3 Practice Tests + Review and Techniques PSAT/NMSQT Prep (2021)

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Acknowledgments
Special thanks to Sara Kuperstein, Amy Minster, and Cynthia Ward for
their contributions to this edition, as well as Aaron Lindh for his expert
guidance.
Thanks also to Anne Bader, Kevin Baldwin, Gabby Budzon, Grace
Cannon, Nicole Cosme, April Davis, Anne Goldberg-Baldwin, Brian
Hong, Brad Kelly, Jomil London, Dave MacKenzie, Amanda Nowotny,
Scott O’Neal, Danielle Perrini, Xander Posner, Jess Thomas, Christina
Torturo, and Jimmy Williams.
The Princeton Review would also like to thank Kris Ogilvie, Liz Dacey,
and Emily Epstein White for their time and attention to each page.
Special thanks to Adam Robinson, who conceived of and perfected
the Joe Bloggs approach to standardized tests, and many other
techniques in this book.

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Contents
Cover
Title Page
Copyright
Acknowledgments
Get More (Free) Content
Part I: Orientation
1 What Is the PSAT/NMSQT?
2 All About the National Merit Scholarships
3 General Strategies
Part II: Practice Test 1
4 Practice Test 1
5 Practice Test 1: Answers and Explanations
Part III: PSAT/NMSQT Prep
6 Reading Comprehension
7 Introduction to Writing and Language Strategy
8 Punctuation
9 Words
10 Questions
11 Math Basics
12 Math Techniques
13 Advanced Math
14 Additional Math Topics
Part IV: Drill Answers and Explanations

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Access printable resources, including a score conversion table, a
study guide, and extra bubble sheets for the practice tests in this
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Chapter 1
What Is the PSAT/NMSQT?
The PSAT/NMSQT—from now on, we’ll just call it the PSAT—is a
standardized test given primarily to high school juniors to give them a
“preliminary” idea of how well they could do on SAT question types.
The test is also used to determine which students are eligible for
National Merit Scholar recognition. This chapter will give you a
general overview of the test and how it is used, along with the basics to
start your preparation. First, a glimpse at the other tests in the College
Board’s Suite of Assessments: the PSAT 8/9 and the PSAT 10.

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PSAT 8/9
Just like the SAT and PSAT, the PSAT 8/9, which is designed for
eighth and ninth graders, contains a Reading Test, a Writing and
Language Test, and a Math Test. The content of each subject is
comparable to the content on the PSAT and SAT.
According to the College Board, the “Evidence-Based Reading and
Writing section asks you to interpret, synthesize, and use evidence
found in a wide range of sources.” The bottom line: be prepared to
justify your selected answer with evidence from the passage and/or
graph provided. This test is still not about making up anything, but
finding the correct answer based on the text.
The College Board also claims that the “Math Test focuses in-depth on
two essential areas of math: Problem Solving and Data Analysis, and
Heart of Algebra.” The bottom line: expect to see Algebra I and II,
some Geometry, as well as questions that have charts, graphs, data
tables, scatterplots, or other form of data display provided.
Psst…
There’s the PSAT 8/9, the PSAT 10, and
PSAT/NMSQT. But when we refer to just the plain
old “PSAT” in this book, we’re referring to the
PSAT/NMSQT.
The Math Test is split into two sections: one in which a calculator may
be used and one in which it may not be used. Even though a calculator
is allowed in one section, it is up to the test-taker to determine
whether the calculator will be a benefit in solving a question.
According to the College Board, “students who make use of structure
or their ability to reason will probably finish before students who use a
calculator.” The bottom line: show your work and use the calculator
for tedious calculations, but a calculator most likely will not be
necessary to solve a majority of the questions.
All questions in the Evidence-Based Reading and Writing section are

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multiple choice. Most of the Math Test questions are multiple choice,
with 18 percent of all Math Test questions in the grid-in, or student-
produced, format. For each question answered correctly, one raw
point is earned, and there is no penalty for an incorrect response or a
question left blank. The bottom line: don’t leave anything blank!
PSAT 10
Though this test is called the PSAT 10, it is identical to the structure of
the PSAT/NMSQT in terms of both number of questions and time
limits per section. The major differences are who takes the test and
when: 10th-graders and schools choose a date in the spring.
Additionally, this test does not qualify you for National Merit
Scholarship consideration.
Just as with the SAT and the PSAT, the PSAT 10 includes an Evidence-
Based Reading and Writing section and a Math Test. The Evidence-
Based Reading and Writing section tests the ability to select, among
the choices provided, the answer that is best evidenced in the provided
passage and/or informational graphics that accompany select
passages. The Math Test is divided into two sections: one in which a
calculator may be used and one in which it may not be used. Even
though the calculator is allowed in one section, it is up to the test-taker
to determine whether or not the calculator will prove necessary.
WHAT’S WITH ALL THESE SCORES?
The PSAT (and the PSAT 8/9, PSAT 10, and SAT) is designed
(according to College Board) to reflect how prepared you are for
college and the working world. While we at The Princeton Review may
take issue with that claim, this idea does inform both how College
Board recommends you prepare and why there are so many different
scores on your score report.
The College Board maintains that the best way to prepare for the test
is to:

