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Reading Guided Tour

The SAT Reading: A Guided Tour

The SAT Reading section doesn’t have a set curriculum. We aren’t expected to have read any of the passages that appear on the test. Our preparation for the Reading section will be less about memorizing specific rules and theorems and more about strategy and sheer practice.

Short Reading Passages
Long Reading Passages


As mentioned in the Introduction to this section, the reading section employs several common types of questions. These questions need you to use different strategies to answer them correctly.

Overarching Questions

It can be helpful to save questions that ask about the passage as a whole for last. If we start small (the questions that direct us to line numbers or specific paragraphs) and work our way up to these overarching questions, we’ll have a surer footing for these larger questions.

Word in Context Questions

These are the questions (like #3) that ask us for the meaning of a designated word in a specific line. The test writers will often put several equally viable synonyms of the word as answer choices, so it’s very important to go back to the specific line mentioned in the question to get a handle on exactly how the word was being used in that sentence.">

We can check our answer to a word in context question by replacing the word in the original sentence with our answer. If we’ve chosen the correct option, the new sentence we’ve made will have the same meaning as the original one.

Open-Ended Questions

These are the questions (like #4) that ask about a specific part of the passage but don’t direct us to the corresponding lines. Since the questions are usually asked in order, we can start looking for the answer to an open-ended questions where we found the answer to the previous question.

Paired Questions

Every passage will have a set of paired questions or two. One question will ask a question about the passage (like #5), then the next one will ask us for the best evidence to support our answer to that general question (like #6).

It’s best to do these questions together: answer the first question using the lines mentioned in the follow-up question. We can tell that a set of paired questions is coming up because all of the answers to one question will be line numbers (like #6).

The Blue Eyes/Brown Eyes Experiment

The Blue Eyes/Brown Eyes Experiment

In 1968, Iowa school teacher Jane Eliot was moved
by the assassination of Martin Luther King Jr. She
wanted to teach her elementary school students,
line most of whom came from a relatively homogeneous
5 community, about discrimination. Her students knew
about racial discrimination in an hypothetical way, but
Eliot wanted her students to understand how it felt to
be the victim of discrimination in a more personal way.
10 With the consent of her students, Ms. Eliot created an
experiment. She divided her class based on eye color.
Blue-eyed children got to sit in the front of the class,
were granted extra privileges, given second helpings
at lunch, and told that the additional melanin that gave
15 their eyes their color have them better genes overall.
Brown-eyed students were made to drink at separate
water fountains, made to wear brown collars around
their necks, and discouraged from playing with the
blue-eyed children.
20 After a few days, the blue-eyed children started acting
superior; the brown-eyed students adopted a
resigned passivity. Even their academic performance
changed. Blue-eyed students outperformed their
brown-eyed classmates on basic tests. Blue-eyed
25 students were so encouraged that they started
outperforming even Ms. Elliot's most hopeful
projections; brown-eyed students were so
discouraged that they started laughing behind their
own recent marks. The next week Ms. Eliot reversed
30 the experiment (now the brown-eyed students were
the privileged group), and the results were the same.
The participants in the experiment related that they
were thoroughly shaken by the first-hand experience
35 of discrimination. They wrote compositions on "How
Discrimination Feels" detailing their new-found
empathy for racial minorities. They unanimously
agreed that this was an invaluable experience that
provided them a prospective they couldn't have ever
40 accessed by simply reading or hearing about racism.
After this initial experiment, Eliot was invited to similar
exercises at schools and corporations. It would be a
tad too much to say that the Blue Eyes/Brown Eyes
45 Experiment instantly cured each of its participants of
racism forever, but it certainly proved an excellent
way to inspire people to think more empathetically.


1.Overall, the author's view of Ms. Elliot's work is:

  1. wildly celebratory
  2. deeply ambivalent
  3. dismissive
  4. approving

2. During the experiment, students in the privileged group:

  1. started acting as if they were better than those in the group being discriminated against.
  2. responded with docility.
  3. wore brown collars as a sign of their elevated position.
  4. failed the experiment.

3. As it's used in line 22, the word “resigned” most nearly means:

  1. to abdicate
  2. compliant
  3. bold
  4. to sign again

4. The author mentions the superior academic performance of the blue-eyed children in lines 22-29 to:

  1. highlight just how deep the effects of the segregation were in such a short period of time.
  2. advance the argument that blue-eyed people are genetically disposed to being more intelligent.
  3. explain what inspired Ms. Eliot to start the experiment.
  4. show that the experiment had surprisingly few effects on the children because they had already learned about the effects of discrimination.

5. The participants in the experiment:

  1. did not consent to being put through this study.
  2. felt unaffected by the experience.
  3. learned how to conclusively defeat racism whenever and wherever they came into contact with it.
  4. felt that they better understood the experience of victims of discrimination.

6. Which of the choices provides the best evidence for the previous answer?

  1. Lines 2-5 ("She… discrimination.")
  2. Lines 10-11 ("With… experiment.")
  3. Lines 29-31 ("The next… same.")
  4. Lines 33-39 ("They… racism. ")
Let Sleeping Children Lie

Let Sleeping Children Lie

Everyone knows the rule of thumb that people need
eight hours of sleep a night to be at their best. This is
true for most adults, but you may be surprised to
line discover that teenagers actually require quite a bit
5 more. The most recent sleep research indicates that
the average high school student actually needs about
nine hours and fifteen minutes of sleep per night.
School schedules do not take this bodily requirement
for good health into account, and it's harming our
10 children physically and intellectually. At my high
school, our first bell was at 7:15 am. The average
student lived about 15 minutes away. To give a
conservative estimate, it takes approximately 30
minutes to wake up, shower, dress, eat breakfast,
15 and be ready for school. This means that the
absolute latest that the average student could wake
up was 6:30 am. In order to get the nine hours and
fifteen minutes of sleep recommended by sleep
scientists, we would have had to be asleep at 9:15
20 pm each night. When a person is getting the right
amount of sleep, it takes him or her 20 minutes to fall
asleep. We would've had to be in bed at 8:55 pm.
Given homework and extracurricular responsibilities,
this was patently impossible. We would've been
25 winding down for the night at 8:30 pm!
Of course, my school system was unusually cruel, but
other schools are almost as bad. Most of the students
at my school were basically zombies until 11 am. That
was already four full periods into my day. I have no
30 idea how much more I would've learned if I'd been
operating at— or anywhere close— to full capacity for
the first half of the school day. Chronic sleep
deprivation is also associated with higher stress
levels, blood pressure, and heart issues, along with
35 increased rates of obesity, Attention Deficit Disorder,
and depression. Who knows what permanent
damage we all inflicted on our bodies just to get to
school on time.
School start times should be pushed back to 10 or 11
40 am, and extra buses should be provided for students
who would no longer be able to be dropped off at
school by their parents on the way to work.
Maybe a cynic would say that American education
isn't ultimately about learning. American education
45 isn't designed to help students fall in love with the
liberating arts of the humanistic tradition; it's trying to
train kids to become corporate drones. The
regimented, unhealthy schedule is a hallmark of the
typical 9-5 job, after all.
50 However, I think that this will come to an end soon
too. Workers in forward-thinking sectors like the tech
world are already allowed to set their own hours. It
won't be long before other industries catch up,
realizing that a well-rested worker is a more efficient,
55 creative, and happy worker. The sleep revolution is
coming— let's have our schools lead the way.


1. The main purpose of the passage is to:

  1. describe the effects of chronic sleep deprivation
  2. argue that school start times should be pushed back.
  3. defend the current school start times as a way of training students for adult life.
  4. propose allowing students to set their own schedules.

2. The author bases his or her argument on:

  1. first-person experience buffered by relevant scientific findings.
  2. careful observation of the scheduling procedures in place at the most successful schools in America and abroad.
  3. third-person observation exclusively.
  4. assertions based on personal experience with no reference to objective sources.

3. As used in line 13, the word “conservative” most nearly means:

  1. reactionary
  2. conventional
  3. steady
  4. moderate

4. One concession to practicality that the author makes is to admit that:

  1. it's possible that schedules will never be changed to allow for sufficient sleep.
  2. schools would have to increase the transportation they provide for students if school start times were pushed back.
  3. even if school start times were pushed back, students might just being going to sleep later too.
  4. the author doesn't really know if he suffered any negative side effects from sleep deprivation.

5. Which of the choices provides the best evidence for the previous answer?

  1. Lines 29-32 (“I have… day.”)
  2. Lines 32-36 (“Chronic… depression.”)
  3. Lines 39-42 (“school… work.”)
  4. Lines 55-56 (“The sleep... way.”)

6. The purpose of the fifth paragraph (lines 43-49) is to:

  1. present a counterargument in order to develop the author’s point further by responding to that argument.
  2. argue that schools ought to focus on learning for the sake of learning rather than on preparing students for becoming corporate drones.
  3. expose the cynicism underpinning the author's critics’ arguments.
  4. remind readers that investing in education is one way to make sure that the economy has an ample supply of capable workers.

Am I a Novelist?

Am I a Novelist?

“Suis-je romancier?”
This sentence translates into English as “Am I a
novelist?” Marcel Proust wrote these quietly
lineanguished words in a diary in 1907. They're ironic to
5 us now— if Proust wasn't a novelist, then no one
was. His million-word novel À la recherche du temps
perdu (variously translated into English as
Remembrance of Things Past or the more literal but
less poetic In Search of Lost Time) is a defining work
10 of modern times. His books were populated by a cast
of dozens of fully-realized characters— Francoise the
cook, Robert Saint-Loup the adventurer, Charles the
imperious aristocrat, Swann the art collector and
romantic obsessive— who still feel like living, real
15 people to readers all these years later. Proust's name
is mentioned in the same breath as the other masters
of the novel form: Tolstoy, Joyce, and Eliot. Perhaps
no one else in all of literature has dissected human
emotion so deftly. As long as imaginative literature is
20 read and appreciated, Proust will continue to be
We can say all of that now, though, only with the
benefit of hindsight. In 1907, “Am I a novelist?” was
hardly a settled question for Proust. The then-36 year
25 old Proust had long harbored literary aspirations.
He'd thought of himself as a writer since
adolescence. He had a few translations and
magazine pieces this name, but he hadn't written
much of substance, nothing that lived up to his lofty
30 artistic standards.
His life up until then wasn't one of acute failure, of
novels rejected by short-sighted publishers or
manuscripts thrown into the fire in the heat of
passion. His was a life of languid leisure; hours,
35 days, even years slipped by with no great tumult
aside from the gnawing self-reproach that he wasn't
writing the capacious novels of his imagination.
By 1908 Proust had written most of what would
become Du côté de chez Swann, which would be the
40 first part of his masterpiece. What changed? How did
the frustrated maybe-novelist of 1907 become the
fruitful writer of 1908? Did some great even transpire
which changed his entire world and forced him to
write about it? Did some change in circumstance
45 finally allow him time to write? Did some lightning bolt
of inspiration finally strike one night?
No. 1908 was not an otherwise eventful year for
Proust, he'd always had plenty of time to write, and
he'd been accumulating ideas for his novel for a
50 while. The only real change was that Proust started
writing. He stopped endlessly wondering what was
keeping him from writing and just began the novel.
Proust found that inspiration didn't make him write;
writing made him inspired. It wasn't some stroke of
55 brilliance which made him turn to his manuscripts;
rather, it was turning to his manuscripts that would
invite strokes of brilliance. These were the golden
hours of pith and productivity when he would stay up
writing in his bed (he always wrote the best in bed)
60 until the small hours of the morning. Proust became a
novelist once he stopped asking himself whether or
not he was one.


1. What is the main point of the passage?

  1. Proust became a productive writer only after a series of personal setbacks inspired him to write.
  2. Proust's novels are as good as those by Tolstoy, Joyce, and Eliot.
  3. Proust because a fruitful writer only after he quit musing about what might be keeping him from being a fruitful writer.
  4. It is unknown how Proust eventually came to start writing.

2. Proust asking himself “Am I a novelist?” is ironic to readers now because:

  1. we know him primarily for his wild success in other fields.
  2. we still don't have a settled answer to the question.
  3. Proust would start writing the novel that enshrined him as one of the world's great novelists soon after.
  4. Proust had already written the books that would secure his legacy.

3. Which of the following choices provides the best evidence for the previous question?

  1. Lines 3-4 ("Marcel… 1907.")
  2. Lines 6-10 ("His million… times.")
  3. Lines 40-42 ("What… 1908.")
  4. Lines 47-50 ("1908… while.")

4. As it's used in line 31, the word “acute” most nearly means:

  1. small
  2. observant
  3. poignant
  4. sharp-angled

5. Proust's life before 1908 was one of:

  1. pointed tragedies but also remarkable literary success.
  2. languor and dissipation
  3. leisure but also unfulfillment
  4. disappointment and poverty

6. What is the point of the rhetorical questions posed in lines 40-46?

  1. To drive home the point that no one really knows what changed for Proust In 1908.
  2. To provide different but equally viable explanations for the big shift that happened in 1908.
  3. To set up a contrast between the life-altering changes one might expect to have taken place and the rather straightforward change that actually did take place.
  4. To introduce a series of various theories that the author is going to elaborate on an support at great length.

