PSAT/NMSQT Prep 2020 - Princeton Review 2020

PSAT Practice Test 2 Answer sheet
Practice tests

You will see an answer sheet like the one below on test day. Review the answer key following the test when finished.

When testing, start with number 1 for each section. If a section has fewer questions than answer spaces, leave the extra spaces blank.

Reading Test

60 Minutes—47 Questions

This section corresponds to Section 1 of your answer sheet.

Directions

Read each passage or pair of passages, then answer the questions that follow. Choose your answers based on what the passage(s) and any accompanying graphics state or imply.

1. Questions 1—9 are based on the following passage.
2. This passage is adapted from “Metamorphosis” by Franz Kafka, a famous story that combines elements of fantasy and reality. This excerpt begins with the protagonist realizing he has literally turned into a giant, beetle-like insect.

 One morning, when Gregor Samsa woke from troubled dreams, he found himself transformed in his bed into a horrible vermin. He lay on his armor-like back, and if he lifted his head a little he could see his brown belly, slightly domed and divided by arches into stiff sections. The bedding was hardly able to cover it and seemed ready to slide off any moment. His many legs, pitifully thin compared with the size of the rest of him, waved about helplessly as he looked.  “What’s happened to me?” he thought. It wasn’t a dream. His room, a proper human room although a little too small, lay peacefully between its four familiar walls. A collection of textile samples lay spread out on the table—Samsa was a travelling salesman—and above it there hung a picture that he had recently cut out of an illustrated magazine and housed in a nice, gilded frame. It showed a lady fitted out with a fur hat and fur boa who sat upright, raising a heavy fur muff that covered the whole of her lower arm towards the viewer.  Gregor then turned to look out the window at the dull weather. Drops of rain could be heard hitting the pane, which made him feel quite sad. “How about if I sleep a little bit longer and forget all this nonsense,” he thought, but that was something he was unable to do because he was used to sleeping on his right, and in his present state couldn’t get into that position. However hard he threw himself onto his right, he always rolled back to where he was. He must have tried it a hundred times, shut his eyes so that he wouldn’t have to look at the floundering legs, and only stopped when he began to feel a mild, dull pain there that he had never felt before.  He thought, “What a strenuous career it is that I’ve chosen! Travelling day in and day out. Doing business like this takes much more effort than doing your own business at home, and on top of that there’s the curse of travelling, worries about making train connections, bad and irregular food, contact with different people all the time so that you can never get to know anyone or become friendly with them.” He felt a slight itch up on his belly; pushed himself slowly up on his back towards the headboard so that he could lift his head better; found where the itch was, and saw that it was covered with lots of little white spots which he didn’t know what to make of; and when he tried to feel the place with one of his legs he drew it quickly back because as soon as he touched it he was overcome by a cold shudder.  He slid back into his former position. “Getting up early all the time,” he thought, “it makes you stupid. You’ve got to get enough sleep. Other travelling salesmen live a life of luxury. For instance, whenever I go back to the guest house during the morning to copy out the contract, these gentlemen are always still sitting there eating their breakfasts. I ought to just try that with my boss; I’d get kicked out on the spot. But who knows, maybe that would be the best thing for me. If I didn’t have my parents to think about I’d have given in my notice a long time ago, I’d have gone up to the boss and told him just what I think, tell him everything I would, let him know just what I feel. He’d fall right off his desk! And it’s a funny sort of business to be sitting up there at your desk, talking down at your subordinates from up there, especially when you have to go right up close because the boss is hard of hearing. Well, there’s still some hope; once I’ve got the money together to pay off my parents’ debt to him—another five or six years I suppose—that’s definitely what I’ll do. That’s when I’ll make the big change. First of all though, I’ve got to get up, my train leaves at five.”

3. According to the passage, Gregor initially believes his transformation is a
1. curse.
2. disease.
3. nightmare.
4. hoax.
4. As used in line 12, “proper” most nearly means
1. called for by rules or conventions.
2. showing politeness.
3. naturally belonging or peculiar to.
4. suitably appropriate.
5. The passage most strongly suggests which of the following about Gregor’s attitude toward his profession?
1. He is resentful.
2. He is diligent.
3. He is depressed.
4. He is eager to please.
6. Which choice provides the best evidence for the answer to the previous question?
1. Lines 14—18 (“A collection . . . gilded frame”)
2. Lines 22—24 (“Gregor then turned . . . quite sad”)
3. Lines 54—60 (“Other . . . the spot”)
4. Lines 66—70 (“And it’s . . . hard of hearing”)
7. What central idea does the passage communicate through Gregor’s experiences?
1. Imagination is a dangerous thing.
2. People are fearful of change.
3. Dreams become our reality.
4. Humankind is a slave to work.
8. The passage most strongly suggests that which of the following is true of Gregor?
1. He feels a strong sense of duty toward his family.
2. He is unable to cope with change.
3. He excels in his profession.
4. He is fearful about his transformation.
9. Which choice provides the best evidence for the answer to the previous question?
1. Lines 11—14 (“What’s happened . . . familiar walls”)
2. Lines 22—24 (“Gregor then turned . . . quite sad”)
3. Lines 36—43 (“Doing business . . . with them”)
4. Lines 70—73 (“Well, there’s still . . . what I’ll do”)
10. As used in line 33, “floundering” most nearly means
1. thrashing.
2. painful.
3. pitiful.
4. trembling.
11. The function of the final sentence of the excerpt (“First of all though, I’ve got to get up, my train leaves at five”) is to
1. provide a resolution to the conflict Gregor faces.
2. foreshadow the conflict between Gregor and his boss.
3. illustrate Gregor’s resilience and ability to move on.
4. emphasize Gregor’s extreme sense of duty.
1. Questions 10—18 are based on the following passage.
2. This passage is adapted from Hillary Rodham Clinton’s speech titled “Women’s Rights Are Human Rights,” addressed to the U.N. Fourth World Conference on Women in 1995.

 If there is one message that echoes forth from this conference, it is that human rights are women’s rights. . . . And women’s rights are human rights.  Let us not forget that among those rights are the right to speak freely and the right to be heard.  Women must enjoy the right to participate fully in the social and political lives of their countries if we want freedom and democracy to thrive and endure.  It is indefensible that many women in nongovernmental organizations who wished to partic ipate in this conference have not been able to attend— or have been prohibited from fully taking part.  Let me be clear. Freedom means the right of people to assemble, organize, and debate openly. It means respecting the views of those who may disagree with the views of their governments. It means not taking citizens away from their loved ones and jailing them, mistreating them, or denying them their freedom or dignity because of the peaceful expression of their ideas and opinions.  In my country, we recently celebrated the seventy-fifth anniversary of women’s suffrage. It took one hundred and fifty years after the signing of our Declaration of Independence for women to win the right to vote. It took seventy-two years of organized struggle on the part of many courageous women and men.  It was one of America’s most divisive philosophical wars. But it was also a bloodless war. Suffrage was achieved without a shot fired.  We have also been reminded, in V-J Day observances last weekend, of the good that comes when men and women join together to combat the forces of tyranny and build a better world.  We have seen peace prevail in most places for a half century. We have avoided another world war. But we have not solved older, deeply-rooted problems that continue to diminish the potential of half the world’s population.  Now it is time to act on behalf of women everywhere.  If we take bold steps to better the lives of women, we will be taking bold steps to better the lives of chil dren and families too. Families rely on mothers and wives for emotional support and care; families rely on women for labor in the home; and increasingly, families rely on women for income needed to raise healthy children and care for other relatives.  As long as discrimination and inequities remain so commonplace around the world—as long as girls and women are valued less, fed less, fed last, overworked, underpaid, not schooled and subjected to violence in and out of their homes— the potential of the human family to create a peaceful, prosperous world will not be realized.  Let this conference be our—and the world’s— call to action.  And let us heed the call so that we can create a world in which every woman is treated with respect and dignity, every boy and girl is loved and cared for equally, and every family has the hope of a strong and stable future.

