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You may wish to remove these sample answer document pages to respond to the practice SAT Essay Test.
You may wish to remove these sample answer document pages to respond to the practice SAT Essay Test.
SECTION 5: ESSAY
You may wish to remove these sample answer document pages to respond to the practice SAT Essay Test.
You may wish to remove these sample answer document pages to respond to the practice SAT Essay Test.
Turn to section 1 of your answer sheet to answer the questions in this section.
Questions 1–10 are based on the following passage and supplementary material.
This passage is adapted from Kevin Drum, “America’s Real Criminal Element: Lead” ©2013 Mother Jones.
In the first paragraph, Karl Smith’s work is presented primarily as
A) a controversial sociological hypothesis.
B) a warning about potentially dangerous economic trends.
C) a useful model for conceptualizing a variety of phenomena.
D) a potential medical solution to a persistent social problem.
The author suggests that promising research in the social sciences is sometimes ignored because it
A) is not presented by authorities with the proper credentials.
B) is not supported by controlled scientific experiments.
C) relies on complex mathematical calculations that are not easily understood.
D) uses historical data that are not necessarily valid in the modern era.
Which of the following provides the strongest evidence for the answer to the previous question?
A) Lines 24–27 (“A recent study … later on”)
B) Lines 49–52 (“In a 2000 paper … America”)
C) Lines 68–72 (“Nevin is … community”)
D) Lines 72–74 (“What’s more … speaking”)
According to the graph, which of the following is closest to the percent increase in violent crime in America from 1963 to 1993?
A) 600%
B) 400%
C) 75%
D) 20%
According to the graph, which decade of violent crime statistics provides the LEAST support to Rick Nevin’s hypothesis?
A) 1963–1973
B) 1980–1990
C) 1983–1993
D) 2003–2013
The author mentions “sales of vinyl LPs” (line 74) primarily as an example of
A) another economic factor that may explain a social trend.
B) how harmful chemicals can be spread via consumer products.
C) a statistic that may be more coincidental than explanatory.
D) a counterintuitive trend in consumer behavior.
The “complications” in line 22 are
A) obstacles to gathering relevant data.
B) controversies about theoretical models.
C) challenges to the implementation of social policies.
D) psychological problems.
The author characterizes the “drivers” in line 60 primarily as
A) inadvertent abettors.
B) unintentional heroes.
C) greedy consumers.
D) devious conspirators.
In line 49, “even better” most nearly means
A) less controversial.
B) more correlative.
C) easier to calculate.
D) more aesthetically engaging.
The final paragraph (lines 85–98) serves primarily to
A) suggest topics for future research.
B) concede a theoretical drawback.
C) propose a novel alternative.
D) describe a supportive implication.
Questions 11–21 are based on the following passages.
Passage 1 is adapted from an essay written by John Aldridge in 1951. ©1951 by John Aldridge. Passage 2 is adapted from Brom Weber, “Ernest Hemingway’s Genteel Bullfight,” published in The American Novel and the Nineteen Twenties. ©1971 by Hodder Education.
Passage 1
Passage 2
On which topic do the authors of the two passages most strongly DISAGREE?
A) The economy of Hemingway’s writing
B) The incisiveness of Hemingway’s prose
C) The sincerity of Hemingway’s portrayals
D) The extent of Hemingway’s reputation
Which pair of sentences provides the strongest evidence for the answer to the previous question?
A) Lines 5–7 (“He was … just shot”) and lines 85–89 (“Hemingway … had value”)
B) Lines 37–39 (“Later writers … his place”) and lines 55–56 (“Our violence … the 1920s”)
C) Lines 24–26 (“The words … stone of life”) and lines 56–58 (“Yet … existence”)
D) Lines 34–36 (“We had much … influence”) and lines 90–93 (“Perhaps the greatest … was ‘flowery’”)
Which of the following best describes how each passage characterizes Hemingway?
A) Passage 1 portrays him as a tortured poet, but Passage 2 portrays him as a crass amateur.
B) Passage 1 portrays him as a master of refinement, but Passage 2 portrays him as a literary revolutionary.
C) Passage 1 portrays him as a hero, but Passage 2 portrays him as a cultural conformist.
D) Passage 1 portrays him as an absurd warmonger, but Passage 2 portrays him as an undisciplined artist.
Which statement about Hemingway is supported by both passages?
A) He was an artistic pioneer, although he was underappreciated in his time.
B) He was a consistent practitioner of spare and evocative prose.
C) His characters serve as archetypes for masculine adventure.
D) His wartime narratives do not fully capture the horrors of war.
In line 26, the phrase “living stone” most nearly means
A) salient experience.
B) inevitable regret.
C) stubborn resistance.
D) durable memorial.
Lines 28–32 (“And so we … aroused in us”) suggests that many of Hemingway’s readers were inclined to
A) emulate his adventures.
B) resent his glorification of war.
C) imitate his literary style.
D) identify with his language.
The “lessons” mentioned in line 43 most likely include stories of
A) transformative romantic love.
B) confidence in the face of danger.
C) indulgent self-examination.
D) corporate or political ambition.
In line 49, the word “tottering” is intended to evoke a sense of
A) infantile frailty.
B) economic instability.
C) artistic immaturity.
D) societal upheaval.
The author of Passage 1 would most likely regard the statement in lines 66–67 (“Hemingway, in effect … conscience”), with
A) journalistic detachment.
B) grudging acquiescence.
C) vehement disagreement.
D) good-natured amusement.
Which statement provides the best evidence for the answer to the previous question?
A) Lines 2–5 (“Like Lord … superb conviction”)
B) Lines 28–32 (“And so … aroused in us”)
C) Lines 34–36 (“We had much … formative influence”)
D) Lines 39–41 (“They have rejected … own time”)
The author of Passage 2 suggests that, in comparison to Hemingway, Frank Lloyd Wright was relatively
A) minimalist.
B) iconoclastic.
C) volatile.
D) traditional.
Questions 22–32 are based on the following passage.
This passage is from Christopher F. Black, “The Mystery of the Strong Nuclear Force.” ©2015 by Christopher F. Black and College Hill Coaching.
ELECTROSTATIC AND STRONG NUCLEAR FORCES BETWEEN PROTONS
The primary purpose of the first paragraph (lines 1–12) is to
A) describe a popular misconception.
B) introduce a physical theory.
C) suggest a scientific conundrum.
D) present a personal account.
In line 7, “aloof” most nearly means
A) impenetrable.
B) formal.
C) retracted.
D) nonreactive.
The question in lines 10–12 (“And why … at all?”) indicates
A) a minor curiosity to scientists exploring deeper questions.
B) a socially significant puzzle that is unfortunately ignored in scientific circles.
C) a humorous irony in an otherwise serious field of investigation.
D) a central conundrum at the heart of an important scientific field.
Which sentence provides the best evidence for the answer to the previous question?
A) Lines 2–5 (“But atoms … stability”)
B) Lines 19–20 (“Even worse … an atom”)
C) Lines 55–56 (“The pion … tweezer’s job”)
D) Lines 68–70 (“If you’re … disappointed”)
In lines 13–16, the repetition of the phrase “We are” serves primarily to emphasize
A) the predominance of certain conceptions.
B) the personal nature of scientific research.
C) the effectiveness of a particular analogy.
D) the deficiencies in public education.
Which of the following best describes the relationship between the electrostatic force and the strong nuclear force between protons at the equilibrium point as shown in the graph?
A) The strong nuclear force is at its maximum, but the electrostatic force is not.
B) The strong nuclear force is at its minimum, but the electrostatic force is near its maximum.
C) The sum of the two forces is zero.
D) The strong nuclear force is zero and the electrostatic force is greater than 100 Newtons.
According to the graph, the electrostatic repulsion between two protons separated by 1.5 femtometers is closest to
A) 2 Newtons.
B) 20 Newtons.
C) 100 Newtons.
D) 1,000 Newtons.
The “mortal blow” (line 51) to Hideki Yukawa’s theory was the fact that
A) the existence of pions was not confirmed by experimental evidence.
B) pions were discovered to be massless, thereby refuting his theory that they were heavy.
C) experiments showed pions to be ineffective in the range required by atomic theory.
D) pions had a destabilizing effect on atomic nuclei, rather than a stabilizing one.
Which of the following best describes the structure of the passage as a whole?
A) a series of intuitive illustrations of a complex physical theory
B) a description of a technical puzzle and the attempts to solve it
C) an account of an experimental finding and its surprising implications
D) a historical overview of a heated scientific controversy
The author’s writing style is particularly notable for its use of all of the following EXCEPT
A) rhetorical questions.
B) illustrative metaphors.
C) technical specifications.
D) appeals to common intuition.
In line 68, “ties up” most nearly means
A) constrains restrictively.
B) resolves neatly.
C) obstructs completely.
D) fastens securely.
Questions 33–42 are based on the following passage.
This passage is adapted from Jean-Jaques Rousseau, “Discourse on Inequality and Social Contract.” Originally published in 1762.
This passage is primarily concerned with
A) restoring the reputation of some widely maligned leaders of the past.
B) comparing the merits of various ancient systems of government.
C) examining the social conditions that foster effective legal systems.
D) establishing the philosophical basis for universal democracy.
In line 2, the word “sounds” most nearly means
A) resonates.
B) enunciates.
C) probes.
D) appears.
In the first paragraph, the author discusses the activities of an architect in order to make the point that
A) the success of a nation’s civil code depends on the nature of its people.
B) good laws must be based on sound philosophical principles.
C) nations that lack good laws cannot support a professional class.
D) effective government requires experts to design civic infrastructure.
The author suggests that long-established societies are characterized primarily by
A) stubborn resistance to political change.
B) an honorable respect for good laws.
C) periodic but predictable social renewal.
D) a tendency toward imperialist expansion.
Which sentence provides the best evidence for the answer to the previous question?
A) Lines 9–12 (“Also, good laws … vice”)
B) Lines 19–21 (“Once customs … reformation”)
C) Lines 30–34 (“Horror … vigor of youth”)
D) Lines 71–73 (“The Tartars … as inevitable”)
In lines 17–18, the distinction between “peoples” and “men” is essentially one between
A) barbarism and civilization.
B) societies and individuals.
C) youth and maturity.
D) rebellion and obedience.
The author mentions “Sparta at the time of Lycurgus” (line 35) primarily as an example of a place where
A) the citizens were paralyzed with fear in the face of invasion.
B) the society was rejuvenated through conflict.
C) the people lost sight of their own sacred traditions.
D) the leaders had become foolish and cowardly.
In lines 37–38, the phrase “particular constitution of the state” refers most specifically to
A) the documented rules by which a nation defines its governmental institutions.
B) the social composition and cultural habits of a population.
C) the enumeration of popular rights in a democratic society.
D) a manifesto about the philosophical motivations for political change.
In lines 51–52, the phrase “amenable to discipline” most nearly means
A) ready to be governed by the rule of law.
B) susceptible to exploitation by neighboring countries.
C) prepared to accept an oppressive ruler.
D) trained for offensive or defensive military activity.
The author suggests that Peter the Great’s main flaw was
A) military ruthlessness.
B) undue reverence for custom.
C) excessive political guile.
D) irresolution in exerting control.
Questions 43–52 are based on the following passage.
This passage is adapted from Bertrand Russell, A History of Western Philosophy. ©1945 by Bertrand Russell, renewed by Edith Russell. Reprinted with permission of Simon & Schuster.
The passage as a whole primarily serves to
A) contrast the ideas of several ancient Greek philosophers.
B) examine the means by which philosophical ideas become popular.
C) describe the conceptions that inform a particular mindset.
D) discuss the debt that modern physics owes to ancient thinkers.
The statement that “animals have lost their importance” (line 29) means that
A) humans no longer treat other species with appropriate respect.
B) animistic beliefs no longer inform our physical theories.
C) scientists no longer regard animal behavior as a productive topic of study.
D) humans do not use animals for transportation to the extent that they once did.
The “simpler system” in line 5 is a
A) method for translating complex writings of ancient thinkers.
B) streamlined system for reaching logically valid conclusions.
C) formal theory based on a very small number of assumptions.
D) relatively unrefined way of thinking.
Which of the following statements about ancient Greek philosophers is best supported by the passage?
A) Their astronomical theories were closely associated with their religious ideas.
B) Their ideas about mechanics inspired many important technological innovations.
C) They regarded human intellect as a divine gift, rather than a cultivated skill.
D) They valued imagination and creativity even more than reason and logic.
Which sentence provides the best evidence for the answer to the previous question?
A) lines 61–65 (“It was natural … simplicity”)
B) lines 45–47 (“To the Greek … of animals”)
C) lines 40–45 (“To the modern … animals and machines”)
D) lines 3–6 (“Every philosopher … quite unaware”)
In line 46, “assimilate” most nearly means
A) incorporate.
B) comprehend.
C) embrace.
D) liken.
The passage suggests that the “men of genius” (line 37) are noteworthy for their
A) creative metaphors for the laws of motion.
B) ability to integrate many different fields of study.
C) effectiveness in articulating their ideas to others.
D) willingness to disregard conventional wisdom.
Which of the following would best bridge the “gulf” in line 45?
A) creating a system of gestures to help humans better communicate with dolphins
B) writing a computer program that analyzes and categorizes mockingbird calls
C) discovering the mechanical laws that describe bumblebee flight
D) teaching modern students more about ancient Greek philosophy
The passage suggests that the “views of Aristotle” (line 1) are characterized primarily by their
A) logical rigor.
B) animistic tendencies.
C) reliance on refutation.
D) unwavering skepticism.
Which sentence provides the best evidence for the answer to the previous question?
A) lines 3–6 (“Every philosopher … quite unaware”)
B) lines 12–14 (“The sophistication … positive result”)
C) lines 19–21 (“In relation … modern student”)
D) lines 45–47 (“To the Greek … animals”)
STOP
If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test.