Poet, Playwright, and... Spy?

Poet, Playwright, and... Spy?

We don't know anything for sure. Records concerning
Christopher Marlowe's life are scant, as they are for
all British commoners of the Elizabethan era. When
line Marlowe was an adolescent, no one knew how
5 interested posterity would be in his life. Who knew
that he'd grow up to write Hero and Leander, Doctor
Faustus, and Tamburlaine. Who knew that he'd be at
the forefront of the birth of British theater and directly
influence William Shakespeare. Even the adult
10 Marlowe's biography is riddled with inexplicable
gaps and frustrating seeming-contradictions. Just as
with Shakespeare, our interest far outpaces the
amount of information we know for certain.
All of that said, there's a lot of evidence pointing to the
15 conclusion that Christopher Marlowe was a spy. The
theory is that he was recruited while an
undergraduate at Cambridge University, one of the
main sources of England's covert agents. During the
1584-1585 academic year, his college's attendance
20 records show that Marlowe started taking
exceptionally long foreign vacations. His absences
were much longer than those usually allowed by the
college, yet he was able to continue at the school and
keep his scholarship. At the same time, he began to
25 spend exorbitant amounts on food and drink during
the increasingly rare occasions when he actually
appeared on campus. He spent far more than his
relatively modest stipend would have financed. After
he graduated, Cambridge was reluctant to grant
30 Marlowe his MA (a formality at the time). For some
reason, the Queen's government stepped in and
made the university grant the degree.
A nascent career in espionage would explain his
long but excused absences, his extras funds, and the
35 government's interest in his credentials. It would also
provide a satisfying, if not completely airtight
explanation for Marlowe's curiously-timed death.
In May of 1593, the 29-year-old Marlowe was
arrested, though there was no formal reason for his
40 arrest provided by the authorities. Twelve days later,
he was found dead in a pub.
The official story is that Marlowe got into a fight with
another customer, attacked the man with a knife, had
the knife turned against him, and sustained an
45 instantly deadly blow.
The only problem with this version of the event is that
it's a rank impossibility. Medical experts have shown
that the blow Marlowe reportedly received couldn't
have possibly killed him instantly. Was this official
50 account— based solely on the testimony of a slim
number of supposed eyewitnesses— merely
mistaken? Or was it fabricated to cover up for a state
murder? Was the man who killed Marlowe swiftly let
free by authorities because they genuinely thought
55 he'd acted in self-defense? Or was he released by
the government because it had actually
commissioned the murder in the first place? Was this
death less than two weeks after a mysterious arrest a
totally random coincidence? Or did the Queen's
60 government realize that Marlowe was somehow
compromised in his role as a spy and send a hitman
to clean up the situation?


1.The author views the theory that Marlowe was a spy as:

  1. an absurdity.
  2. the reason Marlowe quit writing poetry at the age of 29.
  3. a viable theory that, tantalizingly, cannot be definitely proven or disproven
  4. an ironclad fact based on extensive documentation that's only recently been declassified.

2.The author states that there's a lack of documentation about Marlowe's life because:

  1. the government destroyed all records of his life after they had him murdered.
  2. no one kept detailed records of the lives of most English citizens at the time.
  3. no one saw any reason to keep records of his life because they doubted his potential as a writer.
  4. they were destroyed in the Great Fire of 1666.

3.Which choice provides the best evidence for the previous answer?

  1. Lines 1-3 {“Records… commoners.”)
  2. Lines 3-5 ("Who… life.")
  3. Lines 5-7 ("Who… Tamburlaine.")
  4. Lines 9-13 ("Even… certain.")

4.Marlowe received his MA degree:

  1. because of his exemplary academic record.
  2. only after the intervention of the government.
  3. during a celebration of his spectacular literary career.
  4. while he was in the middle of a lengthy foreign vacation.

5.As used in line 47, the word “rank” most nearly means:

  1. absolute
  2. foul-smelling
  3. seeded
  4. unrelated

6.The author uses “supposed” (line 51), “swiftly” (line 53), and “totally random” (line 59) in order to:

  1. introduce doubts about the official version of the story.
  2. underline the viability of the official account of Marlowe's death.
  3. add a sense of precision to the government's faithful reporting of the events.
  4. completely undermine the idea that Marlowe could have possibly been killed in connection to espionage work.



Despite our sometimes-romantic view of the
supposedly unceasing forward march of Reason, the
progress of scientific knowledge is rarely quite so linear.
line We usually take two steps forward while taking one
5 step back. Oftentimes, huge breakthroughs are
coupled with thoroughly mistaken conclusions. Some
ideas that helped to shape the modern world were
worked out by scientists whose other hypotheses
have long been discredited. Entire fields of inquiry
10 have been revealed to be pseudoscience, but only
after they formulate one or two theories which
become the unshakeable basis for the -ologies of
future the future, the sciences that take their place.
Phrenology was one such field. Simply put,
15 phrenology was based on the idea that the shape of a
person’s skull was indicative of his or her personality.
The physical attributes of certain modules of the scalp
determined one’s capacity for secretiveness, wit,
hope, wonder, love of life, etc. One might
take a complicated set of measurements of a
20 child’s cranium and predict what type of
adult the child would grow
In the 19th century, phrenology was widely popular.
As difficult as it might be to imagine today, science
25 lectures were a hugely popular form of entertainment
for all sectors of society. Theorists such as George
Cowler and Luigi Ferravesu were minor celebrities.
Phrenology’s adherents ranged from the working
class to aristocrats. Queen Victoria and Prince Philip
30 had their children’s heads measured.
The specific conclusions of the phrenologists have
been resoundingly debunked. It turns out that the
shape of the skull has little to do with the functioning
of the brain underneath it. However, the field
35 inaugurated the systematic study of the connection
between personality and the brain. Most people had
previously supposed that personality, if it was
intertwined with any bodily organ, was lodged in the
heart. Furthermore, phrenology trained scientists to
40 study the brain with objective, third-person, physical
techniques, rather than the subjective introspective
methods that scientists had previously thought
sufficient. Finally, phrenologist nudged further
researchers towards the idea that different parts of
45 the brain were related to specific, localized functions.
Though phrenology is the butt of jokes today—
perhaps most famously, nonagenarian C.
Montgomery Burns is an adherent of phrenology on
The Simpsons— these three insights have formed the
50 bedrock of decades of psychological and neurological
research. One is led to wonder which of the fields of
study that are widely popular today will be looked
back upon with derision in 150 years after new
findings enabled by technological progress provides
55 access to evidence that renders our current theories
obsolete, even laughable. On the other hand, what
will be the few, momentous insights that survive our
generation and shape the science of the future?


1. The author’s view of phrenology can be best described as:

  1. utterly scornful
  2. hopeful
  3. mixed
  4. indifferent

2. The main purpose of the first paragraph (lines 1-13) is to:

  1. argue for the resuscitation of fields of study that have fallen out of favor.
  2. open the passage with an illuminating anecdote, the full meaning of which will only become clear as the passage goes on.
  3. develop the idea that scientific discovery is an often imprecise process.
  4. introduce some of the main theorists behind phrenology.

3. As used in line 1, “romantic” most nearly means:

  1. amourous
  2. originating in Rome
  3. overly idealized
  4. roaming

4. According to the passage, phrenology:

  1. was only popular with members of the upper class, such as Queen Victoria and Prince Philip.
  2. was confined to the halls of academia.
  3. achieved widespread popularity.
  4. is still a respected field of inquiry.

5. Which choice provides the best evidence for the previous answer?

  1. Lines 9-13 (“Entire… place.”)
  2. Lines 24-26 (“As difficult… society.”)
  3. Lines 26-29 (“Theorists… aristocrats.”)
  4. Lines 29-30 (“Queen… measured.”)

6. According to the passage, contemporary science:

  1. is completely uninformed by phrenology.
  2. was too hasty in dispensing with phrenology.
  3. is liable to having its conclusions revised as future technologies unearth new data.
  4. reaches the public through universally popular scientific lectures attending by people from all walks of life.

The Longshoreman Philosopher

The Longshoreman Philosopher

Few intellectuals' live lives as interesting as the topics
they study and write about. Academics, by and large,
live quietly, pleasantly productive lives.
5 That's not the case for Eric Hoffer. His life story is as
much of a page turner as his well-regarded books.
Born in the Bronx to recent German immigrants,
Hoffer grew up among the working poor. Tragedy
struck early and often in his life. When Hoffer was a
10 child, his mother was carrying him from a bath when
she fell. She died from complications of her injuries.
He lost his sight and, for a very short time, his
memory. His father would pass a few years later.
15 Then, a miracle happened: when Hoffer was 15, his
vision suddenly returned. Doctors couldn't explain
why. Hungry for books after a childhood without then
(Braille books weren't available to him) and afraid that
he could lose his sight again at any moment, he
20 became a voracious reader. It turns out that Hoffer's
recovered eyesight was permanent; his appetite for
books was too.
Lacking a formal education or a familial safety net,
25 Hoffer was reduced to living in Skid Row and working
odd jobs. He spent years as a migrant farmer.
Everywhere he went, he got a library card. He started
writing extensively in book notebooks; these jottings
eventually took the shape of his first book, The True
30 Believer. Published in the wake of World War II and
the various revolutions that preceded and precipitated
it, The True Believer is a study of mass movements
like— the Nazi uprising, the Bolshevik Revolution, the
French Revolution, etc.— and the people drawn to
35 them. Hoffer didn't write from the perch of a detached
observer. Hoffer wrote from the perspective of the
underclass, which peoples mass movements.
The True Believer was an instant classic of sociology,
40 and it enabled Hoffer to keep publishing. Notable later
works include The Ordeal of Change (which Hoffer
himself cited as his most important work) and
Reflections on the Human Condition. His work won
him acclaim both inside of academia and outside it,
45but Hoffer kept his day job as a longshoreman
throughout his rise to acclaim. Scribbling aphorisms
into notebooks during breaks from work on the docks
of California's coast, Hoffer became known as the
“longshoreman philosopher.”


1. What is the overall structure of the passage?

  1. A discussion of a work of sociology is followed by an explanation of some of that work's limitations.
  2. A writer gives a first-hand account of his ride to intellectual acclaim.
  3. A story of the rise of the mass movements that preceded World War II leads to a lengthy exposé of the underclass that peoples them.
  4. A brief biographical sketch of a writer's trying early life leads to a quick discussion of the writer's most famous work and how it was informed by his background.

2. According to the author of the passage, most intellectuals’ lives are:

  1. torturously boring.
  2. fruitful but somewhat uneventful.
  3. more interesting than the topics they write about.
  4. action-packed and riveting.

3. As used in line 23, the word “odd” most nearly means:

  1. various
  2. uncanny
  3. uneven
  4. comical

4. One thing that set The True Believer apart from other works of history and sociology is its:

  1. extensive use of data that was previously unavailable to writer's.
  2. detached, third-person perspective.
  3. use of extensive first-hand reporting from Hoffer's experience with the leaders of mass movements.
  4. basis in Hoffer's own background living and working with the sort of people who often fill the ranks of mass movements.

5. Which choice provides the best evidence for the previous answer?

  1. Lines 27-32 (“Published… them.”)
  2. Lines 32-34 (“Hoffer… movements.”)
  3. Lines 35-36 (“The True Believer…publishing.”)
  4. Lines 39-42 (“His work… acclaim.”)

6. The final paragraph (lines 35-45) relates that:

  1. Hoffer's literary success finally enabled him to leave his life as a laborer.
  2. Hoffer quickly became the most important sociologist in the United States.
  3. despite the success of The True Believer, Hoffer decided to give up writing and return to his life as a longshoreman.
  4. even though Hoffer attained literary success, he didn't abandon the life that had so influenced his work.

Fund the Metro!

Fund the Metro!