3. What is the primary purpose of the passage?
1. To chastise those who have prevented women from attending the conference
2. To argue that women continue to experience discrimination
3. To explain that human rights are of more concern than women’s rights
4. To encourage people to think of women’s rights as an issue important to all
4. Which choice provides the best evidence for the answer to the previous question?
1. Lines 4—5 (“Let us . . . be heard”)
2. Lines 9—12 (“It is indefensible . . . taking part”)
3. Lines 37—39 (“But we have . . . population”)
4. Lines 44—48 (“Families . . . other relatives”)
5. As used in line 28, “divisive” most nearly means
1. conflict-producing.
2. carefully watched.
3. multi-purpose.
4. time-consuming.
6. Based on the speech, with which statement would Clinton most likely agree?
1. More men should be the primary caregivers of their children in order to provide career opportunities for women.
2. Women do not need the support and cooperation of men as they work toward equality.
3. Solutions for global problems would be found faster if women had more access to power.
4. The American movement for women’s suffrage should have been violent in order to achieve success more quickly.
7. Which choice provides the best evidence for the answer to the previous question?
1. Lines 6—8 (“Women . . . endure”)
2. Line 30 (“Suffrage . . . shot fired”)
3. Lines 44—48 (“Families . . . other relatives”)
4. Lines 49—55 (“As long . . . realized”)
8. As used in line 26, “organized” most nearly means
1. arranged.
2. cooperative.
3. hierarchical.
4. patient.
9. Which claim does Clinton make in her speech?
1. The conference itself is a model of nondiscrimination toward women.
2. Democracy cannot prosper unless women can participate fully in it.
3. Women’s rights are restricted globally by the demands on them as parents.
4. Women are being forced to provide income for their families as a result of sexism.
10. Clinton uses the example of V-J Day observations to support the argument that
1. campaigns succeed when they are nonviolent.
2. historical wrongs against women must be corrected.
3. many tragedies could have been avoided with more female participation.
4. cooperation between men and women leads to positive developments.
11. The fifth paragraph (lines 13—20) can be described as
1. a distillation of the author’s main argument.
2. an acknowledgment of a counterargument.
3. a veiled criticism of a group.
4. a defense against an accusation.
1. Questions 19—28 are based on the following passages and supplementary material.
2. The following passages discuss the history and traditions associated with tea.

Passage 1

 Europe was a coffee-drinking continent before it became a tea-drinking one. Tea was grown in China, thousands of miles away. The opening of trade routes with the Far East in the fifteenth and sixteenth centuries gave Europeans their first taste of tea.  However, it was an unpromising start for the beverage, because shipments arrived stale, and European tea drinkers miscalculated the steeping time and measurements. This was a far cry from the Chinese preparation techniques, known as a “tea ceremony,” which had strict steps and called for steeping in iron pots at precise temperatures and pouring into porcelain bowls.  China had a monopoly on the tea trade and kept their tea cultivation techniques secret. Yet as worldwide demand grew, tea caught on in Europe. Some proprietors touted tea as a cure for maladies. Several European tea companies formed, including the English East India Company. In 1669, it imported 143.5 pounds of tea—very little compared to the 32 million pounds that were imported by 1834.  Europeans looked for ways to circumvent China’s monopoly, but their attempts to grow the tea plant (Latin name Camellia sinensis) failed. Some plants perished in transit from the East. But most often the growing climate wasn’t right, not even in the equatorial colonies that the British, Dutch, and French controlled. In 1763, the French Academy of Sciences gave up, declaring the tea plant unique to China and unable to be grown anywhere else. Swedish and English botanists grew tea in botanical gardens, but this was not enough to meet demand.  After trial and error with a plant variety discovered in the Assam district of India, the British managed to establish a source to meet the growing demands of British tea drinkers. In May 1838, the first batch of India-grown tea shipped to London. The harvest was a mere 350 pounds and arrived in November. It sold for between 16 and 34 shillings per pound. Perfecting production methods took many years, but ultimately, India became the world’s largest tea-producing country. By the early 1900s, annual production of India tea exceeded 350 million pounds. This voluminous source was a major factor in tea becoming the staple of European households that it is today.

Passage 2

 In Europe, there’s a long tradition of taking afternoon tea. Tea time, typically four o’clock, means not just enjoying a beverage, but taking time out to gather and socialize. The occasion is not identical across Europe, though; just about every culture has its own way of doing things.  In France, for example, black tea is served with sugar, milk, or lemon and is almost always accompanied by a pastry. Rather than sweet pastries, the French prefer the savory kind, such as the gougère, or puff pastry, infused with cheese.  Germans, by contrast, put a layer of slowly melting candy at the bottom of their teacup and top the tea with cream. German tea culture is strongest in the eastern part of the country, and during the week tea is served with cookies, while on the weekend or for special events, cakes are served. The Germans think of tea as a good cure for headaches and stress.  Russia also has a unique tea culture, rooted in the formalism of its aristocratic classes. Loose leaf black tea is served in a glass held by a podstakannik, an ornate holder with a handle typically made from silver or chrome—though sometimes it may be goldplated. Brewed separately, the tea is then diluted with boiled water and served strong. The strength of the tea is seen as a measure of the host’s hospitality. Traditionally, tea is taken by the entire family and served after a large meal with jams and pastries.  Great Britain has a rich tradition of its own. Prior to the introduction of tea into Britain, the English had two main meals, breakfast and a second, dinner-like meal called “tea,” which was held around noon. However, during the middle of the eighteenth century, dinner shifted to an evening meal at a late hour; it was then called “high tea.” That meant the necessary introduction of an afternoon snack to tide one over, and “low tea” or “tea time” was introduced by British royalty. In present-day Britain, your afternoon tea might be served with scones and jam, small sandwiches, or cookies (called “biscuits”), depending on whether you’re in Ireland, England, or Scotland.  Wherever they are and however they take it, Europeans know the value of savoring an afternoon cup of tea.

Data from Euromonitor International and World Bank.

3. Based on the information provided in Passage 1, it can be inferred that
1. European nations tried to grow tea in their colonies.
2. European tea growers never learned Chinese cultivation techniques.
3. Europeans’ purpose in opening trade routes with the Far East was to gain access to tea.
4. Europeans believed tea was ineffective as a treatment against illness.
4. Which choice provides the best evidence for the answer to the previous question?
1. Lines 6—9 (“However . . . measurements”)
2. Lines 17—18 (“Some . . . maladies”)
3. Lines 26—29 (“But . . . French controlled”)
4. Lines 40—42 (“The harvest . . . per pound”)
5. As used in line 23, “circumvent” most nearly means
1. destroy.
2. get around.
3. ignore.
4. compete with.
6. It can be inferred from both Passage 1 and the graphic that
1. English botanical gardens helped make the United Kingdom one of the highest tea-consuming countries in the world.
2. if the French Academy of Sciences hadn’t given up growing tea in 1763, France would be one of the highest tea-consuming countries in the world.
3. Britain’s success at growing tea in India in the 1800s helped make the United Kingdom one of the highest tea-consuming nations in the world.
4. China’s production of tea would be higher if Britain hadn’t discovered a way to grow tea in India in the 1800s.
7. It is reasonable to infer, based on Passage 2, that
1. serving tea is an important part of hosting guests in Russia.
2. Germans generally avoid medicine for stress.
3. drinking tea in modern Britain is confined to the upper classes.
4. the usual hour for drinking tea varies across Europe.
8. Which choice provides the best evidence for the answer to the previous question?
1. Lines 50—52 (“Tea time . . . socialize”)
2. Lines 65—66 (“The Germans . . . stress”)
3. Lines 73—74 (“The strength . . . hospitality”)
4. Lines 84—86 (“That meant . . . royalty”)
9. As used in line 68, “aristocratic” most nearly means
1. culinary.
2. political.
3. rigid.
4. noble.
10. Compared with France’s tradition of tea-drinking, having tea in Germany
1. is more formal.
2. involves sweeter food.
3. requires greater solitude.
4. is more of a meal than a snack.
11. Which statement is the most effective comparison of the two passages’ purposes?
1. Passage 1’s purpose is to describe the early history of tea in Europe, while Passage 2’s purpose is to compare European cultural practices relating to tea.
2. Passage 1’s purpose is to argue against the Chinese monopoly of tea, while Passage 2’s purpose is to argue that Europeans perfected the art of tea drinking.
3. Passage 1’s purpose is to express admiration for the difficult task of tea cultivation, while Passage 2’s purpose is to celebrate the rituals surrounding tea.
4. Passage 1’s purpose is to compare Chinese and European relationships with tea, while Passage 2’s purpose is to describe the diffusion of tea culture in Europe.
12. Both passages support which generalization about tea?
1. Tea drinking in Europe is less ritualized than in China.
2. Coffee was once more popular in Europe than tea was.
3. India grows a great deal of tea.
4. Tea is a staple of European households.
1. Question 29—38 are based on the following passage.
2. The following passage is adapted from an article about the Spinosaurus, a theropod dinosaur that lived during the Cretaceous period.

