AI Transcription, Pages 301-325
Page 301
If the area of a triangle is one-half the product of two sides, one side
must serve as the base and the other side as the altitude. This occurs
only in the case of the two legs of a right triangle.
16. If an arrow (→) between two expressions indicates that the expres-
sion on the right exceeds the expression on the left by 1, then which
of the following is (are) true?
I. x²→(x + 1)²
II. x/y → (x + 1)/(y + 1)
III. x(x + 2) → (x + 1)²
(A) None (B) I only (C) II only (D) III only (E) I and II
In this question, you must work with a new symbol that has been
defined. In cases I and III the right expressions must be expanded
before comparison. In I, the right member exceeds the left by 2x + 1.
In II, the right member exceeds the left by (y - x) / (y(y + 1)). In III, the right
member exceeds the left by 1, making (D) the correct answer.
17. If rain is falling at the rate of 2 inches per hour, how many inches of
rain will fall in x minutes?
(A) 1/30x (B) x/30 (C) 30/x (D) 60/x (E) 30x
This question requires relational thinking with rates. Since inches
per hour times hours equals inches, 2 × x/60 = x/30 inches of rain.
18. If the radius of circle X is 40% of the radius of circle Y, the area of
circle X is what per cent of the area of circle Y?
(A) 16 (B) 20 (C) 40 (D) 80 (E) 160
If the radius of circle X is R, that of circle Y is .4R. Therefore, the
area of circle X is πR² and of circle Y is .16πR². The per cent is
(.16πR² / πR²) × 100 = 16.
16
[Stamp] ⟦illegible⟧
Page 302
[Marginalia] School Report Form
[Marginalia] V
Princeton, New Jersey
U.S.A.
1. All used answer sheets
2. " " Sect II math exam books (pink covers)
3. Coordinators Report (to be printed)
4. Voucher ⟦Form⟧ Bill (By special letter)
2. Envelope No. 2. First class mail
Educational Testing Service
Box 592, Princeton, New Jersey
U.S.A.
1. Master Record Cards
2. Completed Irregularity report
3. " Coordinator's Comment Sheet (not ⟦...⟧)
4. School Report Form
3. Envelope No. 3
To:
Shipping Center, Educational Testing Service
⟦...⟧
Page 305
1960 Bulletin for Students:
Preliminary
Scholastic Aptitude Test
This leaflet is written for high school students who have registered
with their principals to take the Preliminary Scholastic Aptitude
Test (PSAT) on Tuesday, October 18, or Saturday, October 22, 1960.
Because the PSAT can be helpful to you in planning your future be-
yond high school, it is important that you understand not only the
value of the PSAT scores but also how to prepare for and to take the
test.
Growing numbers of students are seeking admission to our col-
leges in response to the increasing national demand for college-
educated men and women. As a student in high school, you should
thoughtfully consider continuing your education. If you decide to
go to college you will need to consider both the choice of suitable
colleges to which you might go and their requirements for admis-
sion. Many factors in addition to your test scores, such as your
grades and your school's recommendations, are of prime importance
in arriving at these decisions.
Your PSAT scores permit a direct comparison of your scores with
those of national and college groups outside of your own school, and
hence can assist you, your parents, and your counselor by providing
an estimate of your ability to succeed at the college of your choice.
The PSAT is a two-hour version of the Scholastic Aptitude Test (SAT),
a test required for admission by about 400 colleges. The PSAT is
intended for use in the high school guidance program as a "pre-
liminary" SAT. The parallel nature of these two tests and the specially
developed interpretive materials that will be provided give the PSAT
a unique value in the guidance of students toward college. As an aid
in interpreting your scores, an interpretive booklet will be sent to
your school in December for distribution with your test scores. In
addition, your counselor will be provided with more detailed infor-
mation so that he can help you to understand your scores.
1
Page 306
Preparing to take the PSAT
Since the PSAT tests your ability to reason and not your ability to
recall facts, short-term specific preparation for it is unprofitable. The
greater part of your preparation for the test has already taken place.
If you have observed the world about you thoughtfully, if you have
read widely and well, and if you have studied conscientiously, you
have completed the most effective preparation for the PSAT. It will be
to your advantage, however, to read attentively the section in this
leaflet that describes the test and explains the various types of
questions you may be asked. You should also become familiar with
the description of the answer sheet which you will be required to
fill out when you take the PSAT.
When you take the PSAT, remember...
• Read the directions carefully.
• Work attentively and rapidly.
• Keep in mind that the test is two hours long and that you will be
allowed one hour on the Verbal section and one hour on the
Mathematical section.
• Take the questions in order; skip the difficult ones and try them
again later if you have time.
• Do not be disturbed if you cannot answer all of the questions in a
section of the test or if you do not have time to finish it. Many of the
students who take the test do not attempt all of the questions, and no
one is expected to know the answers to all of them.
• When the test is scored, a percentage of the wrong answers is sub-
tracted from the number of right answers as a correction for hap-
hazard guessing. It is improbable, therefore, that mere guessing will
improve your scores significantly; it may even lower your score. If,
however, you are not sure of the correct answer but have some
knowledge of the question and are able to eliminate one or more of
the answer choices as wrong, your chance of getting the right answer
is improved, and it is to your advantage to answer such a question.
• No books, slide rules, or papers of any kind may be used during the
test.
2
Copyright 1960 by College Entrance Examination Board
• No student may give assistance to any other student during the test.
Test booklets and answer sheets must be handed back to the super-
visor; they may not be removed from the test room.