The state of public transportation in the city of Los
Angeles is frankly unacceptable. The Metro System's
buses are few and far between— we have to show up
line to our stops ten minutes early just to make sure that
5 we arrive at our destinations no more than ten
minutes late. There are delay delays on every line in
every direction, delays that have become so common
that they go unexplained, apologized for, and
unremarked upon. The trains are, somehow, worse.
10 They have the same utterly unpredictable schedule
and run so infrequently that missing a train by 20
seconds usually means we have to wait 20 minutes
for the next one. Train stations are so sparse that one
stop typically serves a radius of several miles. We
15 almost always have to connect from a train to a bus
to actually get anywhere close to our final destination.
It doesn't have to be this way. Other cities with even
larger populations have public transportation systems
that blow LA's away. Tokyo has a population four
20 times the size of LA's, but their rail system is
impeccable. A bullet train company recently issued an
apology to its commuters when a train departed
twenty seconds early. In Tokyo, this is an occasion for
heartfelt mea culpas; in LA… well, who knows how
25 LA would handle this?! None of its trains are ever
even close to being on time (let alone actually on time,
let alone slightly early).
LA needs to appropriate more funds for public
transportation. The typical argument against
30 transportation funding is that everyone in LA just
drives everywhere anyways. This type of reasoning
just gets us into a vicious cycle: we don't find buses
or trains, so everyone drives, so we spend even less
on buses and trains, so even more people have to
35 drive, etc. It's not as if the roads are in great shape
either. They were built decades ago for a population a
fraction of the size of our city currently. Our roads are
world-famous for potholes and endless traffic.
However, the city is never going to be able to fix the
40 roads or add extra lanes because the construction
would make the city literally unnavigable. Even if we
woke up tomorrow and all the roads were suddenly
perfect, the burden of constant congestion means
we'd just have to fix them again in a few years.
45 Investing the public transportation is a much
longer-term solution.
Increasing funding to the Metro might seem like a
waste of money to the city's car-bound taxpayers, but
it will actually save money in the long run. If we can
50 make riding the bus or train a reliable, cheap, and
convenient alternative to driving, we'll save millions of
dollars on construction costs. We'll also take a large
bite out of the city's traffic nightmare, saving citizens
countless wasted hours and immeasurable emotional
55 distress from being trapped in the highways. It's time
for Los Angeles to become a modern, first-world
city— it's time to finally find the Metro.
Creation and Destruction of the Globe

The Creation and Destruction of the Globe

In the late 1592, Lord Chamberlain's Men found
themselves in a seemingly intractable situation. The
theatre company— whose in-house playwright was
line William Shakespeare— was in a long-running dispute
5 with its landlord. He was constantly trying to raise the
rent on the increasingly successful troupe. It seemed
as if he had them in a vice: though Lord
Chamberlain's Men owned the wooden theater
building itself, he owned the land on which it was
10 situated. If they stayed, they'd have to pay exorbitant
rent. If they left and started performing elsewhere,
they'd throw away all the money they'd spent on the
The owners of the company can up with an
15 ingenious fix. On December 29, 1598— two days
before they would be forced to re-up their lease—
they hired a dozen workmen to dismantle the theater
in the dead of night. They took the theater apart
beam-by-beam and scurried it across the frozen
20 Thames River to a new plot of land they'd purchased
in secret. It was a farce for a play— just imagine a
restless Londoner trying to cure a bout of insomnia
with a midnight stroll only to stumble upon a pack of
men ferrying an entire theater across the river!
25 The crew set about rebuilding the theater in its new
location. The new performance space, audaciously
named The Globe after it's circular design, took
months to finish. During this minor creative
sabbatical, Shakespeare conceived of As You Like It
30 and Julius Caesar, two of his finest accomplishments.
When The Globe finally opened in the middle of 1599,
he was starting to figure out his next blockbuster:
Hamlet. One could say this time off was rather fruitful
for Shakespeare.
35 The theater would stand in its new location for 14
years, playing host to the opening performances of
such timeless plays as Twelfth Night, Othello,
Macbeth, Antony & Cleopatra, King Lear, and The
Tempest. However, the theater was destroyed in a
40 fire started at the neighboring Blackfriars Theater in
1613. Just as the building of The Globe was
concurrent with the heights of Shakespeare's
writing, the destruction of the theater preceded the
end of his theatrical career. The hassle of having to
45 rebuild the troupe's primary performance space
almost certainly played a role in Shakespeare's early
retirement that year at the age of 49.


1. The primary purpose of the passage is to:

  1. argue that Hamlet Is one of the seminal works in the history of imaginative literature.
  2. present the story of the building and destruction of The Globe, highlighting the ways this chronology intersected with Shakespeare's writing.
  3. evaluate various theories for why Shakespeare retired.
  4. examine the arcane property laws of Elizabethan England.

2. As used in line 7, the word “vice” most nearly means:

  1. tight spot
  2. immorality
  3. a tool for gripping materials
  4. second-in-command

3. The time that it took to build The Globe in 1599:

  1. was such a hassle that Shakespeare decided on an early retirement.
  2. was only so protracted because of a fire in a neighboring theater.
  3. permanently ruined Shakespeare's troupe's popularity.
  4. gave Shakespeare time to think through two new plays.

4. In the third paragraph (lines 25-34), the author states that the new theater's name was inspired by:

  1. its global reach.
  2. its geometric shape.
  3. the farcical manner in which the theater came to be.
  4. the fact that it was being rebuilt on the site of a burned-down theater.

5. According to the passage, the destruction of The Globe:

  1. was, according to Shakespeare's memoirs, the specific reason he quit the stage.
  2. most likely played a role in Shakespeare's retirement.
  3. gave Shakespeare sufficient time off to work on two of his finest plays.
  4. had little effect on the ever-resilient Shakespeare.

6. Which of the following choices provides the best evidence for the previous answer?

  1. Lines 28-30 ("During… accomplishments.")
  2. Lines 35-39 ("The… Tempest.")
  3. Lines 39-41 ("However… 1613.")
  4. Lines 44-47 ("The hassle… 49.")

Postcards from 100 Boots

Postcards from 100 Boots

The art world of the 1960s was dominated by Pop Art.
Andy Warhol was printing screens of Campbell Soup
cans. Roy Lichtenstein was recreating scenes from
line comic books and soapy pulp fiction. Jasper Johns was
5 putting together iconographic works centered around
archetypal American images. The work was broadly
accessible. It was commenting on mass consumption,
sure, but it was also itself designed for mass
10 Then came minimalism and Eleanor Antin. Pop Art
was the much-needed antidote to the extremes of the
obscure Abstract Expressionism of the 50s;
minimalism was the much-needed antidote to the
extremes of the commercial Pop Art of the 60s. If
15 Andy Warhol was the elixir to Mark Rothko, Eleanor
Antin was the elixir to Warhol.
Anton's conceptual art projects were deliberately
uncommercial, personal, and hard-to-find. One of her
earliest projects was called Blood of the Poet Box.
20 Inspired by Jean Cocteau's Blood of the Poet, Antin
collected physical samples of the blood of poets she
admired, preserved on microscopic slides. Her
collection included samples from era-defining talents
like Allen Ginsberg and Lawrence Ferlingetti, eminent
25 members of the Beat Generation. This work was at
once highly personal (is there anything more personal
than an individual's blood?), truly avant-garde, and
utterly unreproducible (that is, unless one was willing
to find and extract blood from the 100 participants in
30 Anton's original project).
Around the same time, Antin started a project called
Carving a Traditional Sculpture, a name which belied
the delightful peculiarity of the work. In 1968, Antin
started taking pictures of herself as she underwent a
35 harsh diet regimen. The pictures document her
gradual weight loss and muscle gain. The 148 photos
were personal (she was literally the object d'art)
without being mawkishly sentimental, playful and yet
pointed at the same time. In a related work from 1972
40 known as The Eight Temptations, Antin captures
herself confronted by an onslaught of delicious foods
which would have destroyed her diet had she not
(mock-) heroically fended them off.
Perhaps Antin's most well-known work from this
45 especially productive period was 100 Boots. Shopping
at a thrift store one day in 1971, Antin purchased 100
tall, plastic boots. Over the next two years, she
proceeded to photograph the boots arranged in
various formations on a journey from the Pacific Coast
50 to New York City. She captured the boots marching
single-file past a family of ducks walking one-by-one
in the opposite direction. She documented a
particularly playful afternoon in which the boots turned
an abandoned car into a makeshift jungle gym. She
55 even discovered the boots taking in high culture,
arrayed in a semi-circle around Marcel DuChamp's
The Treachery of Images, a painting of a pipe
ironically subtitled “This is not a pipe.” Antin, of
course, gave her picture of the boots’ visit the subtitle
60 “This is not 100 boots.”
Although the they always pictured in black-and-white
and are completely unadorned, the 100 boots seem
to take on different moods depending on the scenario.
Passing the ducks, they appear energetic and
65 buoyant. Climbing about the abandoned two-door
sedan, they're indulging in childlike, anarchic fun.
Aligned in front of the DuChamp, they're unusually
Antin's distribution of the pictures is just as
70 idiosyncratic as the art itself. She copied the photos
and sent them to specially-chosen recipients as
“postcards” every few days.
Antin's work, however, was too compelling and
inventive to stay invitation-only for long. 100 Boots is
75 exhibited at the Museum of Modern Art in New York
City. Much of Antin's other work is in the collection at
the Tate Museum in London. Even though it is no
longer exclusively available to those on Antin's mailing
list, these works maintain the good-humored
80 experimentalism that made them so distinctive in the
first place.


1. The main purpose of the passage is to:

  1. discuss the works and artistic environment of a singular artist.
  2. criticize the Pop Art movement that was dominant in the 60s.
  3. explain why Eleanor Antin was the most important artist of the 1970s.
  4. detail Eleanor Antin's weight loss regiment.

2. Lines 2-6 ("Andy… images.") serve to:

  1. provide instances of the kind of art the writer of the passage is advocating for.
  2. supply examples of the kind of art Antin was surrounded by and reacting to.
  3. list Antin's favorite paintings.
  4. introduce the reader to the main works by the notable artists of the 1960s.

3. In the passage, Mark Rothko was associated with which artistic movement?

  1. Pop Art
  2. minimalism
  3. Abstract Expressionism
  4. conceptual art

4. Antin's work can be described as:

  1. serious and political
  2. progressive and realistic
  3. personal and avant-garde
  4. commercial but not easily reproduced

5. Which of the choices provides the best evidence for the previous answer?

  1. Lines 6-9 (“The work… consumption.”)
  2. Lines 10-14 (“Pop… 60s.”)
  3. Lines 17-22 (“One off… slides.”)
  4. Lines 25-30 (“This work… project.)”)

6. Starting with the third paragraph (lines 17-30) the passage transitions from:

  1. a discussion of Abstract Expressionism to an explanation of Pop Art.
  2. a general introduction to Antin's historical context to a discussion of several specific works.
  3. an introduction of Antin's most popular works to a discussion of her overall impact.
  4. Antin's minimalist phase to her more mainstream one.

7. The title of Carving a Traditional Sculpture is ironic because:

  1. the work was rejected by all of the traditional venues.
  2. there was no carving or traditional sculpture involved; Antin herself was the medium.
  3. Antin did none of the carving herself, leaving the work to trained assistants.
  4. Antin uses metals not typically used by or even available to classical sculptors.

8. As used in line 39, “pointed” most nearly means:

  1. sharp-angled
  2. directed at
  3. incisive
  4. covered in small points.

9. How frequently did Antin send “postcards” from the 100 boots?

  1. daily
  2. every few days
  3. 100 times
  4. once a month for two years

10. As used in line 73, “compelling” most nearly means:

  1. forcible
  2. fascinating
  3. coercive
  4. compulsory

11. The main purpose of the final paragraph (lines 73-81) is to:

  1. explore how Antin's reputation soured once her work started being exhibited in more mainstream venues.
  2. discuss how the particular attributes of Antin's work remain, even though the work is displayed in a new context.
  3. trace the development from Pop Art to minimalism.
  4. explore the historical importance of Andy Warhol.

