Junior
PSATTraining
Packet
2017-18
FrequentlyAskedQuestions
1.WhatisthePSAT/NMQST?
ThePreliminarySAT(PSAT)orTheNationalMeritQualifyingScholarshipTest
(NMSQT)isatestthathelpsyoupracticefortheSAT.ForJuniors,thetestenables
studentstoentertheNationalMeritScholarshipCorporation(NMSC)scholarship
program.
2.HowmanytimescanItakethetest?
YoucantakethePSATonceayearinOctoberasasophomoreandajunior.
3.WhatisthedifferencebetweentheSATandPSAT?
Thereareimportantdifferencesbetweenthetwoexams.First,thePSATisshorter
thantheSAT.Second,itdoesnotincludeanessayquestion.Third,thePSATdoesnot
testmorecomplextopicssuchasimaginarynumbersortrigonometry.
4.HowdoIregisterforthePSAT?
AllMittysophomoresandjuniorsareautomaticallyregisteredforthetest.Youwill
takethePSAT/NMQSTonWednesday,October11,2017.
5.CanIguessonthePSAT?
Yes.Thereisnopenaltyforwronganswers,sodonotleaveaPSATquestionblank!
6.DocollegescareaboutmyPSATscores?
PSATscoresareNEVERusedforcollegeadmissions.Ifyouwererecognizedasa
CommendedorNationalMeritScholar,youcanreporttherecognitiononyour
collegeapplications.
7.HowdoIgetmyscores?
PSATscoresandtestbookletswillbemailedtostudentsinJanuary2018.
PSAT%Reading%Test%
%
Time%Allotted%
Total%Questions%
%
%
Passage%Content%
U.S.%and%World%Literature%
60%minutes%(SAT%65)%
47%(SAT%52)%
%
%
%
1%passage;%9%questions%
History%and%Social%Studies%
2%passages,%or%1%passage%and%I%pair;%
9L10%questions%
Science%
2%passages,%or%1%passage%and%I%pair;%
9L10%questions%
Graphs%
1L2%Graphics%in%1%History/Social%Studies%and%in%1%
Science%passage%
Types%of%Questions%
Information%and%Ideas%
30%questions%est.%
Information%and%Ideas:%
Questions%Stems%
%
%
Determining%explicit%and%implicit%meaning%
Citing%textual%evidence%
Determining%central%ideas%and%themes%
Summarizing%
Understanding%relationships%
Interpreting%words%and%phrases%in%context%
%
What%choice%best%summarizes…%
The%narrator/author%indicates/implies/suggests…%
As%used%in%line%25,%“%%%“%most%nearly%means…%
It%can%be%inferred…%
Which%situation%is%most%similar…%
It%is%reasonable%to%conclude…%
Based%on%the%passage…%
The%author’s%main%point…%
Note:%
The%following%question%stem%will%often%follow%any%
one%of%the%above%stems,%creating%a%double%threat:%
%
What%choice%provides%the%best%evidence%to%the%previous%
question?%
%
There%will%usually%be%two%of%the%above%stem%
questions%per%passage.%
3
Analyzing%word%choice%
Analyzing%text%structure%
Analyzing%point%of%view%
Analyzing%purpose%
Analyzing%arguments%
%
The%main%purpose%of%the%passage…%
The%reference%to%the%……%primarily%serves%to……%
The%passage%primarily%serves%to%…%
The%author%recognizes%counterarguments…by…%
What%main%effects%do%the….have%on%the%tone…%
What%choice%best%describes%the%structure%of%the%
….paragraph?%
The%author%uses….as%examples%of…%
%
%
Rhetoric%
10%questions%est.%
Rhetoric%
Questions%stems%
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Synthesis%
7%questions%est.%
%
Analyzing%multiple%texts%
Analyzing%quantitative%information%(tables,%charts,%
graphs)%
%
Which%statement%best%summarizes%the%information%
presented%in%the%graph/table/chart.%
%
According%the%graph,%which%statement….%
What%information%discussed%in%…%is%represented%by%the%
graph?%
What%choice%best%states%the%relationship%between%the%
two%passages?%
How%would%Author%1%respond%to%Author%2?%
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Synthesis%
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4
Reading Comprehension Strategies
• Read the passage carefully and thoroughly.
• Do not read the questions first and then try to search out the answer.
• When you are ready to answer the questions, do not use outside knowledge.
Only use information located in the passage, and eliminate any answers that
cannot be directly supported by the text.
• For charts, graphs, and tables, note the title, how the axes are labeled, and any
correlations
• If you are unfamiliar with a vocabulary word, use the context of the reading and
root words or suffixes to make an educated guess.
• As you read, underline/highlight key points (see below)
o The actual information presented. Question stems:
Based on the passage……
The author’s main point…..
The narrator/author indicates/implies/suggests……..
It is reasonable to conclude...
o How the information is presented- written, tables, graphs. Question
stems:
According to the graph, which statement………
What information discussed in…… is presented by the graph?
How would Author 1 respond to Author 2?
o Primary purpose of the passage. Question stems:
The main purpose of the passage…
The author uses...as examples of…
•
The redesigned SAT uses follow-up questions. These questions require you to
identify the precise text selection that supports your answer to the previous
problem. In other words, you will be expected to provide evidence that supports
your claims.
5
U.S/%World%Literature%
%
%
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6
1
1
L1
Reading Test
65 M I NU TES, 5 2 QUESTIONS
Turn to Section 1 of your answer sheet to answer the questions in this section.
DIRECTIONS
Each passage or pair of passages below is followed by a number of questions. After reading
each passage or pair, choose the best answer to each question based on what is stated or
implied in the passage or passages and in any accompanying graphics (such as a table or
graph).
This passage is adapted from Saki, “The
Schartz-Metterklume Method.” Originally published in 1911.
Line
5
10
15
20
25
Lady Carlotta stepped out on to the platform of
the small wayside station and took a turn or two up
and down its uninteresting length, to kill time till the
train should be pleased to proceed on its way. Then,
in the roadway beyond, she saw a horse struggling
with a more than ample load, and a carter of the sort
that seems to bear a sullen hatred against the animal
that helps him to earn a living. Lady Carlotta
promptly betook her to the roadway, and put rather a
different complexion on the struggle. Certain of her
acquaintances were wont to give her plentiful
admonition as to the undesirability of interfering on
behalf of a distressed animal, such interference being
“none of her business.” Only once had she put the
doctrine of non-interference into practice, when one
of its most eloquent exponents had been besieged for
nearly three hours in a small and extremely
uncomfortable may-tree by an angry boar-pig, while
Lady Carlotta, on the other side of the fence, had
proceeded with the water-colour sketch she was
engaged on, and refused to interfere between the
boar and his prisoner. It is to be feared that she lost
the friendship of the ultimately rescued lady. On this
occasion she merely lost the train, which gave way to
the first sign of impatience it had shown throughout
the journey, and steamed off without her. She bore
the desertion with philosophical indifference; her
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Questions 1-10 are based on the following
passage.
30
35
40
45
50
55
2 7
friends and relations were thoroughly well used to
the fact of her luggage arriving without her.
She wired a vague non-committal message to her
destination to say that she was coming on “by
another train.” Before she had time to think what her
next move might be she was confronted by an
imposingly attired lady, who seemed to be taking a
prolonged mental inventory of her clothes and looks.
“You must be Miss Hope, the governess I’ve come
to meet,” said the apparition, in a tone that admitted
of very little argument.
“Very well, if I must I must,” said Lady Carlotta to
herself with dangerous meekness.
“I am Mrs. Quabarl,” continued the lady; “and
where, pray, is your luggage?”
“It’s gone astray,” said the alleged governess,
falling in with the excellent rule of life that the absent
are always to blame; the luggage had, in point of fact,
behaved with perfect correctitude. “I’ve just
telegraphed about it,” she added, with a nearer
approach to truth.
“How provoking,” said Mrs. Quabarl; “these
railway companies are so careless. However, my
maid can lend you things for the night,” and she led
the way to her car.
During the drive to the Quabarl mansion
Lady Carlotta was impressively introduced to the
nature of the charge that had been thrust upon her;
she learned that Claude and Wilfrid were delicate,
sensitive young people, that Irene had the artistic
temperament highly developed, and that Viola was
CO NTI N U E
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something or other else of a mould equally
commonplace among children of that class and type
in the twentieth century.
“I wish them not only to be TAUGHT,” said Mrs.
Quabarl, “but INTERESTED in what they learn. In
their history lessons, for instance, you must try to
make them feel that they are being introduced to the
life-stories of men and women who really lived, not
merely committing a mass of names and dates to
memory. French, of course, I shall expect you to talk
at meal-times several days in the week.”
“I shall talk French four days of the week and
Russian in the remaining three.”
“Russian? My dear Miss Hope, no one in the
house speaks or understands Russian.”
“That will not embarrass me in the least,” said
Lady Carlotta coldly.