• For use in taking the PSAT, you must bring with you several sharp-
ened No. 2 pencils or a mechanical pencil with soft lead and an
eraser. You should make solid black marks that completely fill the
boxes on your answer sheet, so that the electronic scoring machines
can record your responses.
Completing the answer sheet
When you take the PSAT, you will be given an answer sheet on which
you will record your answers by blackening-in one of the five boxes
that follow the number of each question. As you will see in the sec-
tion that describes the test, each question has five possible answers,
lettered (A), (B), (C), (D), or (E). When you have selected your
answer, fill in the appropriate box completely. If you make an era-
sure, be sure to do a thorough job. The following example illustrates
how the answer to a question should be indicated on your answer
sheet:
30. Chicago is a
(A) state
(B) city
(C) country
(D) town
(E) village
Sample Answer Spaces:
A B C D E
30 [ ] [■] [ ] [ ] [ ]
There will also be a section of the answer sheet on which, if you
are eligible, you will be asked to blacken the appropriate box for any
scholarship program for which you would like to be considered.
In the center of the answer sheet you will find a series of boxes
that have been set off by a dark rule from the rest of the answer sheet.
The information that you will provide here is important, because it
will be used by electronic machines to “read” automatically the in-
formation you have given and to compute a code number for you.
3
Page 307
Sample of completed center portion of answer sheet
F I E L D I N G A L E X A N D C R O M W
⟦grid of bubbles A-Z with marks corresponding to the name above⟧
SEX: 1 MALE
GRADE: JUNIOR
YOUR BIRTH DATE Month: 1 0
YOUR BIRTH DATE Day: 0 3
YOUR STATE OF BIRTH: 1 4
MONTH PARENTS WERE BORN Mother: 0 2
MONTH PARENTS WERE BORN Father: 0 5
SECONDARY SCHOOL Code Number: 0 5 0 8 1 5
4
You will need to provide the following information in the center
portion of your answer sheet: your last and first names, your moth-
er’s maiden name, the month and day of your birth, your sex, your
grade in school, the state where you were born, the month of your
mother’s birth, and the month of your father’s birth. It will be very
helpful if you will make sure beforehand that you can record all of
the above information readily and correctly at the time you take the
PSAT. With this in mind, a blank sample and a completed sample of
this portion of the answer sheet have been included here. After you
have studied the completed sample, fill in the blank sample with your
own information for practice.
Looking first at the completed sample portion of the answer sheet,
you will notice that the top two-thirds of the sheet has three main
groups of boxes running down the alphabet from A to Z. If you look
from left to right across the top of the columns and count, you will
see that the first group of columns has 13 boxes for the letters of the
student’s last name, the second set of columns has boxes for 7 letters
of his first name, and the third set has boxes for the first 5 letters of
his mother’s maiden name.
Our hypothetical student, Alexander Fielding, whose mother’s
maiden name was Cromwell, first printed his last name in the empty
boxes at the top of the left-hand set of columns. If his last name had
contained more than thirteen letters, he would have filled in only the
first thirteen. Moving to the right to the “First Name” column, he
filled in seven letters of his first name: “Alexand.” Over the columns
to the far right he printed the first five letters of his mother’s maiden
name: “Cromw.”
Alexander was then asked to blacken the lettered box in each
column that corresponded to the letter in his name at the top of that
column. Note that he blackened only one box in each column.
The bottom third of the center portion of the answer sheet has five
groups of columns of boxes to be filled in: (1) your sex, and your
grade in school, (2) the month and day of your birth, (3) the code
number of the state in which you were born, (4) the month in
which your mother was born and your father’s month of birth, and
(5) the code number of your secondary school. (A list of state code
numbers and your secondary school code number will be provided
at the time you take the PSAT.)
To return to our example, Alexander blackened the boxes labeled
“male” and “junior” in the first lower column. Since he was born on
5
Page 308
October 3, he wrote the digits “10” and “03” in the empty boxes at
the top of the birth-date columns. Note that, since the day of Alex-
ander’s birth has only one digit, “3,” he wrote “03” in the boxes.
Two digits must be placed in each set of this series of boxes. (For
instance, if Alexander had been born in January, he would have
written “01” in the first two of this series of boxes.) Then Alexander
blackened the appropriate box below each number that corre-
sponded to the number at the top of each column.
The third column has a double series of boxes running from
1 to 0 (standing for “10”). Alexander was born in Chicago and
therefore he wrote “14,” the Illinois code number, in the empty
boxes at the top of the state of birth columns. He then blackened
the corresponding number below in each column. In the fourth set
of columns he blackened the box for his mother’s month of birth,
February. Then he blackened the box for May, his father’s month
of birth.
You are now ready to fill in the blank sample answer sheet on page
7 for practice. Make up your own code numbers for the state in
which you were born and for your secondary school.
A description of the PSAT
The two-hour PSAT uses the same kinds of multiple-choice questions
and measures the same verbal and mathematical abilities as the
three-hour SAT. In order that each student may have the best possible
chance to demonstrate his ability, the test includes several different
types of questions, some verbal and some mathematical. These types
have been chosen because they are closely related to skills that are
needed in college work. The Verbal section emphasizes materials
that test your ability to understand word relationships and to com-
prehend what you read; the Mathematical section emphasizes mate-
rials that test your ability to understand and solve problems.
The sample questions that follow are examples of the kinds of
questions you will find in the PSAT and of the general range of diffi-
culty within parts of the test. Do not consider them as a complete
sample test, either in the number of questions given or in the order
in which they appear.
