . squandered
(B) cruel . . destroyed
(C) amenable . . bore
(D) celebrated . . initiated
(E) ruthless . . forged
theory of morality. So impressed was Kant by
the insights of Rousseau that he hung a picture
of him on the wall of his study, convinced that
Rousseau was the Newton of the moral world.
PASSAGE 2
The roses we lay at Rousseau’s feet for this the-
ory of Natural Rights tend to overwhelm the
less fragrant of his ideas. He persisted in believ-
ing in the nobility of the primitive state of
nature, and that women’s nature was to serve
men. His assertions about Natural Rights of
Man laid the philosophical foundation of
American independence, but his worship of
emotion over reason and of “negative educa-
tion” gave generations of parents permission to
ignore the need to discipline and teach their
children.
6. Passage 1 suggests that Goethe
(A) was at the forefront of the Age of
Reason
(B) was a traditionalist
(C) was influenced by Rousseau

(D) opposed the Romantic movement
(E) inspired much of Rousseau’s work
7. Passage 1 mentions Kant’s “daily walk” (line
16) in order to emphasize
(A) Kant’s forgetfulness
(B) Kant’s commitment to healthful
practices
(C) the dogmatic nature of Rousseau’s writ-
ings
(D) the effect of Rousseau’s philosophy on
Kant
(E) Kant’s close friendship with Rousseau
8. Unlike Passage 1, Passage 2 characterizes
Rousseau’s emphasis on emotion as
(A) insincere
(B) innovative
(C) harmful
(D) temporary
(E) necessary
First passage: from “Rousseau: A Romantic in the Age of
Reason,” from
Socrates to Sartre,
McGraw-Hill, 1999, p. 278
Second passage: Copyright 2005 Christopher Black. All rights
reserved.
Line
5
10
15
20

25
30
35
The passages below are followed by questions
based on their content; questions following a
pair of related passages may also be based on
the relationship between the paired passages.
Answer the questions on the basis of what is
stated
or implied in the passage and in any
introductory material that may be provided.
Questions 6–9 are based on the following passages.
PASSAGE 1
The following is from a recent commentary on
Jean-Jacques Rousseau (1712–1778), a French
philosopher during the Enlightenment.
Taken as a whole, Rousseau’s writings at-
tacked the Age of Reason, gave impetus to the
Romantic movement by emphasizing feeling
(leading Goethe to say that “feeling is all”),
revived religion even though he had doubts
about some traditional teachings, provided a
new direction for education (his book Émile
was considered by some the best work on edu-
cation since Plato’s Republic), inspired the
French Revolution, made a unique impact on
political philosophy, and, more than the writ-
ing of any of his contemporaries, influenced
several subsequent philosophers, especially
Immanuel Kant. On one occasion, Kant was

so absorbed in reading Rousseau’s Émile that
he forgot to take his celebrated daily walk.
While Kant admitted that it was David Hume
who awakened him from his dogmatic slum-
bers regarding the theory of knowledge, it was
Rousseau who showed him the way to a new
CHAPTER 16 / PRACTICE TEST I 605
6 6 666 6
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9. Both passages credit Rousseau with
(A) attacking the Age of Reason
(B) inspiring revolutionary thought
(C) encouraging discipline
(D) praising the primitive state of nature
(E) establishing the Romantic movement
This isn’t an idle example. India developed
a pharmaceutical industry many years ago
that could produce drugs very cheaply that
would have saved tens of thousands of lives
each year. In a free-market economy, the Indian
pharmaceutical industry would have been
allowed to make drugs and get them to the
people who needed them. But that would
mean that western pharmaceutical companies
would make less profit. Of course, it’s not that
the American pharmaceutical companies
don’t care about Indian children dying be-
cause they can’t get drugs; it’s just that their
responsibility is to their stockholders. They
must maximize profits. But the “free market”