Mrs. Quabarl, to use a colloquial expression, was
knocked off her perch. She was one of those
imperfectly self-assured individuals who are
magnificent and autocratic as long as they are not
seriously opposed. The least show of unexpected
resistance goes a long way towards rendering them
cowed and apologetic. When the new governess
failed to express wondering admiration of the large
newly-purchased and expensive car, and lightly
alluded to the superior advantages of one or two
makes which had just been put on the market, the
discomfiture of her patroness became almost abject.
Her feelings were those which might have animated a
general of ancient warfaring days, on beholding his
heaviest battle-elephant ignominiously driven off the
field by slingers and javelin throwers.
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60
1
L1
3 8
1
Which choice best summarizes the passage?
A) A woman weighs the positive and negative
aspects of accepting a new job.
B) A woman does not correct a stranger who
mistakes her for someone else.
C) A woman impersonates someone else to seek
revenge on an acquaintance.
D) A woman takes an immediate dislike to her new
employer.
2
In line 2, “turn” most nearly means
A) slight movement.
B) change in rotation.
C) short walk.
D) course correction.
3
The passage most clearly implies that other people
regarded Lady Carlotta as
A) outspoken.
B) tactful.
C) ambitious.
D) unfriendly.
4
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 10-14 (“Certain . . . business”)
B) Lines 22-23 (“It is . . . lady”)
C) Lines 23-26 (“On this . . . her”)
D) Lines 30-32 (“She . . . train”)
CO NTI N U E
1
The description of how Lady Carlotta “put the
doctrine of non-interference into practice”
(lines 14-15) mainly serves to
A) foreshadow her capacity for deception.
B) illustrate the subtle cruelty in her nature.
C) provide a humorous insight into her character.
D) explain a surprising change in her behavior.
6
In line 55, “charge” most nearly means
A) responsibility.
B) attack.
C) fee.
D) expense.
7
The narrator indicates that Claude, Wilfrid, Irene,
and Viola are
B) unusually creative and intelligent.
C) hostile to the idea of a governess.
D) more educated than others of their age.
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5
A) similar to many of their peers.
1
L1
8
The narrator implies that Mrs. Quabarl favors a form
of education that emphasizes
A) traditional values.
B) active engagement.
C) artistic experimentation.
D) factual retention.
9
As presented in the passage, Mrs. Quabarl is best
described as
A) superficially kind but actually selfish.
B) outwardly imposing but easily defied.
C) socially successful but irrationally bitter.
D) naturally generous but frequently imprudent.
10
4 9
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 49-50 (“How . . . careless”)
B) Lines 62-68 (“I wish . . . memory”)
C) Lines 70-73 (“I shall . . . Russian”)
D) Lines 77-82 (“She was . . . apologetic”)
CO NTI N U E
History%and%%
Social%Studies%
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10
1
As used in line 61, “document” most nearly means
A) portray.
B) record.
C) publish.
D) process.
29
What can reasonably be inferred about gliding
animals from the passage?
A) Their young tend to hop along beside their
parents instead of flying beside them.
B) Their method of locomotion is similar to that of
ground birds.
C) They use the ground for feeding more often than
for perching.
30
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 4-6 (“They jumped . . . air”)
B) Lines 28-29 (“They really . . . traveling”)
C) Lines 57-59 (“The birds . . . slopes”)
D) Lines 72-74 (“something . . . theory”)
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28
D) They do not use a flapping stroke to aid in
climbing slopes.
1
H1
Questions 31-41 are based on the following
passages.
Passage 1 is adapted from Talleyrand et al., Report on Public
Instruction. Originally published in 1791. Passage 2 is
adapted from Mary Wollstonecraft, A Vindication of the
Rights of Woman. Originally published in 1792. Talleyrand
was a French diplomat; the Report was a plan for national
education. Wollstonecraft, a British novelist and political
writer, wrote Vindication in response to Talleyrand.
Passage 1
Line
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10 11
That half the human race is excluded by the other
half from any participation in government; that they
are native by birth but foreign by law in the very land
where they were born; and that they are
property-owners yet have no direct influence or
representation: are all political phenomena
apparently impossible to explain on abstract
principle. But on another level of ideas, the question
changes and may be easily resolved. The purpose of
all these institutions must be the happiness of the
greatest number. Everything that leads us farther
from this purpose is in error; everything that brings
us closer is truth. If the exclusion from public
employments decreed against women leads to a
greater sum of mutual happiness for the two sexes,
then this becomes a law that all Societies have been
compelled to acknowledge and sanction.
Any other ambition would be a reversal of our
primary destinies; and it will never be in women’s
interest to change the assignment they have received.
It seems to us incontestable that our common
happiness, above all that of women, requires that
they never aspire to the exercise of political rights
and functions. Here we must seek their interests in
the wishes of nature. Is it not apparent, that their
delicate constitutions, their peaceful inclinations, and
the many duties of motherhood, set them apart from
strenuous habits and onerous duties, and summon
them to gentle occupations and the cares of the
home? And is it not evident that the great conserving
principle of Societies, which makes the division of
powers a source of harmony, has been expressed and
revealed by nature itself, when it divided the
functions of the two sexes in so obviously distinct a
manner? This is sufficient; we need not invoke
principles that are inapplicable to the question. Let us
not make rivals of life’s companions. You must, you
truly must allow the persistence of a union that no
interest, no rivalry, can possibly undo. Understand
that the good of all demands this of you.
CO NTI N U E
1
45
50
55
60
65
70
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80
85
Contending for the rights of woman, my main
argument is built on this simple principle, that if she
be not prepared by education to become the
companion of man, she will stop the progress of
knowledge and virtue; for truth must be common to
all, or it will be inefficacious with respect to its
influence on general practice. And how can woman
be expected to co-operate unless she know why she
ought to be virtuous? unless freedom strengthen her
reason till she comprehend her duty, and see in what
manner it is connected with her real good? If
children are to be educated to understand the true
principle of patriotism, their mother must be a
patriot; and the love of mankind, from which an
orderly train of virtues spring, can only be produced
by considering the moral and civil interest of
mankind; but the education and situation of woman,
at present, shuts her out from such investigations. . . .
Consider, sir, dispassionately, these
observations—for a glimpse of this truth seemed to
open before you when you observed, “that to see one
half of the human race excluded by the other from all
participation of government, was a political
phenomenon that, according to abstract principles, it
was impossible to explain.” If so, on what does your
constitution rest? If the abstract rights of man will
bear discussion and explanation, those of woman, by
a parity of reasoning, will not shrink from the same
test: though a different opinion prevails in this
country, built on the very arguments which you use
to justify the oppression of woman—prescription.
Consider—I address you as a legislator—
whether, when men contend for their freedom, and
to be allowed to judge for themselves respecting their
own happiness, it be not inconsistent and unjust to
subjugate women, even though you firmly believe
that you are acting in the manner best calculated to
promote their happiness? Who made man the
exclusive judge, if woman partake with him the gift
of reason?
In this style, argue tyrants of every
denomination, from the weak king to the weak
father of a family; they are all eager to crush reason;
yet always assert that they usurp its throne only to be
useful. Do you not act a similar part, when you force
all women, by denying them civil and political rights,
to remain immured in their families groping in
the dark?
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Passage 2
1
H1
11 12
31
As used in line 21, “common” most nearly means
A) average.
B) shared.
C) coarse.
D) similar.
32
It can be inferred that the authors of Passage 1
believe that running a household and raising
children
A) are rewarding for men as well as for women.
B) yield less value for society than do the roles
performed by men.
C) entail very few activities that are difficult or
unpleasant.
D) require skills similar to those needed to run a
country or a business.
33
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 4-6 (“they are . . . representation”)
B) Lines 13-17 (“If the . . . sanction”)
C) Lines 25-30 (“Is it . . . home”)
D) Lines 30-35 (“And . . . manner”)
34
According to the author of Passage 2, in order for
society to progress, women must
A) enjoy personal happiness and financial security.
B) follow all currently prescribed social rules.
C) replace men as figures of power and authority.
D) receive an education comparable to that of men.
CO NTI N U E
1
As used in line 50, “reason” most nearly means
A) motive.
B) sanity.
C) intellect.
D) explanation.
36
In Passage 2, the author claims that freedoms granted
by society’s leaders have
A) privileged one gender over the other.
B) resulted in a general reduction in individual
virtue.
C) caused arguments about the nature of happiness.
D) ensured equality for all people.
37
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 41-45 (“Contending . . . virtue”)
B) Lines 45-47 (“truth . . . practice”)
C) Lines 65-66 (“If so . . . rest”)
D) Lines 72-75 (“Consider . . . happiness”)
38
In lines 61-65, the author of Passage 2 refers to a
statement made in Passage 1 in order to
A) call into question the qualifications of the
authors of Passage 1 regarding gender issues.
B) dispute the assertion made about women in the
first sentence of Passage 1.
C) develop her argument by highlighting what she
sees as flawed reasoning in Passage 1.