6
Blank sample
⟦Two grids of bubbles for letters A through Z; left grid has 20 columns, right grid has 5 columns⟧
YOUR BIRTH YOUR MONTH PARENTS SECONDARY SCHOOL
DATE STATE WERE BORN
SEX Month Day OF Mother Father Code Number
1 □ MALE BIRTH
2 □ FEMALE
GRADE
SOPHOMORE □
JUNIOR □
SENIOR □
OTHER □
7
Page 309
Verbal section
Four kinds of questions are used in the verbal section of the PSAT:
opposites, sentence completions, analogies, and reading comprehen-
sion. Each type is described and illustrated in the following sections:
Opposites. These questions are designed to test the extent of your
vocabulary. In each question a word is given and you are asked to
select from the five choices that follow it the one most nearly oppo-
site in meaning to it. The vocabulary used in this section includes
words most high school students should have met in their general
reading, although they may not be the kind you use in everyday
speech.
Directions: Each question below consists of a word printed in capital
letters, followed by five words or phrases lettered A through E.
Choose the lettered word or phrase that is most nearly opposite in
meaning to the word in capital letters. Since some of the questions
require you to distinguish fine shades of meaning, consider all the
choices before making your decision.
1. AGILE: (A) humble (B) clumsy (C) useless (D) timid (E) ugly
Since agile means quick, dexterous, and easy in movement, the best
answer is "clumsy" (B), which means slow, awkward, and ungainly
in movement. If you know the meaning of this word, answers (A),
(C), (D), and (E) are obviously incorrect. This is a relatively easy
question.
2. ALLEVIATE: (A) lower (B) aggravate (C) finish (D) control
(E) amuse
This is a relatively difficult question. "Alleviate" means to lighten or
lessen (usually physical or mental troubles). The meaning most
nearly opposite is "aggravate" (B), which means to increase (usu-
ally physical or mental troubles). To one who understands the
meaning of "alleviate," (C) and (E) are obviously incorrect.
"Control" (D) can be thought of in relation to physical or mental
troubles, but the act of controlling would not provide the opposite
of "lightening or lessening"; the correct answer must imply increas-
ing or magnifying. "Lower" (A), in a sense, carries the same mean-
ing as alleviate, although alleviate usually refers to physical or
mental problems, while the word "lower" is much more general.
It is certainly not the opposite of alleviate.
8
Handbook Order Card
Tear off this tab to release card from book.
you to complete a
g. They provide a
n: your ability to
d style with other
mplications of the
that best fulfils its
of topics familiar
widely and studied
depend on special-
philosophy, social
, a broad general
kely to be helpful.
more spaces, each
neath the sentence
to choose the one
ntence, best fits in
ern to him; that it
ws (E) triumphs
individual words
o decide what idea
ld is going" of the
"moves" (C) pro-
or where the world
s" or "grows" or
ey all imply some-
es is sufficient.
y the experience of
.
uires some under-
that it enables us
Notice that if (B),
space, they would
om the experience
Page 310
Handbook Order Card
Tear off this tab to release card from book.
Verbal section
Four kinds of ques
opposites, sentence
sion. Each type is d
Opposites. These q
vocabulary. In eac
select from the five
site in meaning to
words most high s
reading, although
speech.
Directions: Each qu
letters, followed b
Choose the lettered
meaning to the wo
require you to dist
choices before mak
1. AGILE: (A) humbl
Since agile means
answer is "clumsy"
in movement. If yo
(C), (D), and (E)
question.
2. ALLEVIATE: (A) low
(E) amuse
This is a relatively
lessen (usually ph
nearly opposite is
ally physical or n
meaning of "allev
"Control" (D) car
troubles, but the a
of "lightening or le
ing or magnifying.
ing as alleviate, a
mental problems,
It is certainly not t
8
you to complete a
ig. They provide a
on: your ability to
nd style with other
implications of the
r that best fulfils its
y of topics familiar
widely and studied
depend on special-
philosophy, social
d, a broad general
ikely to be helpful.
r more spaces, each
eneath the sentence
e to choose the one
entence, best fits in
cern to him; that it
ows (E) triumphs
e individual words
to decide what idea
rld is going" of the
"moves" (C) pro-
or where the world
"ts" or "grows" or
hey all imply some-
es is sufficient.
by the experience of
a.
quires some under-
, that it enables us
Notice that if (B),
space, they would
rom the experience
D70R1100—254180
Allow three weeks for delivery.
Be sure to fill in the other side!
or Box 27896, Los Angeles 27, California
Box 592, Princeton, New Jersey
College Entrance Examination Board
mail to:
The price of the Handbook is $2. If you wish to order a copy, fill out the address lines on the
back of this card, enclose the card in an envelope with a check or money order for $2, and
and ROTC information.
statements were prepared by the colleges themselves. General sections contain scholarship
freshman year, costs, financial assistance, and where to write for further information. These
Board, together with information about location, size, terms of admission, programs of study,
The College Handbook presents in comparable form descriptions of member colleges of the College
Handbook Order Card
Page 311
Verbal section
Four kinds of que
opposites, sentence
sion. Each type is ⟦...⟧
Opposites. These ⟦...⟧
vocabulary. In eac
select from the fiv
site in meaning to
words most high s
reading, although
speech.
Directions: Each q
letters, followed b
Choose the lettere
meaning to the wo
require you to dis
choices before mak
1. AGILE: (A) humb⟦l⟧
Since agile means
answer is "clumsy"
in movement. If y
(C), (D), and (E)
question.