 At long last, paleontologists have solved a century- old mystery, piecing together information discovered by scientists from different times and places.  The mystery began when, in 1911, German paleontologist Ernst Stromer discovered the first evidence of dinosaurs having lived in Egypt. Stromer, who expected to encounter fossils of early mammals, instead found bones that dated back to the Cretaceous period, some 97 to 112 million years prior. His finding consisted of three large bones, which he preserved and transported back to Germany for examination. After careful consideration, he announced that he had discovered a new genus of sauropod, or a large, four-legged herbivore with a long neck. He called the genus Aegyptosaurus, which is Greek for Egyptian lizard. One of these Aegyptosaurs, he claimed, was the Spinosaurus. Tragically, the fossils that supported his claim were destroyed during a raid on Munich by the Royal Air Force during World War II. The scientific world was left with Stromer’s notes and sketches, but no hard evidence that the Spinosaurus ever existed.  It was not until 2008, when a cardboard box of bones was delivered to paleontologist Nizar Ibrahim by a nomad in Morocco’s Sahara desert, that a clue to solving the mystery was revealed. Intrigued, Ibrahim took the bones to a university in Casablanca for further study. One specific bone struck him as interesting, as it contained a red line coursing through it. The following year, Ibrahim and his colleagues at Italy’s Milan Natural History Museum were looking at bones that resembled the ones delivered the year before. An important clue was hidden in the cross-section they were examining, as it contained the same red line Ibrahim had seen in Morocco. Against all odds, the Italians were studying bones that belonged to the very same skeleton as the bones Ibrahim received in the desert. Together, these bones make up the partial skeleton of the very first Spinosaurus that humans have been able to discover since Stromer’s fossils were destroyed.  Ibrahim and his colleagues published a study describing the features of the dinosaur, which point to the Spinosaurus being the first known swimming dinosaur. At 36 feet long, this particular Spinosaurus had long front legs and short back legs, each with a paddle-shaped foot and claws that suggest a carnivorous diet. These features made the dinosaur a deft swimmer and excellent hunter, able to prey on large river fish.  Scientists also discovered significant aquatic adaptations that made the Spinosaurus unique compared to dinosaurs that lived on land but ate fish. Similar to a crocodile, the Spinosaurus had a long snout, with nostrils positioned so that the dinosaur could breathe while part of its head was submerged in water. Unlike predatory land dinosaurs, the Spinosaurus had powerful front legs. The weight of these legs would have made walking upright like a Tyrannosaurus rex impossible, but in water, their strong legs gave the Spinosaurus the power it needed to swim quickly and hunt fiercely. Most notable, though, was the discovery of the Spinosaurus’s massive sail. Made up of dorsal spines, the sail was mostly meant for display.  Ibrahim and his fellow researchers used both modern digital modeling programs and Stromer’s basic sketches to create and mount a life-size replica of the Spinosaurus skeleton. The sketches gave them a starting point, and by arranging and rearranging the excavated fossils they had in their possession, they were able to use technology to piece together hypothetical bone structures until the mystery of this semiaquatic dinosaur finally emerged from the murky depths of the past.

3. Which of the following best summarizes the central idea of this passage?
1. Paleontologists were able to identify a new species of dinosaur after overcoming a series of obstacles.
2. Most dinosaur fossils are found in pieces and must be reconstructed using the latest technology.
3. The first evidence of the Spinosaurus was uncovered by German paleontologist Ernst Stromer.
4. Fossils of an aquatic dinosaur called the Spinosaurus were first found in Egypt in the early twentieth century.
4. Based on the information in the passage, the author would most likely agree that
1. aquatic dinosaurs were more vicious than dinosaurs that lived on land.
2. too much emphasis is placed on creating realistic models of ancient dinosaurs.
3. most mysteries presented by randomly found fossils are unlikely to be solved.
4. the study of fossils and ancient life provides important scientific insights.
5. Which choice provides the best evidence for the answer to the previous question?
1. Lines 13—15 (“After careful . . . long neck”)
2. Lines 53—56 (“Scientists also . . . fish”)
3. Lines 59—61 (“Unlike . . . front legs”)
4. Lines 72—78 (“The sketches . . . past”)
6. As used in line 37, the phrase “against all odds” most nearly means
1. by contrast.
2. at the exact same time.
3. to their dismay.
4. despite low probability.
7. The author uses the phrases “deft swimmer” and “excellent hunter” in line 51 to
1. produce a clear visual image of the Spinosaurus.
2. show how the Spinosaurus searched for prey.
3. create an impression of a graceful but powerful animal.
4. emphasize the differences between aquatic and land dinosaurs.
8. The information presented in the passage strongly suggests that Ibrahim
1. chose to go into the field of paleontology after reading Stromer’s work.
2. was familiar with Stromer’s work when he found the fossils with the red lines.
3. did not have the proper training to solve the mystery of the Spinosaurus on his own.
4. went on to study other aquatic dinosaurs after completing his research on the Spinosaurus.
9. Which choice provides the best evidence for the answer to the previous question?
1. Lines 24—27 (“It was . . . revealed”)
2. Lines 44—47 (“Ibrahim . . . swimming dinosaur”)
3. Lines 53—56 (“Scientists also . . . fish”)
4. Lines 69—72 (“Ibrahim and . . . skeleton”)
10. As used in line 76, “hypothetical” most nearly means
1. imaginary.
2. actual.
3. possible.
4. interesting.
11. Which statement best describes the relationship between Stromer’s and Ibrahim’s work with fossils?
1. Stromer’s work was dependent on Ibrahim’s work.
2. Stromer’s work was contradicted by Ibrahim’s work.
3. Ibrahim’s work built on Stromer’s work.
4. Ibrahim’s work copied Stromer’s work.
12. Which of the following is most similar to the methods used by Ibrahim to create a life-size replica of the Spinosaurus?
1. An architect using computer software and drawings to create a scale model of a building
2. A student building a model rocket from a kit in order to demonstrate propulsion
3. A doctor using a microscope to study microorganisms unable to be seen with the naked eye
4. A marine biologist creating an artificial reef in an aquarium to study fish
1. Questions 39—47 are based on the following passage and supplementary material.
2. The following passage is adapted from an essay about intricacies and implications of laughter.

 Today’s technology and resources enable people to educate themselves on any topic imaginable, and human health is one of particular interest to all. From diet fads to exercise trends, sleep studies to nutrition supplements, people strive to adopt healthier lifestyles. And while some people may as sociate diets and gym memberships with sheer enjoy ment, most of the population tends to think of per sonal healthcare as a necessary but time-consuming, energy-draining, less-than-fun aspect of daily life.  Yet for centuries, or perhaps for as long as conscious life has existed, sneaking suspicion has suggested that fun, or more accurately, funniness, is essential to human health. Finally, in recent years this notion, often phrased in the adage, “Laughter is the best medicine,” has materialized into scientific evidence.  When a person laughs, a chemical reaction in the brain produces hormones called endorphins. Other known endorphin-producing activities include exercise, physical pain, and certain food choices, but laughter’s appearance on this list has drawn increasing empirical interest. Endorphins function as natural opiates for the human body, causing what are more commonly referred to as “good feelings.” A boost of endorphins can thwart lethargy and promote the mental energy and positivity necessary to accomplish challenging tasks. Furthermore, recent data reveal that the laughter-induced endorphins are therapeutic and stress reducing.  This stress reduction alone indicates significant implications regarding the role of laughter in personal health. However, humor seems to address many other medical conditions as well. One study from Loma Linda University in California found that the act of laughing induced immediate and significant effects on senior adults’ memory capacities. This result was in addition to declines in the patients’ cortisol, or stress hormone, measurements. Another university study found that a mere quarter hour of laughter burns up to 40 calories. Pain tolerance, one group of Oxford researchers noticed, is also strengthened by laughter—probably due to the release of those same endorphins already described. And a group of Maryland scientists discovered that those who laugh more frequently seem to have stronger protection against heart disease, the illness that takes more lives annually than any other in America. Studies have shown that stress releases hormones that cause blood vessels to constrict, but laughter, on the other hand, releases chemicals that cause blood vessels to dilate, or expand. This dilation can have the same positive effects on blood flow as aerobic exercise or drugs that help lower cholesterol.  Already from these reputable studies, empirical data indicates that laughter’s health benefits include heart disease prevention, good physical exertion, memory retention, anxiety reduction, and pain resilience—not to mention laughter’s more self-evident effects on social and psychological wellness. Many believe that these findings are only the beginning; these studies pave the way for more research with even stronger evidence regarding the powerful healing and preventative properties of laughter. As is true for most fields of science, far more can be learned.  As for how laughter is achieved, these studies used various methods to provoke or measure laughter or humor. Some used comedy films or television clips; others chose humor-gauging questionnaires and social—or group—laughter scenarios. Such variance suggests that the means by which people incorporate laughter into their daily routine matters less than the fact that they do incorporate it. However, it should be said that humor shared in an uplifting community probably offers greater benefits than that found on a screen.  It is believed that young people begin to laugh less and less as they transition to adulthood. Time-pressed millennials might, in the interest of wellness, choose isolated exercise instead of social- or fun-oriented leisure activities. However, this growing pool of evidence exposes the reality that amusement, too, can powerfully nourish the health of both mind and body. Humor is no less relevant to well-being than a kale smoothie or track workout. But, then, some combination of the three might be most enjoyable (and, of course, beneficial) of all.