D) validate the concluding declarations made by the
authors of Passage 1 about gender roles.
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35
H1
1
39
Which best describes the overall relationship
between Passage 1 and Passage 2?
A) Passage 2 strongly challenges the point of view in
Passage 1.
B) Passage 2 draws alternative conclusions from the
evidence presented in Passage 1.
C) Passage 2 elaborates on the proposal presented
in Passage 1.
D) Passage 2 restates in different terms the
argument presented in Passage 1.
40
The authors of both passages would most likely agree
with which of the following statements about women
in the eighteenth century?
A) Their natural preferences were the same as those
of men.
B) They needed a good education to be successful in
society.
C) They were just as happy in life as men were.
D) They generally enjoyed fewer rights than
men did.
41
12 13
How would the authors of Passage 1 most likely
respond to the points made in the final paragraph of
Passage 2?
A) Women are not naturally suited for the exercise
of civil and political rights.
B) Men and women possess similar degrees of
reasoning ability.
C) Women do not need to remain confined to their
traditional family duties.
D) The principles of natural law should not be
invoked when considering gender roles.
CO NTI N U E
1
This passage is adapted from Taras Grescoe, Straphanger:
Saving Our Cities and Ourselves from the Automobile. ©2012
by Taras Grescoe.
5
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20
25
30
35
40
45
Though there are 600 million cars on the planet,
and counting, there are also seven billion people,
which means that for the vast majority of us getting
around involves taking buses, ferryboats, commuter
trains, streetcars, and subways. In other words,
traveling to work, school, or the market means being
a straphanger: somebody who, by choice or necessity,
relies on public transport, rather than a privately
owned automobile.
Half the population of New York, Toronto, and
London do not own cars. Public transport is how
most of the people of Asia and Africa, the world’s
most populous continents, travel. Every day, subway
systems carry 155 million passengers, thirty-four
times the number carried by all the world’s airplanes,
and the global public transport market is now valued
at $428 billion annually. A century and a half after
the invention of the internal combustion engine,
private car ownership is still an anomaly.
And yet public transportation, in many minds, is
the opposite of glamour—a squalid last resort for
those with one too many impaired driving charges,
too poor to afford insurance, or too decrepit to get
behind the wheel of a car. In much of North
America, they are right: taking transit is a depressing
experience. Anybody who has waited far too long on
a street corner for the privilege of boarding a
lurching, overcrowded bus, or wrestled luggage onto
subways and shuttles to get to a big city airport,
knows that transit on this continent tends to be
underfunded, ill-maintained, and ill-planned. Given
the opportunity, who wouldn’t drive? Hopping in a
car almost always gets you to your destination more
quickly.
It doesn’t have to be like this. Done right, public
transport can be faster, more comfortable, and
cheaper than the private automobile. In Shanghai,
German-made magnetic levitation trains skim over
elevated tracks at 266 miles an hour, whisking people
to the airport at a third of the speed of sound. In
provincial French towns, electric-powered streetcars
run silently on rubber tires, sliding through narrow
streets along a single guide rail set into cobblestones.
From Spain to Sweden, Wi-Fi equipped high-speed
trains seamlessly connect with highly ramified metro
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Questions 11-20 are based on the following
passage and supplementary material.
Line
1
H2
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85
networks, allowing commuters to work on laptops as
they prepare for same-day meetings in once distant
capital cities. In Latin America, China, and India,
working people board fast-loading buses that move
like subway trains along dedicated busways, leaving
the sedans and SUVs of the rich mired in
dawn-to-dusk traffic jams. And some cities have
transformed their streets into cycle-path freeways,
making giant strides in public health and safety and
the sheer livability of their neighborhoods—in the
process turning the workaday bicycle into a viable
form of mass transit.
If you credit the demographers, this transit trend
has legs. The “Millenials,” who reached adulthood
around the turn of the century and now outnumber
baby boomers, tend to favor cities over suburbs, and
are far more willing than their parents to ride buses
and subways. Part of the reason is their ease with
iPads, MP3 players, Kindles, and smartphones: you
can get some serious texting done when you’re not
driving, and earbuds offer effective insulation from
all but the most extreme commuting annoyances.
Even though there are more teenagers in the country
than ever, only ten million have a driver’s license
(versus twelve million a generation ago). Baby
boomers may have been raised in Leave It to Beaver
suburbs, but as they retire, a significant contingent is
favoring older cities and compact towns where they
have the option of walking and riding bikes. Seniors,
too, are more likely to use transit, and by 2025, there
will be 64 million Americans over the age of
sixty-five. Already, dwellings in older neighborhoods
in Washington, D.C., Atlanta, and Denver, especially
those near light-rail or subway stations, are
commanding enormous price premiums over
suburban homes. The experience of European and
Asian cities shows that if you make buses, subways,
and trains convenient, comfortable, fast, and safe, a
surprisingly large percentage of citizens will opt to
ride rather than drive.
CO NTI N U E
1
1
H2
Primary Occupation of Public
Transportation Passengers
in US Cities
unemployed
6.4%
employed
outside
the home
72%
student
10.7%
6.7%
homemaker
2.0%
retired
other
2.2%
Figure 2
Purpose of Public Transportation
Trips in US Cities
other
personal
5.7%
business
medical/dental
3.0%
shopping/dining
social
6.3%
8.5%
6.8%
work
59.1%
10.6%
school
Figure 1 and figure 2 are adapted from the American Public
Transportation Association, “A·Profile of Public Transportation
Passenger Demographics and Travel Characteristics Reported in
On-Board Surveys.” ©2007 by American Public Transportation
Association.
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Figure 1
11
What function does the third paragraph (lines 20-34)
serve in the passage as a whole?
A) It acknowledges that a practice favored by the
author of the passage has some limitations.
B) It illustrates with detail the arguments made in
the first two paragraphs of the passage.
C) It gives an overview of a problem that has not
been sufficiently addressed by the experts
mentioned in the passage.
D) It advocates for abandoning a practice for which
the passage as a whole provides mostly
favorable data.
12
Which choice does the author explicitly cite as
an advantage of automobile travel in North America?
A) Environmental impact
B) Convenience
C) Speed
D) Cost
13
6 15
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 5-9 (“In . . . automobile”)
B) Lines 20-24 (“And . . . car”)
C) Lines 24-26 (“In . . . experience”)
D) Lines 32-34 (“Hopping . . . quickly”)
CO NTI N U E
1
The central idea of the fourth paragraph (lines 35-57)
is that
A) European countries excel at public
transportation.
B) some public transportation systems are superior
to travel by private automobile.
D) much international public transportation is
engineered for passengers to work while on
board.
15
Which choice provides the best evidence for the
answer to the previous question?
A) Line 35 (“It . . . this”)
B) Lines 35-37 (“Done . . . automobile”)
C) Lines 37-40 (“In . . . sound”)
D) Lines 44-48 (“From . . . cities”)
16
As used in line 58, “credit” most nearly means
A) endow.
B) attribute.
C) believe.
D) honor.
17
As used in line 61, “favor” most nearly means
A) indulge.
B) prefer.
C) resemble.
D) serve.
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...............................................................................................................................................................................................................................................................................................................
14
C) Americans should mimic foreign public
transportation systems when possible.
1
H2
7 16
18
Which choice best supports the conclusion that
public transportation is compatible with the use of
personal electronic devices?
A) Lines 59-63 (“The . . . subways”)
B) Lines 63-67 (“Part . . . annoyances”)
C) Lines 68-70 (“Even . . . ago”)
D) Lines 77-81 (“Already . . . homes”)
19
Which choice is supported by the data in the
first figure?
A) The number of students using public
transportation is greater than the number of
retirees using public transportation.
B) The number of employed people using public
transportation and the number of unemployed
people using public transportation is roughly
the same.
C) People employed outside the home are less likely
to use public transportation than are
homemakers.
D) Unemployed people use public transportation
less often than do people employed outside the
home.
20
Taken together, the two figures suggest that most
people who use public transportation
A) are employed outside the home and take public
transportation to work.
B) are employed outside the home but take public
transportation primarily in order to run errands.
C) use public transportation during the week but
use their private cars on weekends.
D) use public transportation only until they are able
to afford to buy a car.
CO NTI N U E
Science%
%
%
%
17
1
This passage is adapted from Geoffrey Giller, “Long a
Mystery, How 500-Meter-High Undersea Waves Form Is
Revealed.” ©2014 by Scientific American.
Line
5
10
15
20
25
30
35
40
Some of the largest ocean waves in the world are
nearly impossible to see. Unlike other large waves,
these rollers, called internal waves, do not ride the
ocean surface. Instead, they move underwater,
undetectable without the use of satellite imagery or
sophisticated monitoring equipment. Despite their
hidden nature, internal waves are fundamental parts
of ocean water dynamics, transferring heat to the
ocean depths and bringing up cold water from below.
And they can reach staggering heights—some as tall
as skyscrapers.