Turn to Section 2 of your answer sheet to answer the questions in this section.
Questions 1–11 are based on the following passage and supplementary material.
Physician Assistants
As the American population grows, ages, and gains better access to affordable health insurance, the demand for primary medical services 1 are expected to skyrocket. As a result, the United States Department of Health and Human Services projects a shortage of about 20,000 primary care physicians by 2020. Therefore, an important challenge facing the healthcare industry is how to address this shortfall without sacrificing quality of care. One possible solution is to 2 elevate more medical school graduates to choose primary care as their field instead of 3 their choosing the more lucrative specialties like surgery and dermatology.
A) NO CHANGE
B) is
C) has been
D) would be
A) NO CHANGE
B) interest
C) incentivize
D) expect
A) NO CHANGE
B) to choose the more lucrative specialties
C) the more lucrative specialties
D) the more lucrative specialties they might choose
PHYSICIAN ASSISTANTS IN THE U.S.
Source: American Academy of Physician Assistants, American Medical News, September 27, 2011
[1] Another option is to incorporate more medical professionals like physician assistants (PAs) and nurse practitioners (NPs) into primary care teams. [2] They can talk with patients about treatment options, prescribe medications, and even 4 perform technical procedures like bone marrow aspirations. [3] Many healthcare providers are moving toward this “team-based” model, 5 where physicians can better focus on their specialties while relying on trained professionals to provide other necessary services. [4] Team-based medicine allows medical practitioners to best utilize their particular skills, 6 still sharing the successes and struggles of the team. [5] If organized around the principles of professionalism, trust, communication, and accountability, these teams may be able to provide better care to patients at less cost. 7
For all the promise of team-based primary medicine, it cannot work without an adequate supply of well-trained health professionals. Although the total number of PAs in the United States more than doubled between 2000 and 2010, 8 the number of PAs going into primary care has decreased by 20% over that same time period. In the years ahead, we must encourage more of these new PAs to choose careers in primary care.
A) NO CHANGE
B) performing technical procedures
C) technical procedures
D) to perform technical procedures
A) NO CHANGE
B) whereby
C) by this
D) when
A) NO CHANGE
B) while at the same time
C) while
D) although
The author is considering inserting the following sentence into this paragraph.
Although they receive less training than physicians do, these professionals have advanced degrees and can provide direct treatment to patients.
Where should it be placed?
A) After sentence 1
B) After sentence 3
C) After sentence 4
D) After sentence 5
Which choice is best supported by the data in the graph?
A) NO CHANGE
B) the number of PAs going into primary care has increased by only 50%
C) more PAs have gone into dermatology than into primary care
D) the fraction of those PAs going into primary care has declined from over one-half to under one-third
Undergraduate students considering a career in medicine have many more options 9 than they did just a generation ago. Graduate PA and NP programs, which take about three years, are becoming increasingly attractive, especially 10 being that MD programs, including residency, lasting seven to ten years and often leave students saddled with tens of thousands of dollars in debt.
Anyone thinking about pursuing a PA or NP degree should keep in mind that these programs aren’t cheap, either, and that most states impose strict limits on the kinds of treatment 11 they can provide.
A) NO CHANGE
B) than
C) than it was
D) to choose from than
A) NO CHANGE
B) when MD programs, including residence, are lasting
C) being that MD programs last, including residency,
D) because MD programs, including residency, can last
A) NO CHANGE
B) he or she
C) these professions
D) these professionals
Questions 12–22 are based on the following passage.
Maria Montessori
What is education? Is it a program of institutionally approved performances, or a collection of self-directed experiences? Such questions absorbed Maria Montessori throughout her life. Born in 1870 in 12 Chiaravalle Italy, Montessori showed a strong independent will even as a child. As a teenager, she told her parents that she wanted to study engineering, 13 a position that was widely thought unladylike. By the age of 20, she had changed her mind and decided to pursue an even less traditional path: medicine. Despite suffering ridicule and isolation, 14 Montessori’s medical studies at the University of Rome were completed and she became one of the first female physicians in Italy.
Although Montessori’s practice focused on psychiatry, her interests gravitated toward education. In 1900, she was appointed co-director of the Scuola Magistrale Ortofrenica, a training institute for special education teachers. Montessori believed that, in order for so-called “deficient” children to thrive, they needed respect and stimulation rather than 15 the regimentation they were receiving in institutions.
A) NO CHANGE
B) Chiaraville, Italy. Montessori showed a strong independent will, even
C) Chiaraville, Italy, Montessori showed a strong, independent will, even
D) Chiaraville, Italy; Montessori showed a strong, independent will even
A) NO CHANGE
B) despite its reputation for being unladylike
C) although widely considered unladylike
D) which was unladylike in reputation
A) NO CHANGE
B) Montessori completed her medical studies at the University of Rome by becoming
C) Montessori’s medical studies were completed, at the University of Rome, and thus she became
D) Montessori completed her medical studies at the University of Rome and became
A) NO CHANGE
B) receiving regimentation in institutions
C) the regimented institutions they were receiving
D) the regimentation of the institutions they were receiving
In 1907 Maria opened the Casa dei Bambini, or “Children’s House,” a daycare center for impoverished children in which she could test her theory that 16 children’s minds each learn according to they’re own schedule. She personalized a curriculum for each child rather than providing a standardized course of study. While learning important academic and life skills, many formerly aggressive and unmanageable children became more emotionally balanced and self-directed. Word of her success with the Casa dei Bambini soon began to 17 distribute internationally, and her methods for child-centered education became widely adopted across Europe.
18 In the 25 years after their founding, Montessori schools were regarded as a remedy to the educational problems associated with rapid urban population growth throughout Europe.
A) NO CHANGE
B) each child’s mind learns according to its own schedule
C) childrens’ minds learn according to its own schedule
D) children’s minds each learn according to their own schedule
A) NO CHANGE
B) increase
C) spread
D) exhibit
Which choice provides the most effective introduction to this paragraph?
A) Montessori dedicated herself to travelling the world and preaching the benefits of child-centered education.
B) Montessori’s first school enrolled 50 students from poor working families.
C) Montessori did not have a particularly nurturing relationship with her own son, Mario, who was raised by another family.
D) As the Montessori method was gaining a foothold, Europe was undergoing dramatic social and political change.
19 So as fascism began to proliferate in the 1930s throughout Spain, Italy, and Germany, child-centered education came to be seen as a threat to the power of the state. In 1933, the totalitarian regimes in Italy and Germany closed all Montessori schools and declared 20 them subversive and that they were undermining their power.
Even outside of Europe, 21 the response to Montessori’s ideas were divided. Many eminent scholars, inventors, and politicians—among them Alexander Graham Bell, Helen Keller, Thomas Edison, Mahatma Gandhi, and Woodrow Wilson—greeted her ideas with enthusiasm. But her theories were challenged by William H. Kirkpatrick, a leading educational reformer and professor at Teachers College, Columbia University. His 1914 book, The Montessori System Examined, declared Montessori’s psychological theories wildly out-of-date. 22
It was not until 1958 that a new generation of Montessorians revived and updated her methods in the United States. In 1958, the first American Montessori school, the Whitby School, was founded in Greenwich, Connecticut, where it thrives today.
A) NO CHANGE
B) When
C) However, as
D) Furthermore, as
A) NO CHANGE
B) that they were subversive in undermining their power
C) them subversive in undermining power
D) them subversive
A) NO CHANGE
B) the response to Montessori’s ideas was
C) Montessori’s ideas had a response that was
D) Montessori’s ideas response was
At this point, the paragraph would benefit most from a discussion of
A) how Kirkpatrick’s book was received among American educators
B) why totalitarian governments regarded Montessori’s methods as a threat
C) those American educators whose influence was comparable to Montessori’s
D) how other reform movements of the era contrasted with Montessori’s
Questions 23–33 are based on the following passage.
Platonic Forms
When we look at the moon, we see a spherical object, but do “spheres” really exist? This may seem to be a silly question, because it’s not hard to understand the definition of a sphere: “the set of all points in space that are a fixed distance (called the radius) from a fixed point (called the center).” We see examples of “spherical” objects all the time, don’t we?
23 First, nothing that we can observe in our physical world 24 complies perfectly to this mathematical definition of a sphere. The moon, a beach ball, and even water droplets are all “bumpy,” at least at the atomic level. So can we say that the concept of “sphere” is real 25 if there is no such thing as a real sphere?
Pondering this question as so many ancient Greek philosophers did, 26 the argument Plato made was that the sphere is an “ideal form,” inaccessible to our physical senses yet 27 the mind can apprehend it through pure reason.
A) NO CHANGE
B) So
C) While
D) In fact,
A) NO CHANGE
B) overlaps
C) corresponds
D) concurs
A) NO CHANGE
B) where no such thing exists
C) as if nothing is
D) if there were nothing
A) NO CHANGE
B) it was Plato who argued
C) Plato had argued
D) Plato argued
A) NO CHANGE
B) it can be apprehended by the mind
C) apprehensible to the mind
D) it is apprehensible to the mind
He also reasoned that, since our senses can be fooled, logic provides a much more reliable path to the truth. Therefore, a Platonic idealist believes that these abstract forms are 28 as effective, if not more so, than sensory experience at revealing the nature of reality. 29
Modern scientists and philosophers are unlikely to be Platonic idealists. Today, we can understand the origin of abstract concepts 30 and not having to believe that they come from a higher, physically inaccessible reality. We simply need to understand 31 the process by which our brains make inferences.
Take an abstract idea like “orangeness.” Most of us would say that orangeness “exists” because we see examples of it every day, such as carrots, traffic cones, and pumpkins. But what if, by some magic, we could remove all orange-colored objects from the universe? In other words, what if, as with “sphereness,” no real examples of “orangeness” 32 would exist? Would “orangeness” still exist?
A) NO CHANGE
B) as effective as, if not more effective than,
C) as effective, if not more effective, than
D) equally as effective, if not more effective than,
At this point, the author is considering adding the following true statement:
The sphere is just one of many ideal forms, like lines and tetrahedrons, that are studied in geometry.
Should the author make this addition here?
A) Yes, because it indicates a particular application of ideal forms.
B) Yes, because explains a claim made in the previous sentence.
C) No, because it detracts from this paragraph’s discussion of philosophy.
D) No, because it undermines the Platonists’ point of view.
A) NO CHANGE
B) in not having to believe
C) and not be believing
D) without having to believe
A) NO CHANGE
B) our brain’s process by which they
C) the process by which our brain’s
D) the process by which our brain
A) NO CHANGE
B) would have existed
C) existed
D) had an existence
In an important sense, the answer is yes. We can demonstrate the existence of “orangeness” without appealing to any higher reality. We could measure the wavelength of red light (about 650 nm), and yellow light (about 570 nm) and make the reasonable inference, because wavelengths fall on a continuum, that a color exists with an intermediate wavelength, of 610 nm, even if we have never directly measured such light.
Our brains do not contain sophisticated instruments for measuring wavelengths of light, but they do make similar inferences constantly. 33 For instance, when you drive, you unconsciously make inferences about quantities like the speeds of surrounding cars and qualities like dangerous driving conditions. Our brains are continually making inferences based on the limited information from our senses, and these inferences are the substance of abstract thought.
Which of the following changes would best improve this sentence’s cohesiveness with the rest of the paragraph?
A) Change “For instance” to “Nevertheless.”
B) Change both instances of “you” to “we.”
C) Change “you unconsciously make changes” to “changes are unconsciously made”
D) Delete the phrase “like dangerous driving conditions.”
Questions 34–44 are based on the following passage and supplementary material.
The Eureka Effect
You’ve probably had the experience. After racking your brain for hours to solve a problem, you finally put it aside and move on to other things. Then, much later, seemingly out of 34 nowhere, perhaps while showering or driving—the answer suddenly strikes you. Psychologists call this the “Eureka effect,” from the ancient Greek word meaning “I have found it,” 35 which Archimides is said to have shouted as he ran naked from his bathtub through the streets of Syracuse upon suddenly solving a vexing physics problem.
Does this feeling arise from our emotional centers or our cognitive centers? In other words, is it simply an emotional response to finding a solution, or does it 36 foretell a fundamentally different way of thinking? Psychologists have tried to answer this question by looking inside subjects’ brains as they solve problems, using electroencephalograms (EEGs) and other tools.
A) NO CHANGE
B) nowhere—perhaps
C) nowhere: perhaps
D) nowhere; perhaps
A) NO CHANGE
B) what Archmides is said to shout
C) that Archimedes shouted, it is said
D) which Archimedes it is said had shouted
A) NO CHANGE
B) indicate
C) provide
D) generate
GAMMA-BAND INTENSITY IN RIGHT ANTERIOR TEMPORAL REGION DURING VERBAL ASSOCIATION TASK
Source: Adapted from Beeman, Bowden et al., “Neural Activity When People Solve Problems with Insight,” PLOS, 2004
In one 37 experiment, subjects performed a word association task, scientists measured the activity in the region of the brain called the right hemisphere anterior superior temporal gyrus (RH aSTG). This region is known to be active in tasks, such as finding a theme in a story, 38 that requires integrating and bringing together information from many distant parts of the brain, but is not particularly active in emotional responses.
The subjects were asked to perform a challenging verbal association task, press a button as soon as 39 solving it, and report whether or not they felt the “Aha!” feeling. If they did, the response was classified as an “insight” solution. If they did not, it was classified as a “non-insight” solution.