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take challenging courses
do your homework
prepare for tests and quizzes
ask and answer lots of questions
How Do You Pronounce PSAT/NMSQT, Anyway?
Ah, yes—first things first. Well, to be honest, we’re
not really sure. You can pronounce it pee-sat-nim-
squit if you want. However, we think it’s easier just
to call it the PSAT.
College admissions advisors wanted a more “well-rounded” picture of
the applicant, so the College Board did its best to meet the demand.
The test provides a measurement of four Evidence-Based Reading and
Writing Subscores (Command of Evidence, Words in Context,
Standard English Conventions, and Expression of Ideas), and three
Math Subscores (Heart of Algebra, Problem Solving and Data
Analysis, and Passport to Advanced Math).
In addition to the seven subscores reported, the College Board now
provides two cross-test scores to offer more insight: one score for
Analysis in History/Social Studies and another for Analysis in Science.
Remain calm; these scores are gathered only from select questions
that deal with appropriate subject matter and are not actual entire test
sections. We will go into PSAT scoring in more detail later.
When Is the PSAT Given?
The PSAT is officially administered twice each year, typically on a
Wednesday and Saturday of the same week in October. Your school
will announce the exact dates at the beginning of the school year, or
you can find out at PrincetonReview.com, or through the College
Board at CollegeBoard.org.
Keep on Schedule
You’ll officially take the PSAT in the fall of your

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junior year. Plan to take the SAT anytime between
the winter of your junior year and the fall of your
senior year.
How Do I Sign Up for the PSAT?
You don’t have to do anything to sign up for the PSAT; your school will
do all the work for you. Test registration fees can vary from school to
school, so be sure to check with your school counselor if you have
questions about how much the PSAT will cost you.
What About Students with Special Needs?
If you have a diagnosed learning difference, you will probably qualify
for accommodations on the PSAT. However, it’s important that you get
the process started early. The first step is to speak to your school
counselor who handles learning differences. Only he or she can file the
appropriate paperwork. You’ll also need to gather some information
(documentation of your condition) from a licensed practitioner and
some other information from your school. Then your school counselor
will file the application for you.
You will need to apply for accommodations only once; with that single
application you’ll qualify for accommodations on the PSAT, SAT, SAT
Subject Tests, and AP Exams. The one exception to this rule is that if
you change school districts, you’ll need to have a counselor at the new
school refile your paperwork.
Does the PSAT Play a Role in College Admissions?
No! The PSAT plays no role in college admissions. It’s really just a
practice test for the SAT.
The one exception is for that very small group of students, about 4
percent of all students nationwide, whose PSAT scores qualify them
for National Merit recognition. (We’ll tell you more than you ever
wanted to know about that in the next chapter.) Recognition as a
commended scholar, semifinalist, or finalist for National Merit is a
fairly impressive addition to your college admissions portfolio, and is

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something that you should certainly pursue if you are seriously in
contention for it.
What Happens to the Score Report from the PSAT?
Only you, your high school, and the National Merit Scholarship
Corporation (which co-sponsors the PSAT) will receive copies of your
score reports. They won’t be sent to colleges.
WHAT DOES THE PSAT TEST?
As you begin your prep, it’s useful to remember that the PSAT is not a
test of aptitude, how good of a person you are, or how successful you
will be in life. The PSAT simply tests how well you take the PSAT.
That’s it. And performing well on the PSAT is a skill that can be
learned like any other. The Princeton Review was founded 40 years
ago on this very simple idea, and—as our students’ test scores show—
our approach is the one that works.
All of these changes to tests that you hear could heavily influence your
college admission strategy can be extremely daunting. However,
remember that any standardized test is a coachable test. A beatable
test. Just remember:
The PSAT doesn’t measure the stuff that matters. It measures
neither intelligence nor the depth and breadth of what you’re learning
in high school. It doesn’t predict college grades as well as your high
school grades do. Colleges know there is more to you as a student—
and as a person—than what you do on a single test.
Who Writes the PSAT?
The PSAT is written and administered by the College Board and used
for scholarships by National Merit Scholarship Corporation. You
might think that the people at the College Board are educators,
professors of education, or teachers. They’re not. They are people who
just happen to make a living writing tests. In fact, they write hundreds
of tests, for all kinds of organizations.