3. The author would most likely characterize the study findings mentioned in the passage as
1. irrelevant.
2. very promising.
3. inconclusive.
4. mildly interesting.
4. Which choice provides the best evidence for the answer to the previous question?
1. Lines 4—6 (“From diet . . . lifestyles”)
2. Lines 14—17 (“Finally, . . . evidence”)
3. Lines 18—19 (“When a person . . . endorphins”)
4. Lines 74—77 (“Such variance . . . incorporate it”)
5. Which statement best explains the relationship between endorphin production and mental outlook?
1. Increasing a person’s amount of endorphins encourages a positive state of mind.
2. The act of laughing produces endorphins, which can offer a person protection against heart disease.
3. Research indicates that chemical reactions in the brain produce endorphins.
4. If a person has more endorphins, he or she has a difficult time tolerating pain.
6. As used in line 57, “reputable” most nearly means
1. honorable.
2. distinguished.
3. celebrated.
4. credible.
7. Which of the following statements can be concluded from the passage?
1. Laughing alone or in the company of others benefits people’s health equally.
2. There is reason for optimism about future research into laughter’s health benefits.
3. Public support for the idea that laughter is healthy is somewhat limited.
4. Physical exercise is sufficient to maintain and improve mental health.
8. Which choice provides the best evidence for the answer to the previous question?
1. Lines 11—14 (“Yet for centuries, . . . health”)
2. Lines 32—35 (“This stress . . . well”)
3. Lines 63—67 (“Many believe . . . of laughter”)
4. Lines 87—91 (“Humor is . . . of all”)
9. Which reason best explains why the author chose to discuss the function of endorphins in lines 23—26 (“Endorphins . . . good feelings”)?
1. To reach a wider audience without a background in physiology
2. To support the claim that laughter affects an individual’s mental state
3. To show that laughter is one of several endorphin-producing activities
4. To demonstrate why scientists have an interest in studying laughter
10. As used in line 15, “adage” most nearly means
1. remark.
2. comment.
3. cliché.
4. proverb.
11. Which value shown on the graph most closely relates to the idea in line 78 that “humor shared in an uplifting community” increases resilience to pain?
1. —25
2. 0
3. 20
4. 75

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

Writing and Language Test

35 Minutes—44 Questions

This section corresponds to Section 2 of your answer sheet.

Directions

Each passage in this section is followed by several questions. Some questions will reference an underlined portion in the passage; others will ask you to consider a part of a passage or the passage as a whole. For each question, choose the answer that reflects the best use of grammar, punctuation, and style. If a passage or question is accompanied by a graphic, take the graphic into account in choosing your response(s). Some questions will have “NO CHANGE” as a possible response. Choose that answer if you think the best choice is to leave the sentence as written.

1. Questions 1—11 are based on the following passage.
2. From Here to the Stars

Gene Kranz hadn’t slept in ages. The flight director, pacing between rows of monitors in NASA’s Mission Control Center, an impossible problem weighing heavy in his weary mind: Three astronauts were operating a crippled spacecraft nearly 200,000 miles from Earth. And time was running out.

Kranz was no stranger to issues. After losing his father at an early age, Kranz turned to the stars for guidance—and found inspiration. His high school thesis was about the possibility of space travel; an idea that prompted Kranz to set a path for the stars. Kranz pursued a degree in aeronautical engineering after high school graduation. After the Wright brothers had pioneered powered, controlled flight only half a century earlier, aviation milestones like breaking the sound barrier changed the future of flight. Aeronautical engineering required a thorough understanding of physics—like lift and drag on wings—as well as proficiency in mathematics to determine maximum weight on an aircraft. After graduating from Saint Louis University’s Parks College of Engineering, Aviation, and Technology, Kranz piloted jets for the Air Force Reserve before performing research and development on missiles and rockets. Kranz later joined NASA and directed the successful Apollo 11 mission to the moon in 1969.

Without his unusual vest, no one would have noticed Kranz in the crowd. One year after the launch, the mood had drastically changed; there were no cheers, no celebratory pats on the back or teary-eyed congratulations. Coffee and adrenaline fueled the scientists and engineers communicating with the astronauts on Apollo 13. Kranz was easy to spot among the avalanche of moving bodies and shifting papers. He was dressed, as ever, in his signature handmade vest. The engineers looked to the calm man in the homemade vest.

Kranz’s wife, Marta, had begun making vests at his request in the early ’60s. Their was power in a uniform, something Kranz understood from his years serving overseas. The vests served not as an authoritative mark or sartorial flair, but a defining symbol for his team to rally behind. During the effort to save the Apollo 13 crew, Kranz wore his white vest around the clock like perspiration-mottled battle armor.

Among meetings and calculations, Kranz and the NASA staff hatched a wild plan. By using the gravitational force of the moon, it could slingshot the injured spacecraft back on an earthbound course. It was a long shot, of course, but also their best and only one. And, due to the tireless efforts of support staff on earth and the intrepid spirit of the Apollo 13 crew, it worked. Six days after takeoff, all three astronauts splashed down safely in the Pacific Ocean.

1. NO CHANGE
2. The flight director paced
3. The pacing flight director
4. The flight director pacing
1. NO CHANGE
2. adversity.
3. deadlines.
4. maladies.
1. NO CHANGE
2. space travel: an idea
3. space travel, an idea
4. space travel. An idea
1. NO CHANGE
2. physics; like lift and drag on wings, as well as proficiency
3. physics like lift and drag on wings, as well as proficiency
4. physics: like lift and drag on wings—as well as proficiency
7. Which sentence would serve as the most effective introduction to the paragraph?
1. NO CHANGE
2. During the mission, Kranz stood out as a pillar of strength in the chaos of the command center.
3. Kranz earned the badges of honor that now adorned his vest.
4. Kranz possessed more years of experience than anyone in the control center.
1. NO CHANGE
2. Among the avalanche of moving bodies and shifting papers, it is easy to spot Kranz.
3. Kranz easily spotted the avalanche of moving bodies and shifting papers.
4. Kranz is easy to spot among the avalanche of moving bodies and shifting papers.
9. Which sentence provides effective evidence to support the main focus of the paragraph?
1. NO CHANGE
2. Many of the men in the Mission Control Center had lengthy military careers.
3. Kranz’s thoughts returned to the many tribulations he had experienced.
4. Several engineers joined together as a bastion of calm in a sea of uncertainty.
1. NO CHANGE
2. They’re was
3. There was
4. They were
1. NO CHANGE
2. sanguine
3. military
4. martial
1. NO CHANGE
2. In spite of
3. Despite
4. Between
1. NO CHANGE
2. he
3. they
4. one
1. Questions 12—22 are based on the following passage.
2. The UK and the Euro

[1] The United Kingdom is a long-standing member of the European Union (EU), a multinational political organization and economic world leader elected over the course of the past half-century. [2] However, there is one key feature of the EU in which the UK does not participate; the monetary union known as the Eurozone, consisting of countries that share the euro as currency. [3] While the nation’s public opinion has remained generally supportive of that decision, evidence suggests that the euro’s benefits for the UK might, in fact, outweigh the risks. [4] When the EU first implemented the euro in 1999, intending to strengthen the collective economy across the union, Britain was permitted exclusion and continued using the pound instead. [5] This, UK leaders hoped, would shield Britain from financial dangers that the euro might suffer.

Proponents for avoiding the euro point to faltering economies in the Eurozone region throughout the Eurozone. To join a massive, multinational economy would involve surrendering taxable wealth from one’s own region to aid impoverished countries that may be some thousands of miles away. If a few economies in the Eurozone suffer, all of the participating nations suffer, too. Other proponents point to details of financial policy such as interest rates and territory responsibilities, fearing loss of agency and political traction. The UK’s taxable wealth would decrease if it assisted impoverished countries.

But complications loom: the UK’s current EU status may be untenable. In recent years, EU leaders seem to want to transition all members toward the Eurozone, for many reasons, this action appears necessary for protecting nations involved and ensuring the monetary union’s long-term success. These conditions may potentially force the UK to choose either the security of its multidecade EU membership, or the pound and all it entails for Britain’s economy. Enjoying both may not remain possible. The UK wants to maintain the pound as its currency.

[1] Regarding Britain’s intent to be protected from the Eurozone’s economic dangers, this hope never quite materialized. [2] The UK saw economic downturns of its own during the euro’s problematic years thus far. [3] Many families in the UK still struggle to pay their bills in the face of higher than normal unemployment rates. [4] It seems that regardless of shared currency, the economies of Britain and its Eurozone neighbors are too closely intertwined for one to remain unscathed by another’s crises.

Perhaps this question of economic security has been the wrong one. Due to Britain’s location and long-standing trade relationships with its neighbors, economies will continue to be somewhat reliant on each other, euro or not. Furthermore, political security, power, and protection bear more significance for the future. If the UK hopes to maintain and expand its influential presence in world leadership, its association and close involvement with greater Europe is invaluable. Considering that the euro probably offers a lower risk margin than many have supposed, the benefits of euro adoption: to secure EU membership and strengthen its cause, made Britain carefully reconsider.