40 What was interesting, experimenters found that the insight solutions were accompanied by an elevated level of “gamma band” activity in the RH aSTG, supporting the theory that the feeling 41 had corresponded
A) NO CHANGE
B) experiment by which subjects
C) experiment where subjects
D) experiment, in which subjects
A) NO CHANGE
B) that require integrating and bringing together
C) that require integrating
D) that requires integrating
A) NO CHANGE
B) it was being solved
C) they solved it
D) it’s solution
A) NO CHANGE
B) The interesting thing was that
C) It was interesting that
D) Interestingly,
A) NO CHANGE
B) corresponds
C) is corresponding
D) will correspond
to a cognitive process rather than purely an emotional one. 42
Interpreting 43 this data is not a very simple matter, however. Many questions remain to be answered. For instance, does the increased gamma-band activity represent a transition of cognitive processing from an unconscious state to a conscious one? 44 If that is true, a question would be what are the unconscious processes that are working? Also, in what way do those processes become conscious all of a sudden?
At this point in the passage, the author wants to mention specific evidence indicated by the graph. Which statement is most justified by the data in this graph?
A) The gamma power in the RH aSTG for the insight solution is more than double that for the non-insight solution.
B) This increase in activity seems to begin about 0.3 seconds prior to the button-press response, and to lasts about 1 second.
C) The gamma activity for the insight solution appears to be roughly equivalent to that for the non-insight solution until the instant the button is pushed.
D) This increase in activity seems to begin about 0.3 seconds after the button-press response, and to last about 0.5 second.
A) NO CHANGE
B) this data are
C) these data are
D) these data is
Which of the following best combines the last two sentences into one?
A) If so, what are the unconscious processes that are working, suddenly becoming conscious?
B) If so, what unconscious processes are at work, and how do they suddenly become conscious?
C) If so, what would be the unconscious processes working, and how would they suddenly become conscious?
D) If so, what are both the unconscious process at work, and how do they suddenly become conscious?
STOP
If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test.
Turn to Section 3 of your answer sheet to answer the questions in this section.
DIRECTIONS
For questions 1–15, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 16–20, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter you answers in the grid. You may use any available space in your test booklet for scratch work.
NOTES
1. The use of a calculator is NOT permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers for which f(x) is a real number.
REFERENCE
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2π.
The sum of the measures in degrees of the angles of a triangle is 180.
If 6x + 9 = 30, what is the value of 2x + 3?
A) 5
B) 10
C) 15
D) 20
x2 + y2 = 9
y = x2 − 4
A system of two equations and their graphs in the xy-plane are shown above. How many solutions does the system have?
A) One
B) Two
C) Three
D) Four
A total of 300 tickets were sold for a performance of a school play. The ticket prices were $5 for each adult and $3 for each child, and the total revenue from tickets was $1,400. Solving which of the following systems of equations would yield the number of adult tickets sold, a, and the number of children’s tickets sold, c?
A) a + c = 1,400
5a + 3c = 300
B) a + c = 300
5a + 3c = 1,400
C) a + c = 300
3a + 5c = 1,400
D) a + c = 300
3a + 5c = 1,400 × 2
Which of the following expressions is equivalent to 2(x − 4)2 − 5x?
A) 2x2 − 21x + 32
B) 2x2 − 21x − 32
C) 2x2 − 13x + 32
D) 2x2 − 16x − 21
Note: Figure not drawn to scale
A rectangular solid above has dimensions 3, a, and b, where a and b are integers. Which of the following CANNOT be the areas of three different faces of this solid?
A) 15, 18, and 30
B) 18, 24, and 48
C) 12, 15, and 24
D) 15, 24, and 40
The cost in dollars, C, to manufacture n necklaces is given by the equation C(n) = an + b, where a and b are positive constants. In this equation, what does a represent?
A) the fixed costs, in dollars, independent of any necklaces being manufactured
B) the total cost, in dollars, to produce n necklaces, not including fixed costs
C) the total cost, in dollars, to produce one necklace, including fixed costs
D) the cost, in dollars, to produce one necklace, not including any fixed costs
Line l intersects the graph of the function f(x) = 2x2 − 4x + 1 at two points where x = −1 and x = 2, respectively. What is the slope of line l?
A) −2
B) 
C) 
D) 2
Which of the following equations represents a parabola in the xy-plane with a vertex that lies on the x-axis?
A) y = (x − 3)2 + 2
B) y = 2(x − 3)2
C) y = 2x2 − 3
D) y = 3x2 + 2
If the function m(x) satisfies the equation 
for all values of x greater than 1, then m(x) =
A) 
B) 
C) 
D) 
In the mesosphere, the atmospheric layer between 50 km and 80 km in altitude, the average atmospheric temperature varies linearly with altitude. If the average temperature at 50 km altitude is 10°C and the average temperature at 80 km is −80°C, then at what altitude is the average temperature −50°C?
A) 60 km
B) 65 km
C) 70 km
D) 75 km
The graph of the equation y = 2x2 − 16x + 14 intersects the y-axis at point A and the x-axis at points B and C. What is the area of triangle ABC?
A) 42
B) 48
C) 54
D) 56
What is the total number of x- and y-intercepts in the graph of the equation y = (x + 2)2(x − 3)2?
A) Two
B) Three
C) Four
D) Five
If the complex number A satisfies the equation A(2 − i) = 2 + i, where 
, what is the value of A?
A) 5 − i
B) 5 + i
C) 
D) 
If k > 2, which of the following could be the graph of y + x = k(x − 1) in the xy-plane?
A)
B)
C)
D)
The function g(x) = ax3 + bx2 + cx + d has zeroes at x = –2, x = 3, and x = 6. If g(0) < 0, which of the following must also be negative?
A) g(−3)
B) g(−1)
C) g(4)
D) g(5)
For questions 16–20, solve the problem and enter your answer in the grid, as described below, on the answer sheet.
1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
5. Mixed numbers such as 
must be gridded as 3.5 or 
.
(If is entered into the grid as 
, it will be interpreted as 
, not 
).
6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.
If 
, what is the value of 4x + 3y?
If 
, what is the value of x?
Note: Figure not drawn to scale.
In the circle above, arc AB has a measure of 7π. What is the value of x?
For what value of k will the system of equations above have at least one solution?
If x represents the radian measure of an angle, where 
, and 
, then what is the value of 
?
STOP
If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test.
Turn to Section 4 of your answer sheet to answer the questions in this section.
DIRECTIONS
For questions 1–30, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 31–38, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 31 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.
NOTES
1. The use of a calculator is permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers for which f(x) is a real number.
REFERENCE
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2π.
The sum of the measures in degrees of the angles of a triangle is 180.
a – 2b = 8
Based on the system of equations above, what is the value of b?
A) −2
B) −1
C) 1
D) 2
The average (arithmetic mean) of three numbers is 50. If two of the numbers have a sum of 85, what is the third number?
A) 75
B) 70
C) 65
D) 55
What number is the same percent of 225 as 9 is of 25?
A) 27
B) 54
C) 64
D) 81
RESULTS OF FAVORABILITY POLL
The table above shows the partial results of a favorability poll for a local politician. If the data shown are correct, how many of the women who were polled viewed the politician unfavorably?
A) 33
B) 43
C) 61
D) It cannot be determined by the information given.
If 22n-2 = 32, what is the value of n?
A) 2.0
B) 2.5
C) 3.0
D) 3.5
A bag of Nellie’s Nut Mix contains x ounces of walnuts, 15 ounces of peanuts, and 20 ounces of pecans. Which of the following expresses the fraction of the mix, by weight, that is walnuts?
A) 
B) 
C) 
D) 
In the triangle above, what is the value of k? (sin 35° = 0.574, cos 35° = 0.819, tan 35° = 0.700)
A) 6.00
B) 6.88
C) 8.40
D) 9.83
The figure above shows a polygon with five sides. What is the average (arithmetic mean) of the measures, in degrees, of the five angles shown?
A) 108°
B) 110°
C) 112°
D) 114°
Questions 9 and 10 are based on the graph below.
ANNUAL REVENUE PER STORE
The scatterplot above shows the annual revenue for each of the individual retail stores operated by a clothing company for each year from 2004 through 2012. Based on the line of best fit to the data shown, which of the following is closest to the average annual increase in revenue per store?
A) $5,000
B) $50,000
C) $100,000
D) $500,000
Which of the following statements is most directly justified by the data shown in the scatterplot above?
A) The average revenue per store increased by over 100% from 2005 to 2009.
B) The total number of retail stores increased by 50% from 2005 to 2012.
C) The total revenue from all stores in 2012 was more than three times the total revenue from all stores in 2004.
D) The total revenue from all stores in 2008 was over $1 million.
Which of the following statements expresses the fact that the product of two numbers, a and b, is 6 greater than their sum?
A) ab + 6 > a + b
B) ab = a + b + 6
C) ab + 6 = a + b
D) ab > a + b + 6
Note: Figure not drawn to scale.
In the figure above, if m || l, what is the area, in square units, of the shaded rectangle?
A) 156
B) 168
C) 180
D) 192
The Glenville Giants have played a total of 120 games and have a win-to-loss ratio of 2 to 3. How many more games have they lost than won?
A) 24
B) 30
C) 40
D) 48
A culture of bacteria initially contained p cells, where p > 100. After one hour, this population decreased by 
. In the second and third hours, however, the population increased by 40% and 50%, respectively. At the end of those first three hours, what was the population of the culture?
A) 1.3p
B) 1.4p
C) 1.5p
D) 1.6p
If 
, what is the value of m2?
A) 
B) 
C) 
D) 
A jar contains only red, white, and blue marbles. It contains twice as many red marbles as white marbles and three times as many white marbles as blue marbles. If a marble is chosen at random, what is the probability that it is not red?
A) 
B) 
C) 
D) 
y = -3(x − 2)2 + 2
In the xy-plane, line l passes through the point (−1, 3) and the vertex of the parabola with equation above. What is the slope of line l?
A) 
B) 
C) 
D)
A certain function takes an input value and transforms it into an output value according to the following three-step procedure:
Step 1: Multiply the input value by 6.
Step 2: Add x to this result.
Step 3: Divide this result by 4.
If an input of 7 to this function yields an output of 15, what is the value of x?
A) 12
B) 16
C) 18
D) 24
The variables x and y are believed to correlate according to the equation y = ax2 + bx + c, where a, b, and c are constants. Which of the following scatterplots would provide the strongest evidence in support of the hypothesis that a < 0?
A) 
B) 
C) 
D) 
On a number line, the coordinates of points P and R are p and r, respectively, and p < r. If the point with coordinate x is closer to p than to r, then which of the following statements must be true?
A) 
B) 
C) |x − p|< r
D) |x + p|< r − p
Let function f(x) be defined by the equation 
. If m is a positive integer, then 
A) 
B) 
C) 
D) 2 − m
The value of y varies with x according to the equation y = a(x − 2)(x + 1), where a < 0. As the value of x increases from 0 to 5, which of the following best describes the behavior of y?
A) It increases and then decreases.
B) It decreases and then increases.
C) It increases only.
D) It decreases only.
If the expression 
is equivalent to the expression 
for all values of n, what is the value of k?
A) −12
B) −6
C) 6
D) 12
An online trading company charges a 3% commission for all stock purchases. If a trader purchases 200 shares of a stock through this company and is charged $3,399 including commission, what is the cost per share for this stock?
A) $16.45
B) $16.48
C) $16.50
D) $16.52
For nonzero numbers w and y, if w is 50% greater than y, then what is the ratio of w−2 to y−2?
A) 4 to 9
B) 2 to 3
C) 9 to 4
D) 4 to 1
Every athlete in a group of 60 female varsity athletes at Greenwich High School either runs track, plays soccer, or does both. If one-third of the athletes in this group who play on the soccer team also run on the track team, and one-half of the athletes in this group who run on the track team also play on the soccer team, which of the following statements must be true?
A) This group contains 40 soccer players.
B) This group contains 20 athletes who play soccer but do not run track.
C) This group contains 20 athletes who play both track and soccer.
D) The number of soccer players in this group is 15 greater than the number of track team members in this group.
A portion of the graph of the quadratic function y = f(x) is shown in the xy-plane above. The function g is defined by the equation g(x) = f(x) + b. If the equation g(x) = 0 has exactly one solution, what is the value of b?
A) −2
B) −1
C) 1
D) 2
If cos x = a, where 
, and cos y = − a, then which of the following could be the value of y?
A) x + 2π
B) x + π
C) 
D) − x + 2π
Questions 29 and 30 refer to the following table.
OPINION POLL ON PROPOSAL 81A
Of those surveyed who expressed an opinion on Proposal 81a, approximately what percentage are under 40 years of age?
A) 30%
B) 38%
C) 68%
D) 72%
If the data in the table above are assumed to be representative of the general voting population, which of the following statements is most directly justified by these data?
A) The approval rate for Proposal 81a generally decreases with the age of the voter.
B) The disapproval rate for Proposal 81a generally increases with the age of the voter.
C) Those who express an opinion on Proposal 81a are more likely to be over 64 than they are to be under 40.
D) In all three age categories, voters are more than twice as likely to approve of Proposal 18a than to have no opinion about it.
Student-Produced Response Questions
DIRECTIONS
For questions 31–38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.
1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
5. Mixed numbers such as 
must be gridded as 3.5 or 
.
(If is entered into the grid as 
, it will be interpreted as 
, not .)
6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.
If y varies inversely as x, and y = ½ when x = 10, then for what value of x does y = 25?
If x2 + 12x = 13, and x < 0, what is the value of x2?
Four triangles are to be cut and removed from a square piece of sheet metal to create an octagonal sign with eight equal sides, as shown in the figure above. If the total area of the removed material is 196 square centimeters, what is the perimeter, in centimeters, of the octagon?
If m and n are integers such that m2 + n2 = 40 and m < 0 < n, what is the value of (m + n)2?
If (cos x)(sin x) = 0.2, what is the value of (cos x + sin x)2?
MONTHLY SALES (FEBRUARY)
The table above shows information about the February sales for five different cell phone models at a local store. What was the median price, to the nearest dollar, of the 240 phones sold in February?