The Stanford Prison Experiment Passage

The Stanford Prison Experiment

Sometimes, the most significant scientific discoveries
come from studies that are ethically dubious. This is
especially true of the social sciences, where the
subjects at hand are typically humans themselves.
5 The Stanford Prison Experiment is a landmark of
social psychology. It gave psychologists invaluable
insights into group dynamics and the roots of
authoritarian tendencies. It was also a monumental
example of ethical malpractice.
10 The 1971 experiment was founded by the US Navy,
who wanted to find out why relationships between
guards and prisoners in naval prisons frequently
turned counter-productively hostile, despite constant
attempts at reform. They turned to Philip Zimbardo, a
15 leading social psychologist at Stanford University. He
set up a makeshift “prison” in the basement of the
school's psychology department building. He
recruited 24 students and local residents to fill his
prison. Half of the participants were randomly
20 assigned to be guards; the other half were prisoners.
Zimbardo and his team of researchers tried to
approximate the conditions of a real prison as much
as possible. Guards attended a special orientation
before the experiment commenced. They were given
25 batons and reflective eyewear (to block eye contact
between guards and prisoners). Guards were
instructed to exclusively call prisoners by numbers
assigned to them upon entry. While physical force
was forbidden, the guards were instructed to instill a
30 sense of fear and lack of privacy in their wards.
Attempts at verisimilitude were even stricter for the
prisoners. To put them into the mindset of real
convicts, prisoners were arrested by local policemen,
taken from their residences, and processed just like
35 actual felons. While the guards had access to
recreation and we're allowed to leave the grounds
during the study, the prisoners were restricted to their
basement cells. Each cell contained three people,
who were allotted just a small, uncomfortable cot.
40 There were no private bathrooms.
Within two days, the prisoners were in open revolt.
One cell of inmates barricaded itself in its room. One
prisoner had a nervous breakdown so severe he was
allowed to leave the experiment after only 36 hours.
45 The wards, who were working in shifts of three, tried
to quell the unrest. They separated out those
prisoners who has remained docile and rewarded
them with extra benefits, such as nicer meals. Others
who were not so easily broken were placed in
50 “solitary confinement” inside a small closet.
Tensions escalated. Guards began punishing
increasingly petty misdeeds, such as flubbing the
prison roll call. Prisoners were threatened with a fire
hose and punished by not being allowed to empty the
55 trash bags they were forced to use as restrooms.
The experiment was planned to last two weeks; they
made it six days. The study was ended abruptly when
Christine Malachi, a graduate research assistant who
came to interview the participants, confronted
60 Zimbardo about the grisly conditions. It should be
noted that more than 50 observers had already taken
part in the study, and none of the others had
challenged Zimbardo's methods. Commenting on her
sense of guilt at having taken part in the study,
65 Malachi said, “I was sick to my stomach. When it's
happening to you, it doesn't feel heroic. It feels real
scary; it feels like you are a deviant.”
The results of the study indicate that both prisoner
and guard mentalities were more situational than
70 dispositional. They're part of the prison environment
itself. Hostilities didn't arise because prisoners were
lawless felons or guards were born sadists. Both
groups had been drawn from an affluent, law-abiding
population. It only took six days for the process of
75 deindividuation to take hold. By the end of the study,
prisoners were asking to be “paroled” (allowed to
leave the experiment, forfeiting their back pay) when
they could’ve simply quit and left of their own accord.
They were so ingrained in their role that they’d started
80 to think of themselves as inmates, forgetting that they
were still free people. If this process could take hold
for prisoners and guards in a fake prison in less than
a week, it seems reasonable to conclude that the
same thing was causing the hostilities in real prisons.
85 It wasn't that prisoners and guards necessarily had
personalities that led to conflict; it seems like the
prison situation itself causes conflict.
The Stanford Prison Experiment has inspired films,
documentaries, and short stories, all of which
90 broadcast the study's important findings while also
highlighting the obviously inhumane way in which
they were uncovered. While it certainly doesn't hold
up to today's ethical standards, the experiment has
led to some much-needed reforms of the prison
95 system. The study has led to changes to the ways
that prisoners are houses and guards are trained, and
it has led to an emphasis on rehabilitating prisoners,
rather than merely punishing them.


1. The main purpose of the passage is to:

  1. discuss an imperfectly designed experiment that, nevertheless, yielded impactful insights.
  2. summarize Philip Zimbardo’s career as a leading social psychologist.
  3. argue that the United States Navy should not be funding psychological experiments.
  4. list a set of guidelines for how to design an ethical experiment in the social sciences.

2. Overall, the author’s view of the Stanford Prison Experiment can be best described as:

  1. unqualified appreciation
  2. ambivalence
  3. indifference
  4. complete disgust

3. As it’s used in line 2, “dubious” most nearly means:

  1. incredulous
  2. certain
  3. vague
  4. questionable

4. How many of the participants were assigned to be prisoners?

  1. 12
  2. 24
  3. 36
  4. 50

5. As it’s used in line 22, “approximate” most nearly means:

  1. guess
  2. adjoin
  3. come close to
  4. exact

6. In the sixth paragraph (lines 41-44), the passage transitions from:

  1. focusing on Philip Zimbardo to focusing on Christine Malachi.
  2. discussing the insights gleaned from the study to excoriating of the ethical malpractice of the experimenters.
  3. introducing the study to describing how it got out of hand.[m]
  4. discussing situational attributes to an examining deindividuation.

7. Why was the Stanford Prison Experiment finally called off?

  1. A research assistant objected to the conditions of the study.
  2. More than 50 outside observers objected to the conditions of the study.
  3. The prisoners revolted, barricading themselves in their rooms.
  4. The prison guards objected to being forced to treat their fellow subjects so inhumanely.

8. What is the difference between a situational attribute and a dispositional one?

  1. Situational attributes apply to the prisoners; dispositional attributes only applied to the guards.
  2. Situational attributes apply to real prisoners; dispositional attributes only applied to the the participants in this study.
  3. While a dispositional attribute arises from an individual’s personality, a situational attribute is one that is induced by environmental factors.
  4. While a situational attribute is part of a person’s innate personality, a dispositional one is learned from the individual’s environment.

9. Which of the choices provides the best evidence for the previous answer?

  1. Lines 70-72 (“They’re... sadists.”)
  2. Lines 74-75 (“It took… hold.”)
  3. Lines 75-78 (“By the… accord.”)
  4. Lines 92-95 (“While… system.”)

10.According to the passage, the process of deindividuation is:

  1. now largely discredited because of the findings of the Stanford Prison Experiment.
  2. the process by which people can lose their personal identities when they get too caught up in playing a social role.
  3. something that only happens to affluent, law-abiding citizens.
  4. something that only happens to career criminals.

11. Which choice provides the best evidence for the previous answer?

  1. Lines 65-67 (“I was… deviant”)
  2. Lines 72-74 (“Both… population”)
  3. Lines 79-81 (“They… people.”)
  4. Lines 88-92 (“The Stanford… uncovered.”)

Connie "The Hawk" Hawkins Passage

Connie “The Hawk” Hawkins

There are few stories in the world of sport that are
more galling than the injustice committed against
Connie Hawkins. Hawkins was a basketball player
line who grew up in desperate poverty in the
5 Bedford-Stuyvesant neighborhood of Brooklyn.
Hawkins was undereducated and undernourished;
when he wasn't on the court, Hawkins was known for
napping constantly because of a lack of energy from
not having enough to eat.
10 Hawkins's story starts out on a familiar trajectory: a
sudden growth spurt matched with the gradual
refinement of his natural talents gave him the
opportunity to escape the cycle of poverty he would
have otherwise likely been caught in. He became a
15 legend at Rucker Park, the stories Harlem court
where all-time greats such as Wilt Chamberlain,
Kareem Abdul-Jabbar, and Julius Erving established
their reputations. “The Hawk” stood out for the
subtleties of his style. Most players from New York—
20 where asphalt courts, unforgiving outdoor rims, and
frequent inclement weather forbade finesse— were
known for their sheer speed and strength. Hawkins's
game, however, was based in slick deception. Instead
of trying to speed past defenders or push through
25 them, Hawkins went around them. He would fake
defenders out so thoroughly they were turned around
the wrong way as he scored easily.
The Hawk was recruited to the University of Iowa for
collegiate ball. This is where his trouble started.
30 Hawkins once borrowed $200 to cover school
expenses from Jack Molinas, a New York attorney
with connections to the basketball world. Even in the
1960s, the NCAA's regulation of benefits accorded to
student athletes was outlandishly harsh, making
35 poorer students resort to desperate financial
arrangements like this. As soon as the Hawkins
family was able to repay the loan, they did.
Later that year, Molinas was implicated in a gambling
scandal. Hawkins hadn't taken part in the
40 point-shaving scheme. He had an airtight alibi—
since he was a freshman, he wasn't even allowed to
play in the varsity games that gamblers were betting
on. He was never arrested for charged with any
wrongdoing stemming from the investigation (an
45 investigation during which, it ought to be noted,
Hawkins was not allowed legal counsel).
Nevertheless, Hawkins was too notable to fly under
the radar. He was summarily expelled from Iowa,
blacklisted from all major collegiate programs, and
50 banned from the National Basketball Association
With nowhere else to play his trade, Hawkins turned
in stints with independent teams and alternate
basketball leagues. He played for the Harlem
55 Globetrotters and various teams in the American
Basketball League (ABL) and the American
Basketball Association (ABA). He was still
dominant— he was recognized as the Most Valuable
Player (MVP) of both the ABL and ABA during his
60 tenures there. When he led the Pittsburgh Pipers to
the ABA Championship in 1968, he was awarded
Playoffs MVP.
Finally, the NBA came to its senses— well, they were
forced to come to their senses. An incendiary
65 magazine profile and ensuing book by David Wolf
excoriating the outrageous treatment of Connie
Hawkins brought his case national attention. The
NBA settled the lawsuit that Hawkins had brought
against them, paying him $1.2 million and allowing
70 him to enter the player draft.
Hawkins was signed by the Phoenix Suns. He was an
instant hit. In his first season, he led the Suns to the
brink of a world championship, only losing in the
playoffs to the eventual champion Los Angeles
75 Lakers. The seven-game series, in which Hawkins
played all-time great Wilt Chamberlain to a draw, is
still known as one of the closest, most dramatically
compelling playoff series in league history. He was
perennially selected to the All-Star team of the
80 league's best players and was inducted into the Hall
of Fame after his retirement.
Still, it's hard not to imagine what might have been.
Hawkins spent his physical peak in fringe leagues. He
was denied the typical player development afforded
85 to collegiate and NBA players and had his talents
atrophy against inferior competition. Even so, he was
able to become one of the NBA's absolute best
players. Who knows how good The Hawk could have
been if he'd been able to train with and test his mettle
90 against the best?


1. The author's attitude towards Hawkins is best described as:

  1. sympathetic
  2. ambivalent
  3. indifferent
  4. apathetic

2. As it's used in line 2, the word “galling” most nearly means:

  1. pleasing
  2. blustery
  3. exasperating
  4. pleasing

3. Hawkins's playing style can be best described as:

  1. harsh and physical
  2. smooth and guileful
  3. subtle but predictable
  4. artful and bruising

4. Which choice provides the best evidence for the previous answer?

  1. Lines 19-22 (“Most… strength.”)
  2. Lines 22-27 (“Hawkins… easily.”)
  3. Lines 28-29 (“The Hawk… ball.”)
  4. Lines 78-81 (“He was… retirement.”)

5. In the third paragraph (lines 28-37), the passage transitions from a brief sketch of Hawkins's childhood to:

  1. a description of the sequence of events that would eventually lead to his legal troubles.
  2. a discussion of his time on the University of Iowa's varsity basketball team.
  3. an excoriation of the NBA's handling of Hawkins's case.
  4. a description of Hawkins's playing style.

6. As it’s used in line 48, the word “summarily” most nearly means:

  1. concluding
  2. immediately
  3. somewhat
  4. largely

7. Which of the following is the most effective piece of evidence supporting Hawkins's innocence:

  1. Hawkins was a freshman at the time of the gambling scandal.
  2. Hawkins was known for deceptive basketball techniques.
  3. Hawkins had already returned the money he'd earned from the gambling scheme.
  4. Hawkins was born into desperate poverty.

8. Why did the NBA eventually let Connie Hawkins into the league?

  1. He completed the term of his temporary expulsion with no further gambling incidents to his name.
  2. Hawkins provided his value with stellar play in the ABL and ABA.
  3. The league realized it had lost millions of dollars by not allowing a player of Hawkins's ability join its ranks.
  4. Public outcry following a journalist's exposé of the situation forced them to rethink their handling of the case.

9. Which choice provides the best evidence for the previous answer?

  1. Lines 48-51 ("He was… (NBA).")
  2. Lines 57-62 ("He was… MVP.")
  3. Lines 63-67 ("Finally… attention.")
  4. Lines 67-70 ("The NBA… draft.")

10. As they are presented in the passage, the ABA and ABL were:

  1. perfect substitutes for the NBA experience.
  2. professional leagues that were somewhat less prestigious than the NBA.
  3. superior to the NBA in every way.
  4. organizations that treated Connie Hawkins unjustly.

11. The main purpose of the final paragraph (lines 81-89) is to:

  1. happily muse on other ways the court case might have turned out.
  2. drive home the tragedy of Hawkins's case by wondering how great he could have been if he'd never been exiled from the NBA.[s]
  3. defend the NBA's handling of the Hawkins case.
  4. list Hawkins's various achievements on NBA teams.