was getting in the way, so they simply
changed the rules.
Thus, in 1994 India “agreed” (that is, gave
in to Western pressure) to “liberalize” its
pharmaceutical industry by allowing its
largest drug companies to be sold to Western
interests, thereby reducing competition.
Drug prices predictably shot up, putting
them out of reach of people who needed
them, but the Western corporations made
more money. It was a big triumph for the
“liberalization” of markets, but a great blow
to free markets.
In a free economy, businesses are also ex-
pected to wager their own capital on success
in the marketplace. The adventurous entre-
preneur is a moral icon in the United States.
The American pharmaceutical industry, how-
ever, receives over half a billion dollars annu-
ally in federal tax dollars in the form of
research grants to develop medications and
vaccines that they can then patent and sell
back to consumers at monopolistic prices.
The legislators who sponsor these grants
know that their campaigns will likely receive
reciprocal monetary benefit as a result. What is
worse, most American voters accept this sys-
tem happily because they believe that they are
simply helping to find cures for diseases. The
reality, however, is very different: by discourag-

ing the competition that leads to real progress,
this system of protectionism is actually a huge
impediment to the elimination of disease.
Questions 10–16 are based on the following passage.
The following passage was written by an
American essayist in 2003 about the status of
capitalism.
In response to a journalist’s question, “What
do you think about Western civilization?”
Mahatma Gandhi is said to have replied, “It
would be a good idea.” Any honest person
who values the concept of the free market,
who believes in the promise of open economic
competition, would say the same thing about
capitalism. We hear our politicians, and of
course the corporate news and entertainment
media, speaking as if the United States were a
model of free-market capitalism, as if anyone
could start a business to create and sell a
product or service without the obstruction of
the government. The truth is quite different.
Those we hear saying such things are quite
often voices that are bankrolled by large cor-
porations, which themselves are often pro-
tected from competition by mutual agreement
with the federal government.
The concept of free trade is simple: if
Company A can produce and distribute a prod-
uct more efficiently and at a higher quality than
Company B, it should be allowed to do so, and

to charge any price for it that free consumers
are willing to pay. Although Company B would
likely suffer as a result, humanity would benefit
from freer and cheaper access to high-quality
goods. Sometimes free trade works nicely, as
when Company A is in the United States and
Company B is in India. Then, agreements are
signed to “open up” India to the cheaper goods
made by Company A, even if doing so crushes
Company B because, we say, consumers have a
right to cheap, high-quality goods. But if Com-
pany A were in India and Company B were in
the United States, the story would likely be very
different.
Line
5
10
15
20
25
Line
5
10
15
20
25
30
35
40
45

50
55
60
65
70
75
80
85
606 MCGRAW-HILL’S SAT
10. The quotation from Mahatma Gandhi
(lines 3–4) suggests that Gandhi believed that
Western civilization was
(A) on the decline
(B) the beneficiary of unfair economic
practices
(C) antithetical to progress in Asia
(D) a great triumph
(E) an unrealized concept
11. The “voices” mentioned in line 16 can be in-
ferred to include all of the following EXCEPT
(A) American politicians
(B) leaders like Mahatma Gandhi
(C) television journalists
(D) some leaders of large corporations
(E) those who believe that the United States
is faithful to the capitalist ideal
12. The primary function of the second paragraph
(lines 20–37) is to
(A) illustrate a debate
(B) provide a statistical analysis