1. NO CHANGE
2. determined
3. advanced
4. built
1. NO CHANGE
2. participate: the monetary
3. participate, the monetary
4. participate. The monetary
5. To make this paragraph most logical, sentence 3 should be placed
1. where it is now.
2. after sentence 1.
3. after sentence 4.
4. after sentence 5.
6. Which choice best completes the sentence?
1. NO CHANGE
2. to financial dangers that the euro might suffer.
3. to faltering economies in most if not all Eurozone countries.
4. to financial dangers and faltering economies in Eurozone countries throughout Europe.
7. Which statement most clearly communicates the main claim of the paragraph?
1. NO CHANGE
2. Economic independence from impoverished countries would still be possible.
3. The UK would take on significant economic risk if it adopted the euro as its currency.
4. Euro adoption would require subsequent economic assistance on the UK’s behalf.
1. NO CHANGE
2. toward the Eurozone. For many reasons,
3. toward the Eurozone, for many reasons.
4. toward the Eurozone. For many reasons.
9. Which sentence most effectively concludes the paragraph?
1. NO CHANGE
2. All EU members may soon have to accept the euro.
3. The UK faces a difficult decision regarding its EU membership.
4. All member nations want to ensure the success of the EU.
1. NO CHANGE
2. disparate
3. identical
4. relevant
11. Which sentence is least relevant to the central idea of this paragraph?
1. Sentence 1
2. Sentence 2
3. Sentence 3
4. Sentence 4
1. NO CHANGE
2. Or,
3. Also,
4. However,
1. NO CHANGE
2. adoption—to secure EU membership and strengthen its cause—
3. adoption: to secure EU membership and strengthen its cause—
4. adoption; to secure EU membership and strengthen its cause,
1. Questions 23—33 are based on the following passage.
2. Coffee: The Buzz on Beans

Americans love coffee. Some days you can find a coffee shop in nearly every American city. But this wasn’t always true. How did coffee, which was first grown in Africa over five hundred years ago, come to America?

The coffee plant, from which makers get the “cherries” that is dried and roasted into what we call beans, first appeared in the East African country Ethiopia, in the province of Kaffa. From there, it spread to the Arabian Peninsula, where the coffeehouse, or qahveh khaneh in Arabic, was very popular. Like spices and cloth, coffee was traded internationally as European explorers reached far lands and establishing shipping routes. The first European coffeehouse opened in Venice, Italy, in 1683, and not long after London displayed over three hundred coffeehouses.

There is no record of coffee being among the cargo of the Mayflower, which reached the New World in 1620. It was not until 1668 that the first written reference to coffee in America was made. The reference described a beverage made from roasted beans and flavored with sugar or honey and cinnamon. Coffee was then chronicled in the New England colony’s official records of 1670. In 1683, William Penn, who lived in a settlement on the Delaware River, wrote of buying supplies of coffee in a New York market, he paid eighteen shillings and nine pence per pound.

Coffeehouses like those in Europe were soon established in American colonies, and as America expanded westward, coffee consumption grew. In their settlement days, Chicago St. Louis and New Orleans each had famous coffeehouses. By the mid-twentieth century, coffeehouses were abundant. In places like New York and San Francisco, they became confused with counterculture, as a place where intellectuals and artists gathered to share ideas. In American homes, coffee was a social lubricant, bringing people together to socialize as afternoon tea had done in English society. With the invention of the electric coffee pot, it became a common courtesy to ask a guest if she wanted “coffee or tea?” “There were many coffee shops n New York and in Chicago.”

However, by the 1950s, U.S. manufacturing did to coffee what it had done to other foods; produced it cheaply, mass-marketed it, and lowered its quality. Coffee was roasted and ground in manufacturing plants and freeze-dried for a long storage life, which compromised its flavor. An “evangelism” began to bring back the original bracing, dark-roasted taste of coffee and spread quickly. In every major city of the world, now travelers around the world, expect to be able to grab an uplifting, fresh, and delicious cup of coffee—and they can.

1. NO CHANGE
2. Many
3. The
4. These
1. NO CHANGE
2. are being dried and roasted
3. are dried and roasted
4. is being dried and roasted
1. NO CHANGE
2. established
3. having established
4. was establishing
1. NO CHANGE
2. bragged
3. highlighted
4. boasted
1. NO CHANGE
2. New York market and William Penn
3. New York market so he paid
4. New York market, paying
8. Which choice best establishes a concluding sentence for the paragraph?
1. Coffee’s appearance in the historical record shows it was becoming more and more established in the New World.
2. The colonies probably used more tea than coffee because there are records of it being imported from England.
3. William Penn founded Pennsylvania Colony, which became the state of Pennsylvania after the Revolutionary War with England ended.
4. The Mayflower did carry a number of items that the colonists needed for settlement, including animals and tools.
1. NO CHANGE
2. Chicago, St. Louis, and New Orleans
3. Chicago, St. Louis, and, New Orleans
4. Chicago St. Louis and, New Orleans
1. NO CHANGE
2. related
3. associated
4. coupled
11. Which choice most effectively concludes the paragraph?
1. NO CHANGE
2. Electric coffee machines changed how people entertained at home.
3. Over time, it was clear that coffee had become a part of everyday American life.
4. People went to coffeehouses to discuss major issues.
1. NO CHANGE
2. other foods produced
3. other foods, produced
4. other foods: produced
1. NO CHANGE
2. Now travelers, in every major city of the world, around the world expect to be able to grab an uplifting, fresh, and delicious cup of coffee—and they can.
3. Now in every major city of the world, travelers around the world expect to be able to grab an uplifting, fresh, and delicious cup of coffee—and they can.
4. Now travelers around the world expect to be able to grab an uplifting, fresh, and delicious cup of coffee in every major city of the world—and they can.
1. Questions 34—44 are based on the following passage and supplementary material.
2. Predicting Nature’s Light Show

One of the most beautiful of nature’s displays is the aurora borealis, commonly known as the Northern Lights. As their informal name suggests, the best place to view this phenomenon is the Northern Hemisphere. How far north one needs to be to witness auroras depends not on conditions here on Earth, but on the Sun.

As with hurricane season on Earth, the Sun observes a cycle of storm activity, called the solar cycle, which lasts approximately 11 years. Also referred to as the sunspot cycle, this period is caused by the amount of magnetic flux that rises to the surface of the Sun, causing sunspots, or areas of intense magnetic activity. The magnetic energy is sometimes so great it causes a storm that explodes away from the Sun’s surface in a solar flare.

These powerful magnetic storms eject high-speed electrons and protons into space. Called a coronal mass ejection, this ejection is far more powerful than the hot gases the Sun constantly emits. The speed at which the atoms are shot away from the Sun is almost triple that of a normal solar wind. It takes this shot of energy one to three days to arrive at Earth’s upper atmosphere. Once it arrives, it is captured by Earth’s own magnetic field. It is this newly captured energy that causes the Northern Lights. Scientists and interested amateurs in the Northern Hemisphere use tools readily available to all in order to predict the likelihood of seeing auroras in their location at a specific time. One such tool is the Kp-Index, a number that determines the potential visibility of an aurora. The Kp-Index measures the energy added to Earth’s magnetic field from the Sun on a scale of 0-9, with 1 representing a solar calm and 5 or more indicating a magnetic storm, or solar flare. The magnetic fluctuations are measured in three-hour intervals (12 a.m. to 3 a.m., 3 a.m. to 6 a.m., and so on) so that deviations can be factored in and accurate data can be presented.

Magnetometers, tools that measure the strength of Earth’s magnetic field, are located around the world. When the energy from solar flares reaches Earth, the strength and direction of the energy is recorded by these tools and analyzed by scientists at the National Oceanic and Atmospheric Administration, who calculate the difference between the average strength of the magnetic field and spikes due to solar flares. They plot this information on the Kp-Index and update the public with information on viewing the auroras as well as other impacts solar flares may have on life on Earth. While solar flares can sometimes have negative effects on our communications systems and weather patterns, the most common effect is also the most enchanting: a beautiful light show, such as the solar flare that took place from 3 p.m. to 6 p.m. on September 11.