Civic Engagement Passage

Civic Engagement

Passage 1
Civic engagement is a privilege. Throughout the entire
history of humankind, only a vanishingly tiny
percentage of people been able to have any say in
line politics. For so much of human history, kings, queens,
5 tyrants and their loyal lackeys have ruled over
thousands of people who weren't allowed to question
or criticize the leadership. Even previous experiments
with democracy restricted enfranchisement so much
that they were essentially oligarchies run by
10 wealthy— usually strictly male— property owners.
Hence, we should be grateful as we wait in line at our
polling centers. It might be easy to take voting for
granted nowadays, but the right to vote was only
granted to every American citizen less than a century
15 ago. Sure, you and all of your neighbors and family
and friends can vote, but you're part of a very
exclusive club, historically speaking.
Voting is a privilege, but it's also a duty. By the nature
of American democracy, there is, indeed, about a fifty
20 percent chance that your preferred candidate is going
to lose any specific election. That likelihood of defeat
rises if you support a third-party ticket. However, duty
isn't about an end result. Duty isn't about you getting
what you want out of the system. It's not about you or
25 your team winning. Duty is about the action itself. We
have an obligation to give our feedback about the way
the country is going. If no one gave our elected
officials any input on the way things were actually
going in America, they'd have only the vaguest, most
30 academic sense of how their policies are affecting
real people.
Voting can be frustrating. Even if you candidate wins,
he or she will probably still disappoint. It might take
years and years to make change, even change that
35 people universally want. It is nothing less than our job
to help steer that ship of state. That job is a rare honor
and a welcome obligation.
Passage 2
Voting is a sheer waste of time and mental energy. In
a country with more than 300 million citizens, each
40 individual vote is mathematically meaningless. It is
impossible for one person's vote to have any sway in
a presidential election.
Sometimes, supporters of civic engagement reference
unusually close elections, citing, say, the fact that if
45 just one vote in every precinct in Illinois had changed
from John Kennedy to Richard Nixon, Nixon would've
won the election in 1960. That number might
encourage you… if you somehow got control of the
votes in hundreds of Illinois precincts. Even in this
50 anomalously close election, one single Illinois vote
was still without real import. Voters spend election day
waiting in line for their chance to fill up a wooden box
with a slip of paper that will have no effect on
55 Commentators bemoan the ignorance of the citizenry,
even— or especially— those who vote. I understand
this ignorance. In fact, I celebrate it. If you're the sole
person making a decision that directly affects you and
the people you care about, it makes a lot of sense to
60 be as informed as possible. If, say, you were given
the responsibility of choosing your family's next car,
you would want to do plenty of research on which
makes and models are safest, most durable, and
most cost-effective. It's reasonable to put in some
65 elbow grease: the decision is all yours. If you're more
knowledgeable, you'll make a better decision.
Now, let's imagine that a committee of 1,000 people
was going to decide your family's next car purchase.
In that case, it doesn't make sense for you to put in as
70 much work. Your effort is no longer all that directly tied
to the outcome of the decision. Chances are, your
level of knowledge on the issue won't have much of
an impact on the final outcome.
Voting in a presidential election is like having a
75 committee of 100,000,000 people choose the next
chief executive. No matter how informed you are, the
outcome of the vote is going to be the same. It doesn't
make sense to waste your mental energy becoming
knowledgeable on the issues when that knowledge
80 won't pay off in a smarter decision.
I invite my fellow Americans to sit out the next
presidential election. If you absolutely must vote
(perhaps you need an excuse to miss hours of work
that Tuesday or you're addicted to collecting “I voted!”
85 stickers), then I beg of you to at least not waste your
time becoming an informed voter.


1. What is the meaning of the word “lackeys” in line 5?

  1. underlings
  2. a key designed for a certain lock
  3. a person who has misplaced his or her keys
  4. a king or a queen

2. The author of Passage 1 likely respond to the argument presented in lines 38-42 of Passage 2 by...

  1. agreeing with the conclusions presented in Passage 2.
  2. countering that voting is an responsibility that doesn't lose its importance simply because an individual doesn't have absolute power.
  3. countering that voting is still the best way for voters to pressure politician into promoting the interests of the voter's interest group.
  4. arguing that it doesn't make that much sense to put effort into becoming an informed voter because no individual voter has much of a say anyways.

3. Which choice provides the best evidence for the above question?

  1. Lines 18-21 (“By the… election.”)
  2. Lines 21-22 (“The likelihood… ticket.”)
  3. Lines 22-25 (“However… itself.”)
  4. Lines 32-33 (“Voting… disappoint.”)

4. The author of Passage 1 mentions voters who support third-party candidates in order to:

  1. convince them to support more mainstream candidates with better odds of winning.
  2. disprove a theory set forth in Passage 2.
  3. expand on the point that voting is often frustrating.
  4. introduce the point that even fringe candidates can have a large effect on the political discourse.

5. As used in line 41, “sway” most nearly means:

  1. rhythmical
  2. moving gently back and forth
  3. influence
  4. bias

6. The author of Passage 2 characterizes voting as:

  1. ultimately unimportant.
  2. a necessary evil.
  3. an honor and an obligation.
  4. a good way of securing favors from those in power.

7. Which choice provides the best evidence for the previous answer?

  1. Lines 43-47 ("Sometimes… 1960.")
  2. Lines 51-54 ("Voters… anything.")
  3. Lines 55-57 ("Commentators… ignorance.")
  4. Lines 67-70 ("Now… work.")

8. In the context of Passage 2, the purpose of lines 57-64 (“If… decision.”) is to:

  1. list the features you should research before purchasing a car for your family.
  2. provide an example of the type of thorough decision-making process one would go through when making a decision that one has direct control over.
  3. detail how a seemingly insignificant choice can have larger ramifications.
  4. show that each person's vote is mathematically meaningless.

9. How would the author of Passage 2 most likely respond to the information presented in the graph?

  1. Decreasing voter turnout is a good thing; if anything, it should go lower.
  2. Decreasing voter turnout is a sign of modern America’s lack of a sense of duty.
  3. Voter turnout isn’t as important as making sure that everyone who does vote is well-informed.
  4. Decreasing voter turnout is an indication that we should be doing more to make it easier for people to get to the polls on election day.

10. What is the relationship between Passage 1 and Passage 2?

  1. The author of passage 2 presents an updated version of a theory presented in Passage 1.
  2. Passage 1 and Passage 2 present slightly different ways of fixing the same problem.
  3. The author Passage 1 presents a theory which the author of Passage 2 supports with a few thought puzzles.
  4. The author of Passage 2 firmly disagrees with an action that the author of Passage 1 encourages.

11. What is one point that the authors of Passage 1 and 2 agree on?

  1. Regardless of one's political ideology, one should still take the time to vote.
  2. There is often a disconnect between how people vote and the policies the government enacts.
  3. The right to vote should be restricted to those who own property.
  4. Voters need to be sure to put in sufficient research before entering the voting booth.

Paired Passages: College Athletics

Collegiate Athletics

Passage 1
The National Collegiate Athletics Association (NCAA)
is an inherently corrupt institution. It brings in billions
of dollars a year in ticket sales, TV revenue, and
line business sponsorships. None of that money goes to
5 players— you know, the entire reason people buy
those tickets and tune into games— who are working
a full-time job on top of attending school. The NCAA
is an outmoded system of minor league athletics
designed before sports became a billion-dollar
10 industry; it's maintained now so that all of those
dollars can flow to those at the top. Executives,
athletics directors, coaches, and administrators are
millionaires; some players can’t afford food.
The NCAA's moralistic rhetoric about preparing its
15 “scholar athletes” for their lives beyond athletics is
merely a justification for cheating teenagers into
providing the NCAA with free labor. The “education”
that athletes are supposed to be grateful to receive is
usually little more than training in how to skirt the
20 rules; comically easy course loads, “tutors” who just
do athletes work for them, and fluff majors are
unlikely to open up “scholar-athletes” to the liberating
wisdom of the ancient humanistic tradition. Athletes
may receive a diploma, but they rarely receive an
25 education.
In other nations, teenaged basketball or soccer
players who are trying to eventually go pro join minor
leagues teams where they get paid and are enabled
to focus on their craft. If they get hurt or fail to make it
30 as professionals, they can then attend further
schooling (when they have the time to actually give
education their full attention). This sort of system
should be our goal. Of course, we couldn't bring that
about tomorrow, even if we followed the most
35 aggressive reform proposals. We could, however,
start the ball rolling by easing the rules on the
material benefits available to players (rules which
every major athletics program already breaks),
allowing student athletes to unionize (just as their
40 professional counterparts are allowed to unionize),
loosening the education requirements applied to
college athletes, and enabling athletes to make
money off of sponsorships and the use of their names
on jerseys and their images in commercials and video
45 games.
Passage 2
In 1979, when Ralph Sampson was recruited to play
basketball for the University of Virginia (UVA), he was
unable to read. By the time he left for the National
Basketball Association (NBA), he could. Without the
50 NCAA rules about attending classes while taking part
in college athletics, he might have lived his entire life
an illiterate.
The NCAA is imperfect, to be sure, but it is worthy of
reform. The way to fix college athletics isn't the
55 replacement of the NCAA's guidelines for athletics
but, rather, stricter enforcement of those rules.
Instead of getting rid of the requirement that
teenagers go to school while pursuing athletics, we
should replace the admittedly phony curriculum
60 followed by most athletes in high-revenue programs
at major schools with better educational guidelines.
We should make athletes challenge themselves like
Ralph Sampson did.
The money that the NCAA brings in is a sign of
65 health. It's an indicator of the value of tradition.
People spend thousands of dollars flying to college
football bowl games because of their histories with
the schools involved. Business slows to a halt during
the first weekend of the men's basketball tournament
70 (March Madness) because everyone knows that it's
the most exciting four days of basketball every year.
The players benefit from this tradition. There's no way
that Steph Curry, who barely received any recruiting
attention during high school, would have found
75 himself drafted in the first round of the NBA draft if
viewers nationwide hadn't seen him lead lowly
Davidson College on a run to the 2008 quarterfinals.
Even if we were able to snap our fingers and
magically replace collegiate athletics with a minor
80 league system tomorrow, it wouldn't have the
sentimental pull within our collective imagination to
allow for a Cinderella story like that.


1. What does the author of Passage 1 argue about the historical roots of the NCAA?

  1. Tradition is important; it benefits athletes just as much as the schools themselves.
  2. The NCAA's long history is one thing that a new minor league system couldn't replicate.
  3. The NCAA was founded under radically different circumstances than exist today.
  4. The NCAA has always been acceptable, but there are some ways to improve it.

2. As it's used in line 14, “moralistic” most nearly means:

  1. improper
  2. esteemed
  3. morale-boosting
  4. virtuous-sounding

3. The author of Passage 1 put quotation marks around “education” in line 17 in order to:

  1. indicate a direct quotation.
  2. indicate sarcasm.
  3. refer back to a previous use of the term.
  4. to highlight the importance of the word.

4. As it's used in line 19, “skirt” most nearly means:

  1. border
  2. a short dress
  3. surround
  4. get around

5. The reference to the “liberating wisdom of the ancient humanistic tradition” in lines 22-23 serves to:

  1. elaborate upon the reforms advocated earlier in the passage.
  2. give an example of how impactful the education scholar-athletes receive can be.
  3. highlight how important humanism still is today.
  4. underscore just how far short of the lofty ideals of higher education the curriculum offered to collegiate athletes falls.

6. How would the author of Passage 1 likely respond to the anecdote presented in the first paragraph (lines 46-52) of Passage 2?

  1. Ralph Sampson learning to read at UVA shows just how vital the NCAA is.
  2. This is an exceedingly rare circumstance that is still remarkable 40 years later precisely because of how unusual it is.
  3. Ralph Sampson learning to read at UVA shows that we should make the education requirements in the NCAA stricter.
  4. UVA should have been opening Ralph Sampson up to the liberating wisdom of the ancient humanistic tradition, not teaching him to read.

7. What is the relationship between Passage 1 and 2?

  1. Both passages argue that changes should be made to collegiate athletics, but they offer free very different proposals.
  2. Passage 1 criticizes an institution that Passage 2 celebrates without reservation.
  3. Passage 2 agrees with the proposals advocated for in Passage 1, but it adds some further suggestions.
  4. Passage 2 rebukes an organization that Passage 1 moderately defends while offering reform proposals of its own.

8. How would the author of Passage 2 likely respond to the suggestions made in lines 35-45 (“We could… video games.”)?

  1. The NCAA should be completely replaced, not merely reformed.
  2. These are fine ideas, but they don't go far enough.
  3. The best course of action is tightening the rules, not loosening them.
  4. These are unnecessary recommendations; the NCAA is fine as it is.

9. Which choice provides the best evidence for the previous answer?

  1. Lines 53-54 (“The NCAA… reform.”)
  2. Lines 54-56 (“The way… rules.”)
  3. Lines 72-77 (“The players… quarterfinals.”)
  4. Lines 78-82 (“Even… that.”)

10. The final paragraph of Passage 2 (lines 72-82) serves to:

  1. highlight how the traditions associated with the NCAA can materially benefit players.
  2. give an example of how an athlete benefited from the college education he received in return for playing for the school's basketball team.
  3. indicate how the reforms advocated earlier in the passage might help individual athletes.
  4. explain just how corrupt the NCAA is.

11. How would the author of Passage 2 most likely respond to the information presented in the graph following the passages?

  1. The more money the coaches make, the more unfair the NCAA becomes.
  2. NCAA coaches should make as much as their players.
  3. It’s a positive sign that salaries for coaches are increasing: everyone benefits when the NCAA is making money.
  4. The fact that coaches are making more and more money is a trivial piece of historical information that has little bearing on the question of athletes’ well-being.

12. The authors of both passages agree that:

  1. It would be impossible to completely replace the NCAA in the short term.
  2. The system of minor league athletics in other countries is superior to the collegiate athletic system in America.
  3. Collegiate athletes should be allowed to unionize.
  4. The NCAA should tighten its education requirements.