Questions 37 and 38 are based on the scenario described below. Enter your responses on the corresponding grids on your answer sheet.
Performance Banner Company creates promotional banners that include company logos. The Zypz Running Shoe Company would like a 4-foot high and 20-foot long banner that includes its logo, which has a height-to-length ratio of 5:8.
If the logo were scaled so that its height matched the height of the banner and then were placed in the center of the banner, then what would be the width, in feet, of each margin on either side of the logo?
Performance Banner Company charges its customers $1.20 per square foot for the banner material, $2.50 per square foot of any printed logo, and $32 in fixed costs per banner. The Zypz Running Shoe Company is considering two options for the banner: one with a single logo, and another with two logos. If these logos are all to be the same size as described in Part 1, what percent of the banner costs would the company save by choosing the single-logo option instead of the two-logo option? (Ignore the % symbol when entering into the grid. For example, enter 27% as 27.)
STOP
If you finish before time is called, you may check your work on this section only. Do not turn to any other section of the test.
Adapted from Steven Pinker, “Mind Over Mass Media.” ©2010 by The New York Times. Originally published June 10, 2010.
1 New forms of media have always caused moral panics: the printing press, newspapers, paperbacks and television were all once denounced as threats to their consumers’ brainpower and moral fiber.
2 So too with electronic technologies. PowerPoint, we’re told, is reducing discourse to bullet points. Search engines lower our intelligence, encouraging us to skim on the surface of knowledge rather than dive to its depths. Twitter is shrinking our attention spans.
3 But such panics often fail reality checks. When comic books were accused of turning juveniles into delinquents in the 1950s, crime was falling to record lows, just as the denunciations of video games in the 1990s coincided with the great American crime decline. The decades of television, transistor radios and rock videos were also decades in which I.Q. scores rose continuously.
4 For a reality check today, take the state of science, which demands high levels of brainwork and is measured by clear benchmarks of discovery. Today, scientists are never far from their e-mail and cannot lecture without PowerPoint. If electronic media were hazardous to intelligence, the quality of science would be plummeting. Yet discoveries are multiplying like fruit flies, and progress is dizzying. Other activities in the life of the mind, like philosophy, history and cultural criticism, are likewise flourishing.
5 Critics of new media sometimes use science itself to press their case, citing research that shows how “experience can change the brain.” But cognitive neuroscientists roll their eyes at such talk. Yes, every time we learn a fact or skill the wiring of the brain changes; it’s not as if the information is stored in the pancreas. But the existence of neural plasticity does not mean the brain is a blob of clay pounded into shape by experience.
6 Experience does not revamp the basic information-processing capacities of the brain. Speed-reading programs have long claimed to do just that, but the verdict was rendered by Woody Allen after he read War and Peace in one sitting: “It was about Russia.” Genuine multitasking, too, has been exposed as a myth, not just by laboratory studies but by the familiar sight of an SUV undulating between lanes as the driver cuts deals on his cellphone.
7 Moreover, the evidence indicates that the effects of experience are highly specific to the experiences themselves. If you train people to do one thing, they get better at doing that thing, but almost nothing else. Music doesn’t make you better at math; conjugating Latin doesn’t make you more logical; brain-training games don’t make you smarter. Accomplished people don’t bulk up their brains with intellectual calisthenics; they immerse themselves in their fields. Novelists read lots of novels; scientists read lots of science.
8 The effects of consuming electronic media are also likely to be far more limited than the panic implies. Media critics write as if the brain takes on the qualities of whatever it consumes, the informational equivalent of “you are what you eat.” As with primitive peoples who believe that eating fierce animals will make them fierce, they assume that watching quick cuts in rock videos turns your mental life into quick cuts or that reading bullet points and Twitter postings turns your thoughts into bullet points and Twitter postings.
9 Yes, the constant arrival of information packets can be distracting or addictive, especially to people with attention deficit disorder. But distraction is not a new phenomenon. The solution is not to bemoan technology but to develop strategies of self-control, as we do with every other temptation in life. Turn off e-mail or Twitter when you work, put away your BlackBerry at dinner time, ask your spouse to call you to bed at a designated hour.
10 And to encourage intellectual depth, don’t rail at PowerPoint or Google. It’s not as if habits of deep reflection, thorough research and rigorous reasoning ever came naturally to people. They must be acquired in special institutions, which we call universities, and maintained with constant upkeep, which we call analysis, criticism and debate. They are not granted by propping a heavy encyclopedia on your lap, nor are they taken away by efficient access to information on the Internet.
11 The new media have caught on for a reason. Knowledge is increasing exponentially; human brainpower and waking hours are not. Fortunately, the Internet and information technologies are helping us manage, search, and retrieve our collective intellectual output at different scales, from Twitter and previews to e-books and online encyclopedias. Far from making us stupid, these technologies are the only things that will keep us smart.
Write an essay in which you explain how Steven Pinker builds an argument to persuade his audience that new media are not destroying our moral and intellectual abilities. In your essay, analyze how Pinker uses one or more of the features listed in the box above (or features of your own choice) to strengthen the logic and persuasiveness of his argument. Be sure that your analysis focuses on the most relevant features of the passage.
Your essay should NOT explain whether you agree with Pinker’s claims, but rather explain how Pinker builds an argument to persuade his audience.
Section 1: Reading
1. C
2. A
3. C
4. B
5. D
6. C
7. D
8. A
9. B
10. D
11. B
12. C
13. C
14. D
15. A
16. D
17. B
18. D
19. C
20. B
21. B
22. C
23. D
24. D
25. A
26. A
27. C
28. C
29. C
30. B
31. A
32. B
33. C
34. C
35. A
36. A
37. B
38. B
39. B
40. B
41. A
42. D
43. C
44. B
45. D
46. A
47. A
48. D
49. D
50. C
51. B
52. D
Total Reading Points (Section 1)
Section 2: Writing and Language
1. B
2. C
3. C
4. A
5. B
6. C
7. A
8. D
9. A
10. D
11. D
12. C
13. B
14. D
15. A
16. B
17. C
18. D
19. C
20. D
21. B
22. A
23. D
24. C
25. A
26. D
27. C
28. B
29. C
30. D
31. A
32. C
33. B
34. B
35. A
36. B
37. D
38. C
39. C
40. D
41. B
42. B
43. D
44. B
Total Writing and Language Points (Section 2)
Section 3: Math (No calculator)
1. B
2. D
3. B
4. A
5. C
6. D
7. A
8. B
9. D
10. C
11. A
12. B
13. C
14. B
15. B
-------
16. 30
17. 25/7 or 3.57
18. 35
19. 1.2
20. 2.4
Total Math Points (Section 3)
Section 4: Math (Calculator)
1. D
2. C
3. D
4. B
5. D
6. C
7. B
8. A
9. B
10. C
11. B
12. D
13. A
14. B
15. B
16. B
17. C
18. C
19. C
20. B
21. A
22. A
23. D
24. C
25. A
26. D
27. D
28. B
29. A
30. B
-------
31. 1/5 or 0.2
32. 169
33. 112
34. 16
35. 1.4
36. 115
37. 6.8
38. 25
Total Math Points (Section 4)
1. Use the answer key to mark your responses on each section.
2. Total the number of correct responses for each section:
3. Add the raw scores for sections 3 and 4. This is your Math Raw Score: _________________
4. Use the Table 1 to calculate your Scaled Test and Section Scores (10–40).
5. Add the Reading Test Scaled Score and the Writing and Language Test Scaled Score and multiply this sum by 10 to get your Reading and Writing Test Section Score (20–80).
Table 1: Scaled Section and Test Scores (10–40)
Section 1: Reading
1. C
Specific Purpose
Let’s translate this question into a “stand-alone” question: “How is Smith’s work presented in the first paragraph?” The passage states (line 3) that Karl Smith has a good rule of thumb for categorizing epidemics, then goes on to describe various types of epidemics in an effort to help visualize the types of spread. In other words, he is proposing a model for conceptualizing phenomena. (Note that the word phenomena refers simply to common occurrences. It has a neutral tone, not a positive one.)
2. A
Inference
The passage states in lines 67–72 that Nevin’s paper was almost completely ignored because Nevin was an economist, not a criminologist, and his paper was published in Environmental Research, not a journal with a big readership in the criminology community. In other words, Nevin’s paper was ignored because it was not presented by authorities with the proper credentials.
3. C
Textual Evidence
As the explanation to question 2 indicates, the evidence for this answer is lines 67–72, which includes the statement in (C).
4. B
Inference from Data
According to the graph, in 1963 there were 150 violent crimes per 100,000 capita, and in 1993 there were 750 violent crimes per 100,000 capita. This is an increase of 600 crimes per 100,000, and 600 is 400% of 150.
5. D
Inference from Data
Nevin’s hypothesis is phrased in the form of a question in lines 27–28: Maybe reducing lead exposure had an effect on violent crime too? Therefore, the portion of the graph that would least support his hypothesis is the portion that shows the least correlation between lead exposure and crime. The biggest gap in the two graphs (and hence the portion that provides the least support for his thesis) corresponds to the set of violent crime statistics from 2003 to 2013.
6. C
Specific Purpose
The sales of vinyl LPs are mentioned to describe a statistic that also happens to correlate with preschool blood lead levels, thereby making the point that a single correlation between two curves isn’t all that impressive, econometrically speaking … No matter how good the fit, if you only have a single correlation it might just be coincidence. Hence, it is a statistic that may be more coincidental than explanatory.
7. D
Interpretation
The sentence in lines 21–24 indicates that lead exposure in small children [had been linked] with a whole raft of complications later in life, including lower IQ, hyperactivity, behavioral problems, and learning disabilities. These complications are psychological problems for those exposed to lead at a young age.
8. A
Interpretation
When the passage states that the drivers were unwittingly creating a crime wave two decades later (lines 63–64), it indicates that they were inadvertent abettors.
9. B
Word in Context
The phrase even better (line 49) refers to the finding mentioned in the previous sentence that the similarity of the curves was as good as it seemed, suggesting that the data showed an even stronger correlation than Nevin had hoped.
10. D
Specific Purpose
The final paragraph discusses the fact that the gasoline lead hypothesis explains many additional phenomena, such as the difference between the murder rates in large cities (where there are lots of cars) and small cities (where there are fewer cars and therefore less lead exhaust exposure). These implications further support the hypothesis.
11. B
Cross-Textual Inference
The author of Passage 1 indicates that Hemingway was a legendary figure whose work seemed … to have been carved from the living stone of life (lines 25–26) and therefore had a great impact on the author and his friends. Passage 2, however, suggests that Hemingway’s works don’t have the impact they once did, saying that they now seem unable to evoke the same sense of a tottering world that in the 1920s established Ernest Hemingway’s reputation (lines 48–50) and no longer seem to penetrate deeply the surface of existence (lines 57–58). Therefore, the two passages disagree most strongly on the incisiveness (deep analytical quality) of Hemingway’s work.
12. C
Textual Evidence
As the answer to the previous question indicates, the best evidence for this answer is found in lines 24–26 and lines 56–58.
13. C
Cross-Textual Interpretation
The author of Passage 1 regards Hemingway as a legend (line 16) whose impact upon us was tremendous (lines 18–19), but the author of Passage 2 calls Hemingway a dupe of his culture rather than its moral-aesthetic conscience (lines 66–67).
14. D
Cross-Textual Inference
The author of Passage 1 indicates that, although Hemingway’s work had a strong formative impact on him, it ultimately could not capture the true horrors of war that he and his friends were later to encounter:
The Hemingway time was a good time to be young. We had much then that the war later forced out of us, something far greater than Hemingway’s strong formative influence (lines 33–36).
Likewise, the author of Passage 2 indicates that Hemingway’s work did not fully capture the horrors of war: We have had more war than Hemingway ever dreamed of (lines 53–54) … yet Hemingway’s great novels no longer seem to penetrate deeply the surface of existence (lines 56–58).
15. A
Word in Context, Purpose
In saying that the words he put down seemed to us to have been carved from the living stone of life (lines 24–26), the author of Passage 1 means that Hemingway’s words represent living truths that have the weight and permanence of stone carvings. In other words, his words represent the salient (prominent and important) experience of life.
16. D
Interpretation
In saying that we began unconsciously to translate our own sensations into their terms and to impose on everything we did and felt the particular emotions they aroused in us (lines 28–32) the author is saying that he and his friends identified with Hemingway’s language.
17. B
Inference
According to Passage 1, the lessons that [Hemingway] had to teach (line 43) included the example he set as a war correspondent writing a play in the Hotel Florida in Madrid while thirty fascist shells crashed through the roof (lines 10–12) and as a soldier defending his post singlehandedly against fierce German attacks (lines 13–15), both of which exemplify confidence in the face of danger.
18. D
Specific Purpose
The phrase a tottering world (line 49) is used to describe the Europe of the 1920s that Ernest Hemingway depicts in his novels. The author compares this world to one whose social structure is … shaken (lines 51–52) and which had more war than Hemingway ever dreamed of (line 54). In other words, a world filled with societal upheaval.
19. C
Cross-Textual Inference
The author of Passage 1 clearly views Hemingway as a personal and literary hero. Hence, a withering accusation such as the one in Passage 2 that Hemingway, in effect, became a dupe of his culture rather than its moral-aesthetic conscience (lines 66–67) would almost certainly be met with vehement disagreement.
Tip: Questions about how the author of one passage might most likely respond to some statement in another passage require us to focus on the thesis and tone of that author. Before attempting to answer such questions, remind yourself of the central theses of the passages.
20. B
Textual Evidence
The best evidence for this answer comes from lines 28–32, where the author of Passage 1 says that we began to unconsciously translate our own sensations into their terms and to impose on everything we did and felt the particular emotions they aroused in us. In other words, Hemingway was in fact a kind of moral-aesthetic conscience for the author of Passage 1 and his friends.