1. NO CHANGE
2. an
3. its
4. that
1. NO CHANGE
2. is through the Northern Hemisphere.
3. is over the Northern Hemisphere.
4. is in the Northern Hemisphere.
5. Which of the following would most strengthen the passage’s introduction?
1. A statement about the Kp-Index and other necessary tracking tools scientists use
2. A mention that the National Oceanic and Atmospheric Administration monitors solar flares
3. An explanation about why conditions on the Sun rather than on Earth affect the Northern Lights
4. A statement about what scientists think people should study before viewing auroras
1. NO CHANGE
2. experiences
3. perceives
4. witnesses
1. NO CHANGE
2. Interested scientists and amateurs
3. Scientists and amateurs interested
4. Scientists interested and amateurs
1. NO CHANGE
2. use tools for prediction
3. use specific tools to predict
4. use all tools readily available to predict
9. Which of the following, if added to this paragraph, would best support the author’s claims?
1. The speeds of normal solar winds and coronal mass ejections
2. The strength of Earth’s magnetic field
3. The temperature of normal solar wind
4. The definition of coronal mass ejection
1. NO CHANGE
2. are
3. will be
4. has been
1. NO CHANGE
2. update aurora viewing information
3. update information on viewing the auroras
4. update aurora viewing information for the public
1. NO CHANGE
2. However,
3. Since
4. Whereas
13. Which choice competes the sentence with accurate data based on the graphic?
1. NO CHANGE
2. 12 a.m. on September 11 to 3 a.m. on September 12.
3. 9 a.m. on September 10 to 12 p.m. on September 12.
4. 9 a.m. on September 11 to 12 a.m. on September 12.

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

Math Test

25 Minutes—17 Questions

1. NO-CALCULATOR SECTION

This section corresponds to Section 3 of your answer sheet.

Directions

For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding oval on the answer sheet. You may use any available space for scratch work.

Notes:

1. Calculator use is NOT permitted.
2. All numbers used are real numbers, and all variables used represent real numbers, unless otherwise indicated.
3. Figures are drawn to scale and lie in a plane unless otherwise indicated.
4. Unless stated otherwise, the domain of any function f is assumed to be the set of all real numbers x, for which f(x) is a real number.

Information:

• The sum of the degree measures of the angles in a triangle is 180.
• The number of degrees of arc in a circle is 360.
• The number of radians of arc in a circle is 2π.

2. What is the average rate of change for the line graphed in the figure above?

3. Which of the following could be the factored form of the equation graphed in the figure above?
0. 
1. 
2. 
3. 
4. Kinetic energy is the energy of motion. The equation represents the kinetic energy in joules of an object with a mass of m kilograms traveling at a speed of v meters per second. What is the kinetic energy in joules of an unmanned aircraft that has a mass of 2 × 10³ kilograms traveling at a speed of approximately 3 × 10³ meters per second?
0. 9 × 5⁹
1. 9 × 10⁸
2. 9 × 10⁹
3. 1.8 × 10¹⁰
5. 

In the equation above, what is the value of k ?

0. 
1. 
2. 
3. 
5. An environmental protection group had its members sign a pledge to try to reduce the amount of garbage they throw out by 3 percent each year. On the year that the pledge was signed, each person threw out an average of 1,800 pounds of garbage. Which exponential function could be used to model the average amount of garbage each person who signed the pledge should throw out each year after signing the pledge?
0. y = 0.97 × 1,800t
1. y = 1,800 × t^0.97
2. y = 1,800 × 1.97t
3. y = 1,800 × 0.97t

7. If the equation of the line shown in the figure above is written in the form , which of the following could be the value of m ?
0. −3
1. 
2. 
3. 3
8. If 4x² + 7x + 1 is multiplied by 3x + 5, what is the coefficient of x in the resulting polynomial?
0. 3
1. 12
2. 35
3. 38

9. The figure above shows worldwide unemployment rates from 2004 to 2013. Which of the following statements is true?
0. The graph is decreasing everywhere.
1. The graph is increasing from 2007 to 2010.
2. The graph is decreasing from 2004 to 2007 and from 2009 to 2011.
3. The graph is increasing from 2007 to 2010 and decreasing from 2011 to 2013.

10. The solution to which inequality is represented in the graph above?
0. 
1. 
2. 
3. 

11. If (a, b) is a solution to the equation above, what is the ratio , given that a ≠ 0 ?
0. −3
1. −2
2. 
3. 

12. If the system of linear equations above has no solution, and a is a constant, what is the value of a ?
0. 
1. 
2. 
3. 3
13. A taxi in the city charges $3.00 for the first mile, plus $0.25 for each additional mile. Eric plans to spend no more than $20.00 on a taxi ride around the city. Which inequality represents the number of miles, m, that Eric could travel without exceeding his limit?
0. 2.5 + 2m ≤ 20
1. 3 + 0.25m ≤ 20
2. 3 + 2m ≤ 20
3. 12 + 2m ≤ 20
14. A projectile is any moving object that is thrown near the Earth’s surface. The path of the projectile is called the trajectory and can be modeled by a quadratic equation, assuming the only force acting on the motion is gravity (no friction). If a projectile is launched from a platform 8 feet above the ground with an initial velocity of 64 feet per second, then its trajectory can be modeled by the equation h = —16t² + 64t + 8, where h represents the height of the projectile t seconds after it was launched. Based on this model, what is the maximum height in feet that the projectile will reach?
0. 72
1. 80
2. 92
3. 108

1. Directions

For questions 14—17, enter your responses into the appropriate grid on your answer sheet, in accordance with the following:

0. You will receive credit only if the circles are filled in correctly, but you may write your answers in the boxes above each grid to help you fill in the circles accurately.

1. Don't mark more than one circle per column.

2. None of the questions with grid-in responses will have a negative solution.

3. Only grid in a single answer, even if there is more than one correct answer to a given question.

4. A mixed number must be gridded as a decimal or an improper fraction. For example, you would grid as 7.5 or 15/2.

(Were you to grid it as , this response would be read as .)

5. A decimal that has more digits than there are places on the grid may be either rounded or truncated, but every column in the grid must be filled in order to receive credit.

2. If , what is the value of 9x + 10y ?
3. How many degrees does the minute hand of an analog clock rotate from 3:20 p.m. to 3:45 p.m.?

4. What is the exponent on x when the expression above is written in simplest form?
5. An exponential function is given in the form f(x) = a • b x. If f(0) = 3 and f(1) = 15, what is the value of f(—2) ?

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

Math Test

45 Minutes—31 Questions

1. CALCULATOR SECTION

This section corresponds to Section 4 of your answer sheet.

Directions

For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding oval on the answer sheet. You may use any available space for scratch work.

Notes:

1. Calculator use is permitted.
2. All numbers used are real numbers, and all variables used represent real numbers, unless otherwise indicated.
3. Figures are drawn to scale and lie in a plane unless otherwise indicated.
4. Unless stated otherwise, the domain of any function f is assumed to be the set of all real numbers x for which f (x) is a real number.

Information:

• The sum of the degree measures of the angles in a triangle is 180.
• The number of degrees of arc in a circle is 360.
• The number of radians of arc in a circle is 2π.
1. A home improvement store that sells carpeting charges a flat installation fee and a certain amount per square foot of carpet ordered. If the total cost for f square feet of carpet is given by the function C(f ) = 3.29f + 199, then the value 3.29 best represents which of the following?

0. The installation fee
1. The cost of one square foot of carpet
2. The number of square feet of carpet ordered
3. The total cost not including the installation fee

3. The United States Constitution requires that any candidate for the presidency be at least 35 years of age, although no president to date has been that young. The figure above shows the distribution of the ages of the presidents through 2012 at the time they were inaugurated. Based on the information shown, which of the following statements is true?
0. The shape of the data is skewed to the left, so the mean age of the presidents is greater than the median.
1. The shape of the data is fairly symmetric, so the mean age of the presidents is approximately equal to the median.
2. The data has no clear shape, so it is impossible to make a reliable statement comparing the mean and the median.
3. The same number of 55-or-older presidents have been inaugurated as ones who were younger than 55, so the mean age is exactly 55.

4. Which value of x satisfies the equation above?
0. —5
1. —3
2. —1
3. 1

5. The following quadratic equations are all representations of the graph shown above. Which equation could you use to find the minimum value of the function without doing any additional work?
0. 
1. 
2. 
3. 
6. Marion is a city planner. The city she works for recently purchased new property on which it plans to build administrative offices. Marion has been given the task of sizing the lots for new buildings, using the following guidelines:

• The square footage of each lot should be greater than or equal to 3,000 square feet, but less than or equal to 15,000 square feet.
• Each lot size should be at least 30 percent greater in area than the size before it.
• To simplify tax assessment calculations, the square footage of each lot must be a multiple of 1,000 square feet.

Which list of lot sizes meets the city guidelines and includes as many lots as possible?