Which Glove Do You Like Best?

Which Glove Do You Like Best?

Epistemology is the study of knowledge. How do we
know what we know? What do know for certain?
Epistemology is often a good source of humility
linehumans, it turns out, don’t know very much with
5 absolute, undeniable objectivity. Even perception is
dubitable. Things in the natural world are inevitably
filtered through our (limited) senses. We have
mountains of evidence that the brain is not a neutral
observer of the world around it; perception is not
10 some transparent glass through which we see, hear,
taste, touch, and smell things are they really are.
Perception is an imperfect mirror with countless,
sometimes surprising, warbles. Our brains edit and
consolidate information. We perceive the present in a
15 biased way, and our memories of the past get fudged
even more.
Okay, fine. Our brains aren’t perfect, disinterested
recorders of the outside world. We can’t know that
much about the external world for sure. We can, at
20 least, know what’s going on inside of our own minds,
if nothing else? Our brains can at least tell us about
what’s going on in our brains, right?
Well, recent studies are showing that even that might
not be the case. First-person introspection, the act of
25 a person scanning his or her own brain to see what
going on in there, might not be as unquestionable as
once thought.
An experiment was completed in which four red
gloves were lined up on a table. Participants were
30 simply asked to choose whichever glove they liked
best and then explain their choice. A comfortable
majority chose the glove on the far right. They
explained that this glove was the most attractive to
them because it was the softest or the most colorful
35 or the most well-hemmed.
All of the gloves, however, were exactly the same:
none of the gloves was softer or more or more neatly
sewn. The implication was that they simply chose the
glove on the far right because of some
40 unacknowledged bias towards the right. After all, this
was a random sample of the population, so most of
the participants would have been right-handed.
Why did none of the participants attribute their choice
correctly? It seems as if they chose a glove, then
45 reverse-engineered a logical reason for preferring it
to the other only after the fact. They chose their
favorite glove, then explained that choice to
themselves incorrectly. No one can really say
whether or not their first order thinking (“I like the
glove on the right the best…”) was flawed, but it
50 certainly appears like their second order thinking
(“... because it was the softest.”) was fictionalized.
The discovery that we might not know why we like the
things we like or why we chose the things we chose
opens a bunch of interesting avenues of inquiry in the
55 fields of psychology, philosophy, literature, politics,
economics, sociology— pretty much every single topic
related to human behavior. This study is
begging for follow-up experiments. For example, it
would be interesting to know how participants in this
60 or a similar study might react to being informed of
their mistakes. The human brain is famous for its
adaptability: maybe participants could learn to
interrogate their thoughts processes more carefully?
Hopefully, epistemologists are inspired to jump down
65 this and countless similar rabbit holes. Maybe we’ll
come to know about more fields of knowledge we
can’t put out faith in.


1. What is the main point of this passage?

  1. We can never trust anything our brains ever tell us.
  2. Human knowledge is fallible, even with regards to types of knowledge we once thought were unquestionable.
  3. Our second order thinking is imperfect, but our first order thinking is always beyond question.
  4. Epistemology is a threat to the storehouse of human knowledge.

2. The author sees the human brain as:

  1. a neutral, faithful observer of the world-at-large.
  2. intentionally misleading.
  3. essentially useless
  4. a somewhat flawed filter for the world around us.

3. Which choice provides the best evidence for the answer to the previous question?

  1. Lines 6-11 (“Things… are.”)
  2. Lines 19-21 (“We can… else.”)
  3. Lines 28-29 (“An experiment… table.”)
  4. Lines 62-64 (“The human… carefully.”)

4. As used in line 15, “fudged” most nearly means:

  1. blurred
  2. perfected
  3. a chocolate confection
  4. lied

5. The writer uses the phrase “Okay, fine” in line 17 to:

  1. directly quote the reactions of the participants in this study to being shown its findings.
  2. verify the accuracy of the studies underpinning the claims made in the first paragraph.
  3. introduce a line of thinking which the writer expects to be a normal layperson’s response to the preceding information.
  4. transition to a field of knowledge we can still put our faith in.

6. As used in line 31, “comfortable” most nearly means:

  1. sizeable
  2. wealthy
  3. complacent
  4. pleasant

7. According to the author, participants misattributed the reasons behind their glove preferences because they:

  1. were embarrassed, so they wanted to seem like they made a more reasonable than they actually were.
  2. wanted to fit in with the reports of the other participants in the study.
  3. didn’t trust the people running the study.
  4. didn’t fully understand their own decision-making.

8. Which choice provides the best evidence for the answer to the previous question?

  1. Lines 32-35 (“They… well-hemmed.”)
  2. Lines 36-38 (“All… sewn.”)
  3. Lines 46-48 (”They… incorrectly.”)
  4. Lines 62-64 (“The human… carefully.”)

9. Which of the following would constitute a second order, introspective thought?

  1. “I think my teacher has a bias towards student athletes.”
  2. “I like the color red.”
  3. “I like the glove on the right.”
  4. “I like this perfume because it reminds me of my mother.”

10. The author reacts to the findings in the study with:

  1. excitement and humility
  2. complete devastation
  3. skepticism and enthusiasm
  4. skepticism and enthusiasm

11. The main point of the final paragraph (lines 53-69) is to:

  1. give an exhaustive list of all of the follow-up studies that have been completed after this study.
  2. explain how this study, while interesting on its own, is really the beginning of a line of inquiry which might stretch over several fields.
  3. tamper any possible enthusiasm about the study discussed in the passage.
  4. indict the researchers in various fields who haven’t had the courage to do the necessary follow-up studies the author suggests.
Diagnostic Qs
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Diagnostic Qs

The Waves

Every Virginia Woolf fanatic has his or her own favorite Woolf book. In high school, my favorite was Mrs. Dalloway. As I get older, however, the book I find myself returning to most frequently is The Waves.

[A] The Waves is not Woolf's most well-known book. [B] Her earlier novels— particularly Dalloway and [1] To the Lighthouse, have become classics of the form. [C] The Waves has failed to find an audience, perhaps, because it pushed beyond the parameters of the novel. [D] It’s so experimental that Woolf invented a new term to describe this [2] work: “playpoem.” [E] These two books certainly push the boundaries of form, but they’re still operating in the tradition of the novel. [3]

[4] Known for her lush, poetic descriptions of the everyday, the book doesn’t contain traditional characters or a classical, detached perspective. [5]. Therefore, the story is told by six voices— three female and three male— which [6] presents less of a scene-by-scene chronology of well-plotted events and more of a record of subjective inner states from childhood through old age. These monologues melt into each other, just as the characters seem to. The voices are [7] commenced by nine short, poetic interludes the ebb and flow of a tide from sunrise to sunset.

[8] Woolf was aiming for a musical effect. At [9] it’s best, the novel does indeed achieve a sort of lyricism, set against the percussive backbeat of the rhythm of the prose. There are [10] some, truly ecstatic scenes and entrancing interludes, in the book. However, these delicious aesthetic pleasures require patient, fully-engaged reading. In our modern era— during which art is little more than mere entertainment, designed to be passively consumed— too few readers are trained to give a work this level of attention. The formal experimentation of the book might have limited its reach. [11] That’s a real shame.



  2. To The Lighthouse—
  3. To The Lighthouse)
  4. To The Lighthouse;

[2] Which of the following options presents the most effective description?

  2. work "playpoem."
  3. work; "playpoem."
  4. work and this term was "playpoem"

[3] The most logical placement for sentence E is:

  1. after sentence A.
  2. after sentence B.
  3. after sentence C.
  4. where it is now.


  2. She wrote the novel in 1931
  3. After publishing five previous novels
  4. Written in 1931


  2. Also
  3. Instead
  4. Thus


  2. present
  3. is presenting
  4. has presented


  2. forwarded
  3. instituted
  4. prefaced

[8]Which of the options provides the best introduction to the paragraph?

  2. Woolf said that this was the first novel that she truly wrote in her own voice.
  3. Woolf was deeply disappointed when the book was received lukewarmly.
  4. Virginia's sister Vanessa Bell did the cover art for the first edition.


  2. its
  3. its'
  4. their


  2. truly, ecstatic scenes, and entrancing interludes
  3. truly, ecstatic, scenes and entrancing interludes,
  4. truly ecstatic scenes and entrancing interludes

[11]The writer is thinking of deleting the previous sentence. Should the writer do so?

  1. Yes, it conflicts with information provided elsewhere in the passage.
  2. Yes, it unnecessarily repeats an idea that has already been discussed.
  3. No, it adds an important conclusion.
  4. No, it provides an illuminating look into Woolf's thinking about the reception of the novel.



Commas probably show up on the test more frequently than any other grammar topic. Luckily, all of the commas used on the test boil down to three basic uses. We'll see commas used to separate items in lists, to mark off dependent clauses, and to connect independent clauses.


We use commas between each of the items in a list:

I had to buy apples, bananas, and cucumbers.

The test defaults to the Oxford comma, the one right before the and. It’s a good idea to do the same on the essay section, just to be safe.



Just to be sure, colons look like : (though rarely in huge font and bolded).

Out and about, we’re probably most likely to see colons before lists.

I bought new editions of books by some of my favorite authors: Evelyn Waugh, Oscar Wilde, and Virginia Woolf.

Notice that I bought new editions of books by some of my favorite authors is an independent clause: it could stand as its own sentence. We always need a full independent clause before a colon. Then, the list of authors after the colon explains precisely what I mean by my favorite authors.



First things first, semicolons are the ones that look like ; (just to be sure).

Semicolons, quite simply, go between independent clauses (strings of words that could stand alone as their own sentences). Stylistically, semicolons indicate a closer connection between two clauses than a period does. However, since the two are so similar grammatically, we can always test whether or not a semicolon is in the right place by switching it with a period. If a period works somewhere (adjusting the capitalization accordingly), then a semicolon would work in the same place.

It started raining; I started moping.

After all of that studying, I knew I’d do well on the test; therefore, I was unsurprised when I found out I’d aced it.

Parentheses and Dashes

Parentheses and Dashes

We use parentheses and dashes to add information to the middle or end of a sentence.


Michael Jordan (who played his college basketball at the University of North Carolina) is widely regarded as the greatest basketball player of all time.

Virginia Woolf wrote several beloved works of fiction and nonfiction (even though women faced countless obstacles to writing and publishing literature during her lifetime).



We use apostrophes for two reasons: to make contractions and to show possession.


This is obviously not an exhaustive list of every possible contraction that humans who speak English could possibly come up with, but, hopefully, it makes the pattern clear.

Several verbs can be combined and contracted with not. For example, do not becomes don’t. We push the two words together, then replace the o in not with an apostrophe.

Pronouns and names can also combine with verbs and be contracted. Hence, she is becomes she's.



A pronoun is just a common noun that we use as a substitute for names to avoid being needlessly wordy by repeating names again and again. Subject pronouns stand in for the person, people, or things performing the verb in a sentence.

I filled the water balloons.

She loaded the water balloons into the catapult.

He ran for his life.

We laughed savagely.

Our parents came outside to see what all the commotion was. They were not pleased.

Who vs. Whom

Who vs. Whom

This is one of the knottiest topics in the grammar section, since people default to who ~100% of the time in casual conversation. Our grammatical ears might not work perfectly here. Even when we use whom correctly, it might still sound a little bit off because we aren’t used to hearing it used at all.

who is a subject pronoun, while whom is an object pronoun.

Who serves the same purpose as I, she, he, we, and they. As a subject pronoun, who is used for the person or people performing the verb.

Who is coming over to study for the test?

Who wants to skip the study group and cover the teacher's car in Post-It notes instead?

Who keeps covering my car with Post-It notes?!

Problematic Possessives

Problematic Possessives

Who’s vs. Whose

Both the contraction of who is and the possessive form of who have a claim to taking an apostrophe, since we use apostrophes to denote possession and contractions.

To avoid confusion, we only use an apostrophe with the contraction: who is becomes who’s. For the possession version of who, then, we just attach an -se, with no apostrophe: whose.

Who’s coming to the study session?

Whose jacket is that?


We conjugate verbs based on number and time: the number of people or things performing the verb and the time it’s being performed.

Yesterday, I went to the Post Office.

Tomorrow, they will go to the DMV.

Weird Verbs

There are three types of verbs that, in our experience, give students the most trouble: gerunds, past perfect, and present perfect.


Seeing that the triangle had sides of 5, 12, and 13, I knew that it must be a right triangle.

The first clause— Seeing that the triangle had sides of 5, 12, and 13— gives the setting, the condition I was in when the rest of the sentence happened. That second clause gives us the rest of the idea and the primary verb: I knew that it must be a right triangle.

Notice that the gerund (seeing) is in a sentence with another clause that has another verb(knew).