2. ALLEVIATE: (A) lov
(E) amuse
This is a relatively
lessen (usually ph
nearly opposite is
ally physical or i
meaning of "alle
"Control" (D) ca
troubles, but the a
of "lightening or l
ing or magnifying
ing as alleviate, i
mental problems,
It is certainly not
8
College Entrance Examination Board
Box 592, Princeton, New Jersey
or Box 27896, Los Angeles 27, California
NAME:
NUMBER AND STREET:
CITY:
ZONE:
STATE:
• To receive The College Handbook, you must give your name and address above.
Sentence completions. These questions require you to complete a
sentence in which one or two words are missing. They provide a
measure of one aspect of reading comprehension: your ability to
select those choices that are consistent in logic and style with other
elements in the sentence. If you understand the implications of the
sentence, you will be able to select the one answer that best fulfils its
meaning. The sentences deal with a wide variety of topics familiar
to the secondary school student who has read widely and studied
seriously. Understanding the sentences does not depend on special-
ized knowledge in science, literature, music, philosophy, social
studies, or other such fields. On the other hand, a broad general
knowledge covering a wide range of topics is likely to be helpful.
Directions: Each of the sentences below has one or more spaces, each
blank indicating that a word has been omitted. Beneath the sentence
are five lettered words or sets of words. You are to choose the one
word or set of words that, when inserted in the sentence, best fits in
with the meaning of the sentence as a whole.
3. Where the world is going is of no particular concern to him; that it
............ is sufficient.
(A) flourishes (B) acts (C) moves (D) grows (E) triumphs
The problem here is to comprehend not only the individual words
in the sentence but also the logic of the sentence—to decide what idea
provides a proper balance for the "where the world is going" of the
first part. A careful analysis will reveal that only "moves" (C) pro-
vides this balance. To a person with no concern for where the world
is going, knowledge that it "flourishes" or "acts" or "grows" or
"triumphs" would also be of no concern since they all imply some-
thing about direction or destination. That it moves is sufficient.
4. ............................ makes it possible for us to profit by the experience of
past generations as if this experience were our own.
(A) Language (B) Democracy (C) Progress
(D) Truth (E) Economy
This relatively difficult sentence completion requires some under-
standing of one important function of language, that it enables us
to profit by the experience of past generations. Notice that if (B),
(C), (D), or (E) were to be fitted into the blank space, they would
fit no better than their opposites. We can profit from the experience
9
Page 312
of past dictatorships as well as from past democracies. Falsehood
has its lessons as well as Truth. Thus there is nothing particularly
fitting about any of the choices except "Language" (A). Lacking a
language, it would be almost impossible for one generation to com-
municate with another. Given a language, the experiences of Democ-
racy, Progress, Truth, or Economy—or their opposites—of one
generation can be used by a succeeding one.
Analogies. These questions test your understanding of relationships
between words and ideas. You are asked to analyze relationships and
to recognize those that are similar to each other. Some of the ques-
tions will involve cause and effect relationships; in others you will
be asked to carry an analogy from a concrete, tangible relationship
to a more abstract and less tangible one. Explore each relationship
thoroughly and select as your answer the choice that comes closest to
satisfying all of the demands.
Directions: In each of the following questions, a related pair of words
or phrases is followed by five lettered pairs of words or phrases.
Select the lettered pair which best expresses a relationship similar to
that expressed in the original pair.
5. FOOTBALL: SPORT::
(A) frame:picture (B) clock:time (C) gourmet:food
(D) cherry:fruit (E) intelligence:personality
This is a relatively easy analogy. Since football is one of a number
of sports, the correct answer must involve some object that is in-
cluded in a larger group described by the second part of the answer.
The choice that best fits this description is (D), "cherry:fruit."
6. AXIOM:HYPOTHESIS::
(A) self-evident:tentative (B) concrete:abstract (C) fact:fancy
(D) assume:conclude (E) adage:maxim
This relatively difficult analogy requires that you analyze the rela-
tionship between "axiom" and "hypothesis" in order to arrive at the
correct answer. Since an axiom is a self-evident truth, while a hy-
pothesis is a tentative statement assumed as a basis for reasoning,
the best answer is (A).
Reading comprehension. Approximately half of the time on the Ver-
bal section of the PSAT is devoted to measures of reading comprehen-
sion, because it is important that college students be able to read with
10
understanding, insight, and discrimination. The selections come
from a variety of fields, such as history, social science, physical sci-
ence, biological science, music, art, literature, and philosophy.
Reading comprehension is tested at several levels. Some of the
questions depend simply on an understanding of the plain sense of
what has been directly stated. To answer other questions, you must
be able to interpret and analyze what you have read. Still other ques-
tions are designed to test your ability to recognize reasonable appli-
cations of the principles or opinions expressed by the author. And
some of the questions require you to judge what you have read—to
observe good and bad points in the presentation, to recognize how
far the author has supported his statements by evidence, and to rec-
ognize and evaluate the means used by the author to get his points
across.
Directions: Each passage in this group is followed by questions based
on its content. After reading a passage, choose the best answer to each
question. Answer all questions following a passage on the basis of
what is stated or implied in that passage.
(The passages for this test have been adapted from published mate-
rials to provide the candidate with significant problems for analysis
and evaluation. The ideas contained in the passages are those of the
original author and do not necessarily represent the opinions of the
College Entrance Examination Board or Educational Testing Service.)
Talking with a young man about success and a career, Doctor Sam-
uel Johnson advised the youth “to know something about everything
and everything about something.” The advice was good—in Doctor
Johnson’s day, when London was like an isolated village and it took a
week to get the news from Paris, Rome, or Berlin. Today, if a man
were to take all knowledge for his province and try to know something
about everything, the allotment of time would give one minute to each
subject, and soon the youth would flit from topic to topic as a butterfly
from flower to flower; life would be as evanescent as the butterfly
that lives for the present honey and moment. Today commercial,
literary, or inventive success means concentration.