21. B
Interpretation
Passage 2 states that Hemingway’s novels yielded to the functionalist, technological aesthetic of the culture instead of resisting in the manner of Frank Lloyd Wright (lines 63–66). In other words, Frank Lloyd Wright was more iconoclastic (culturally rebellious) than Hemingway.
22. C
Specific Purpose
The first paragraph establishes the idea that atoms, the building blocks of everything we know and love … don’t appear to be models of stability, a fact that represents a scientific conundrum (riddle), because instability is not a quality that we expect of building blocks.
23. D
Word in Context
By asking [w]hy are some atoms, like sodium, so hyperactive while others, like helium, are so aloof? the author is drawing a direct contrast between chemical reactivity and relative nonreactivity.
24. D
Inference
This question, about why protons stick together in atomic nuclei, is the guiding question for the passage as a whole. The next paragraph analyzes this question in more detail, explaining why this well-known fact is actually so puzzling. The remainder of the passages discusses attempts to resolve this puzzle, which remains at the heart of quantum physics.
25. A
Textual Evidence
The evidence that this question represents a central conundrum is found in lines 1–5, where the author makes the uncontroversial claim that a sound structure requires stable materials, but then makes the paradoxical claim that atoms, the building blocks of everything we know and love … don’t appear to be models of stability.
26. A
Specific Purpose
The two sentences in lines 13–19 (We are told … electrons. We are also told … closer) indicate that we, the educated public, have been taught two seemingly contradictory facts about atoms. In other words, these are predominant conceptions.
27. C
Inference from Data
In the graph, the equilibrium point is indicated by a dashed vertical line labeled Equilibrium. If we notice where this line intersects the two curves, we can see that the corresponding electrostatic force is precisely opposite to the corresponding strong nuclear force. That is, the equilibrium point is where the two forces “cancel out” and have a sum of 0.
28. C
Inference from Data
Tip: When a question asks about a graph or table, it helps to circle the words or phrases in the question that correspond to the words or phrases in the graph or table. In this case, circle the key phrases electrostatic repulsion and separated by 1.5 femtometers in both the question and the graph.
Now, if we go to the graph and find the vertical line that corresponds to a separation of 1.5 femtometers, we can see that it intersects the curve for electrostatic force at the horizontal line representing 102, or 100, Newtons.
29. C
Interpretation
In the fourth paragraph, we are told that Hideki Yukawa proposed that the nuclear force was conveyed by a then-undiscovered heavy subatomic particle he called the pi meson (or “pion”), which (unlike the photon) decays very quickly and therefore conveys a powerful force only over a very short distance (lines 44–49). However, his theory was dealt a mortal blow by a series of experiments … that demonstrated that pions carry force only over distances greater than the distance between bound protons (lines 50–55). In other words, pions are ineffective in the range required by atomic theory, so they cannot be the carriers of the strong nuclear force.
30. B
General Structure
The first paragraph of this passage introduces the scientific conundrum of how protons adhere in atomic nuclei. The second paragraph analyzes this strange situation. The third paragraph describes a force, the strong nuclear force, that could solve the conundrum. The fourth paragraph describes a particular theory, now refuted, about what might convey this strong nuclear force. The fifth and sixth paragraphs indicate that the problem has yet to be satisfactorily resolved. Thus, the passage as a whole is a description of a technical puzzle and the attempts to solve it.
31. A
Literary Devices
A rhetorical question is a question intended to convey a point of view, rather than suggest a point of inquiry. Although the first and second paragraphs include five questions, they are all inquisitive, not rhetorical.
The passage includes illustrative metaphors in lines 15–16 (a cloud of speedy electrons) and lines 55–56 (a plumber’s wrench trying to do a tweezer’s job), technical specifications in lines 29–40 (First, it can’t have … each other), and appeals to common intuition in lines 1–2 (a sound structure … materials) and lines 13–16 (We are . . . electrons).
32. B
Word in Context
The hope that QCD ties up atomic behavior with a tidy little bow is the hope that the QCD theory resolves the problem in a tidy way.
33. C
General Purpose
The passage as a whole develops the thesis that the wise legislator does not begin by laying down laws good in themselves, but by investigating the fitness of the people, for which they are destined, to receive them (lines 3–6). In other words, the passage is concerned with examining the social conditions that foster effective legal systems.
34. C
Word in Context
In saying that the architect sounds the site to see if it will bear the weight, the author means that the architect probes the proposed location for a building to make sure that it is safe to build upon.
35. A
Specific Purpose
The analogy of the architect in the first paragraph illustrates the thesis of the passage that the wise legislator does not begin by laying down laws good in themselves, but by investigating the fitness of the people, for which they are destined, to receive them (lines 3–6). That is, that a nation’s civil code depends on the nature of its people. Choice (B) is incorrect because the analogy is not about the foundational principles of laws, but rather the fitness of the people for whom they are intended.
36. A
Inference
The author states that as a nation grows older, its citizens become incorrigible (unable to be improved) . Once customs have become established and prejudices inveterate (deep-seated), it is dangerous and useless to attempt their reformation (lines 19–21). That is, the people become stubbornly resistant to political change.
37. B
Textual Evidence
As the explanation to the previous question indicates, the relevant evidence is found in lines 20–21.
38. B
Interpretation
When the author says that [m]ost peoples, like most men, are docile only in youth (lines 17–18), he is saying that societies (the peoples) as well as individuals (men) become less manageable as they age.
39. B
Specific Purpose
The author refers to Sparta at the time of Lycurgus (line 35) as an example of a state, set on fire by civil wars, [which] is born again (lines 31–32). That is, a society rejuvenated by conflict. Choice (A) may seem tempting, because the beginning of the paragraph mentions the fact that periods of violence (lines 28–29) can make people forget the past, but the paragraph explains that this forgetting has the effect of renewal, not paralysis.
40. B
Interpretation
Although the word constitution can be used to mean the documented rules by which a nation defines its governmental institutions (as in the Constitution of the United States of America), the phrase the constitution of the state, as it is used in this passage, clearly refers to the composition of the state, that is, the people who constitute the nation.
41. A
Interpretation
In saying that [o]ne people is amenable to discipline from the beginning; another, not even after ten centuries (lines 51–53), the author means that some nations are ready to be governed by the rule of law as soon as they are founded, but others require much more time.
42. D
Inference
The passage states that Peter the Great … lacked true genius [because he] did not see that [his nation] was not ripe for civilization: he wanted to civilize it when it needed only hardening (lines 55–61). In other words, he did not give his nation the hardening it needed: his flaw was his irresolution (hesitancy due to a lack of conviction) in exerting control.
43. C
General Purpose
The first sentence of the passage establishes its central purpose: to understand the views of Aristotle, and asserts that to do this it is necessary to apprehend his imaginative background (lines 1–3). In other words, the purpose of this passage is to describe the conceptions that inform a particular mindset.
44. B
Interpretation
When the author states that Animals have lost their importance in our imaginative pictures of the world (lines 29–30), he is reinforcing his point that modern students are accustomed to automobiles and airplanes; they do not, even in the dimmest recesses of their subconscious imagination, think that an automobile contains some sort of horse inside, or that an airplane flies because its wings are those of a bird possessing magical powers (lines 23–29). In other words, animistic beliefs no longer inform our physical theories.
45. D
Interpretation
When the author states that every philosopher, in addition to the formal system that he offers to the world, has another much simpler system of which he may be quite unaware (lines 3–6), the simpler system refers to the imaginative background (line 3) that informs a scientist’s formal theories. However, if a scientist is aware of this simpler system, he probably recognizes that it won’t do (line 7). Therefore, this system is a relatively unrefined way of thinking.
46. A
Inference
In lines 61–65, the author states that It was natural that a philosopher who could no longer regard the heavenly bodies themselves as divine should think of them as moved by the will of a Divine Being who had a Hellenic love of order and geometric simplicity. In other words, the astronomical theories of some ancient Greek philosophers were closely associated with their religious ideas.
47. A
Textual Evidence
As the explanation to the previous question indicates, the evidence for this answer is in lines 61–65.
48. D
Word in Context
When the author states that, to the Greek, it seemed more natural to assimilate apparently lifeless motions to those of animals (lines 46–47), he means that the ancient Greeks found it easy to liken the motion of machines to the motion of animals.
49. D
Inference
The passage states that To the ancient Greek, attempting to give a scientific account of motion, the purely mechanical view hardly suggested itself, except in the case of a few men of genius such as Democritus and Archimedes. In other words, most Greeks were not inclined toward the mechanical view, except for the men of genius, who had more accurate metaphors for the laws of motion, and therefore were “willing to disregard conventional wisdom.”
50. C
Inference
As it is discussed in the passage, the apparent gulf between animals and machines (lines 44–45) is the ever-shrinking gap between the animistic and the mechanistic view of animal physiology. To the modern scientist, each piece of evidence that demonstrates how the body of an animal is a very elaborate machine, with an enormously complex physical and chemical structure (lines 41–43) serves to bridge this gulf. One example of such evidence might be the mechanical laws that describe bumblebee flight.
51. B
Inference
The first paragraph discusses the fact that the views of Aristotle (line 1) are due to his imaginative preconceptions, or to what Santayana calls “animal faith” (lines 17–18), which the author goes on to explain include animistic tendencies, that is, tendencies toward seeing living spirits in all physical phenomena .
52. D
Textual Evidence
Lines 45–47 also reinforce the author’s point that Aristotle, like other ancient Greeks, was inclined toward an animistic view of the world: To the Greek, it seemed more natural to assimilate apparently lifeless motions to those of animals.
Section 2: Writing and Language
1. B
Subject-Verb Agreement
The subject of this verb is demand, which is singular. Therefore, are must be changed to is.
2. C
Diction
This question asks you to choose the word that best fits the semantic context of the sentence, that is, the word that helps the sentence to convey a logical idea in the context of the paragraph.
This previous sentence states that an important challenge facing the healthcare industry is how to address this shortfall without sacrificing quality of care. Among our options, the only one that suggests a possible solution to this problem is to incentivize more medical school graduates to choose primary care.
Although it may seem that interest is a reasonable choice, notice that its use would violate idiom in this sentence: the correct idiom is not interest someone to do something, but rather interest someone in doing something.
3. C
Logical Comparisons
This portion of the sentence is part of a parallel construction in the form A instead of B. In such constructions, the words or phrases in A and B must have the same grammatical form and describe logically comparable (or contrastable) things. Since in this case A is primary care (a noun phrase indicating a medical specialty), the most logical choice for B is the more lucrative specialties (a noun phrase indicating medical specialties). The original phrasing is incorrect because their choosing does not indicate a medical specialty, (B) is incorrect because to choose does not indicate a medical specialty, and choice (D) is incorrect because it is redundant.
4. A
Parallelism
Words or phrases in a list should have the same grammatical form. In the original phrasing, the three items in the list are all present tense verbs: talk … prescribe … perform.
5. B
Diction
Because a “team-based” model is not a location, the use of the pronoun where is incorrect. Likewise, choice (D) when is incorrect because a “team-based” model is not a time. Choice (C) is incorrect because it produces a comma splice. The correct answer is (B) whereby, which means by which.
6. C
Diction
The adverb still means even now or nevertheless, neither of which fit the logical context of this sentence. Only choice (C) while, meaning at the same time, fits logically. Choice (B) while at the same time is redundant, and choice (D) although implies a contrast, which is illogical.
7. A
Coordination of Ideas, Cross-References
The subject of the inserted sentence is these professionals. The pronoun these requires an antecedent, which is best provided if the sentence is placed after sentence 1, which specifies medical professionals like physician assistants (PAs) and nurse practitioners (NPs).
8. D
Data Analysis
The descending line in the graph shows clearly that the percentage of PAs in primary care has declined from 51% in 2000 (over one-half) to 31% in 2010 (under one-third).
9. A
Logical Comparisons, Pronoun-Antecedent Agreement
This sentence is correct as written. The pronoun they agrees in number and kind with its antecedent students, and the comparison is logical. Choice (D) is redundant.
10. D
Idiom, Pronoun-Antecedent Agreement
Using the phrase being that to mean because is colloquial and nonstandard for written American English, therefore choices (A) and (C) are incorrect. Choice (B) is incorrect because when should only be used to refer to a time.
11. D
Pronoun-Antecedent Agreement, Cross-References
The definite pronoun they must refer to some plural noun, but the only possible plural antecedent in this sentence is programs, which would be illogical. Choice (D) clarifies the reference.
12. C
Punctuation
The four choices differ only in their punctuation. Any reference to a city-and-country or city-and-state must separate the two with commas: e.g. London, England or Providence, Rhode Island. Therefore the original punctuation in (A) is incorrect. Choice (B) is incorrect because it produces a sentence fragment. Choice (D) is incorrect because it misuses the semicolon: the two phrases on either side of the semicolon should be independent clauses.
13. B
Logic, Dangling Participles
Since engineering is a class of profession and not a position, the original phrasing is illogical. Choice (C) is incorrect because it is a dangling participial phrase: the past participle considered does not share a subject with the main clause. Choice (D) is incorrect because the phrase in reputation is not idiomatic.
14. D
Dangling Participles
The sentence begins with the participial phrase suffering ridicule and isolation. Any participial phrase must have the same subject as the main clause. In the original phrasing, the subject of the main clause is Montessori’s medical studies, but this cannot be the subject of suffering ridicule and isolation. Therefore, choices (A) and (C) are both incorrect. Choices (B) and (D) both correct this problem by changing the subject of the main clause to Montessori, but (B) is incorrect because the phrase by becoming is illogical.
15. A
Parallelism
This sentence contains the parallel construction A rather than B. The original phrasing provides parallel phrasing: respect and stimulation shares the same grammatical form and semantic category as the regimentation. Choice (D) provides a parallel phrasing but illogically implies that the students were receiving institutions.