Verb Practice

Practice Questions #1

1. Yesterday, Throckmorton tries to convince them that he didn’t eat all of their donuts.

  2. tried
  3. try
  4. will try

Surprising Singularity

Surprising Singularity

Collective nouns and singular indefinite pronouns can be tricky because they describe large groups of people, but they act as singular units grammatically.

Collective Nouns

The study group meets at lunch.

The team practices at 6pm.

Parallel Structure

Parallel Structure

According to parallel structure, we should always use the same phrasing for similar ideas within the same sentence.

Danny wants to be a triathlete, so he’s been running, swimming, and biking every day.

Here, we maintain parallel structure by putting each of the verbs in the gerund form (with the -ing): running, swimming, and biking.

Misplaced Modifiers

Misplaced Modifiers

A misplaced modifier is a description that doesn’t align with the correct noun, the noun it’s actually describing. We tend to let them slide in conversation-- we can usually tell what someone’s trying to say from context clues. In formal English, however, misplaced modifiers are unacceptable. Here are a few examples:

Waiting for the school bus, a dog ran up to me.

After a long morning workout, a glutinous lunch was called for.

Struggling to return home after the Trojan War, Odysseus’s epic adventures have entranced readers for centuries.

Lightning Round

Lightning Round

There are a few finicky usage issues we’ll want to just memorize for the test


We use then to indicate cause and effect or to place an event in a chronological sequence.

If you steal the Jade Monkey, then the Princess’s guards will come after you with all they’ve got.

My friend got caught trying to sneak into the Princess’s treasure lair. Then, he was banished from the kingdom forever.


We use than when we’re comparing things.

The Jade Monkey is worth more money than you could possibly imagine.

We also use than to shift focus, as in the phrases rather than and other than.

Rather than stealing the Princess’s Jade Monkey, why don’t you try to find your own?

Insertions, Deletions, and Revisions

Insertions, Deletions, and Revisions

The SAT test writers value straightforwardness over all else. Outside of the test, there’s definitely a place for poetic repetition, whimsical wordiness, or sly elusion. Not on the SAT. On the test, we want to phrase everything in the most direct, concise manner.

When we’re adding, omitting, or changing a phrase, our thinking boils down to one overarching idea: we want to make sure that every single word in a passage is adding something concrete to the text.

Introductions, Transitions, and Conclusions


Whenever we’re asked to choose the best introduction to a paragraph, we’ll really just be looking for the answer choice that best matches the information that follows in the rest of the paragraph.

The Life You Save Might Be Your Own

Teddy Roosevelt was the 26th president of the United States. [1] One day, this long-windedness literally saved his life. Before a speech during the 1912 presidential election, TR was shot in the chest. The bullet would have almost certainly punctured Roosevelt’s lung if it hadn’t been slowed by 50 pages of notes for his speech that he was keeping folded up in his chest pocket. Roosevelt survived the assassination attempt and was actually able to give a 90-minute speech (without the aid of his notes).

1. Which option provides the best introduction to the paragraph?

  2. Teddy Roosevelt was known for giving lengthy addresses.
  3. Teddy Roosevelt was one of the founding fathers of American Progressivism.
  4. Teddy Roosevelt earned the colorful nickname "The Bull Moose."

Moving Sentences

Moving Sentences

The test will sometimes require us to edit for logical flow by moving sentences around within a paragraph. This can feel odd at first because it's probably not something you do with your own writing: hopefully you aren't writing your paragraphs out of order and then trying to reconfigure them at the end to make sense.

Luckily, there will always be a hook that we can use to latch one sentence onto another. Once we find the hook, this type of question becomes reasonably straightforward.

Transitional Expressions

Transitional Expressions

Transitional expressions are words or phrases that connect two sentences or paragraphs and indicate the relationship between the two.

We couldn’t hope to make an exhaustive list of every single transitional expression that exists in the English language— there are dozens and dozens. We will, however, spend some time with examples that show up frequently on the test.

Transitional expressions can indicate that one idea supports another, they can set up contrasts, and they can give us a sense of chronology.

They act as dependent clauses that are usually separated from the rest of the sentence with commas, but they can also appear inside a pair of dashes or parentheses.

Combining Sentences

Combining Sentences

Sometimes the test writers will have us combine two sentences into one. Typically, the most effective way to combine sentences is to rework any repetitions.

I tried to bribe my French teacher. She was in the process of deciding if my 89.45% in her class deserved an A.

Both of these sentences are talking about my French teacher. We can combine these sentences by merging the references to her.

I tried to bribe my French teacher, who was in the process of deciding if my 89.45% in her class deserved an A.

Word Choice

Word Choice

When we're editing for word choice, we aren't applying strict, universal rules. Instead, we'll be analyzing word choice on the subtler grounds of function, tone, and phrasing.


Oftentimes, we’ll be tasked with choosing between two or more words that have very similar meanings but slightly different functions. Even though two options might mean basically the same thing, one choice will be much more appropriate given the specific context of the sentence.

Grammar Practice
Grammar Practice Set 1

Practice Questions #1

1. Everyone needs to make sure that they are in class on time tomorrow.

  2. we are
  3. they is
  4. he or she is

Grammar Practice Set 2

Practice Questions #2

1. Throckmorton and me might never let go of our grudge.

  2. Throckmorton and I
  3. Throckmorton and also me
  4. DELETE the underlined portion

Grammar Practice Set 3

Practice Questions #3

1. I may be the star quarterback on the football team, but my real dream is to be a ballet dancer!

  2. team, however
  3. team,
  4. team, so

Grammar Practice Set 4
Practice Questions #4

1. The teachers’ students threw them a surprise party.

  2. teacher’s students
  3. teacher’s student’s
  4. teacher’s students’

Grammar Practice Set 5
Practice Questions #5

1. The nurses didn’t know who stole there babie’s candy.

  2. their babies’
  3. they’re baby’s
  4. their babys

Grammar Practice Set 6
Practice Questions #6

1. I don’t like sand. It’s coarse, rough, and irritating.

Which of the following is NOT an appropriate way of combining these sentences?

  1. I don’t like sand: it’s coarse, rough, and irritating.
  2. I don’t like sand because it’s coarse, rough, and irritating.
  3. I don’t like sand, it’s coarse, rough, and irritating.
  4. I don’t like sand— it’s coarse, rough, and irritating.


Blue Nights and Magical Thinking

Joan Didion has always been well-respected within the literary community for her stark novels and penetrating journalism. [1] However, it wasn’t until she published a pair of memoirs in her 70s that she achieved mainstream popularity.

The first of these personal tales was The Year of Magical Thinking. In it, Didion described her grief after her husband’s sudden death in 2003 in painstaking detail. [A] The late John Gregory Dunne had been her husband for almost forty years. [B] A writer himself, he was the first person Didion showed her work to, [2] since he was also an author. [C]The book is neither an uplifting memoir of overcoming bereavement nor an excessively macabre book. Instead, Magical Thinking is a frank reporting of Didion’s grief written in her trademark style: cool and detached. [D] Didion likens grief to insanity: the magical thinking of the title was Didion’s unreasonable, unconscious belief that she could undo her husband’s death if only she wished strongly enough or performed the right set of rituals. In the book’s most famous incident, Didion is unable to throw away a pair of Dunne’s shoes. What if he comes back and needs them? The book [3] received lots of praise.[4]

[A] While Didion was preparing The Year of Magical Thinking for publication, another personal tragedy struck.[5][B] In 2005, her daughter Quintana died from complications following a head wound. [C] In this book, Didion departs for the linear narrative format that had structured her previous work. [D] The digressive work circles around themes of aging, parenthood, and meaningless. [E] Didion finds no consolation in Quintana’s death; there is no [6] grand illumination, [7] only agonising “twilights that turn long and blue.” [F] This second blow inspired the book Blue Nights. [8]

The Year of Magical Thinking and Blue Nights are appreciated for many reasons. [9]


[1] The writer is thinking about adding the following sentence:
Didion was raised in Sacramento, a city she would return to many times in her life and in her writing.
Should the writer make this addition here?

  1. Yes, because it provides important details about Didion's biography.
  2. Yes, because it explains a reference made later in the passage.
  3. No, because it repeats information from elsewhere in the passage.
  4. No, because it interrupts the flow of the paragraph with information that isn't made use of again in the passage.

[2] How would you change the unnderlined text?

  2. since he was the author of several novels.
  3. as he was a writer too
  4. DELETE the underlined portion and replace the preceding comma with a period.

[3] How How should I change the underlined text?

  2. was much-discussed when it came out.
  3. was very well-received.
  4. won the National Book Award and was a Finalist for the Pulitzer Prize.

[4] If the writer were to break this paragraph into two, which would be the best place to start the new paragraph?

  1. A
  2. B
  3. C
  4. D

[5] Which of the choices provides the best transition from the previous paragraph to the one that follows?

  2. Magical Thinking even inspired a Broadway play.
  3. In 2011, Didion published a memoir.
  4. Didion had previously published two collections of her spectacular journalism: Slouching Towards Bethlehem and The White Album.

[6] Which option is most consistent with the tone established in the passage?

  2. ginormous
  3. preeminent
  4. blinding

[7] The writer is thinking of deleting the underlined portion. If the writer were to make this deletion, the passage would lose:

  1. an image that both finishes the idea of this sentence and explains the title of the book.
  2. an unnecessary repetition of an idea that's already been thoroughly introduced in the passage.
  3. an idea of the consolation Didion gleaned from Quintana's death.
  4. a lengthy examination of how Didion's grief always seemed to well up in the early evening.

[8] What's the most logical and effective placement for sentence F?

  1. where it is now
  2. before sentence B
  3. before sentence C
  4. before sentence D

[9] Which of the following options provides the best conclusion for the passage?

  2. Recently, Netflix released a documentary about Didion's life.
  3. Though The Year of Magical Thinking and Blue Nights eschew the sentimentalism and easy answers of most popular memoirs, they have become cherished by readers for their understated artistry and unflinching honesty.
  4. These are just two of the 16 books Didion has published; many of her books are still in print and can be found at booksellers or local libraries.

Whole Passages
The Mexican Phoenix

The Mexican Phoenix

If the verified facts about Juana Ines de la Cruz’s life were presented in a work of fiction, they might be dismissed as being too outlandish to be true. [1] Born in Mexico in 1651, her parents were a Spanish Captain and a Creole woman to whom she was an illegitimate child. Juana was fluent in [2] several languages by the time she was eight. She was [3] hugely self-taught. She had to [4] be, girls were granted little access to education then. Juana herself was forbidden from entering her grandfather’s [5] library; she had to break in and read in secret.

[A] When she was a teenager, de la Cruz [6]devises a plan to dress as a boy and attend college (which was restricted to young men at the time) in [7] disguise, and her family didn’t allow her to go through with it. [B] She impressed the colonial court so much that the viceroy invited learned men from all over New Spain to visit and test de la Cruz’s knowledge. [C] The 17-year-old Juana aced these impromptu examinations on philosophy, theology, science, math, and literature. [D] Instead, she became a lady-in-waiting to the viceroy’s wife. [8]

As an adult, de la Cruz entered a monastery, eschewing the more traditional path of marriage in order to continue focusing on her studies. [9] Sor Juana ([10] who’s literary career started when she

wrote a poem about the Eucharist at the age of [11] eight— wrote plays, poems, and [12]completed the composition of philosophical tracts. Revelatory works such as First Dream (a 975-line poem meditating on human knowledge) and The Divine Narcissus (a play synthesizing Christian theology and classical mythology) earned her the nicknames “The Mexican Phoenix” and “The Tenth Muse.”

In 1692, however, a friend-turned-rival leaked a private critique Juana had written of a decades-old sermon. This was enough to convince the authorities to take away the liberties that Sor Juana had been granted: she had to stop writing and was forced to sell her extensive library containing [13] no less then 4,000 volumes. She died while tending to plague victims three years later. For 200 years, Sor Juana was lost to history.

[14] Recently, however, Sor Juana has received renewed interest. A 1982 biography by Octavio Paz brought Sor Juana’s story to a mainstream audience. Dozens of critical studies of her work have followed. Collections of Sor Juana’s work have become available in Spanish and English. Everyone who has the pleasure of coming across an anthology of her work [15] is bound to be blown away by the depth of her talent and the breadth of her learning.



  2. Born in Mexico in 1651, her parents were a Spanish Captain and a Creole woman for whom she was an illegitimate child.
  3. Born in Mexico in 1651, an illegitimate child was what she was for her parents, a Spanish Captain and a Creole woman.
  4. Born in Mexico in 1651, she was the illegitimate child of a Spanish Captain and a Creole woman.

[2] Which of the following options presents the most effective description?

  2. a few languages
  3. Spanish, Latin, and Nahuatl (the Aztec language)
  4. three languages


  2. largely
  3. decidedly
  4. vastly


  2. be (girls
  3. be,
  4. be: girls


  2. library, she
  3. library, but she
  4. library, had


  2. devised
  3. devising
  4. to devise

The Undead Merchant of Death

The Undead Merchant of Death


Nobel was born in Sweden and was the son [1]of, famous inventor, Immanuel Nobel. Alfred made a fortune investing in oil refineries and held 355 [2] patents, however, he was most well-known for inventing dynamite. Furthermore, while he was a pacifist himself, his [3] families business ran about 100 armaments facilities.