(C) explain a concept
(D) give historical background
(E) describe a popular viewpoint
13. By saying that “the story would likely be very dif-
ferent” (lines 36–37), the passage suggests that
(A) the rules of a free market are selectively
applied
(B) trade laws favor smaller countries
(C) American companies produce the best
products
(D) Asian countries are moving away from
the free market
(E) American companies share the same
interests as Indian companies
6 6 666 6
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14. The quotation marks around particular words in
the fourth paragraph (lines 55–65) serve pri-
marily to indicate that those words are
(A) being used ironically
(B) technical economic terms
(C) adaptations of foreign words
(D) recently coined
(E) direct quotations from a document
described earlier
15. The “triumph” described in line 63 is charac-
terized as
(A) a rare success for free markets
(B) a legislative victory
(C) a breakthrough in the development of

inexpensive drugs
(D) a tragic violation of the principle of free
trade
(E) a success that was based on luck
16. The passage suggests that the “entrepreneur”
(lines 68–69) differs from executives in the
pharmaceutical industry in that the entre-
preneur
(A) does not abide by free-market ideals
(B) risks his or her own money
(C) does not hire employees from overseas
(D) works more closely with representatives
in Washington
(E) needs less money to start a typical
business
CHAPTER 16 / PRACTICE TEST I 607
6 6 666 6
GO ON TO THE NEXT PAGE
Questions 17–24 are based on the following passage.
The following passage is an excerpt from Mary
Shelley’s Frankenstein, written in 1831.
Natural philosophy, and particularly chem-
istry, became nearly my sole occupation.
I read with ardor those works, so full of ge-
nius and discrimination, that modern inquir-
ers have written on these subjects. I attended
the lectures and cultivated the acquaintance
of the men of science of the university. In
M. Waldman I found a true friend. His gentle-
ness was never tinged by dogmatism, and his

instructions were given with an air of frank-
ness and good nature that banished every idea
of pedantry. In a thousand ways he smoothed
for me the path of knowledge and made the
most abstruse inquiries clear and facile to my
apprehension.
As I applied so closely, it may be easily
conceived that my progress was rapid. My
ardor was indeed the astonishment of the
students, and my proficiency that of the mas-
ters. None but those who have experienced
them can conceive of the enticements of sci-
ence. A mind of moderate capacity which
closely pursues one study must infallibly ar-
rive at great proficiency in that study; and I,
who continually sought the attainment of
one object of pursuit and was solely wrapped
up in this, improved so rapidly that at the
end of two years I made some discoveries in
the improvement of some chemical instru-
ments, which procured me great esteem and
admiration at the university. When I had
arrived at this point and had become as well
acquainted with the theory and practice of
natural philosophy as depended on the
lessons of any of the professors at Ingolstadt,
my residence there being no longer con-
ducive to my improvements, I thought of
returning to my friends and my native town,
when an incident happened that protracted

my stay.
Whence, I often asked myself, did the prin-
ciple of life proceed? It was a bold question,
and one which has never been considered as a
mystery; yet with how many things are we
upon the brink of becoming acquainted, if
cowardice or carelessness did not restrain our
inquiries. I revolved these circumstances in
my mind and determined thenceforth to apply
myself more particularly to those branches of
natural philosophy which relate to physiology.
Unless I had been animated by an almost su-
pernatural enthusiasm, my application to this
study would have been irksome and almost in-
tolerable. To examine the causes of life, we
must first have recourse to death. I became
acquainted with the science of anatomy, but
this was not sufficient; I must also observe the
natural decay and corruption of the human
body. In my education my father had taken
the greatest precautions that my mind should
be impressed with no supernatural horrors. I
do not ever remember to have trembled at a
tale of superstition or to have feared the ap-
parition of a spirit. Darkness had no effect
upon my fancy, and a churchyard was to me
merely the receptacle of bodies deprived of
life, which, from being the seat of beauty and
strength, had become food for the worm. I
saw how the fine form of man was degraded

and wasted; I beheld the corruption of death
succeed to the blooming cheek of life; I saw
how the worm inherited the wonders of the
eye and brain. I paused, examining and ana-
lyzing all the minutiae of causation, as exem-
plified in the change from life to death, and
death to life, until from the midst of this dark-
ness a sudden light broke in upon me—a light
so brilliant and wondrous, yet so simple, that
while I became dizzy with the immensity of
the prospect which it illustrated, I was sur-
prised that among so many men of genius
who had directed their inquiries towards the
same science, that I alone should be reserved
to discover so astonishing a secret.
Line
5
10
15
20
25
30
35
40
45
50
55
60
65
70