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The folks at the College Board aren’t really paid to educate; they’re
paid to write and administer tests. And even though you’ll be paying
them to take the PSAT, you’re not their customer. The actual
customers the College Board caters to are the colleges, which get the
information they want at no cost. This means that you should take
everything that the College Board says with a grain of salt and realize
that its testing “advice” isn’t always the best advice. (Getting testing
advice from the College Board is a bit like getting baseball advice from
the opposing team.)
Every test reflects the interests of the people who write it. If you know
who writes the test, you will know a lot more about what kinds of
answers will be considered “correct” answers on that test.
WHAT IS THE PRINCETON REVIEW?
The Princeton Review is the nation’s leading test-preparation
company. In just a few years, we became the nation’s leader in SAT
preparation, primarily because our techniques work. We offer courses
and private tutoring for all of the major standardized tests, and we
publish a series of books to help in your search for the right school. If
you’d like more information about our programs or books, give us a
call at 800-2-Review, or check out our website at
PrincetonReview.com.
Shortcuts
The Princeton Review’s techniques are the closest
thing there is to a shortcut to the PSAT. However,
there is no shortcut to learning these techniques.
HOW TO USE THIS BOOK
This book is divided into five parts. The first three parts of the book
contain Practice Test 1 and general testing strategies and question-
specific problem-solving instruction. Use the first practice test as a
diagnostic to see which sections of the test you need to work when you

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read through the content chapters. The last two parts of the book
contain Practice Test 2 and drill answers and explanations. After
working through the content chapters and checking your answers and
the explanations to the chapter drills, take Practice Test 2 and apply
everything you’ve learned to improve your score. The “Session-by-
Session Study Guide” starting on this page will give you a plan of
attack for these tests and the rest of the book. There is no single plan
that will fit everyone, so be prepared to adapt the plan and use it
according to your own needs. For additional practice, you can
download one more practice test online by registering your book on
our website and following the steps to access your online resources.
(See “Get More (Free) Content on this page.)
Practice Test 1 will give you an idea of your strengths and weaknesses,
both of which can be sources of improvement. If you’re already good at
something, additional practice can make you great at it; if you’re not
so good at something, what you should do about it depends on how
important it is. If the concept is one that frequently appears on the
test, you should spend a lot of time on it; if it comes up only once in a
while, you should spend very little time working on it and remember
that it’s something you should either put off until you’ve completed
easier things or skip it entirely.
How do you know what’s important? We’ll tell you throughout this
book, when we discuss techniques like Plugging In and so forth, but
you can also get an idea of what to focus on simply by observing how
this book is laid out. The most important concepts in each section
appear first in the corresponding section of this book. For example, if
you’re shaky on critical reading, you know you’ll need to devote some
time to Reading questions because there are a total of 47 such
questions on the test. And if you’re not so confident when it comes to
geometry, don’t panic: geometry questions appear only in the
Advanced Math chapter, which tells you that this topic isn’t as much of
a priority as Plugging In or Math Basics.
Time Management

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To manage your PSAT preparation, make use of the study guide on the
following pages. This guide will break down the seemingly daunting
task of PSAT prep into bite-sized pieces we call “sessions.” We have
mapped out tasks for each session to be sure you get the most out of
this book. The tests will be the first and last sessions, so you should be
sure to plan to have about three hours for these sessions. Most other
sessions will last between an hour and two hours, so plan to take a
short break in the middle, and if it looks like the session is going to
exceed two hours, feel free to stop and pick up where you left off on the
next day.
When You Take a Practice Test
You’ll see when to take practice tests in the session outlines. Here are
some guidelines for taking these tests:
Time yourself strictly. Use a timer, watch, or stopwatch that will
ring, and do not allow yourself to go over time for any section. If
you try to do so at the real test, your scores will probably be
canceled.
Take a practice test in one sitting, allowing yourself breaks of no
more than two minutes between sections. You need to build up
your endurance for the real test, and you also need an accurate
picture of how you will do. However, do take 5-minute breaks after
the Reading and Math (No Calculator) sections. On the real test
you will have a break, so it’s important not to skip it on the
practice tests.
Always take a practice test using an answer sheet with bubbles to
fill in, just as you will for the real test. For the practice tests in the
book, use the answer sheets provided at the back of this book. You
need to be comfortable transferring answers to the separate sheet
because you will be skipping around a bit.
Each bubble you choose should be filled in thoroughly, and no
other marks should be made in the answer area.
As you fill in the bubble for a question, check to be sure you are on