Because these waves are involved in ocean mixing
and thus the transfer of heat, understanding them is
crucial to global climate modeling, says Tom
Peacock, a researcher at the Massachusetts Institute
of Technology. Most models fail to take internal
waves into account. “If we want to have more and
more accurate climate models, we have to be able to
capture processes such as this,” Peacock says.
Peacock and his colleagues tried to do just that.
Their study, published in November in Geophysical
Research Letters, focused on internal waves generated
in the Luzon Strait, which separates Taiwan and the
Philippines. Internal waves in this region, thought to
be some of the largest in the world, can reach about
500 meters high. “That’s the same height as the
Freedom Tower that’s just been built in New York,”
Peacock says.
Although scientists knew of this phenomenon in
the South China Sea and beyond, they didn’t know
exactly how internal waves formed. To find out,
Peacock and a team of researchers from M.I.T. and
Woods Hole Oceanographic Institution worked with
France’s National Center for Scientific Research
using a giant facility there called the Coriolis
Platform. The rotating platform, about 15 meters
(49.2 feet) in diameter, turns at variable speeds and
can simulate Earth’s rotation. It also has walls, which
means scientists can fill it with water and create
accurate, large-scale simulations of various
oceanographic scenarios.
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...............................................................................................................................................................................................................................................................................................................
Questions 43-52 are based on the following
passage and supplementary material.
S1
45
50
55
60
65
70
75
14 18
1
Peacock and his team built a carbon-fiber resin
scale model of the Luzon Strait, including the islands
and surrounding ocean floor topography. Then they
filled the platform with water of varying salinity to
replicate the different densities found at the strait,
with denser, saltier water below and lighter, less
briny water above. Small particles were added to the
solution and illuminated with lights from below in
order to track how the liquid moved. Finally, they
re-created tides using two large plungers to see how
the internal waves themselves formed.
The Luzon Strait’s underwater topography, with a
distinct double-ridge shape, turns out to be
responsible for generating the underwater waves.
As the tide rises and falls and water moves through
the strait, colder, denser water is pushed up over the
ridges into warmer, less dense layers above it.
This action results in bumps of colder water trailed
by warmer water that generate an internal wave.
As these waves move toward land, they become
steeper—much the same way waves at the beach
become taller before they hit the shore—until they
break on a continental shelf.
The researchers were also able to devise a
mathematical model that describes the movement
and formation of these waves. Whereas the model is
specific to the Luzon Strait, it can still help
researchers understand how internal waves are
generated in other places around the world.
Eventually, this information will be incorporated into
global climate models, making them more accurate.
“It’s very clear, within the context of these [global
climate] models, that internal waves play a role in
driving ocean circulations,” Peacock says.
CO NTI N U E
1
1
S1
CHANGES IN DEPTH OF ISOTHERMS*
IN AN INTERNAL WAVE OVER A 24-HOUR PERIOD
0:
00
1:
12
2:
24
3:
36
4:
48
6:
00
7:
12
8:
24
9:
36
10
:4
12 8
:0
13 0
:1
14 2
:2
15 4
:3
16 6
:4
18 8
:0
19 0
:1
20 2
:2
21 4
:3
22 6
:4
24 8
:0
0
Time (hours)
Depth Below
Surface (meters)
0
40
80
120
160
13°C
11°C
10°C
9°C
* Bands of water of constant temperatures
Adapted from Justin Small et al., “Internal Solitons in the Ocean: Prediction from SAR.” ©1998 by Oceanography, Defence Evaluation and Research Agency.
The first paragraph serves mainly to
A) explain how a scientific device is used.
B) note a common misconception about an event.
C) describe a natural phenomenon and address its
importance.
D) present a recent study and summarize its
findings.
44
As used in line 19, “capture” is closest in meaning to
A) control.
B) record.
C) secure.
D) absorb.
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43
15 19
45
According to Peacock, the ability to monitor internal
waves is significant primarily because
A) it will allow scientists to verify the maximum
height of such waves.
B) it will allow researchers to shift their focus to
improving the quality of satellite images.
C) the study of wave patterns will enable regions to
predict and prevent coastal damage.
D) the study of such waves will inform the
development of key scientific models.
46
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 1-2 (“Some . . . see”)
B) Lines 4-6 (“they . . . equipment”)
C) Lines 17-19 (“If . . . this”)
D) Lines 24-26 (“Internal . . . high”)
CO NTI N U E
1
As used in line 65, “devise” most nearly means
A) create.
B) solve.
C) imagine.
D) begin.
48
Based on information in the passage, it can
reasonably be inferred that all internal waves
A) reach approximately the same height even
though the locations and depths of continental
shelves vary.
B) may be caused by similar factors but are
influenced by the distinct topographies of
different regions.
C) can be traced to inconsistencies in the tidal
patterns of deep ocean water located near
islands.
D) are generated by the movement of dense water
over a relatively flat section of the ocean floor.
49
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 29-31 (“Although . . . formed”)
B) Lines 56-58 (“As the . . . it”)
C) Lines 61-64 (“As these . . . shelf”)
D) Lines 67-70 (“Whereas . . . world”)
.....................................................................................................................................................................................................................................................
47
1
S1
50
In the graph, which isotherm displays an increase in
depth below the surface during the period 19:12 to
20:24?
A)
9°C
B) 10°C
C) 11°C
D) 13°C
51
Which concept is supported by the passage and by
the information in the graph?
A) Internal waves cause water of varying salinity
to mix.
B) Internal waves push denser water above layers of
less dense water.
C) Internal waves push bands of cold water above
bands of warmer water.
D) Internal waves do not rise to break the ocean’s
surface.
52
How does the graph support the author’s point that
internal waves affect ocean water dynamics?
A) It demonstrates that wave movement forces
warmer water down to depths that typically are
colder.
B) It reveals the degree to which an internal wave
affects the density of deep layers of cold water.
C) It illustrates the change in surface temperature
that takes place during an isolated series of deep
waves.
D) It shows that multiple waves rising near the
surface of the ocean disrupt the flow of normal
tides.
STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
Unauthorized copying or reuse of any part of this page is illegal.
16 20
1
Data in the graph provide most direct support for
which idea in the passage?
A) Acting on empathy can be counterproductive.
B) Ethical economics is defined by character.
C) Ethical economics is still possible.
D) People fear losses more than they hope for gains.
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21
1
S2
Questions 22-32 are based on the following
passages.
Passage 1 is adapted from Nicholas Carr, “Author
Nicholas Carr: The Web Shatters Focus, Rewires Brains.”
©2010 by Condé Nast. Passage 2 is from Steven Pinker,
“Mind over Mass Media.” ©2010 by The New York Times
Company.
Passage 1
Line
5
10
15
20
25
30
35
40
8 21
The mental consequences of our online
info-crunching are not universally bad.
Certain cognitive skills are strengthened by our use
of computers and the Net. These tend to involve
more primitive mental functions, such as hand-eye
coordination, reflex response, and the processing of
visual cues. One much-cited study of video gaming
revealed that after just 10 days of playing action
games on computers, a group of young people had
significantly boosted the speed with which they could
shift their visual focus between various images and
tasks.
It’s likely that Web browsing also strengthens
brain functions related to fast-paced problem
solving, particularly when it requires spotting
patterns in a welter of data. A British study of the
way women search for medical information online
indicated that an experienced Internet user can, at
least in some cases, assess the trustworthiness and
probable value of a Web page in a matter of seconds.
The more we practice surfing and scanning, the more
adept our brain becomes at those tasks.
But it would be a serious mistake to look narrowly
at such benefits and conclude that the Web is making
us smarter. In a Science article published in early
2009, prominent developmental psychologist Patricia
Greenfield reviewed more than 40 studies of the
effects of various types of media on intelligence and
learning ability. She concluded that “every medium
develops some cognitive skills at the expense of
others.” Our growing use of the Net and other
screen-based technologies, she wrote, has led to the
“widespread and sophisticated development of
visual-spatial skills.” But those gains go hand in hand
with a weakening of our capacity for the kind of
“deep processing” that underpins “mindful
knowledge acquisition, inductive analysis, critical
thinking, imagination, and reflection.”
We know that the human brain is highly
plastic; neurons and synapses change as
circumstances change. When we adapt to a new
cultural phenomenon, including the use of a new
CO NTI N U E
1
50
medium, we end up with a different brain, says
Michael Merzenich, a pioneer of the field of
neuroplasticity. That means our online habits
continue to reverberate in the workings of our brain
cells even when we’re not at a computer. We’re
exercising the neural circuits devoted to skimming
and multitasking while ignoring those used for
reading and thinking deeply.
Passage 2
55
60
65
70
75
80
85
90
Critics of new media sometimes use science itself
to press their case, citing research that shows how
“experience can change the brain.” But cognitive
neuroscientists roll their eyes at such talk. Yes, every
time we learn a fact or skill the wiring of the brain
changes; it’s not as if the information is stored in the
pancreas. But the existence of neural plasticity does
not mean the brain is a blob of clay pounded into
shape by experience.