16. B
Diction, Agreement
The original phrasing is incorrect because they’re is a contraction of they are, which is illogical in this context. Choice (C) is incorrect because childrens’ is not a word at all. Children is the plural form of child, and the possessive form of children is children’s. Choice (D) is incorrect because their disagrees in number with the antecedent each.
17. C
Diction
This sentence discusses how word of Montessori’s success with her school began to spread of its own merit and accord. Choices (A) and (D) are incorrect because both distribute and exhibit imply intentional action. Choice (B) is illogical: word of someone’s success cannot increase.
18. D
Logical Cohesiveness
To understand which sentence most effectively introduces this paragraph, we must first understand what the paragraph is about. As a whole, the paragraph discusses how Montessori schools were regarded as a remedy to the educational programs associated with rapid urban population growth in Europe … but then came to be seen as a threat to the power of the state. Choice (D) encapsulates this idea the best.
19. C
Logical Transitions
Choice (C) provides the most logical transition between ideas in the paragraph: the shift from a positive view of Montessori’s work to a negative view requires a contrasting transition like however.
20. D
Redundancy
The original phrasing is redundant: being subversive is the same as undermining power. The most concise correct phrasing is that in (D).
21. B
Subject-Verb Agreement
In the original phrasing, the subject response (singular) disagrees with the verb were (plural) divided. Choice (B) provides the most effective correction.
22. A
Logical Cohesiveness
The remarkable thing about this paragraph is its introduction of dissenting views on Montessori’s work from within the field of education, rather than merely from political opponents. Any additional discussion in this paragraph should elaborate on the nature of that dissent in the educational community. Only choice (A) extends the discussion in a relevant way.
23. D
Redundancy
This sentence is asserting a claim that directly contrasts the point of view presented in the previous paragraph. Choice (D) In fact, introduces just such an assertion. Choice (A) First is incorrect because this claim is not part of an enumerated list. Choice (B) So is incorrect, because this sentence is not asserting a logical consequence of the previous claim. Choice (C) While is incorrect because it produces a sentence fragment.
24. C
Diction, Idiom
The original phrasing is incorrect because the phrase complies [to] is not idiomatic. The same is true of (B) overlaps [to] and (D) concurs [to]. Choice (C) corresponds [to], however, is idiomatic and logical.
25. A
Coordination of Ideas
This phrase is correct as written. It is expressing a condition, and so the use of the conjunction if is correct.
26. D
Dangling Participles
The participle pondering and the main clause must share the same subject, or else the participle “dangles.” Who was pondering? Plato. Therefore Plato must be the subject of the main clause. Choice (C) is incorrect, however, because there is no need for the past participle form had argued.
27. C
Parallelism
The sentence contains the parallel construction A yet B. The phrasing inaccessible … yet apprehensible provides a parallel form, since both inaccessible and apprehensible are adjectives.
28. B
Modifier Usage
The phrase between the commas is an interrupting modifier. Any sentence should remain grammatically complete even when any interrupting modifier is removed. Notice that if we did this with the original sentence, it would read as effective … than sensory experience, which is clearly unidiomatic. (The correct comparative idiom is as effective as.) The only choice that corrects this problem is (B).
29. C
Logical Cohesiveness
The information the author is proposing does not fit with the discussion about the philosophy of Platonic idealism.
30. D
Modifier Form
In the original phrasing, the conjunction and is incorrect because it does not conjoin comparable words or phrases; therefore, choices (A) and (C) are incorrect. In choice (B) the prepositional phrase in not having to believe is illogical. Choice (D) is correct because the prepositional phrase without having to believe logically modifies the verb understand.
31. A
Possessives
This sentence is correct as written. Choice (B) is incorrect because the pronoun they has no clear antecedent. Choice (C) misuses the possessive brain’s, and choice (D) yields the subject-verb disagreement brain make.
32. C
Verb Mood
This clause is part of a counterfactual hypothesis. As we discuss in Chapter 4, Lesson 30, a present counterfactual hypothesis takes the form of the present subjunctive mood, which is usually the same form as the simple past tense: existed.
33. B
Pronoun Consistency
Since the previous sentence refers to our brains, pronoun consistency requires that this sentence continue to use the first-person plural pronoun we.
34. B
Coordination of Clauses
The interrupting modifier (perhaps while showering or driving) must be “bracketed” on either end by commas, em dashes, or parentheses. Since it clearly ends with an em dash, it must start with an em dash as well.
35. A
Pronoun Form
This sentence is correct as written. Choice (B) uses the wrong pronoun form what and incorrectly implies that Archimedes is shouting in the present. Choice (C) uses the wrong pronoun form that and misplaces the modifying clause it is said. Choice (D) misuses the past perfect form had shouted.
36. B
Diction
The sentence discusses the relationship between the feeling of the Eureka effect and a fundamentally different way of thinking. In the context of the discussion, the only choice that indicates a logical relationship is (B): this feeling indicates a different way of thinking.
37. D
Coordination of Clauses
The original phrasing is incorrect because it includes a comma splice. Choice (B) is incorrect because the prepositional phrase by which is illogical. In choice (C), the use of the pronoun where is incorrect because an experiment is not a place.
38. C
Subject-Verb Agreement, Redundancy
The verb requires (singular) disagrees with the subject tasks (plural), therefore choices (A) and (D) are incorrect. Choice (B) is redundant.
39. C
Subject-Verb Agreement
The modifying phrase as soon as solving it is vague and awkward. Choice (C) clarifies the modifier by indicating that the subjects are solving the task.
40. D
Awkwardness, Logical Transitions
The underlined phrase is a sentence modifier, that is, a phrase that modifies the statement in the main clause experimenters found. Choices (A), (B), and (C) are needlessly awkward and wordy, but choice (D) provides a concise and clear modifier.
41. B
Verb Tense
This clause is describing a general fact (the theory that . . .), not an event. To express general facts, we use the simple present tense: corresponds.
42. B
Data Analysis
According to the graph, the line indicating the Insight condition separates from the line representing the Non-insight condition approximately 0.3 seconds prior to the button being pushed, and remains elevated until about 0.7 seconds after the button is pushed, for a duration of approximately 1 second.
43. D
Pronoun-Antecedent Agreement, Subject-Verb Agreement
The verb is agrees with the subject interpreting (both are singular), but the pronoun this disagrees with its antecedent data (this is singular, but data is plural).
44. B
Coordinating Clauses
The correct choice should combine the two questions into a single sentence. Choice (A) misstates the second question. Choice (C) inappropriately uses the subjunctive mood. Choice (D) misuses the parallel construction both A and B.
Section 3: Math (No Calculator)
1. B
Algebra (solving equations) EASY
6x + 9 = 30
To solve in one step, just divide both sides by 3:
2x + 3 = 10
Most students waste time solving for x, which will work, but takes longer:
6x + 9 = 30
Subtract 9:
6x = 21
Divide by 6:
x = 3.5
Evaluate 2x + 3 by
substituting x = 3.5:
2x + 3 = 2(3.5) + 3 = 7 + 3 = 10
2. D
Advanced Mathematics (nonlinear systems)
EASY
The solutions to the system correspond to the points of intersection of the two graphs. The figure shows four such intersection points.
3. B
Algebra (algebraic expressions) EASY
Let a = # of adult tickets sold, and c = # of child tickets sold. If 300 tickets were sold altogether:
c + a = 300
The revenue for a adult tickets sold at $5 each is $5a, and the revenue for c child tickets sold at $3 each is $3c. Since the total revenue is $1,400:
5a + 3c = 1,400
4. A
Advanced Mathematics (polynomials) EASY
2(x − 4)2 − 5x
Factor:
2[(x − 4)(x − 4)] − 5x
FOIL:
2[ x2 − 4x − 4x + 16] − 5x
Simplify:
2[ x2 − 8x + 16] − 5x
Distribute:
2x2 − 16x + 32 − 5x
Combine like terms:
2x2 − 21x + 32
5. C
Special Topics (three-dimensional geometry) MEDIUM
On the drawing, we should first mark the areas of the three faces. The front and back faces both have an area of 3a. The left and right faces both have an area of 3b. The top and bottom faces both have an area of ab. We should now try to find integer values for a and b so that these areas match those given in the choices.
(A) 15, 18, and 30
This is possible if a = 5 and b = 6.
(B) 18, 24, and 48
This is possible if a = 6 and b = 8.
(C) 12, 15, and 24
This cannot work for any integer values of a and b.
(D) 15, 24, and 40
This is possible if a = 5 and b = 8.
6. D
Algebra (linear equations) MEDIUM
C(n) = an + b
Since this expression is linear in n (the input variable, which represents the number of necklaces produced), the constant a represents the slope of this line, which in turn represents the “unit rate of increase,” in other words, the increase in total cost for each individual necklace produced.
The constant b represents the “y-intercept” of this line, which in this case means the costs when n = 0 (that is, the fixed costs before any necklaces are produced).
7. A
Algebra (lines) MEDIUM
To find the slope of line l, we can find two points on l and then use the slope formula.
f(x) = 2x2 − 4x +1
Plug in −1 for x:
f(−1) = 2(−1)2 − 4(−1) + 1
Simplify:
f(−1) = 2(1) + 4 + 1 = 2 + 4 + 1 = 7
Therefore line l intersects the function at (−1, 7).
Plug in 2 for x:
f(2) = 2(2)2 − 4(2) + 1
Simplify:
f(2) = 2(4) − (8) + 1 = 8 − 8 + 1 = 1
Therefore line l intersects the function at (2, 1). Now we find the slope of the line containing these two points.
slope 
8. B Advanced Mathematics (parabolas) MEDIUM
The general equation of a parabola in the xy-plane is y = a(x − h)2 + k, in which (h, k) is the vertex. Now let’s express each choice in precisely this form.
(A) y = (x − 3)2 + 2 y = 1(x − 3)2 + 2a = 1, h = 3, k = 2
(B) y = 2(x − 3)2 y = 2(x − 3)2 + 0a = 2, h = 3, k = 0
(C) y = 2x2 − 3 y = 2(x − 0)2 − 3a = 2, h = 0, k = −3
(D) y = 3x2 + 2 y = 3(x − 0)2 + 2a = 3, h = 0, k = 2
If this vertex is on the x-axis, then k = 0. The only equation in which k = 0 is (B).
9. D Advanced Mathematics (rational equations) MEDIUM
Add 
:
Express right side in terms of a common denominator:
Combine terms on right into one fraction:
Combine terms:
Multiple by x + 3:
10. C
Algebra (linear relationships) MEDIUM
We are told that the temperature varies linearly with altitude, so if y represents the temperature (in °C) and x represents altitude (in km), these variables are related by the equation y = mx + b, where m (the slope) and b (the y-intercept) are constants.
We are given two points on this line: (50 km, 10°) and (80 km, −80°). We can use these points to find the slope, m:
slope 
Recall that the slope of a linear relationship is the “unit rate of change.” In other words, the slope of −3 means that the temperature declines by 3° for every 1 km of additional altitude. Since we want the altitude at which the temperature is −50°, we want the value of x such that (x, −50°) is on this line. To find x, we can simply use the slope formula again, using either of the other two points: Slope formula using (50, 10) and (x, −50):
slope 
Multiply by 50 − x:
60 = −3(50 − x)
Distribute:
60 = −150 + 3x
Add 150:
210 = 3x
Divide by 3:
70 = x
11. A Advanced Mathematics (triangles/quadratics) MEDIUM-HARD
Any point that intersects the y-axis has an x-value of 0. So, to find point A, plug in 0 for x and solve for y:
y = 2x2 − 16x + 14
Plug in 0 for x:
y = 2(0)2 − 16(0) + 14 = 14
Any point that intersects the x-axis has a y-value of 0. So, to find points B and C, plug in 0 for y and solve for x:
y = 2x2 − 16x + 14
Substitute 0 for y:
0 = 2x2 − 16x + 14
Divide by 2:
0 = x2 − 8x + 7
Factor:
0 = (x − 7)(x − 1)
Use the Zero Product Property:
x = 7 and x = 1
If we connect these three points, we get a triangle with a height of 14 (from y = 0 to y = 14) and a base of 6 (from x = 1 to x = 7).
Use the triangle area formula 
bh:
12. B Advanced Mathematics (polynomials) MEDIUM-HARD
Given equation:
y = (x + 2)2 (x − 3)2
To find the y-intercept, set x = 0:
y = (0 + 2)2(0 − 3)2
Simplify:
y = (2)2(-3)2 = (4)(9) = 36
Therefore the y-intercept is at (0, 36).
To find the x-intercepts, set y = 0:
0 = (x + 2)2 (x − 3)2
By the Zero Product Property, the only solutions to this equation are x = −2 and x = 3, so there are two x-intercepts and a total of three x- and y-intercepts.
13. C
Special Topics (complex numbers) HARD
A(2 − i) = 2 + i
Divide by (2 − i):
Multiply numerator and denominator by the conjugate (2 + i):
FOIL:
Combine terms:
Substitute i2 = − 1:
Simplify:
Combine terms:
Distribute to express in standard a + bi form:
14. B
Algebra (graphs of linear equations) HARD
Given equation:
y + x = k(x − 1)
Subtract x:
y = k(x − 1) − x
Distribute:
y = kx − k − x
Collect like terms:
y = (k − 1)x − k
The slope of this line is k − 1 and its y-intercept is − k. If k > 2, then k − 1 > 1, and − k < −2. In other words, the slope of the line is greater than 1 and the y-intercept is less than −2. The only graph with these features is the one in choice (B).
15. B
Advanced Mathematics (analyzing polynomial functions) HARD
Because this polynomial has a degree of 3 (which is the highest power of any of its terms), it cannot have more than 3 zeros. These three zeros are given as −2, 3, and 6. We also know that g(0), the y-intercept of the graph, is negative. This gives us enough information to make a rough sketch of the graph.