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the correct number on the answer sheet. If you fill in the wrong
bubble on the answer sheet, it won’t matter if you’ve worked out
the problem correctly in the test booklet. All that matters to the
machine scoring the test is the No. 2 pencil mark.
Session-by-Session Study Guide
Session Zero You’re involved in this session right now. Finish
reading the first chapter so you’ll know what the test is about, why it is
important for you to take, and what to expect from the rest of the
book. This step probably won’t take you long, so if you have about
three hours after you complete Chapter 1, you can go on to Session
One and take the first practice test.
Session One Take Practice Test 1 and score it. You’ll use this result to
get an idea of how many questions on each section you should attempt
before guessing strategically, and the parts of each section you should
concentrate on. Note that our explanations refer to concepts discussed
elsewhere in this book, so you may want to wait until after Session
Four before reviewing this test.
Session Two Work through Chapters 2 and 3 of the Orientation and
Chapter 6, Reading Comprehension.
Session Three Read Chapter 7, Introduction to Writing and
Language Strategy, along with Chapter 8, Punctuation.
Session Four Work through the Math Basics in Chapter 11 and the
corresponding drills.
Session Five Work through the Math Techniques section in Chapter
12 and associated drills. Take a look at Chapter 9, Words.
Session Six Review Advanced Math, Chapter 13. As you work through
this chapter, be sure to apply techniques like Plugging In that you
learned in Chapter 12. Since these techniques are central to doing well
on the math sections, you can never practice them too much. If there’s

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time, start Chapter 14.
Session Seven Work through the Additional Math Topics in Chapter
14. When you finish, read through Chapter 10, Questions. This will
give you a good idea of how the PSAT will put together all the things
you’ve gone over for the Writing and Language section of the test.
Session Eight Take Practice Test 2. Use the techniques you’ve been
practicing throughout the book. Score your test and go through the
explanations, focusing on where you may have missed the opportunity
to use a technique and your decisions about whether you should have
attempted a question or not, given your pacing goals and Personal
Order of Difficulty.
Some of the terminology in the study guide may be unfamiliar to you
now, but don’t worry, you’ll get to know it soon. Also, you’ll want to
refer back to this study guide at each session to keep yourself on track.
Don’t forget to download Practice Test 3 from your online student
tools for more prep!
…The Less to Study
While higher-level math may sound scary at first,
stay tuned for further information from us on the
most effective techniques to use on the PSAT that
can, sometimes, drastically reduce the math
complexity for many questions.
One important note: In this book, some sample questions do not
appear in numerical order within a chapter. For example, you might
see a question 4 followed by a question 14. This is because on the Math
sections of PSAT, a higher question number generally indicates a
higher level of difficulty (this is not the case with Reading or Writing
and Language). Chapter 3 has great advice on how to crack some of
the most difficult questions.
HOW IS THE PSAT STRUCTURED AND

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SCORED?
According to the College Board, the PSAT redesign of 2015 raised the
complexity of questions across the board. For the Reading and Writing
and Language Tests, this refers in part to the way in which all
questions are now connected to full passages, which are written at the
same level as writing expected in introductory college and vocational
training programs. This means that there will be a good amount of

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history- and science-based reading material. Additionally, there are no
longer any fill-in-the-blank sentence completion questions or stand-
alone sentence-editing questions. Instead, the PSAT tests your ability
to demonstrate a full understanding of a source’s ideas.
Moreover, the scope of math content focuses on a specific set of
problem-solving and analytical topics, and it includes high-level
content like trigonometry. You will also encounter more grid-in
questions, and you will face topics that are both specifically geared to
test your ability to use a calculator and for which calculators are not
permitted.
The Math Test is divided into two sections, one without a calculator,
with 17 questions over the course of 25 minutes, followed by one with
a calculator, with 31 questions administered in 45 minutes. Because of
the tight time limit, particularly in the No Calculator section, you
should work as efficiently as possible. To help you do this, even if you
answer a question correctly, we recommend that you review the
explanations for the questions in the drills and the practice tests. You
may discover techniques that help to shave seconds from your
solutions. A large part of what’s being tested is your ability to use the
appropriate tools in a strategic fashion, and while there may be
multiple ways to solve a given problem, you’ll want to focus on the
most efficient.
Scoring on the PSAT
The PSAT is scored on a scale of 320–1520, which is the sum of the
two section scores that range from 160–760. The two sections are the
Evidence-Based Reading and Writing section and the Mathematics
section. Wrong answers to multiple-choice questions are not
penalized, so you’re advised never to leave a question blank—even if
that means blindly picking a letter and bubbling it in for any
uncompleted questions before time runs out.