Experience does not revamp the basic
information-processing capacities of the brain.
Speed-reading programs have long claimed to do just
that, but the verdict was rendered by Woody Allen
after he read Leo Tolstoy’s famously long novel
War and Peace in one sitting: “It was about Russia.”
Genuine multitasking, too, has been exposed as a
myth, not just by laboratory studies but by the
familiar sight of an SUV undulating between lanes as
the driver cuts deals on his cell phone.
Moreover, the effects of experience are highly
specific to the experiences themselves. If you train
people to do one thing (recognize shapes, solve math
puzzles, find hidden words), they get better at doing
that thing, but almost nothing else. Music doesn’t
make you better at math, conjugating Latin doesn’t
make you more logical, brain-training games don’t
make you smarter. Accomplished people don’t bulk
up their brains with intellectual calisthenics; they
immerse themselves in their fields. Novelists read
lots of novels, scientists read lots of science.
The effects of consuming electronic media are
likely to be far more limited than the panic implies.
Media critics write as if the brain takes on the
qualities of whatever it consumes, the informational
equivalent of “you are what you eat.” As with ancient
peoples who believed that eating fierce animals made
them fierce, they assume that watching quick cuts in
rock videos turns your mental life into quick cuts or
that reading bullet points and online postings turns
your thoughts into bullet points and online postings.
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45
1
S2
9 22
22
The author of Passage 1 indicates which of the
following about the use of screen-based technologies?
A) It should be thoroughly studied.
B) It makes the brain increasingly rigid.
C) It has some positive effects.
D) It should be widely encouraged.
23
Which choice provides the best evidence for the
answer to the previous question?
A) Lines 3-4 (“Certain . . . Net”)
B) Lines 23-25 (“But . . . smarter”)
C) Lines 25-29 (“In a . . . ability”)
D) Lines 29-31 (“She . . . others”)
24
The author of Passage 1 indicates that becoming
adept at using the Internet can
A) make people complacent about their health.
B) undermine the ability to think deeply.
C) increase people’s social contacts.
D) improve people’s self-confidence.
25
As used in line 40, “plastic” most nearly means
A) creative.
B) artificial.
C) malleable.
D) sculptural.
CO NTI N U E
1
The author of Passage 2 refers to the novel
War and Peace primarily to suggest that
Woody Allen
A) did not like Tolstoy’s writing style.
B) could not comprehend the novel by
speed-reading it.
C) had become quite skilled at multitasking.
D) regretted having read such a long novel.
27
According to the author of Passage 2, what do
novelists and scientists have in common?
A) They take risks when they pursue knowledge.
B) They are eager to improve their minds.
C) They are curious about other subjects.
D) They become absorbed in their own fields.
28
The analogy in the final sentence of Passage 2 has
primarily which effect?
A) It uses ornate language to illustrate a difficult
concept.
B) It employs humor to soften a severe opinion of
human behavior.
C) It alludes to the past to evoke a nostalgic
response.
D) It criticizes the view of a particular group.
29
The main purpose of each passage is to
A) compare brain function in those who play games
on the Internet and those who browse on it.
B) report on the problem-solving skills of
individuals with varying levels of Internet
experience.
C) take a position on increasing financial support
for studies related to technology and intelligence.
D) make an argument about the effects of electronic
media use on the brain.
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...............................................................................................................................................................................................................................................................................................................
26
1
S2
30
Which choice best describes the relationship between
the two passages?
A) Passage 2 relates first-hand experiences that
contrast with the clinical approach in Passage 1.
B) Passage 2 critiques the conclusions drawn from
the research discussed in Passage 1.
C) Passage 2 takes a high-level view of a result that
Passage 1 examines in depth.
D) Passage 2 predicts the negative reactions that the
findings discussed in Passage 1 might produce.
31
On which of the following points would the authors
of both passages most likely agree?
A) Computer-savvy children tend to demonstrate
better hand-eye coordination than do their
parents.
B) Those who criticize consumers of electronic
media tend to overreact in their criticism.
C) Improved visual-spatial skills do not generalize
to improved skills in other areas.
D) Internet users are unlikely to prefer reading
onscreen text to reading actual books.
32
10 23
Which choice provides the best evidence that the
author of Passage 2 would agree to some extent with
the claim attributed to Michael Merzenich in
lines 41-43, Passage 1?
A) Lines 51-53 (“Critics . . . brain”)
B) Lines 54-56 (“Yes . . . changes”)
C) Lines 57-59 (“But . . . experience”)
D) Lines 83-84 (“Media . . . consumes”)
CO NTI N U E
Writing%and%Language%
Test%
%
%
%
%
24
PSAT%Writing%and%Language%Test%
%
Time%Allotted%
Total%Questions%
%
%
Passage%Content%
Careers%
35%minutes%(same%as%SAT)%
44%(same%as%SAT)%
%
%
%
1%passage;%11%questions%
History/Social%Studies%
1%passage;%11%questions%
Humanities%
1%passage;%11%questions%
Science%
1%passage;%11%questions%
Types%of%Questions%
%
Expression%of%Ideas.%
Development%
8%questions%est.%
%
These questions focus on revising text in relation
to rhetorical purpose. (Prior knowledge of the
topic is not assessed, though consistency of the
material within a passage may be.)
Organization%
8%questions%est.%
These questions focus on revision of text to
improve the logic and cohesion of text at the
sentence, paragraph, and whole-text levels.
Effective%Language%Use%
8%questions%est.%
%
These questions focus on revision of text to
improve the use of language to accomplish
particular rhetorical purposes.
Standard%English%Conventions%
Sentence%Structures%
7%questions%est.%
%
These questions focus on editing text to correct
problems in sentence formation and inappropriate
shifts in construction within and between
sentences.
Conventions%of%Usage%
8%questions%est.%
These questions focus on editing text to ensure
conformity to the conventions of standard written
English usage.
Conventions%of%Punctuation%
5%questions%est.%
These questions focus on editing text to ensure
conformity to the conventions of standard written
English punctuation.
%
%
25
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39
New Information about the Math SAT
1. The Math section of the Redesigned SAT will increase its focus on algebraic and
general problem solving, as well as data interpretation. Geometry will still be
present, but it will account for a much smaller portion of the test (10% instead of
25%) with trigonometry (<5%).
2. There is now a calculator-free portion.
3. Extended-thinking questions: these questions will be word problems followed by
several related questions, all of which test your problem solving skills. The
answers to these questions will be “open” (or student produced), rather than
multiple-choice. These questions are not only based on realistic scenarios but
also present more complicated situations that require understanding what math
concepts to employ.
4. More real-life situations and word problems.
5. Questions are more straightforward.
SAT Math Tips:
1. Answer the question that is being asked (solve for x, then plug it back
in). Underline key portions of the problem to remind yourself what it is ultimately
asking of you.
2. Translate words into math (i.e. of = multiplication)
3. Look for consecutive problems that pull from the same graph/data chart to ask
questions. To start preparing for these extended thinking questions, treat all math
problems as essentially “open” – solve each practice question with the possible
responses covered, and write your answer in the margin. After you finish,
compare your result with the answer key.
4. Answer all the beginning questions before moving on to the more difficult
questions. Questions go from easy to difficult. First third are easy, second third
are medium, and last third are difficult.
5. Look for wrong answers to eliminate because you are no longer penalized for
answering incorrectly, eliminating one answer will increase your odds of getting it
correct.
6. Use the figure shown to help solve the problem when it does NOT say “figure not
drawn to scale”
7. Plug in numbers to the given formula (backsolve) in order to save time
8. Pick numbers for variables (never 0 or 1 because they have special properties) to
skip using involved algebraic equations
%
%
40
3
3
M1
Math Test – No Calculator
25 M I NU TES, 2 0 QUESTIONS
Turn to Section 3 of your answer sheet to answer the questions in this section.
For questions 1-15, solve each problem, choose the best answer from the choices
provided, and fill in the corresponding circle on your answer sheet. For questions 16-20,
solve the problem and enter your answer in the grid on the answer sheet. Please refer to
the directions before question 16 on how to enter your answers in the grid. You may use
any available space in your test booklet for scratch work.
1. The use of a calculator is not permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for
which f(x) is a real number.
ℓ
r
w
A = pr 2
C = 2pr
r
w
V = ℓwh
a
c 2 = a2 + b 2
r
h
2x
c
b
b
1
A = bh
2
A = ℓw
h
ℓ
h
4
V = pr 3
3
x
s 45°
s√2
30°
45°
s
x√3
Special Right Triangles
h
h
r
V = pr 2h
60°
1
V = pr 2h
3
ℓ
V = 1 ℓwh
3
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2p.
The sum of the measures in degrees of the angles of a triangle is 180.
Unauthorized copying or reuse of any part of this page is illegal.
32 41
w
CO NTI N U E
3
If 5x + 6 = 10 , what is the value of 10x + 3 ?