75
80
Excerpted from
Frankenstein
by Mary Shelley, public domain,
edited for length
608 MCGRAW-HILL’S SAT
17. In the first paragraph, the narrator indicates
that the instruction given to him by M. Wald-
man was
(A) haughty
(B) challenging
(C) easily understood
(D) obscure
(E) expensive
18. In line 15, the word “apprehension” most
nearly means
(A) fear
(B) reservation
(C) imprisonment
(D) understanding
(E) arrest
19. The narrator indicates that proficiency in an
academic study requires which of the follow-
ing?
I. genius
II. diligence
III. financial resources
(A) I only
(B) II only

(C) I and II only
(D) II and III only
(E) I, II, and III
20. The narrator indicates that he considered leav-
ing Ingolstadt because he
(A) had learned all he could from its instruc-
tors
(B) was acutely homesick
(C) was offered another job
(D) had a negative experience with a profes-
sor there
(E) had become ill
6 6 666 6
21. In saying that he was “animated by an almost
supernatural enthusiasm” (lines 51–52), the
narrator suggests that he
(A) was easily influenced by superstition
(B) loved lecturing at Ingolstadt
(C) was passionate about studying the physi-
ology of life and death
(D) was excited about the prospect of return-
ing home
(E) wanted to learn more about the origin of
certain superstitions
22. The “seat of beauty and strength” (lines 67–68) is
a reference to
(A) the churchyard
(B) the human body
(C) the worm
(D) the university at Ingolstadt

(E) the narrator’s studies
23. In line 71, the phrase “succeed to” most nearly
means
(A) inspire
(B) thrive
(C) replace
(D) proceed to
(E) promote
24. The final sentence of the passage suggests that
the narrator feels
(A) intimidated by the enormous task
before him
(B) grateful to those who instructed him
(C) anxious about the moral dilemma posed
by his work
(D) baffled by particular scientific
principles
(E) privileged to be on the verge of a mo-
mentous discovery
STOP
If you finish before time is called, you may
check your work on this section only. Do not
turn to any other section of the test.
CHAPTER 16 / PRACTICE TEST I 609
7 7 777 7
GO ON TO THE NEXT PAGE
1. Which of the following integers is 2 greater
than a multiple of 7?
(A) 14
(B) 15

(C) 16
(D) 17
(E) 18
2. A store sells oranges for 20 cents each, but for
every four oranges you buy, you may buy a
fifth for only 5 cents. How many oranges can
you buy from this store for $3.40?
(A) 14
(B) 17
(C) 18
(D) 19
(E) 20
3. If r is a positive number and s is a negative
number, all of the following must represent
positive numbers EXCEPT.
(A) −r + s
(B) r − s
(C)
(D) rs
2
(E) (rs)
2
r
s
2
SECTION 7
Time—20 minutes
16 questions
Turn to Section 7 of your answer sheet to answer the questions in this section.
Directions: For this section, solve each problem and decide which is the best of the choices

given. Fill in the corresponding circle on the answer sheet. You may use any available space for
scratchwork.
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide information useful in solv-
ing the problems. They are drawn as accurately as possible EXCEPT when it is stated in a spe-
cific problem that the figure is not drawn to scale. All figures lie in a plane unless otherwise
indicated.
4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real num-
bers x for which f(x) is a real number.
The number of degrees of arc in a circle is 360.
The sum of the measures in degrees of the angles of a triangle is 180.
Notes
Reference Information
r
A = πr
2
C=2πr
ᐉ
w
A =
ᐉw V = ᐉwh V = πr
2
h
Special right triangles
c
2
= a
2
+ b

2
A =
1
/
2
bh
h
b
ᐉ
w
h
r
h
b
c
a
2x
x
x
s
s
s
3
2
30°
60°
45°
45°