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Scoring Your Practice Tests
As you can see, scoring is a little tricky. That’s why
we provide scoring tables to help you determine
your approximate score. When we say that the
score is “approximate,” we mean that the score is
accurate for that particular test. However, the
number of questions you need to get right or wrong
to earn a certain score can vary depending on the
PSAT’s scale from test to test. For example, if you
miss 10 Math questions and get a 680 on a practice
test, that does not necessarily mean that 10 missed
Math questions on the actual exam will result in a
680 as well; you may get that score from missing 8
questions or 12 questions.
In addition to the overall total score and the section scores, you’ll find
several subscores on your PSAT score report.
Analysis in History/Social Studies and Analysis in Science
cross-test scores are generated based on questions from all three of the
subject tests (Math included!). These cross-test scores assess the
cross-curricular application of the tested skills to other contexts.
Relax! This doesn’t mean that you have to start cramming dates and
anatomy—every question can be answered from the context of a given
reading passage or the data included in a table or figure. The only
changes have to do with the content of the passages and questions
themselves.
Additionally, the Math Test is broken into several categories, as we’ve
done in this book. The Heart of Algebra subscore looks specifically
at how well students understand how to handle algebraic expressions,
work with a variety of algebraic equations, and relate real-world
scenarios to algebraic principles. Problem Solving and Data
Analysis focuses more on interpretation of mathematical

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expressions, graphical analysis, and data interpretation. Your ability to
understand what the question is asking will come in handy here.
Passport to Advanced Mathematics questions showcase the
higher-level math that’s been added to the test, from quadratics and
their graphs to the creation and translation of functions. Finally, there
is an Additional Topics domain that’s filled with what you might
consider wild-card material. Although these questions might not
correlate directly to a subscore, two of these miscellaneous types will
show up on the redesigned test.
In the Verbal portions of the test, the Command of Evidence
subscore measures how well you can translate and cite specific lines
that back up your interpretation, while the Words in Context
subscore ensures that you can select the best definition for how a word
is used in a passage. The Writing and Language Test additionally
measures Expression of Ideas, which deals with revising language
in order to make more logical and cohesive arguments, and Standard
English Conventions, which assesses your ability to conform to the
basic rules of English structure, punctuation, and usage.
HOW DOES THE SAT DIFFER FROM THE
PSAT?
The SAT does not differ significantly from the PSAT in structure and
timing! Indeed, the PSAT’s Reading Test, which contains 5 fewer
questions, is only 5 minutes shorter than the SAT’s Reading Test. The
Writing and Language Test is the same in terms of length and timing
for both tests. The PSAT’s Math Test has only 10 fewer total questions
as compared to those of the SAT’s Math Test. The tables below
summarize the differences—or actually, the similarities!—of the two
tests.
Here’s a breakdown of how the tests differ:

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Are You Ready for the SAT?
If you want to start preparing for the SAT, pick up a
copy of our SAT Premium Prep, which is chock full
of content review, strategy, and realistic practice!
What Does the PSAT Score Mean for My SAT Score?
The SAT is scored on a 1600 scale, whereas the PSAT is scored on a
1520 scale. However, because the PSAT and SAT are aligned by the
College Board to be scored on the same scale, your PSAT score
indicates the approximate SAT score you would earn were you to have
taken the SAT on that same day.
How Much Should I Prepare for the PSAT?
If you’re in that very small percentage of students who are in
contention for National Merit recognition, it may be worth your while
to put in a good deal of time to prepare for this test. After all, your
extra hard work may well put you in a better position for National
Merit recognition. Otherwise, you should prepare enough so that you

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feel more in control of the test and have a better testing experience.
(Nothing feels quite as awful as being dragged through a testing
experience feeling like you don’t know what you’re being tested on or
what to expect—except perhaps dental surgery.) The other reason to
prepare for the PSAT is that it will give you some testing skills that will
help you begin to prepare for the tests that actually count, namely the
SAT and SAT Subject Tests.
The bottom line is this: the best reason to prepare for the PSAT is that
it will help you get an early start on your preparation for the SAT.
Study
If you were getting ready to take a biology test,
you’d study biology. If you were preparing for a
basketball game, you’d practice basketball. So, if
you’re preparing for the PSAT (and eventually the
SAT), study the PSAT. The PSAT can’t test
everything, so concentrate on learning what it does
test.

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Preliminary Scholastic Aptitude Test

3 Practice Tests + Review and Techniques PSAT/NMSQT Prep (2021)

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