4
B)
9
C) 11
D) 20
2
x+y =0
3x − 2y = 10
Which of the following ordered pairs (x, y ) satisfies
the system of equations above?
A) (3, −2)
B) (2, −2)
C) (−2, 2)
D) (−2, −2)
Unauthorized copying or reuse of any part of this page is illegal.
...............................................................................................................................................................................................................................................................................................................
1
A)
3
M1
33 42
3
A landscaping company estimates the price of a job,
in dollars, using the expression 60 + 12nh , where n
is the number of landscapers who will be working
and h is the total number of hours the job will take
using n landscapers. Which of the following is the
best interpretation of the number 12 in the
expression?
A) The company charges $12 per hour for each
landscaper.
B) A minimum of 12 landscapers will work on
each job.
C) The price of every job increases by
$12 every hour.
D) Each landscaper works 12 hours a day.
4
9a4 + 12a2b 2 + 4b4
Which of the following is equivalent to the
expression shown above?
2
A) (3a2 + 2b 2)
B) (3a + 2b)4
2
C) (9a2 + 4b 2)
D) (9a + 4b)4
CO NTI N U E
3
2k 2 + 17 − x = 0
If k > 0 and x = 7 in the equation above, what is the
value of k ?
A) 2
B) 3
C) 4
D) 5
6
y
ℓ
(0, 2)
k
O
( p, 0)
(0, ! 4)
In the xy-plane above, line
What is the value of p ?
A)
4
B)
5
C)
8
is parallel to line k.
D) 10
Unauthorized copying or reuse of any part of this page is illegal.
x
...............................................................................................................................................................................................................................................................................................................
5
(! 5, 0)
3
M1
7
If
xa
x
2
b2
= x16 , x > 1, and a + b = 2, what is the value
of a − b ?
A)
8
B) 14
C) 16
D) 18
8
34 43
nA = 360
The measure A, in degrees, of an exterior angle of a
regular polygon is related to the number of sides, n,
of the polygon by the formula above. If the measure
of an exterior angle of a regular polygon is greater
than 50° , what is the greatest number of sides it
can have?
A) 5
B) 6
C) 7
D) 8
CO NTI N U E
3
The graph of a line in the xy-plane has slope 2 and
contains the point (1, 8). The graph of a second line
passes through the points (1, 2) and (2, 1). If the
two lines intersect at the point (a, b), what is the
value of a + b ?
A)
4
B)
3
C) −1
D) −4
10
Which of the following equations has a graph in the
xy-plane for which y is always greater than or equal
to −1 ?
A) y = x − 2
B) y = x 2 − 2
C) y = (x − 2)2
D) y = x 3 − 2
Unauthorized copying or reuse of any part of this page is illegal.
...............................................................................................................................................................................................................................................................................................................
9
3
M1
35 44
11
Which of the following complex numbers is
equivalent to
A)
3 5i
−
8 2
B)
3 5i
+
8 2
C)
7
23i
−
34 34
D)
7
23i
+
34 34
3 − 5i
? (Note: i = −1 )
8 + 2i
12
F
N+F
A website uses the formula above to calculate a
seller’s rating, R, based on the number of favorable
reviews, F, and unfavorable reviews, N. Which of
the following expresses the number of favorable
reviews in terms of the other variables?
R=
A) F =
RN
R−1
B) F =
RN
1−R
C) F =
N
1−R
D) F =
N
R−1
CO NTI N U E
3
What is the sum of all values of m that satisfy
2m2 − 16m + 8 = 0 ?
A)
−8
B) −4 3
C) 4 3
D) 8
14
A radioactive substance decays at an annual rate of
13 percent. If the initial amount of the substance is
325 grams, which of the following functions f
models the remaining amount of the substance, in
grams, t years later?
A) f (t ) = 325(0.87)t
B) f (t ) = 325(0.13)t
C) f (t ) = 0.87(325)t
D) f (t ) = 0.13(325)t
Unauthorized copying or reuse of any part of this page is illegal.
...............................................................................................................................................................................................................................................................................................................
13
M1
3
15
36 45
The expression
5x − 2
is equivalent to which of the
x+3
following?
A)
5−2
3
B) 5 −
2
3
C) 5 −
2
x+3
D) 5 −
17
x+3
CO NTI N U E
3
3
M1
7
Answer: 12
DIRECTIONS
For questions 16–20, solve the problem and
enter your answer in the grid, as described
below, on the answer sheet.
1. 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. You will receive credit only if the
circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one
correct answer. In such cases, grid only one
answer.
5. Mixed numbers such as 3 1 must be gridded
2
Write
answer
in boxes.
7 / 12
.
1
2
3
4
5
6
7
8
9
Grid in
result.
/
grid, it will be interpreted as 31 , not 3 1 .)
2
2
6. 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.
2 . 5
.
1
2
3
4
5
6
7
8
9
/ /
. . .
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
2 / 3
. 666
Decimal
point
201
201
. 667
/ /
/ /
. . . .
. . . .
.
0 0 0
0 0 0
1 1 1 1
1 1 1 1
1
2 2 2 2
2 2 2 2
2
3 3 3 3
3 3 3 3
3
4 4 4 4
4 4 4 4
4
5 5 5 5
5 5 5 5
5
6 6 6 6
6 6 6 6
6
7 7 7 7
7 7 7 7
7
8 8 8 8
8 8 8 8
8
9 9 9 9
9 9 9 9
9
Answer: 201 – either position is correct
/ /
. . .
0 0 0
1 1 1 1
2 2 2 2
3 3 3 3
.
Unauthorized copying or reuse of any part of this page is illegal.
Fraction
line
2
Acceptable ways to grid 3 are:
as 3.5 or 7/2. (If 3 1 / 2 is entered into the
/
/ /
. . .
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
Answer: 2.5
37 46
/ /
. . .
0 0 0
1 1 1 1
2 2 2 2
3 3 3 3
.
/ /
. . .
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
NOTE: You
may start your
answers in any
column, space
permitting.
Columns you
don’t need to
use should be
left blank.
CO NTI N U E
3
3
M1
The sales manager of a company awarded a total of
$3000 in bonuses to the most productive salespeople.
The bonuses were awarded in amounts of $250 or
$750. If at least one $250 bonus and at least one $750
bonus were awarded, what is one possible number of
$250 bonuses awarded?
17
2x(3x + 5) + 3(3x + 5) = ax 2 + bx + c
In the equation above, a, b, and c are constants. If
the equation is true for all values of x, what is the
value of b ?
Unauthorized copying or reuse of any part of this page is illegal.
...............................................................................................................................................................................................................................................................................................................
16
18
38 47
C
D
B
10
A
5
8
E
In the figure above, AE CD and segment AD
intersects segment CE at B. What is the length of
segment CE ?
CO NTI N U E
3
3
M1
y
A (√3, 1)
O
B
x
In the xy-plane above, O is the center of the circle,
π
and the measure of ∠AOB is
radians. What is
a
the value of a ?
........................................................................................................................................................................................................................................................
19
20
ax + by = 12
2x + 8y = 60
In the system of equations above, a and b are
constants. If the system has infinitely many
solutions, what is the value of
a
?
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.
Unauthorized copying or reuse of any part of this page is illegal.
39 48
4
4
M2
Math Test – Calculator
55 M I NU TES, 3 8 QUESTIONS
Turn to Section 4 of your answer sheet to answer the questions in this section.
For questions 1-30, solve each problem, choose the best answer from the choices
provided, and fill in the corresponding circle on your answer sheet. For questions 31-38,
solve the problem and enter your answer in the grid on the answer sheet. Please refer to
the directions before question 31 on how to enter your answers in the grid. You may use
any available space in your test booklet for scratch work.
1. The use of a calculator is permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for
which f(x) is a real number.
ℓ
r
w
A = pr 2
C = 2pr
r
w
V = ℓwh
a
c 2 = a2 + b 2
r
h
2x
c
b
b
1
A = bh
2
A = ℓw
h
ℓ
h
4
V = pr 3
3
x
s 45°
s√2
30°
45°
s
x√3
Special Right Triangles
h
h
r
V = pr 2h
60°
1
V = pr 2h
3
ℓ
V = 1 ℓwh
3
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2p.
The sum of the measures in degrees of the angles of a triangle is 180.
Unauthorized copying or reuse of any part of this page is illegal.
40 49
w
CO NTI N U E
4
A musician has a new song available for
downloading or streaming. The musician earns
$0.09 each time the song is downloaded and $0.002
each time the song is streamed. Which of the
following expressions represents the amount, in
dollars, that the musician earns if the song is
downloaded d times and streamed s times?
A) 0.002d + 0.09s
B) 0.002d − 0.09s
C) 0.09d + 0.002s
D) 0.09d − 0.002s
2
A quality control manager at a factory selects
7 lightbulbs at random for inspection out of every
400 lightbulbs produced. At this rate, how many
lightbulbs will be inspected if the factory produces
20,000 lightbulbs?