3. 3,000; 5,000; 10,000; 15,000
4. 3,000; 4,500; 6,000; 7,500; 10,000; 15,000
5. 3,000; 4,000; 6,000; 8,000; 11,000; 15,000
6. 3,000; 3,900; 5,100; 6,600; 8,600; 11,200; 14,600
6. One function of the Environmental Protection Agency (EPA) is to reduce air pollution. After implementing several pollution reduction programs in a certain city, EPA calculated that the air pollution should decrease by approximately 8 percent each year. What kind of function could be used to model the amount of air pollution in this city over the next several years, assuming no other significant changes?
0. A linear function
1. A quadratic function
2. A polynomial function
3. An exponential function
7. Escape velocity is the speed that a traveling object needs to break free of a planet or moon’s gravitational field without additional propulsion (for example, without using fuel). The formula used to calculate escape velocity is  , where G represents the universal gravitational constant, m is the mass of the body from which the object is escaping, and r is the distance between the object and the body’s center of gravity. Which equation represents the value of r in terms of v, G, and m ?
0. 
1. 
2. 
3. 
8. A movie rental kiosk dispenses DVDs and Blu-rays. DVDs cost $2.00 per night and Blu-rays cost $3.50 per night. Between 5 p.m. and 9 p.m. on Saturday, the kiosk dispensed 209 movies and collected $562.00. Solving which system of equations would yield the number of DVDs, d, and the number of Blu-rays, b, that the kiosk dispensed during the 4-hour period?
0. 
1. 
2. 
3. 
9. The United States Senate has two voting members for each of the 50 states. The 113th Congress had a 4:1 male-to-female ratio in the Senate. Forty-five of the male senators were Republican. Only 20 percent of the female senators were Republican. How many senators in the 113th Congress were Republican?
0. 20
1. 49
2. 55
3. 65
10. According to the Project on Student Debt prepared by The Institute for College Access and Success, 7 out of 10 students graduating in 2012 from a four-year college in the United States had student loan debt. The average amount borrowed per student was $29,400, which is up from $18,750 in 2004. If student debt experiences the same total percent increase over the next eight years, approximately how much will a college student graduating in 2020 owe, assuming he takes out student loans to pay for his education?
0. $40,100
1. $44,300
2. $46,100
3. $48,200
11. Annalisa has 10 beanbags to throw in a game. She gets 7 points if a beanbag lands in the smaller basket and 3 points if it lands in the larger basket. If she gets b beanbags into the larger basket and the rest into the smaller basket, which expression represents her total score?
0. 3b
1. 3b + 7
2. 30 + 4b
3. 70 — 4b
1. Questions 12 and 13 refer to the following information.
2. In a 2010 poll, surveyors asked registered voters in four different New York voting districts whether they would consider voting to ban fracking in the state. Hydraulic fracturing, or “fracking,” is a mining process that involves splitting rocks underground to remove natural gas. According to ecologists, environmental damage can occur as a result of fracking, including contamination of water. The results of the 2010 survey are shown in the following table.

3. According to the data, which district had the smallest percentage of voters with no opinion on fracking?
0. District A
1. District B
2. District C
3. District D
4. A random follow-up survey was administered to 500 of the respondents in District C. They were asked if they planned to vote in the next election. The follow-up survey results were 218 said they planned to vote, 174 said they did not plan to vote, and 108 said they were unsure. Based on the data from both the initial survey and the follow-up survey, which of the following is most likely an accurate statement?
0. Approximately 19,000 people in District C who support a ban on fracking can be expected to vote in the next election.
1. Approximately 21,000 people in District C who support a ban on fracking can be expected to vote in the next election.
2. Approximately 43,000 people in District C who support a ban on fracking can be expected to vote in the next election.
3. Approximately 48,000 people in District C who support a ban on fracking can be expected to vote in the next election.

5. Based on the system of equations above, what is the value of the sum of x and y ?
0. 
1. 3
2. 
3. 4

6. Ian, Mae, and Jin bowled five games during a bowling tournament. The table above shows their scores. According to the data, which of the following conclusions is correct?
0. Ian bowled the most consistently because the mean of his scores is the highest.
1. Mae bowled the least consistently because the standard deviation of her scores is the lowest.
2. Mae bowled the most consistently because the standard deviation of her scores is the lowest.
3. Jin bowled the most consistently because the standard deviation of his scores is the highest.
7. Which of the following are solutions to the quadratic equation (x + 3)² = 16 ?
0. x = —19 and x = 13
1. x = —7 and x = 1
2. x = —1 and x = 1
3. x = —1 and x = 7
8. An architect is building a scale model of the Statue of Liberty. The real statue measures 305 feet, 6 inches from the bottom of the base to the tip of the torch. The architect plans to make her model 26 inches tall. If Lady Liberty’s nose on the actual statue is 4 feet, 6 inches long, how long in inches should the nose on the model be?
0. 
1. 
2. 
3. 
9. If f(x) = 3x + 5, what is f(6) — f(2) ?
0. 11
1. 12
2. 17
3. 23

10. The United States Fish and Wildlife Service classifies animals whose populations are at low levels as either threatened or endangered. Endangered species are animals that are currently on the brink of extinction, whereas threatened species have a high probability of being on the brink in the near future. Since 1990, the Northern Spotted Owl has been listed as threatened. The figure above shows the populations of the Northern Spotted Owl in a certain region in Oregon from 1994 to 2014. Based on the line of best fit shown in the figure, which of the following values most accurately reflects the average change per year in the number of Northern Spotted Owls?
0. —25
1. —0.04
2. 0.04
3. 25
11. The x-coordinates of the solutions to a system of equations are — 4 and 2. Which of the following could be the system?
0. 
1. 
2. 
3. 

12. The White-footed Mouse, named for its darker body fur and white feet, is primarily found on the east coast of the United States, living in warm, dry forests and brushland. A scientist in Virginia studied a sample of 200 white-footed mice to see how many offspring they had per birth. The results of the study are recorded in the figure above. Based on the data, given a population of 35,000 female white-footed mice living in Virginia, how many would you expect to have a litter of seven or more pups?
0. 3,325
1. 4,375
2. 7,700
3. 15,400
13. Human beings have a resting heart rate and an active heart rate. The resting heart rate is the rate at which the heart beats when a person is at rest, engaging in no activity. The active heart rate rises as activity rises. For a fairly active woman in her 20s, eight minutes of moderate exercise results in a heart rate of about 90 beats per minute. After 20 minutes, the same woman’s heart rate will be about 117 beats per minute. If the human heart rate increases at a constant rate as the time spent exercising increases, which of the following linear models represents this same woman’s heart rate, r, after t minutes of moderate exercise?
0. r = 0.15t — 5.3
1. r = 0.44t — 32
2. r = 2.25t + 72
3. r = 6.75t + 36
14. Chantal buys new furniture using store credit, which offers five-year, no-interest financing. She sets up a payment plan to pay the debt off as soon as possible. The function 40x + y = 1,400 can be used to model her payment plan, where x is the number of payments Chantal has made and y is the amount of debt remaining. If a solution to the equation is (21, 560), which of the following statements is true?
0. Chantal pays $21 per month.
1. Chantal pays $560 per month.
2. After 21 payments, $560 remains to be paid.
3. After 21 payments, Chantal will have paid off $560 of the debt.

15. Which of the following equations best represents the trend of the data shown in the figure above?
0. y = —2.4x + 30
1. y = —1.2x + 40
2. y = —0.8x + 40
3. y = —0.4x + 36
16. The graph of f(x) passes through the point (5, 1). Through which point does the graph of —f(x + 3) — 2 pass?
0. (—2, —1)
1. (2, —3)
2. (2, 1)
3. (8, —3)
17. When a certain kitchen appliance store decides to sell a floor model, it marks the retail price of the model down 25 percent and puts a “Floor Model Sale” sign on it. Every 30 days after that, the price is marked down an additional 10 percent until it is sold. The store decides to sell a floor model refrigerator on January 15th. If the retail price of the refrigerator was $1,500 and it is sold on April 2nd of the same year, what is the final selling price, not including tax?
0. $820.13
1. $825.00
2. $911.25
3. $1,012.50
18. When New York City built its 34th Street subway station, which has multiple underground levels, it built an elevator that runs along a diagonal track approximately 170 feet long to connect the upper and lower levels. The angle formed between the elevator track and the bottom level is just under 30 degrees. What is the approximate vertical distance in feet between the upper and lower levels of the subway station?
0. 85
1. 98
2. 120
3. 147

1. Directions

For questions 28—31, enter your responses into the appropriate grid on your answer sheet, in accordance with the following:

0. You will receive credit only if the circles are filled in correctly, but you may write your answers in the boxes above each grid to help you fill in the circles accurately.

1. Don’t mark more than one circle per column.

2. None of the questions with grid-in responses will have a negative solution.

3. Only grid in a single answer, even if there is more than one correct answer to a given question.

4. A mixed number must be gridded as a decimal or an improper fraction. For example, you would grid as 7.5 or .

(Were you to grid it as , this response would be read as .)

5. A decimal that has more digits than there are places on the grid may be either rounded or truncated, but every column in the grid must be filled in order to receive credit.