7. The author implies that a modern scientist
(A) makes discoveries by accident
(B) must bend his mind in a specific direction
(C) is able to contribute only if he has a background of general
knowledge
11
Page 313
(D) must be well versed in the arts
(E) must be successful, whatever the cost
This is a "plain-sense" question. The author gives Dr. Johnson's
view, which he says was good in Dr. Johnson's day, and then gives
his own view of what is true today. He says that success in a particu-
lar field—science, as well as any other—today demands concentration
within that field. The answer, then, is (B). Some students answer
(C); but (C) is true of Dr. Johnson's view and is directly contrary
to the author's.
Question 8 is harder, but still requires only an understanding of
the plain sense of the selection.
8. According to the passage, if we tried now to follow Doctor Johnson's
advice, we would
(A) lead a more worthwhile life
(B) have a slower-paced, more peaceful, and more productive life
(C) fail in our attempts
(D) hasten the progress of civilization
(E) perceive a deeper reality
The author has tried to show that it is impossible today to follow
Dr. Johnson's advice; in one minute per topic, no one could learn
much of anything. So the answer to question 8 is (C). Some students
answer (B) and some answer (D); however, the author nowhere
implies that we could or should turn the clock back. These may
be the students' own views, but the question is not asking for them.
9. Why does the author compare the youth to a butterfly (next-to-last
sentence)?
(A) Butterflies symbolize a life of luxury and ease.
(B) The butterfly, like the youth, exhausts a present source of energy.
(C) The butterfly, like the youth, has no clear single objective.
(D) The butterfly, like the youth, is unaware of the future.
(E) The butterfly lives but a short time and thus retains the inno-
cence of youth.
To answer this question, you should understand why it suits the
author's purpose to compare the youth to a butterfly. All five of the
choices state comparisons that could reasonably be made. But only
one of the comparisons, (C), deals with "concentration," or the
"single objective," which the author is driving at.
12
10. In which one of the following comparisons made by the author is the
parallelism of the elements least satisfactory?
(A) Topics and flowers
(B) The youth and the butterfly
(C) London and an isolated village
(D) Knowledge and province
(E) Life and the butterfly
Sometimes an author uses comparisons that are not very reasonable
ones. In question 10 you are asked to look critically at what has
been said.
The same kind of thinking needed in the analogies is called for
here. The comparisons in (A) and (B) are satisfactory. The au-
thor's statement that "the youth would flit from topic to topic as a
butterfly from flower to flower" is a clear and effective comparison.
Choice (C) is also satisfactory; by today's standards, Johnson's
London was very much like an isolated village. The word "province"
(D) is often used to refer to a person's sphere of interest or activity
and the philosopher who took all knowledge as his province is well
known--whether or not his name comes to mind; so (D) is satisfac-
tory. But in (E) the comparison is a little shaky. What the author
really means is that human life would be like the life of a butterfly--
aimless and evanescent—not that human life would be like the butter-
fly itself. The least satisfactory comparison, then, is (E).
Mathematical section
Some questions in the Mathematical section require you to apply
graphical, spatial, numerical, symbolical, and logical techniques to
situations already familiar to you; these may be similar to exercises
in your textbooks. In other questions you are presented with novel
situations and are called upon to do original thinking and problem-
solving. You will not be expected to use mathematical knowledge
beyond elementary algebra or the geometry implied by the formulas
printed for your reference at the beginning of each Mathematical
section of the test. Although no specific knowledge of subject matter
beyond that just described is required, well-taught courses in mathe-
matics preceding and following the ninth grade will probably im-
prove your performance on the PSAT and will provide a stronger
foundation for your college-level work.
13
Page 314
The following sample questions illustrate both the types of prob-
lems and the range of difficulty to be expected in the PSAT.
Directions: In this section solve each problem, using any blank space
in the booklet for figuring. Then select the one correct answer.
The following information is for your reference in solving some of
the problems:
Circle:
area = πr²
circumference = 2πr
degrees of arc in a circle = 360°
Straight angle = 180°
Triangle:
sum of the angles of a triangle = 180°
If CD is perpendicular to AB, then
(1) area of △ABC = AB × CD / 2
(2) AC² = AD² + DC²
C
A D B
Definitions of symbols:
< means "is less than"; > means "is greater than";
≤ means "is less than or equal to"; ≥ means "is greater than or equal
to";
⊥ means "is perpendicular to"; ∥ means "is parallel to."
Note: Figures accompanying problems are not necessarily drawn to
scale.
11. If there are P girls and R boys in a class, what is the ratio of the num-
ber of girls to the total number of boys and girls in the class?
(A) P - R / P + R (B) P / P + R (C) P / R (D) R / P (E) P + R / P
This question requires the construction of a ratio. One might first
think of the answer in this form: girls / class and then in this form:
girls / girls + boys. Direction letter substitution gives us: P / P + R.
14
12. City R is 200 miles directly east of city T, and city H is 150 miles
directly north of T. What is the shortest distance (in miles) between
H and R?
(A) 50√7 (B) 175 (C) 250 (D) 300 (E) 350
This question involves the Pythagorean Theorem and the recogni-
tion of a right triangle. One must see that the ratio 150/200 is the same
as 3/4, thus making this a 3-4-5 right triangle or a 150-200-250 right
triangle.