A) 300
B) 350
C) 400
D) 450
Unauthorized copying or reuse of any part of this page is illegal.
...............................................................................................................................................................................................................................................................................................................
1
4
M2
41 50
3
= 24 + 3.5m
One end of a spring is attached to a ceiling. When an
object of mass m kilograms is attached to the other
end of the spring, the spring stretches to a length of
centimeters as shown in the equation above. What
is m when is 73 ?
A)
14
B)
27.7
C)
73
D) 279.5
CO NTI N U E
4
4
M2
The amount of money a performer earns is directly
proportional to the number of people attending the
performance. The performer earns $120 at a
performance where 8 people attend.
4
How much money will the performer earn when
20 people attend a performance?
A) $960
B) $480
C) $300
D) $240
5
The performer uses 43% of the money earned to pay
the costs involved in putting on each performance.
The rest of the money earned is the performer’s
profit. What is the profit the performer makes at a
performance where 8 people attend?
A) $51.60
B) $57.00
C) $68.40
D) $77.00
▲
Unauthorized copying or reuse of any part of this page is illegal.
...............................................................................................................................................................................................................................................................................................................
▼
Questions 4 and 5 refer to the following information.
6
When 4 times the number x is added to 12, the
result is 8. What number results when 2 times x is
added to 7 ?
A) −1
B)
5
C)
8
D)
9
7
42 51
y = x 2 − 6x + 8
The equation above represents a parabola in the
xy-plane. Which of the following equivalent forms of
the equation displays the x-intercepts of the parabola
as constants or coefficients?
A) y − 8 = x 2 − 6x
B) y + 1 = (x − 3)2
C) y = x(x − 6) + 8
D) y = (x − 2)(x − 4)
CO NTI N U E
4
In a video game, each player starts the game with
k points and loses 2 points each time a task is not
completed. If a player who gains no additional
points and fails to complete 100 tasks has a score of
200 points, what is the value of k ?
A)
0
B) 150
C) 250
D) 400
9
A worker uses a forklift to move boxes that weigh
either 40 pounds or 65 pounds each. Let x be the
number of 40-pound boxes and y be the number of
65-pound boxes. The forklift can carry up to either
45 boxes or a weight of 2,400 pounds. Which of the
following systems of inequalities represents this
relationship?
⎪⎧ 40x + 65y ≤ 2,400
A) ⎪
⎨
⎪⎪⎩ x + y ≤ 45
⎪⎧⎪ x + y ≤ 2,400
B) ⎪
⎨ 40 65
⎪⎪ x + y ≤ 45
⎩⎪
⎪⎧ 40x + 65y ≤ 45
C) ⎪
⎨ x + y ≤ 2,400
⎩⎪⎪
⎧⎪ x + y ≤ 2,400
D) ⎪
⎨
⎪⎪⎩ 40x + 65y ≤ 2,400
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...............................................................................................................................................................................................................................................................................................................
8
M2
43 52
4
10
A function f satisfies f (2) = 3 and f (3) = 5. A
function g satisfies g(3) = 2 and g(5) = 6 . What is
the value of f ( g (3)) ?
A) 2
B) 3
C) 5
D) 6
11
Number of hours Tony plans to read the
novel per day
3
Number of parts in the novel
8
Number of chapters in the novel
239
Number of words Tony reads per minute
250
Number of pages in the novel
1,078
Number of words in the novel
349,168
Tony is planning to read a novel. The table above
shows information about the novel, Tony’s reading
speed, and the amount of time he plans to spend
reading the novel each day. If Tony reads at the rates
given in the table, which of the following is closest to
the number of days it would take Tony to read the
entire novel?
A)
6
B)
8
C)
23
D) 324
CO NTI N U E
4
A) 325,000 − 7,500 ≤ y
B) 325,000 ≤ 7,500y
C) 150,000 ≥ 7,500y
D) 175,000 + 7,500y ≥ 325,000
13
A researcher conducted a survey to determine
whether people in a certain large town prefer
watching sports on television to attending the
sporting event. The researcher asked 117 people who
visited a local restaurant on a Saturday, and 7 people
refused to respond. Which of the following factors
makes it least likely that a reliable conclusion can be
drawn about the sports-watching preferences of all
people in the town?
A) Sample size
B) Population size
C) The number of people who refused to respond
D) Where the survey was given
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4
14
44 53
Number of miles traveled
(billions)
On January 1, 2000, there were 175,000 tons of trash
in a landfill that had a capacity of 325,000 tons. Each
year since then, the amount of trash in the landfill
increased by 7,500 tons. If y represents the time, in
years, after January 1, 2000, which of the following
inequalities describes the set of years where the
landfill is at or above capacity?
...............................................................................................................................................................................................................................................................................................................
12
M2
Miles Traveled by Air Passengers
in Country X, 1960 to 2005
600
500
400
300
200
100
0
1960 1970 1980 1990 2000 2010
Year
According to the line of best fit in the scatterplot
above, which of the following best approximates the
year in which the number of miles traveled by air
passengers in Country X was estimated to be
550 billion?
A) 1997
B) 2000
C) 2003
D) 2008
CO NTI N U E
4
M2
The distance traveled by Earth in one orbit around
the Sun is about 580,000,000 miles. Earth makes
one complete orbit around the Sun in one year. Of
the following, which is closest to the average speed of
Earth, in miles per hour, as it orbits the Sun?
A)
66,000
B)
93,000
C) 210,000
D) 420,000
16
Results on the Bar Exam of Law School Graduates
Took review course
Did not take
review course
Passed
bar exam
Did not pass
bar exam
18
82
7
93
The table above summarizes the results of 200 law
school graduates who took the bar exam. If one of
the surveyed graduates who passed the bar exam is
chosen at random for an interview, what is the
probability that the person chosen did not take the
review course?
A)
18
25
B)
7
25
C)
25
200
D)
7
200
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...............................................................................................................................................................................................................................................................................................................
15
45 54
4
17
The atomic weight of an unknown element, in
atomic mass units (amu), is approximately 20% less
than that of calcium. The atomic weight of calcium
is 40 amu. Which of the following best approximates
the atomic weight, in amu, of the unknown element?
A)
8
B) 20
C) 32
D) 48
18
A survey was taken of the value of homes in a county,
and it was found that the mean home value was
$165,000 and the median home value was $125,000.
Which of the following situations could explain the
difference between the mean and median home
values in the county?
A) The homes have values that are close to each
other.
B) There are a few homes that are valued much less
than the rest.
C) There are a few homes that are valued much
more than the rest.
D) Many of the homes have values between
$125,000 and $165,000.
CO NTI N U E
4
4
M2
A sociologist chose 300 students at random from each of
two schools and asked each student how many siblings he
or she has. The results are shown in the table below.
Students! Sibling Survey
Number of
siblings
Lincoln
School
Washington
School
0
120
140
1
80
110
2
60
30
3
30
10
4
10
10
There are a total of 2,400 students at Lincoln School and
3,300 students at Washington School.
19
What is the median number of siblings for all the
students surveyed?
A) 0
B) 1
C) 2
D) 3
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...............................................................................................................................................................................................................................................................................................................
▼
Questions 19 and 20 refer to the following
information.
20
Based on the survey data, which of the following
most accurately compares the expected total number
of students with 4 siblings at the two schools?
A) The total number of students with 4 siblings is
expected to be equal at the two schools.
B) The total number of students with 4 siblings at
Lincoln School is expected to be 30 more than at
Washington School.
C) The total number of students with 4 siblings at
Washington School is expected to be 30 more
than at Lincoln School.
D) The total number of students with 4 siblings at
Washington School is expected to be 900 more
than at Lincoln School.
▲
21
46 55
A project manager estimates that a project will take
x hours to complete, where x > 100 . The goal is for
the estimate to be within 10 hours of the time it will
actually take to complete the project. If the manager
meets the goal and it takes y hours to complete the
project, which of the following inequalities
represents the relationship between the estimated
time and the actual completion time?
A) x + y < 10
B) y > x + 10
C) y < x − 10
D) −10 < y − x < 10
CO NTI N U E
4
4
M2
I=
P
4πr 2
At a large distance r from a radio antenna, the intensity
of the radio signal I is related to the power of the
signal P by the formula above.
22
Which of the following expresses the square of the
distance from the radio antenna in terms of the
intensity of the radio signal and the power of the
signal?
IP
A) r =
4π
2
B) r 2 =
P
4πI
C) r 2 =
4πI
P
D) r 2 =
I
4πP
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...............................................................................................................................................................................................................................................................................................................
▼
Questions 22 and 23 refer to the following
information.
47 56
23
For the same signal emitted by a radio antenna,
Observer A measures its intensity to be 16 times the
intensity measured by Observer B. The distance of
Observer A from the radio antenna is what fraction
of the distance of Observer B from the radio
antenna?