Hence, when [4] it thought he’d died, it ran an obituary calling him “the merchant of death.” Nobel was shocked to see his impact on the world put in such stark terms. He committed himself to leaving a more positive legacy. [5]


In 1888, Alfred Nobel’s brother died. [6] However, some newspapers misreported it as Alfred’s death. [7] Much akin with Tom Sawyer listening in on his own funeral service, Nobel got the chance to see what people would say about him after he died. What he read would change his life.


Nobel was [8]displaced to devote his time and resources to philanthropy. His most famous attempt to inspire positive change was his endowment of the Nobel Prize, for which he allocated [9]94% of his fortune. To this day, the Nobel Prize is awarded [10] to recipients who have distinguished themselves in physical science, literature, and medicine. Another prize, the Nobel Peace Prize, is given in recognition of those who perform great services in the name of international fraternity. Nobel’s name is now associated with human excellence and international cooperation. [11] As of 2018, 584 prizes have been given out. [12]



  2. of famous inventor,
  3. of famous, inventor,
  4. of famous inventor

[2] Which of the following options presents the most effective description?

  2. patents, but
  3. patents,
  4. patents. But

[3]How should we correct the underlined word?

  2. families'
  3. family's
  4. familys

[4]Again, how should we correct this underlined word?

  2. they
  3. a French newspaper
  4. them

[5]What's the most effective way of combining the two underlined sentences into one?

  1. Nobel, shocked to see his impact on the world put in such stark terms, committed himself to leaving a more positive legacy.
  2. Nobel committed himself to leaving a more positive legacy, for it was shocking to him to see his impact on the world put into such stark terms.
  3. Nobel committed, having been shocked to see his impact on the world put into such stark terms, to leaving a more positive legacy.
  4. Nobel, who then committed himself to leaving a more positive legacy, was shocked to see his impact on the world put into such stark terms.

[6]How would you change the underlined text that follows?

  2. Thus
  3. Alternatively
  4. Finally

[7]How would you change the underlined text that follows?

  2. Much like
  3. Much alike
  4. Much similar to

[8]How would you change the underlined text that follows?

  2. moved
  3. lifted
  4. affected

[9]How would you change the underlined text that follows?

  2. a huge portion of his fortune.
  3. a quantifiable sum of money.
  4. a whole lot of his money

[10]How would you change the underlined text that follows?

  2. those people who achieve great things
  3. people deemed worthy of awards
  4. DELETE the underlined portion

[11]Which option provides the best conclusion to the passage?

  2. As he hoped for, Nobel has become known as a merchant of peace.
  3. There is a similar prize in mathematics called the Fields Medal.
  4. Some of the awards have, unsurprisingly, inspired controversy.

[12]What is the most logical and effective placement for paragraph 3?

  1. where it is now
  2. before paragraph 1
  3. after paragraph 1
  4. after paragraph 4

My Beloved Hoodie

My Belovèd Hoodie

I’ve never cared much [1] in fashion. I’d rather be comfortable [2] then look good relative to some arbitrary, ever-changing definition of “well-dressed.” [3] Nonetheless, my all-time favorite article of clothing was a ratty, old hooded sweatshirt that was worn out at the elbows. It was my favorite [4] color Carolina blue. [5] More importantly, it was almost superfluously [6] soft, it fit absolutely perfectly. I really liked the way it looked, and I loved the way it fit me. [7]

This makes it all the more tragic that I am personally guilt of accidentally destroying my belovèd hoodie one summer. [8] I’d been wearing it even more than usual: in class, at meals, and [9] I wore the hoodie during my nightly basketball games. [10]I wore my blue hoodie almost as much as any other hoodie I owned. [11] In May however it got so hot that I couldn’t wear the hoodie comfortably anymore. I threw it in the back of my car and forgot about it until September, when it was finally chilly enough to justify [12] wearing it again. To my shock, it now had misshapen stripes up and down the back, and it didn’t fit very well anymore. Flung haphazardly onto my backseat, it had been bleached by the sun. Balled up for an entire summer, it had lost [13] it’s shape. I had to remove the hoodie from my rotation. I’ve worn many hooded sweatshirts since [14] then, but sadly, none of them have ever felt the same.



  2. towards
  3. for
  4. into

[2] Which of the following options presents the most effective description?

  2. as
  3. to
  4. than

[3]How should I start the next sentence?

  2. However
  3. Instead
  4. In fact

[4]How should I change the underlined phrase?

  2. color:
  3. color (
  4. color;

[5]At this point, the writer is thinking of adding the following sentence:
Three of my favorite basketball players— Rasheed Wallace, Vince Carter, and Michael Jordan— played at the University of North Carolina at Chapel Hill, whose school color is Carolina blue.
Should the writer make this addition here?

  1. Yes, because it describes Carolina blue for those who might not be familiar with it.
  2. Yes, because it gives some much-needed information that is referred to later in the passage.
  3. No, because it contradicts information presented later in the passage.
  4. No, because it provides unnecessary information that distracts from the focus of the paragraph.

[6]How should I correct the underlined phrase?

  2. soft; fitting
  3. soft, but it
  4. soft, and it

[7]The writer is thinking of deleting the preceding sentence. Should the writer make this deletion?

  1. Yes, because it unnecessarily repeats information presented earlier in the paragraph.
  2. Yes, because it distracts from the explanation of why the writer liked that sweatshirt so much.
  3. No, because it provides an important clue into why the writer liked that sweatshirt so much.
  4. No, because it sets up the paragraph that follows.

[8]Which is the best transition from the previous paragraph to the one that follows?

  2. I used to wear this hoodie a lot.
  3. I wish I hadn't left this hoodie in my car all summer.
  4. I have an ever-expanding collection of hoodies of different colors.

[9]How should I correct the underlined portion?

  2. I also was known to wear it
  3. also wore the hoodie
  4. DELETE the underlined portion

[10]Which of the following options best relates the information presented in the pie chart following the passage?

  2. I wore my blue hoodie more than all of my other hoodies combined.
  3. I wore my blue hoodie twice as much as my purple one.
  4. I wore my blue hoodie frequently.

[11]How should I correct the underlined portion?

  2. In May, however,
  3. In May, however
  4. In May however,

[12]How should I correct the underlined word?

  2. wore
  3. had worn
  4. wear

[13]How should I correct the underlined word?

  2. its
  3. its'
  4. one's

[14]How should I/we correct the underlined phrase?

  2. then but sadly.
  3. then, but, sadly,
  4. then, but sadly


Writing Review

This is an overview of all of the writing topics. These pages are just a collection of all of the final Review pages from each of the individual sections. Don’t expect anything more from these pages; don’t expect anything less.

This section is a good thing to look at two or three days before the test. Skim through and refresh yourself on all of the guidelines (you want, say, the rules for using colons on the tip of your tongue on the day of the test). If you see something that you don’t remember very well, it would be a good idea to go back and read through that individual section itself.



Comma questions on the test will task us with correctly placing commas in lists, around dependent clauses, and in between independent clauses.


We use commas to separate items in a list.

In order to make dinner tonight, I needed to buy pasta, diced tomatoes, cream, and bread.

Dependent clauses

We can also use commas to set a dependent clause apart from the beginning, middle, or end of an independent clause.

First, I left to go to the grocery store.

I realized, however, that I’d locked my keys inside my house.

I had to break in through the window, even though it’s my own house.

Independent Clauses

Finally, we can use a comma and an appropriate FANBOYS to connect two independent clauses that are related to each other.

A policeman saw me trying to smash my window, and he arrested me for trespassing.

You’ll probably want to have your phone in landscape mode for most of these Math sections.

You’ll probably want to have your phone in landscape mode for most of these Math sections.

Diagnostic Qs

a + b = 4
a - b = 8

What is the value of ab?

  1. -12
  2. -4
  3. 4
  4. 12

Exponents and Radicals

Exponent Rules

We aren’t provided with the exponent rules on the cheat sheet that accompanies the SAT Math sections, so it’s best to memorize them.

We use exponents to show that we’re multiplying a number by itself.

x · x = x2

The exponent (the number attached to the top-right corner of a term) tells us how many times we’re multiplying the term by itself. Here, we see x two times, so that gets rewritten as x2. We refer to x, the number being raised to an exponent, as the base.

If we were, say, multiplying 37 x terms together, we’d write that as x37.

Combining Like Terms

When we have the same base and the same exponent, we can add

xa + xa = 2xa

When we have the same base and the same exponent, we can also subtract

5xa - 3xa = 2xa




Erliss got a new job at a law office. Her main duty is filing memos. She can file 15 memos in 30 seconds. If Erliss is able to maintain this pace, how many memos will she be able to file in four minutes?

If Erliss is able to work keep filing memos at the same speed, then the number of memos she files in 4 minutes should be proportionate to the number she could file in 30 seconds. The relationship between memos and time should stay the same. We can solve this time of question using a proportion:

It’s helpful to verbalize the proportion, to put into words what goes into each part of each fraction. Maybe 70% of the time that students get proportions questions wrong, it’s because they accidentally flip one of the proportions. If we write out what each part of the fraction is supposed to mean, it’s easier to check ourselves and make sure that we have memos over seconds for each part of the proportion.



We calculate the value of a variable by getting that variable alone on one side of the equation.


43 = 6x - 5

What is x - 3?

We’re going to need to get x alone on the right side of the equation.

To get rid of the - 5 we add 5 to both sides. We always do the opposite function of the original when we’re trying to get rid of a number.

To detach the 6 from x, we’ll divide both sides by 6. Originally, we were multiplying 6 and x, so the opposite function is division. When we do something to one side of the equation, we also have to do the same thing to the other side.

Remember, however, that the question asks us to find x - 3.

The test writers love to throw in these little side tasks to the end of questions. We don’t just find the value of the variable itself; we have to plug that into some other expression. Be very careful about what questions are actually asking— the test writers will always put 8 as one of the distracting answer choices.

Fun With Functions


f(x) = 8x + 3

This equation might be read as “the function of x equals 8x + 3.” The f(x) just means that we’re plugging in x for the variable to find the value of the function, f.

This gets more interesting when we’re asked to plug something else in for the variable.

Here, f(6) means that we’re plugging in 6 every time we see the variable

We can plug plenty of other terms into the function beyond integers.

We could plug in another term involving x itself.

We handle 3x the same way we dealt with 6.

Linear Equations

Linear Equations

A linear equation that we graph on the (x, y) coordinate plane models the relationship between x and y.

Let’s say that we’re given the equation y = 2x + 2. We could plug in any value for x and calculate the corresponding value for y.

Let’s say x is 1.

When x is 1, y is 4.

We can write this relationship as an ordered pair: (1, 4). We always write ordered pairs in the format (x, y).

Let’s say x is -2.

When x is -2, y is -2.

This could be summarized in another ordered pair: (-2, -2).

What if x = 0?

When x = 0, y = 2

This gives us the ordered pair (0, 2).

Quadratic Functions

Quadratic Functions

Quadratic functions model the relation between x and y when we have an x term raised to the second power (x2).

Let’s play around with the function y = x2 - 4x + 3.

When x = 0

y = (0)2 - 4(0) + 3
y = 0 - 0 + 3
y = 3

Let’s plot this point.

Factoring Practice

Factoring Practice

We pull the solutions— a.k.a. the zeros— for quadratic functions out of the factors. The factored form restates the function as a pair of parenthetical binomials.

For example, the factored form of the equation……

If we were to multiply the factored form of the equation back out, we’d arrive back at the original function.

When we multiply two parentheses like this, we want to be sure to multiply every term in the first parenthesis by every term in the second.

When we put this all back together, we have…

Combining our like terms leaves us with…

When we factor, we’re reversing this process. We’re looking for the terms to put inside our parentheses which multiply back out to our original function.

For the sake of convenience, we usually filter quadratic functions into an ax2 + bx + c template.

Factoring is usually a matter of finding the integers that will add up to b (3 + 3 = 6) and multiply out to c (3 · 3 = 9).

Quadratic Formula

Quadratic Formula

A few times per test, we’ll be given quadratic functions that don’t factor out nicely. In those cases, we’ll have to use the quadratic formula.

There’s no convenient way to factor this function:
No numbers that multiply to -2 add up to -4. Hence, we’ll use the quadratic formula.

y = x2 - 4x - 2

To plug our equation into the quadratic formula, we’ll have to put it into the template ax2 + bx + c.

The number in front of the x2 is a.
The number in front of the x is b.
The integer is c.

a = 1
b = -4
c = -2

The quadratic formula allows us to solve for x.

We start by plugging our values for a, b, and c into the formula.

This gives us...

...which simplifies to...