13. A square and an equilateral triangle have equal perimeters. What is
the length of a side of the triangle if the area of the square is 9?
(A) 3 (B) 4 (C) 6 (D) 9 (E) 12
If the area of the square is 9, its side is 3 and its perimeter is 12. If
the perimeter of an equilateral triangle is also 12, its side is 4.
▬▬▬▬▬▬▬▬▬
│
(◌)← 80 pounds
(◌)← 20 pounds
(◌)← 35 pounds
(◌)← 45 pounds
(◌)← 20 pounds
│
┌───┐
│ W │
└───┘
14. The chain in the figure above has 5 links. The maximum weight that
each link can hold is shown. What is the maximum weight W, in
pounds, that the chain can hold?
(A) 20 (B) 35 (C) 45 (D) 80 (E) 200
Since "a chain is no stronger than its weakest link," this chain can
hold no more than 20 pounds.
15. If the area of a certain triangle is equal to one-half the product of two
of its sides, what kind of triangle is it?
(A) Equilateral (B) Acute (C) Right (D) Obtuse
(E) It cannot be determined from the information given.
15
Page 315
If the area of a triangle is one-half the product of two sides, one side
must serve as the base and the other side as the altitude. This occurs
only in the case of the two legs of a right triangle.
16. If an arrow (→) between two expressions indicates that the expres-
sion on the right exceeds the expression on the left by 1, then which
of the following is (are) true?
I. x² → (x + 1)²
II. x/y → (x + 1)/(y + 1)
III. x(x + 2) → (x + 1)²
(A) None (B) I only (C) II only (D) III only (E) I and II
In this question, you must work with a new symbol that has been
defined. In cases I and III the right expressions must be expanded
before comparison. In I, the right member exceeds the left by 2x + 1.
In II, the right member exceeds the left by (y - x) / y(y + 1). In III, the right
member exceeds the left by 1, making (D) the correct answer.
17. If rain is falling at the rate of 2 inches per hour, how many inches of
rain will fall in x minutes?
(A) 1/30x (B) x/30 (C) 30/x (D) 60/x (E) 30x
This question requires relational thinking with rates. Since inches
per hour times hours equals inches, 2 × x/60 = x/30 inches of rain.
18. If the radius of circle X is 40% of the radius of circle Y, the area of
circle X is what per cent of the area of circle Y?
(A) 16 (B) 20 (C) 40 (D) 80 (E) 160
If the radius of circle X is R, that of circle Y is .4R. Therefore, the
area of circle X is πR² and of circle Y is .16πR². The per cent is
.16πR² / πR² × 100 = 16.
16
Page 316
Affix label with student's name and scores here
⟦Y⟧our scores on the
Preliminary Scholastic
Aptitude Test
The numbers above are the scores you made
several weeks ago on the Preliminary Scholastic
Aptitude Test of the College Entrance Exam-
ination Board. The purpose of this leaflet is to tell
you what these scores mean and to suggest how
to use this information in planning for college.
The questions you answered on the Verbal and
Mathematical parts of the PSAT measured your
ability to reason with verbal and quantitative
Page 317
2
material — to read with skill and understanding
and use words correctly, and to understand
numbers and their use in solving problems.
Since these abilities are important for good work
in college, your test scores give an indication
of how well you might do in college.
Scores on the PSAT run from a low of 20 to
high of 80 points on a scale similar to the
200 to 800-point scale used for the College
Board’s Scholastic Aptitude Test, which is taken
by many seniors for admission to college. Both
the PSAT and the SAT score scales are arbitrary
ones that were chosen to avoid resemblance to
other marking scales in use, like the one running
up to 100. “Scaled scores” are simply your
marks on the test expressed in terms of its special
score scale. The 20 to 80-point PSAT score scale
has no passing or failing marks.
To give you some idea of what your PSAT scores
mean on a national basis, Figures 1 and 2
show how all high school juniors and seniors
might have done if they had taken the PSAT when
you did. You can use these charts to figure o⟦ut⟧
where your scores place you among all juniors o⟦r⟧
seniors. For example, suppose that a junior,
Paul, scored 46 on the Verbal part of the test.
You can see from the “PSAT Verbal” part of
Figure 1 that 5% of all juniors would receive
scores near Paul’s—between 45 and 49.
By adding up the per cents above the 45-49
group you see that about 6% of all juniors would
get higher scores than Paul’s. Similarly, if you
add up the per cents below 45, you will find that
about 89% would do worse than Paul did.
Now, looking at the “PSAT Mathematical” part
of Figure 1, suppose Paul’s Mathematical score
Copyright 1959 by College Entrance Examination Board
3
Figure 1: Scores of all school juniors
(if all juniors took the PSAT)
| PSAT Verbal |
| ⟦60⟧ & above | 1% |
| 55-59 | 2% |
| ⟦50-54⟧ | 3% |
| 45-49 | 5% |
| 40-44 | 10% |
| 35-39 | 24% |
| 30-34 | 31% |
| Below 30 | 24% |
| PSAT Mathematical |
| 60 & above | 2% |
| 55-59 | 7% |
| 50-54 | 12% |
| 45-49 | 17% |
| 40-44 | 16% |
| 35-39 | 19% |
| 30-34 | 21% |
| Below 30 | 6% |
Note: Students who have taken the Preliminary
Scholastic Aptitude Test in competing for
sponsored scholarships should await direct word
from scholarship program sponsors, who will
notify only those applicants who qualify for
further consideration or awards. The College
Board does not select potential scholarship
winners, notify finalists, or award scholarships.