A)
1
4
B)
1
16
C)
1
64
D)
1
256
▲
24
x 2 + y 2 + 4x − 2y = −1
The equation of a circle in the xy-plane is shown
above. What is the radius of the circle?
A) 2
B) 3
C) 4
D) 9
CO NTI N U E
4
A) It is positive.
B) It is negative.
C) It equals zero.
D) It is undefined.
26
y
y = f (x)
1
O
1
x
The complete graph of the function f is shown in the
xy-plane above. Which of the following are
equal to 1 ?
I. f (−4)
⎛3⎞
II. f ⎜⎜ ⎟⎟
⎜⎝ 2 ⎟⎠
III. f (3)
III only
I and III only
II and III only
I, II, and III
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27
48 57
70
Temperature (! C)
The graph of the linear function f has intercepts at
(a, 0) and (0, b) in the xy-plane. If a + b = 0 and
a ≠ b , which of the following is true about the slope
of the graph of f ?
...............................................................................................................................................................................................................................................................................................................
25
A)
B)
C)
D)
4
M2
60
insulated
non! insulated
50
40
30
20
10
0
0 10 20 30 40 50 60 70
Time (minutes)
Two samples of water of equal mass are heated to
60 degrees Celsius (°C ). One sample is poured into
an insulated container, and the other sample is
poured into a non-insulated container. The samples
are then left for 70 minutes to cool in a room having
a temperature of 25°C . The graph above shows the
temperature of each sample at 10-minute intervals.
Which of the following statements correctly
compares the average rates at which the temperatures
of the two samples change?
A) In every 10-minute interval, the magnitude of
the rate of change of temperature of the
insulated sample is greater than that of the
non-insulated sample.
B) In every 10-minute interval, the magnitude of
the rate of change of temperature of the
non-insulated sample is greater than that of the
insulated sample.
C) In the intervals from 0 to 10 minutes and from
10 to 20 minutes, the rates of change of
temperature of the insulated sample are of
greater magnitude, whereas in the intervals from
40 to 50 minutes and from 50 to 60 minutes, the
rates of change of temperature of the
non-insulated sample are of greater magnitude.
D) In the intervals from 0 to 10 minutes and from
10 to 20 minutes, the rates of change of
temperature of the non-insulated sample are of
greater magnitude, whereas in the intervals from
40 to 50 minutes and from 50 to 60 minutes, the
rates of change of temperature of the insulated
sample are of greater magnitude.
CO NTI N U E
4
y
B
6
4
C
2
E
A
! 4
! 2
! 2
2
4
6
x
! 4
! 6
D
In the xy-plane above, ABCD is a square and
point E is the center of the square. The coordinates
of points C and E are (7, 2) and (1, 0),
respectively. Which of the following is an equation
of the line that passes through points B and D ?
A) y = −3x − 1
B) y = −3(x − 1)
1
C) y = − x + 4
3
1
D) y = − x − 1
3
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28
! 6
4
M2
49 58
29
y=3
y = ax 2 + b
In the system of equations above, a and b are
constants. For which of the following values of a
and b does the system of equations have exactly two
real solutions?
A) a = −2, b = 2
B) a = −2, b = 4
C) a = 2, b = 4
D) a = 4, b = 3
30
The figure above shows a regular hexagon with sides
of length a and a square with sides of length a. If
the area of the hexagon is 384 3 square inches,
what is the area, in square inches, of the square?
A) 256
B) 192
C)
64 3
D) 16 3
CO NTI N U E
4
4
M2
7
Answer: 12
DIRECTIONS
For questions 31-38, solve the problem and
enter your answer in the grid, as described
below, on the answer sheet.
1. 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. You will receive credit only if the
circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one
correct answer. In such cases, grid only one
answer.
5. Mixed numbers such as 3 1 must be gridded
2
Write
answer
in boxes.
7 / 12
.
1
2
3
4
5
6
7
8
9
Grid in
result.
/
grid, it will be interpreted as 31 , not 3 1 .)
2
2
6. 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.
2 . 5
.
1
2
3
4
5
6
7
8
9
/ /
. . .
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
2 / 3
. 666
Decimal
point
201
201
. 667
/ /
/ /
. . . .
. . . .
.
0 0 0
0 0 0
1 1 1 1
1 1 1 1
1
2 2 2 2
2 2 2 2
2
3 3 3 3
3 3 3 3
3
4 4 4 4
4 4 4 4
4
5 5 5 5
5 5 5 5
5
6 6 6 6
6 6 6 6
6
7 7 7 7
7 7 7 7
7
8 8 8 8
8 8 8 8
8
9 9 9 9
9 9 9 9
9
Answer: 201 – either position is correct
/ /
. . .
0 0 0
1 1 1 1
2 2 2 2
3 3 3 3
.
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Fraction
line
2
Acceptable ways to grid 3 are:
as 3.5 or 7/2. (If 3 1 / 2 is entered into the
/
/ /
. . .
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
Answer: 2.5
50 59
/ /
. . .
0 0 0
1 1 1 1
2 2 2 2
3 3 3 3
.
/ /
. . .
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
NOTE: You
may start your
answers in any
column, space
permitting.
Columns you
don’t need to
use should be
left blank.
CO NTI N U E
4
A coastal geologist estimates that a certain country’s
beaches are eroding at a rate of 1.5 feet per year.
According to the geologist’s estimate, how long will it
take, in years, for the country’s beaches to erode by
21 feet?
32
If h hours and 30 minutes is equal to 450 minutes,
what is the value of h ?
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31
M2
4
33
In the xy-plane, the point (3, 6) lies on the graph of
the function f (x ) = 3x 2 − bx + 12. What is the value
of b ?
34
51 60
In one semester, Doug and Laura spent a combined
250 hours in the tutoring lab. If Doug spent 40 more
hours in the lab than Laura did, how many hours did
Laura spend in the lab?
CO NTI N U E
4
4
M2
a = 18t + 15
Jane made an initial deposit to a savings account.
Each week thereafter she deposited a fixed amount
to the account. The equation above models the
amount a, in dollars, that Jane has deposited after
t weekly deposits. According to the model, how
many dollars was Jane’s initial deposit? (Disregard
the $ sign when gridding your answer.)
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35
52 61
36
L
60!
O
M
N
In the figure above, point O is the center of the
circle, line segments LM and MN are tangent to the
circle at points L and N, respectively, and the
segments intersect at point M as shown. If the
circumference of the circle is 96, what is the length of
minor arc LN ?
CO NTI N U E
4
4
M2
A botanist is cultivating a rare species of plant in a
controlled environment and currently has 3000 of these
plants. The population of this species that the botanist
expects to grow next year, Nnext year , can be estimated
from the number of plants this year, Nthis year , by the
equation below.
⎛
Nthis year ⎞
⎟⎟
Nnext year = Nthis year + 0.2 Nthis year ⎜⎜1 −
⎟⎟
⎜⎜⎝
K
⎠
(
)
The constant K in this formula is the number of plants
the environment is able to support.
37
According to the formula, what will be the number of
plants two years from now if K = 4000 ? (Round
your answer to the nearest whole number.)
.....................................................................................................................................................................................................................................................
▼
Questions 37 and 38 refer to the following
information.
38
The botanist would like to increase the number of
plants that the environment can support so that the
population of the species will increase more rapidly.
If the botanist’s goal is that the number of plants will
increase from 3000 this year to 3360 next year, how
many plants must the modified environment
support?
▲
STOP
If you finish before time is called, you may check your work on this section only.
Do not turn to any other section.
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53 62
FrequentlyAskedQuestions
1.WhatisthePSAT/NMQST?
ThePreliminarySAT(PSAT)orTheNationalMeritQualifyingScholarshipTest
(NMSQT)isatestthathelpsyoupracticefortheSAT.ForJuniors,thetestenables
studentstoentertheNationalMeritScholarshipCorporation(NMSC)scholarship
program.
2.HowmanytimescanItakethetest?
YoucantakethePSATonceayearinOctoberasasophomoreandajunior.
3.WhatisthedifferencebetweentheSATandPSAT?
Thereareimportantdifferencesbetweenthetwoexams.First,thePSATisshorter
thantheSAT.Second,itdoesnotincludeanessayquestion.Third,thePSATdoesnot
testmorecomplextopicssuchasimaginarynumbersortrigonometry.
4.HowdoIregisterforthePSAT?
AllMittysophomoresandjuniorsareautomaticallyregisteredforthetest.Youwill
takethePSAT/NMQSTonWednesday,October11,2017.
5.CanIguessonthePSAT?
Yes.Thereisnopenaltyforwronganswers,sodonotleaveaPSATquestionblank!
6.DocollegescareaboutmyPSATscores?
PSATscoresareNEVERusedforcollegeadmissions.Ifyouwererecognizedasa
CommendedorNationalMeritScholar,youcanreporttherecognitiononyour
collegeapplications.
7.HowdoIgetmyscores?
PSATscoresandtestbookletswillbemailedtostudentsinJanuary2018.