This shows that the only values of x for which the function is negative are −2 < x < 3 and x > 6. Therefore the only negative value among the choices is (B) g(−1).
16. 30
Algebra (linear equations) EASY
Multiply by 6 (the common denominator):
Distribute:
Simplify:
4x + 3y = 30
17. 25/7 or 3.57
Advanced Mathematics (rational equations) EASY
Add :
Simplify:
Cross multiply:
25 = 7x
Divide by 7:
18. 35
Special Topics (radians and arcs) MEDIUM-HARD
Since an arc is simply a portion of a circumference, let’s first calculate the circumference of the circle:
C = 2πr = 2π(36) = 72π
Because arc AB has a measure of 7π, it is 
of the entire circumference. Since x° is the measure of the central angle that corresponds to this arc, it must be the same fraction of the whole:
Cross multiply:
72x = 7(360)
Divide by 72:
x = 7(5)
Simplify:
x = 35
19. 1.2
Algebra (linear systems) MEDIUM-HARD
First, we should simplify the first equation:
Subtract y:
Multiply by 12:
6x − 4y = 1.2
This equation represents a line with slope of 
. The second equation, 6x − 4y = k, also represents a line with slope 
. In order for this system of equations to have at least one solution, these two lines must have an intersection. How can two lines with the same slope intersect? They must be identical lines, and therefore intersect in all of their points. If this is the case, then k must equal 1.2.
20. 2.4
Special Topics (trigonometry) HARD
Since x represents the radian measure of an acute angle, and sin 
, we can use the definition of sine 
to draw a right triangle:
We might notice that this is a 5-12-13 special right triangle, or simply use the Pythagorean Theorem to show that m = 12. We can also show that the other acute angle in the triangle must be complementary to x (that is, together they form a right angle), and so must have a measure of 
− x.
To find tan 
, we simply have to use the angle with measure 
as our new reference angle, and use TOA:
tan
1. D
Algebra (systems) EASY
When faced with a system of equations, notice whether the two equations can be combined in a simple way—either by subtracting or adding the corresponding sides—to get the expression the question is asking for.
a − b = 10
a − 2b = 8
Subtract corresponding sides:
b = 2
2. C
Data Analysis (central tendency) EASY
The average of three numbers is 50:
Multiply by 3:
150 = a + b + c
Two of the numbers have a sum of 85:
85 = a + b
Substitute into the previous equation:
150 = 85 + c
Subtract 85 to find c:
65 = c
3. D
Problem Solving/Data Analysis (proportions) EASY
Set up a proportion:
Cross multiply:
2,025 = 25x
Divide by 25:
81 = x
4. B
Data Analysis (tables) EASY
Let’s fill in the table with the information we’re given and work our way to the value the question asks us to find. First, use the information in the FAVORABLE column to determine how many women viewed the politician favorably:
26 + w = 59
Subtract 26:
w = 33
Next, go to the WOMEN row:
33 + x + 13 = 89
Combine terms:
46 + x = 89
Subtract 46:
x = 43
5. D
Algebra (exponentials) EASY
22n − 2 = 32
When dealing with exponential equations, it helps to see if we can express the two sides of the equation in terms of the same base. Since 32 = 25, we can express both sides in base 2:
22n − 2 = 25
If xa = xb and x > 1, then a = b (if the bases are equal, the exponents are equal):
2n − 2 = 5
Add 2:
2n = 7
Divide by 2:
6. C
Algebra (representing quantities) EASY
The question asks us to find the “part-to-whole” ratio of walnuts: walnut fraction 
.
Since the walnuts weigh x ounces, and the total weight of all the nuts is x + 15 + 20 = x + 35 ounces,
walnut fraction 
7. B
Advanced Mathematics (triangle trigonometry) EASY
Remember the definitions of the basic trigonometric functions: SOH CAH TOA. Since the “side of interest” (k) is the OPPOSITE side to the given angle (35°), and since we know the length of the HYPOTENUSE (12), we should use SOH.
Plug in the values:
Substitute sin 35° = 0.574:
Multiply by 12:
(12)(0.574) = 6.88 = k
8. A
Special Topics (polygons) EASY
The sum of the measures if the interior angles of any polygon is (n − 2)180°, where n is the number of sides in the polygon. Since this is a 5-sided polygon, the sum of its interior angles is (5 − 2)(180°) = 3(180°) = 540°. Therefore the average of these measures is 540°/5 = 108°.
9. B
Data Analysis (scatterplot) MEDIUM
We want to find the slope of the line of best fit because it represents the average annual increase in revenue per store. Although the question asks about the years 2004 and 2012, we can choose ANY two points on this line to find its slope. We should choose points on the line of best fit that are easy to calculate with, such as (2005, $300,000) and (2011, $600,000).
10. C
Data Analysis (scatterplot) MEDIUM-HARD
When faced with a question like this, we must analyze each statement individually.
(A) The average revenue per store increased by over 100% from 2005 to 2009. True or false? In 2005, according to the line of best fit, the average revenue per store was approximately $300,000. In 2009, the average revenue per store was approximately $500,000. This is a percent increase of
(B) The total number of retail stores increased by 50% from 2005 to 2012. True or false? According to the scatterplot, in 2005 there were 3 stores corresponding to the three dots above 2005. In 2012 there were 6 stores corresponding to the 6 dots above 2012. This is a percent increase of
FALSE
(C) The total revenue for all stores in 2012 is more than three times the total revenue from all stores in 2004. True or false? In 2004, there were 3 stores with an average revenue per store of approximately $250,000. Therefore the total revenue in 2004 was approximately 3 × $250,000 = $750,000. In 2012, there were 6 stores with an average revenue per store of approximately $650,000. Therefore the total revenue in 2012 was approximately 6 × $650,000 = $3,900,000. Since $3,900,000 is more than three time $750,000, this statement is TRUE.
11. B
Algebra (translating quantitative information) MEDIUM
This question tests your ability to translate words into algebraic expressions. Systematically translate the sentence phrase by phrase.
The product of two numbers, a and b is 6 greater than their sum.
Translation:
ab = 6 + a + b
Use commutative law of equality on right side:
ab = a + b + 6
12. D
Special Topics (coordinate geometry) MEDIUM
First, find the slope of l using the points (0, −9) and (12, 0):
Since the two lines are parallel, line m must also have a slope of 
. Now we can solve for k using the slope equation and the two points on line m, (0, 0) and (k, 12):
Cross multiply:
4(12) = 3(k)
Simplify:
48 = 3k
Divide by 3:
16 = k
Notice that the coordinates of the point (16, 12) correspond to the width and the length of the rectangle, respectively. Therefore, the area of the rectangle is 16 × 12 = 192 square units.
13. A
Problem Solving/Data Analysis (ratios) MEDIUM
If the Giants’ win-loss is 2:3, then they won 2n games and lost 3n games, where n is some unknown integer. (For instance, perhaps they won 2 games and lost 3, in which case n = 1, or perhaps they won 20 games and lost 30, in which case n = 10, etc.) This means that the total number of games they played is 2n + 3n = 5n. Since they won 120 games,
5n = 120
Divide by 5:
n = 24
Therefore they won 2n = (2)(24) = 48 games and lost 3n = (3)(24) = 72 games, and so they lost 72 − 48 = 24 more games than they won.
14. B
Advanced Mathematics (exponential growth) MEDIUM
We might begin by plugging in a number for p. Let’s say p = 120 cells to start. We are told that after one hour the population decreased by . Since of 120 is 40, the population decreased by 40 and the population was then 120 − 40 = 80 cells. In the second hour, the population increased by 40%. Increasing a number by 40% is equivalent to it by 1.40 (because it becomes 140% of what it was), so the population was then 80(1.40) = 112 cells. In the third hour, the population increased by 50%, so it became 112(1.50) = 168 cells.
Substituting p = 120 into each of the answer choices yields (A) 1.3p = 1.3(120) = 156, (B) 1.4p = 1.4(120) = 168, (C) 1.5p = 1.5(120) = 180, and (D) 1.6p = 1.6(120) = 192. Therefore the answer is (B).
Alternately, you can solve this problem algebraically: p(2/3)(1.40)(1.50) = 1.40p.
15. B
Advanced Mathematics (exponentials) MEDIUM
For this one, we’ll need the Laws of Exponentials from
Chapter 9, Lesson 9.
Translate by using Exponential Law #3:
Multiply by m2:
Multiply by 16:
Simplify:
16. B
Data Analysis (probability) MEDIUM
Let R = the number of red marbles, W = the number of white marbles, and B = the number of blue marbles. If the jar contains twice as many red marbles as white marbles, then R = 2W. If the jar contains three times as many white marbles as blue marbles, then W = 3B. We can substitute numbers to these equations to solve the problem. Let’s say B = 10. This means there are 3(10) = 30 white marbles and 2(30) = 60 red marbles. The total number of marbles is therefore 10 + 30 + 60 = 100, and the number of non-red marbles is therefore 10 + 30 = 40 marbles, so the probability that the marble is not red is 
.
17. C
Advanced Mathematics (parabolas) MEDIUM
The vertex of a parabola with the equation y = A(x − h)2 + k is (h, k). For this parabola, h = 2 and k = 2. So, the vertex is (2, 2). The slope of the line that passes through (1, −3) and (2, 2) is
18. C
Advanced Mathematics (functions) MEDIUM-HARD
Let the input number be 7.
Step 1: Multiply the input value by 6:
42
Step 2: Add x to that result:
42 + x
Step 3: Divide this result by 4:
This must yield an output of 15:
Multiply by 4:
60 = 42 + x
Subtract 42:
18 = x
19. C
Data Analysis (graphing data) MEDIUM-HARD
The graph of the quadratic y = ax2 + bx + c is a parabola. If a < 0, the parabola is “open-down” like a frowny-face. The only graph with this feature is (C).
20. B
Algebra (expressing relationships) MEDIUM-HARD
Draw a number line, and to show that p < r, place p to the left of r on the number line. The points that are closer to p than to r are all the points to the left of their midpoint. The midpoint is the average of the endpoints: 
, so if the point with coordinate x is closer to p than to r, then 
.
21. A
Algebra (simplifying expressions) MEDIUM-HARD
Substitute 
for x:
Simplify the denominator:
Divide by multiplying by the reciprocal:
22. A
Advanced Mathematics (quadratics) MEDIUM-HARD
The graph of y = a(x − 2)(x + 1) is a quadratic with zeros (x-intercepts) at x = 2 and x = −1. The axis of symmetry of this parabola is halfway between the zeros, at x = (2 + −1)/2 = 1/2. Since a < 0, the parabola is “open down,” and so we have a general picture like this:
If you trace the curve from x = 0 to x = 5, that is, from the y-intercept and then to the right, you can see that the graph goes up a bit (until x = 1/2), and then goes down again.
Alternately, you can pick a negative value for a (like − 2) and graph the equation on your calculator.
23. D
Advanced Mathematics (rational equations) HARD
Given equation:
Add 
:
Combine the fractions into one:
Multiply by n2 + 3:
n2 − 9 + k = n2 + 3
Subtract n2 :
−9 + k = 3
Add 9:
k = 12
24. C
Problem Solving (percentages) MEDIUM-HARD
Let p = the price per share of the stock. The cost of 200 of these shares (before commission) is therefore 200p. With a 3% commission, the cost becomes (1.03)(200p)
(1.03)(200p) = $3,399
200p = $3,300
Divide by 200:
p = $16.50 per share
25. A
Algebra (expressing quantities) MEDIUM-HARD
It may be easiest to choose number for w and y. Assume y = 4. If w is 50% greater than y, then w = 1.5(4) = 6. Therefore w−2 = 6−2 = 1/36, and y−2 = 4−2 = 1/16. Therefore the ratio of w−2 to y−2 is
26. D
Data Analysis (set relations) HARD
Let’s let s = the total number of athletes in the group who play soccer, and t = the number of athletes in the group who run track. We can set up a Venn diagram to show the relationship between these two overlapping sets.
Since one-third of the soccer players also run track, we must put s in the overlapping region between soccer and track, and therefore the number who play only soccer is 
s. Likewise, since one-half of the athletes who run track also play soccer, we must put 
t in the overlapping region, and therefore the number of athletes who only run track is t.
Sincer there are 60 athletes in total:
Simplify:
Multiply by 3 to simplify:
2s + 3t = 180
The number of soccer players who run track must equal the number of track athletes who play soccer:
Multiply by 6 (the common denominator):
2s = 3t
Substitute 2s = 3t into the previous equation:
3t + 3t = 180
Simplify:
6t = 180
Divide by 6:
t = 30
Substitute t = 30 into the other
equation to solve for s:
2s = 3(30)
Simplify:
2s = 90
Divide by 2:
s = 45
Now we can use these values to complete the Venn diagram:
From this diagram, we can see that the only true statement among the choices is (D).
27. D
Advanced Mathematics (transformations) HARD
The graph of y = g(x) = f(x) + b is the graph of f vertically shifted up by b units. If g(x) = 0 has exactly one solution, the graph of y = g(x) can touch the x-axis at only one point: the vertex. Since the vertex of f has a y-coordinate of −2, this can only happen if f is shifted up 2 units, so b = 2.
28. B
Special Topics (trigonometry) HARD
The statement 
indicates that x is an angle in quadrant II, where the cosine is negative. Let’s draw this situation on the unit circle so we can visualize it. (We don’t want to confuse the angles called x and y in the problem with the x-coordinates and y-coordinates in the xy-plane. For this reason, let’s label the terminal rays for the angles “angle x” and “angle y.”) Recall that the cosine of any angle is the x-coordinate of the point on the unit circle that corresponds to that angle. If cos x = a, then a is the x-coordinate of the point on the unit circle that corresponds to “angle x,” as shown in the diagram.