Inquiries concerning particular scholarship
programs that require the PSAT should
be addressed to the individual programs.
Page 318
4
is 43. This puts him among those who had scores
between 40 and 44. Sixteen per cent of all
juniors would have scores in this vicinity. About
38% would have scores higher than Paul's and
about 46% would have Mathematical scores
lower than his.*
See where your own scores place you on these
charts. If you are a senior, use Figure 2 to ⟦...⟧
where you stand among all seniors.
Should you go to college? Because the PSAT is
a shorter version of the Scholastic Aptitude Test,
your PSAT scores can also tell something about
your chances of being successful at a variety of
colleges. The Scholastic Aptitude Test is required
of applicants at several hundred colleges. It
enables these colleges to compare the academic
promise of all their applicants on the same basis.
PSAT scores, available to you early in your junior
or senior year, make it possible for you to begin
now to think seriously about your chances for
success at different types of colleges.
Of course, test scores do not tell the whole
story about you, for no test is a perfect indic⟦...⟧r
of future college success. In fact, your high
school record—your grades, the academic sub-
jects you studied, your rank in class—agrees
better than anything else with what your achieve-
ment in college will be. This is because your
desire to learn as well as your ability to
learn are both reflected in your school record.
Later on, therefore, colleges will use both what-
*In general, girls do less well than boys on the
Mathematical part of the test and should not be surprised
if their Mathematical scores are lower than their
Verbal scores.
5
Figure 2: Scores of all school seniors
(if all seniors took the PSAT)
| PSAT Verbal |
| 60 & above | 3% |
| 55-59 | 2% |
| ⟦50-54⟧ | 5% |
| 45-49 | 8% |
| 40-44 | 13% |
| 35-39 | 23% |
| 30-34 | 27% |
| Below 30 | 19% |
| PSAT Mathematical |
| 60 & above | 6% |
| 55-59 | 7% |
| 50-54 | 11% |
| 45-49 | 16% |
| 40-44 | 17% |
| 35-39 | 18% |
| 30-34 | 19% |
| Below 30 | 6% |
ever test scores they have for you and your
school record to evaluate your application. If you
have high scores and a mediocre school record,
you may not be working hard in school. Low
scores can often be outweighed by a school
record that shows that you are serious about your
school work. In general, though, your test
scores should agree with your day-by-day per-
formance. If both are good, the chances are that
you will do well in college. If both are low, you
may have difficulty with college work.
Page 319
6
In addition to the information revealed by
your scores and school record, colleges like to
know about you as a person. This they learn
from your school, from interviews, and from
accounts of your outside activities. Colleges know
that the adjustment to independent study
and responsibility requires that students have
developed some degree of maturity and hence
often look for evidence of this. Thus, no single
part of your total record will be all-important;
colleges will judge your promise by a com-
bination of school work, test scores, and outside
activities. You should judge your readiness
for college in the same way.
The majority of the students who enter college
comes from the top half of their high school
classes. If you stand well up in your class and, in
addition, have PSAT scores that place you in
the upper half of all juniors or seniors—scores
around 35 or better—you should seriously
consider going on to college. If you do have
scores this high and have decided against college,
you should take up this question with your
school advisers. These people are in a good pos⟦i-⟧
tion to help you review your plans and to
assist you in exploring ways of financing your
college education if lack of funds has
prompted your decision against college.
On the other hand, if you scored below 35 but
are doing good work in academic subjects
and planning on college, you should not at all
alter your course. When you begin to think about
possible colleges, see your school adviser early,
for his experience with many students and his
knowledge of many colleges and their require-
ments will help to put you on the right track.
Page 320
8
Your prospects of admission: There are well
over 1,000 four-year colleges and universities in
the country and more than 600 two-year junior
colleges and technical schools. Some are state
universities, others are private or church-related
colleges. Some of these colleges have rigorous
academic standards and admit only those stude⟦illegible⟧
who have high ability and superior school
records. Other colleges, with a smaller ratio of
applicants to available openings, admit almost all
of the qualified students who apply. Still other
colleges admit all applicants, although many of
these colleges expect their students to meet high
academic standards and give failing grades to
those who do poorly. Sometimes a large university
will have stricter requirements for one division,
like its engineering school, than for another.
Thus, as you see, colleges have different require-
ments, serve different purposes, and educate
different groups of students.
Because admissions requirements at different
types of colleges vary widely, it may be
helpful for you to compare your PSAT scores w⟦illegible⟧
the estimated PSAT scores of enrolled freshmen
at three actual colleges of good reputation.
These are charted in Figure 3. The scores shown
are those that would have been made by
these freshmen when they were high school
juniors. If you are a senior, subtract 4 points
from each of your PSAT scores to see where your
PSAT scores place you in relation to these three
college freshman classes.
Let us consider what Figure 3 means for
individual students like yourself. College X is
typical of a relatively small group of colleges that
have very high admissions standards. Their
Figure 3: Scores of freshmen at three colleges (if they had been tested as high school juniors)
| College X | College Y | College Z |
| PSAT
Verbal | PSAT
Mathematical | PSAT
Verbal | PSAT
Mathematical | PSAT
Verbal | PSAT
Mathematical |
| 1% | 1% | 75-80 | | 75-80 | |
| 4% | 3% | 70-74 | 1% | 70-74 | |
| 13% | 14% | 65-69 | 1% | 1% | 65-69 | |
| 20% | 17% | 60-64 | 3% | 3% | 60-64 | 1% | 2% |
| 24% | 22% | 55-59 | 16% | 9% | 55-59 | 2% | 3% |
| 17% | 19% | 50-54 | 22% | 16% | 50-54 | 7% | 6% |
| 12% | 13% | 45-49 | 26% | 23% | 45-49 | 14% | 12% |
| 7% | 8% | 40-44 | 17% | 25% | 40-44 | 22% | 22% |
| 2% | 3% | 35-39 | 10% | 15% | 35-39 | 27% | 28% |
| | | 30-34 | 4% | 6% | 30-34 | 15% | 17% |
| | 1% | 25-29 | 1% | 1% | 25-29 | 8% | 7% |
| | | 20-24 | | | 20-24 | 4% | 3% |
Page 321
10
students usually come from the top 5 to 10 per
cent of their high school classes and have
correspondingly high test scores. Students
admitted to colleges like X rarely fail academi-
cally because these colleges accept only
highly qualified students.
To use our earlier example of Paul, whose
Verbal and Mathematical scores are 46 and 43,
you can see from Figure 3 that his chances
of success at College X are slim. Only 12 per cent
of the enrolled freshmen have Verbal PSAT
scores near his. Nine per cent have lower scores,
while 79 per cent have higher scores. Paul’s
Mathematical score of 43 is also very low at
College X, falling in the bottom 11 per cent.
This college has learned that students with scores
like Paul’s and with only fair high school
grades usually fail if admitted. Although some
students with these scores were admitted, the out-
look for students like Paul is not very bright
at X, unless they have unusually good school
records or other outstanding accomplishments.
Such students would probably do better to
consider a college where the prospects for
admission and success are better. Remember that
test scores do not tell the whole story—many
students with very high scores were not admitted
at X because they lacked other qualifications.
College Y is, of course, typical of a great many
more colleges than the small number of colleges
like X. Here, our hypothetical student looks
more promising. A Verbal score of 46 is better
than 32 per cent of the class and exceeded by
about 42 per cent, while a Mathematical score of
43 is better than 22 per cent and worse than
53 per cent. Thus Paul stands at about the middle
Page 322
13
of the class at College Y and, if his other
credentials are equally favorable, his chances for
admission and success are good.
Turning now to College Z—representative of a
much larger group of colleges than all those
similar to X and Y put together—we see that Paul's
scores, 46 Verbal and 43 Mathematical, place
⟦him⟧ in about the top quarter of the class. With a
good school record Paul should do very well
academically at College Z. Perhaps College Z is a
college that accepts all applicants and then
gives failing marks to the sizable group of
students who do unsatisfactory academic work
according to its standards. But even if it is, Paul
would stand high enough in its freshman class
to indicate that he has the ability to do
successful work at this college.
A simple way to see where Paul would stand
among the freshmen at all three colleges is
to draw a line representing each of his scores
right across all three charts. If this were done
first for his Verbal score, the picture of his rela-
⟦tive⟧ standing would look in outline like Figure 4.
Figure 4
Verbal
Paul Verbal
X Y Z
46
From Figure 4 you can see that, in PSAT
Verbal score, Paul would stand below most of the
freshmen at College X, at about the middle of
the freshmen at College Y, and above most of the
freshmen at College Z. His actual standings
in percentages can be read from the full charts as
already explained.
Page 323
15
To see where Paul stands with respect to his
Mathematical score, we would draw another
line across all three charts as in Figure 5.
We could then make similar observations about
where he would stand among the freshmen at
each college on the basis of Mathematical score.
⟦Figu⟧re 5 Mathematical Paul Mathematical
X Y Z 43
Now, by drawing lines across the three charts
in Figure 3 in just the same way for your
own scores, see where you would stand among
the freshmen at Colleges X, Y, and Z.
One more comparison of the relative standing
at the three colleges of an individual student
—like yourself or Paul—may be worth while. To
illustrate in Paul's case, let us again draw a
line for his PSAT Verbal score across the charts of
all three colleges. But this time, let us also include
⟦illegible⟧ part of the Figure 1 chart showing how all
⟦illegible⟧nior-year students in the country would score in
PSAT Verbal if all took the test. The result would
appear in outline as shown in Figure 6.
Figure 6 Verbal Paul Verbal
All juniors X Y Z 46
The important thing to notice in Figure 6
is that, although Paul would stand higher than
most juniors in the country, he would stand
lower than most others in the entering class at
Page 324
16
College X and only at about the middle of
the class at College Y.
Of course, you would rather know how you
compare with the freshmen at those colleges you
are considering rather than at X, Y, and Z.
But many colleges do publish and send to school
officials the type of information shown for
X, Y, and Z. These freshman class descriptions
usually present information not only on test
scores, but on high school grades and many other
factors used by the college in selecting a class.
Your school adviser has leaflets like these as well
as much other information about colleges' require-
ments. In addition, conferences with college
admissions officers, either at your school or at the
colleges, will prove helpful in assessing your
prospects.
College Entrance Examination Board
425 West 117 Street, New York 27, N. Y.
[Stamp] ceeb
Photos by George Zimbel
Page 325
Your College Board Scores
Several weeks ago, you spent three hours taking the Scholastic Aptitude
Test of the College Entrance Examination Board. Since that time, your
test has been carefully graded and a report of the scores you made has
been sent to the various colleges you named and to your secondary school.
The colleges are now comparing your scores with all of the other evidence
they have collected about you (such information as secondary school
record, principal's recommendation, and evidences of extracurricular
activities). They are also comparing all of your credentials with those of
the other applicants they are considering for admission.
We cannot, of course, tell you whether you will be admitted to one or
more of the colleges to which you have applied. This is a decision which
only those colleges can make. We can, however, tell you something about