Now notice that, since a is a negative number, −a (that, is, the opposite of a), is a positive number. More specifically, it is the reflection of the point labeled a over the x-axis, as shown in the diagram. Now, if cos y = −a, then “angle y” corresponds to a point on the unit circle with an x-coordinate of −a. There are two possible locations for this point on the circle, and both are shown in the diagram above. Notice that one of these angles is the reflection of “angle x” over the y-axis. This is the supplement of “angle x,” that is, π − x. The other is the reflection of “angle x” over the origin, that is x + π. Therefore, the correct answer is (B).
Alternately, we could use the calculator to solve this problem by process of elimination. We can choose a value of “angle x” between π/2 and π. (In radian mode this is an angle between 1.57 and 3.14, and in degree mode it is an angle between 90° and 180°.) Let’s pick “angle x” to be 2 radians (about 115°). According to the calculator, cos(2) = −.416. Therefore, cos y must equal .416. Now we can substitute x = 2 into all of the choices and see which angle has a cosine of .416.
(A) cos(2 + 2π ) = −.416
(B) cos(2 + π) = .416
(C) cos(2 + π/2) = −.909
(D) cos(−2 + 2π) = −.416
Therefore the correct answer is (B).
29. A
Data Analysis (table) HARD
Since the question asks about those “who expressed an opinion on Proposal 81a,” we must ignore those who are listed as having No Opinion.
The number at the bottom right of the table indicated that there were 4,407 total people surveyed. But 719 of those had No Opinion, so 4,407 − 719 = 3,688 did have an opinion. What percentage of those are under 40? The answer is in the first row of the table (18 to 39): 917 of these Approve and 204 of these Disapprove. Therefore 917 + 204 = 1,121 of those showing an opinion are under 40 years of age.
Therefore the percentage of those showing an opinion who are under 40 is 
30. B
Data Analysis (table) HARD
(A) The approval rate for Proposal 81a generally decreases with the age of the voter.
Age 18 to 39:
918 out of 1,624 approve (56%)
Age 40 to 64:
1,040 out of 1,644 approve (64%)
Age 65 and older:
604 out of 1,139 approve (53%)
The approval rate increases and then decreases with age, so (A) is not correct.
(B) The disapproval rate for Proposal 81a generally increases with the age of the voter:
Age 18 to 39:
204 out of 1,624 disapprove (13%)
Age 40 to 64:
502 out of 1,644 disapprove (31%)
Age 65 and older:
420 out of 1,139 disapprove (37%)
The disapproval rate INCREASES as age increases, therefore (B) is correct.
31. 1/5 or 0.2
Data Analysis (variation) MEDIUM
If y varies inversely as x:
Substitute ½ = y and 10 = x:
Cross multiply:
10 = 2k
Divide by 2:
5 = k
Therefore the general equation is:
Substitute 25 = y:
Multiply by x:
25x = 5
Divide by 25:
32. 169
Advance Mathematics (quadratics) MEDIUM
x2 = 12x = 13
Subtract 13:
x2 + 12x − 13 = 0
Factor:
(x + 13)(x − 1) = 0
Use the Zero Product Property:
x = −13 or x = 1
If x < 0, x must be −13. Therefore x2 = (−13)2 = 169.
Alternately, if you have QUADFORM (a quadratic formula program) programmed into your calculator, select PROGRAM, QUADFORM, and input a = 1, b = 12 and c = −13 to find the zeros (−13 and 1).
33. 112
Special Topics (polygons) MEDIUM-HARD
Notice that the “cutouts” can be reassembled to form two squares with side x and diagonal y, leaving an octagon with perimeter 8y.
Since each of the cutout triangles is a right triangle:
x2 + x2 = y2
Simplify:
2x2 = y2
If the total area of the “cutouts” is 196 square centimeters:
2x2 = 196
Substitute 2x2 = y2:
y2 = 196
Take square root:
y = 14
Therefore the perimeter of the octagon is 8 × 14 = 112.
34. 16
Algebra (solving equations) HARD
Because m2 + n2 = 40, where m and n are both integers, we must look for two perfect squares that have a sum of 40. The perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … and the only two of these with a sum of 40 are 4 and 36. So either m2 = 4 and n2 = 36 or m2 = 36 and n2 = 4.
CASE 1:
m2 = 4 and n2 = 36
Take square root:
m = ±2 and n = ±6
Since m < 0 < n:
m = −2 and n = 6
Evaluate (m + n)2:
(m + n)2 = (−2 + 6)2 = 42 = 16
CASE 2:
m2 = 36 and n2 = 4
Take square root:
m = ±6 and n = ±2
Since m < 0 < n:
m = −6 and n = 2
Evaluate (m + n)2:
(m + n)2 = (−6 + 2)2 = (−4)2 = 16
35. 1.4
Advanced Mathematics (trigonometry) MEDIUM-HARD
Recall the Pythagorean Trigonometric Identity, which is true for all x:
sin2 x + cos2 x = 1
Expression to be evaluated:
(sin x + cos x)2
FOIL:
(sin x + cos x)(sin x + cos x) = sin2 x + 2(sin x)(cos x) + cos2 x
Rearrange with Commutative and Associative Laws of Addition:
2(sin x)(cos x) + (sin2 x + cos2 x)
Substitute sin2 x + cos2 x = 1:
2(sin x)(cos x) + 1
Substitute (sin x)(cos x) = 0.2:
2(0.2) + 1 = 1.4
36. 115
Data Analysis (central tendency) MEDIUM
Begin by putting the data in order from least expensive to most expensive:
80 phones sold for $98
40 phones sold for $110
20 phones sold for $120
62 phones sold for $140
38 phones sold for $162
We don’t have to actually write out the prices of all 240 phones to find the median price. We can divide any set of 240 numbers, in ascending order, into two sets of 120 numbers. The median is in the middle of these, so it is the average of the 120th and 121st numbers. Since the first two categories account for 40 + 80 = 120 of these numbers, the 120th number in the set is $110, and the 121st number in the set is in the next higher category, $120. The median price is therefore ($110 + $120)/2 = $115.
37. 6.8
Problem Solving (extended thinking) HARD
If the height of the logo is to match the height of the banner, it must have a height of 4 feet. Let x be the corresponding length of the logo.
Since the logo has a height-to-length
ratio of 5:8:
Cross multiply:
5x = 32
Divide by 5:
x = 6.4
Since the banner is 20 feet long, there are 20 - 6.4 = 13.6 feet in total for the side margins. If the logo is centered, then each margin is half this length, 13.6 ÷ 2 = 6.8 feet.
38. 25
Problem Solving (extended thinking) HARD
The banner has dimensions of 20 feet by 4 feet, so its area is 20 × 4 = 80 square feet. If the company charges $1.20 per square foot for the banner material, this cost is 80 × $1.20= $96. Based on the logo dimensions we determined in the previous problem, the area of the logo is 4 × 6.4 = 25.6 square feet. If the company charges $2.50 per square foot for the logo, the cost per printed logo is 25.6 × $2.50 = $64.
If the company charges a fixed cost of $32 per banner, then the total cost of a banner with ONE logo would be $96 + $64 + $32 = $192. The total cost of a banner with TWO logos would be $96 + $64 + $64 + $32 = $256.
We can calculate the percent savings with the “percent change” formula, since we are considering a “change” from the more expensive banner to the less expensive banner.
Therefore the percent savings is 25(%).
Sample Response
Reading Score: 8 out of 8
Analysis Score: 8 out of 8
Writing Score: 8 out of 8
In this essay, Steven Pinker examines the “moral panics” surrounding new forms of media and the supposed cognitive and moral decline they cause. His essay provides a measure of balance to our modern discussions of social media and instantaneous digital information. He supports his thesis, that “such panics often fail reality checks,” with examples dating back as far as the 1950s, logical analysis, vibrant illustrative images, and touches of humor. He provides historical and scientific context for his claims and effectively encapsulates the broad misconceptions that cultural critics have about the relationship between modern media and the human brain. Although his argument could have been bolstered with more specific scientific support, his essay as a whole effectively argues for a reprieve from the hysteria about intellectual and moral decline allegedly caused by Twitter and Facebook.
Pinker makes use of “reductio ad absurdum,” or indirect proof, to make his case. This technique proceeds by arguing that if the point to be refuted were true, it would lead necessarily to a contradiction, and therefore it cannot be true. For instance, Pinker hints at this logical technique in the second paragraph: “When comic books were accused of turning juveniles into delinquents in the 1950s, crime was falling to record lows, just as the denunciations of video games in the 1990s coincided with the great American crime decline.” Here, Pinker is suggesting that sociological and psychological evidence refutes claims of social decline.
He uses reductio ad absurdum even more explicitly in the third paragraph: “If electronic media were hazardous to intelligence, the quality of science would be plummeting. Yet discoveries are multiplying like fruit flies, and progress is dizzying. Other activities in the life of the mind, like philosophy, history and cultural criticism, are likewise flourishing.” Unfortunately, Pinker does not provide substantial evidence to bolster these claims. He fails to address the common counterclaim that much of the “science” published on the Internet is flimsy, and the “cultural criticism” lazy.
Pinker then goes on to outline a basic lesson in human information processing, in an attempt to ground his argument in science. To Pinker, the claim that “information can change the brain” is facile (“it’s not as if the information is stored in the pancreas”) and misleading (“the existence of neural plasticity does not mean the brain is a blob of clay pounded into shape by experience”). Rather, Pinker suggests, “the effects of experience are highly specific to the experiences themselves. … Music doesn’t make you better at math; conjugating Latin doesn’t make you more logical; brain-training games don’t make you smarter.” Unfortunately, Pinker here seems to mistake assertion for argumentation. He is directly contradicting the claims of thousands of music and Latin teachers, as well as dozens of Lumosity commercials. But he is only gainsaying. Here again, we might expect some data to support his points.
Next, Pinker attempts to refute cultural critics by drawing analogies between their reasoning and the faulty reasoning of “primitive peoples” who believe that “eating fierce animals will make them fierce.” He likens this to the thinking of modern observers who believe that “reading bullet points and Twitter postings turns your thoughts into bullet points and Twitter postings.” But of course just because one line of reasoning parallels another does not mean that both are equally incorrect. Here again, Pinker’s argument would benefit from information about the actual cognitive effects of reading Twitter feeds.
Next, Pinker provides a qualification: “Yes, the constant arrival of information packets can be distracting or addictive, especially to people with attention deficit disorder.” But here again, even in conceding a point, Pinker doesn’t quite offer the information a reader might want: How significant is this distraction or addiction, and does it have any harmful long-term effects? We don’t get this information from Pinker, but we do get some practical advice: “Turn off e-mail or Twitter when you work …” We get even more substantial advice in the next paragraph: to cultivate “intellectual depth,” we must avail ourselves of “special institutions, which we call universities” and engage in “analysis, criticism, and debate.” But why, a reader might wonder, should we moderate our use of electronic media if it doesn’t have any real harmful effects?
Finally, Pinker ends with a broader perspective and a note of hope: “the Internet and information technologies are helping us manage, search, and retrieve our collective intellectual output. … Far from making us stupid, these technologies are the only things that will keep us smart.” Perhaps Pinker is right, but his argument would be stronger with more substantial quantitative evidence and more direct refutation of our real concerns about how the Internet might be changing our brains.
Reading—8 (both readers gave it a score of 4)
This response demonstrates extremely thorough comprehension of Pinker’s essay through skillful use of summary, paraphrase, and direct quotations. The author summarizes Pinker’s central thesis and modes of persuasion (His thesis, that “such panics often fail reality checks,” is supported with examples dating back as far as the 1950s, careful logical analysis, vibrant illustrative images, and touches of humor) and shows a clear understanding of Pinker’s supporting ideas and overall tone (He provides historical and scientific context for his claims and effectively encapsulates the broad misconceptions that cultural critics have about the relationship between modern media and the human brain. … Pinker ends with a broader perspective and a note of hope). Each quotation is accompanied by insightful commentary that demonstrates that this author thoroughly understands Pinker’s central and secondary ideas, and even recognizes when Pinker seems occasionally to fall short of his own purpose.
This response provides a thoughtful and critical analysis of Pinker’s essay and demonstrates a sophisticated understanding of the analytical task. The author has identified Butler’s primary modes of expression (logical analysis, vibrant illustrative images, and touches of humor) and has even provided a detailed examination of Pinker’s preferred logical method, reductio ad absurdum, with a discussion of several examples. Perhaps even more impressively, the author indicates where Pinker’s evidence falls short, providing critical analysis and suggesting alternatives (Unfortunately, Pinker does not provide substantial evidence to bolster these claims. He doesn’t address the common counterclaim that much of the “science” published on the Internet is flimsy, and the “cultural criticism” lazy. … Pinker here seems to mistake assertion for argumentation. … Here again, Pinker’s argument would benefit from information about the actual cognitive effects of reading Twitter feeds). Overall, the author’s analysis of Pinker’s essays demonstrates a thorough understanding not only of the rhetorical task that Pinker has set for himself, but also the means by which it is best accomplished.
This response shows a masterful use of language, sentence structure to establish a clear and insightful central claim (Although his argument could have been bolstered with more specific scientific support, his essay as a whole effectively argues for a reprieve from the hysteria about intellectual and moral decline allegedly caused by Twitter and Facebook). The response maintains a consistent focus on this central claim and supports it with a well-developed and cohesive analysis of Pinker’s essay. The author demonstrates effective verb choice (effectively encapsulates the broad misconceptions. … He likens this to the thinking of modern observers), strong grasp of relevant analytical terms, like reduction ad absurdum, facile, sociological and psychological evidence, counterclaim, assertion, argumentation, and gainsaying. The response is well-developed, progressing from general claim to specific analysis to considered evaluation. Largely free from grammatical error, this response demonstrates strong command of language and proficiency in writing.