2. The table above shows the seating configuration for several commercial airplanes. The day before a particular flight departs, a travel agent books the last seat available for a client. If the seat is on one of the two Boeing 777s, what is the probability that the seat is a Business Class seat, assuming that all seats have an equal chance of being the last one available?
3. Heating water accounts for a good portion of the average home’s energy consumption. Tankless water heaters, which run on natural gas, are about 22 percent more energy efficient on average than electric hot water heaters. However, a tankless hot water heater typically costs significantly more. Suppose one tankless water heater costs $160 more than twice as much as a conventional hot water heater. If both water heaters cost $1,000 together, how many more dollars does the tankless water heater cost than the conventional one?
4. Questions 30 and 31 refer to the following information.
5. 

Daniel works for a pest control company and is spraying all the lawns in a neighborhood. The figure above shows the layout of the neighborhood and the times that Daniel started spraying the lawns at two of the houses. Each lawn in the neighborhood is approximately 0.2 acres in size and takes the same amount of time to spray.

6. How many minutes will it take Daniel to spray all of the lawns in the neighborhood?
7. Daniel uses a mobile spray rig that holds 20 gallons of liquid. It takes 1 gallon to spray 2,500 square feet of lawn. How many times, including the first time, will Daniel need to fill the spray rig, assuming he fills it to the very top each time? (Note: 1 acre = 43,560 square feet.)

If you finish before time is called, you may check your work on this section only. Do not turn to any other section in the test.

Answer key

READING TEST

1. C
2. D
3. A
4. C
5. D
6. A
7. D
8. A
9. D
10. D
11. D
12. A
13. C
14. D
15. B
16. B
17. D
18. C
19. A
20. C
21. B
22. C
23. A
24. C
25. D
26. B
27. A
28. D
29. A
30. D
31. B
32. D
33. C
34. B
35. D
36. C
37. C
38. A
39. B
40. B
41. A
42. D
43. B
44. C
45. B
46. D
47. D

Answer key

WRITING AND LANGUAGE TEST

1. B
2. B
3. C
4. A
5. B
6. A
7. A
8. C
9. A
10. D
11. C
12. D
13. B
14. D
15. B
16. C
17. B
18. C
19. A
20. C
21. D
22. B
23. D
24. C
25. B
26. D
27. D
28. A
29. B
30. C
31. C
32. D
33. D
34. C
35. D
36. C
37. B
38. B
39. C
40. A
41. B
42. B
43. A
44. D

Answer key

MATH TEST—NO-CALCULATOR

1. B
2. D
3. C
4. B
5. D
6. C
7. D
8. C
9. A
10. C
11. D
12. A
13. A
14. 144
15. 150
16. 8
17. 3/25 or .12

Answer key

MATH TEST—CALCULATOR

1. B
2. B
3. A
4. A
5. C
6. D
7. A
8. D
9. B
10. C
11. D
12. D
13. A
14. B
15. C
16. B
17. C
18. B
19. A
20. D
21. C
22. C
23. C
24. D
25. B
26. C
27. A
28. 1/6 or .166 or .167
29. 440
30. 252
31. 4

Answers and explanations

READING TEST

1. Suggested passage map notes:
• ¶1: Gregor woke up not himself
• ¶2: description of Gregor’s room, job
• ¶3: thought sleep would make him normal, couldn’t roll over
• ¶4: thought job stress was to blame for how he was
• ¶5: thinks he needs more sleep, wants more luxury but has to help parents
2. C

Difficulty: Easy

Category: Detail

Getting to the Answer: Skim the passage to locate Gregor’s first reaction to his transformation. The first sentence states that Gregor woke “from troubled dreams.” He only realizes “it wasn’t a dream” (lines 11—12) after he has examined his new body and looked around his room to orient himself. Choice (C) is the correct answer. “Nightmare” describes a dream that is “troubled.”

3. D

Difficulty: Hard

Category: Vocab-in-Context

Getting to the Answer: Use context clues and tone to help determine the meaning of the word. Use the surrounding text to paint a mental picture of descriptive words. Finally, make sure the answer choice does not alter the meaning of the sentence when inserted. The paragraph in which the word appears describes an average room appropriate for a person. Therefore, (D) is the correct answer. “Proper” means “suitably appropriate” in this context.

4. A

Difficulty: Medium

Category: Inference

Getting to the Answer: Look for Gregor’s thoughts and statements about work. Use this as evidence of his attitude. Paragraphs 4 and 5 are essentially rants about Gregor’s dissatisfaction with his job. He dislikes travelling, feels that he works much harder than others, and expresses anger toward his boss. Gregor feels that it is unfair that other salesmen have a life of “luxury” while he has to wake up early. Choice (A) is the correct answer. Gregor is resentful and bitter about his job.

5. C

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Review your answer to the previous question. Decide which lines of text give clues to how Gregor feels about his job. Choice (C) offers the best support. These lines describe Gregor’s bitterness and the unfairness he perceives. He feels he works much harder than the other salesmen, but that he would be fired if he asked for better treatment or less work.

6. D

Difficulty: Hard

Category: Global

Getting to the Answer: Ask yourself what purpose the author has in writing the passage. What main point does the majority of the excerpt support? The events in the passage show that despite a dramatic physical transformation, Gregor still plans to go to work. Gregor consistently expresses unhappiness and bitterness about his job but ignores his transformation into an insect because he feels he must still go to work or he will be fired. In this situation, (D) is the correct answer. Gregor’s duty to his job overrides reason and sense when he plans to attend work despite the physical transformation that has left him inhuman and helpless.

7. A

Difficulty: Medium

Category: Inference

Getting to the Answer: Reread the text, looking for evidence to support each of the answer choices. Examine Gregor’s thoughts and statements for clues about his personality. Based on Gregor’s statements about his work, it is clear that he continues to work at a job he dislikes in order to support his parents. He largely ignores his physical transformation, and there is no evidence as to whether he excels at his work. Choice (A) is the correct answer.

8. D

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Review your answer to the previous question. Read each choice and figure out which one provides specific support for that answer. Choice (D) provides the best support. These lines show that Gregor thinks it may be best to quit the job he hates, but he will continue to work until he can pay off his parents’ debt.

9. A

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Use context clues from the target sentence and surrounding sentence. Predict the meaning of the word and look for a match in the answer choices. Gregor is attempting to turn over in his bed, but finds his legs and body are useless and unable to turn him over into his preferred position. Choice (A) is the nearest match to the meaning of “floundering” in this context.

10. D

Difficulty: Medium

Category: Function

Getting to the Answer: Contrast Gregor’s thoughts with the dark tone of the rest of the excerpt. Think about how this phrase adds to or supports the interpretations you made in previous questions. The author ends the excerpt with Gregor completely disregarding the fact that he is now an insect. Gregor plans to go to work as he always does, and the author draws attention to the absurdity of this decision. Choice (D) is the correct choice. The author uses the matter-of-fact tone in the sentence to emphasize that Gregor will ignore his physical condition and go to work because he has such a strong sense of duty to his family.

11. Suggested passage map notes:
• ¶1—3: women are equal and deserve to be treated as such
• ¶4: what freedom is
• ¶5—6: history of women fighting for equality
• ¶7—8: men and women do great things when they work together
• ¶9—13: must help women in other countries achieve equality and fight discrimination
12. D

Difficulty: Easy

Category: Global

Getting to the Answer: Consider the word choices Clinton uses throughout her speech. Notice any recurring themes. Choice (D) is the correct answer. Clinton says that working to improve the lives of women will improve others’ lives as well.

13. D

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Beware of answer choices that are only vaguely related to Clinton’s point. The correct answer will follow her purpose closely. Clinton indicates that women’s rights issues affect more than just women. Choice (D) is the best fit. These lines from the text provide concrete examples of how improving the lives of women improves their families’ lives as well.

14. A

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Sometimes you can recognize similarities between the word in question and a more familiar word. “Divisive” is similar to “divide” and “division,” both of which have to do with things being split or made separate. Clinton is saying that though suffrage produced great conflict and divided people more than other philosophical wars, it was “bloodless.” Choice (A) is correct; “divisive” means “conflict-producing.”

15. C

Difficulty: Hard

Category: Inference

Getting to the Answer: You’re being asked to decide which statement Clinton is most likely to agree with. Because the statement isn’t explicitly mentioned in the speech, you must infer, or make a logical guess, based on information in the speech. Clinton states that the world would be improved if women were able to contribute more. She provides specific examples of her vision for an improved world. Choice (C) is correct as it suggests that if women did not experience discrimination and had more power, the world would be better off.

16. D

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Try paraphrasing the answer you chose for the previous test item. Then, decide which quote from the speech supports this idea. Choice (D) provides the best evidence. This quote notes that women are discriminated against and that it is not just women who suffer from this discrimination; there are global problems that could benefit from women’s ideas.

17. B

Difficulty: Hard

Category: Vocab-in-Context

Getting to the Answer: A word like “organized” can have several meanings, depending on the context. Beware of choosing the most common meaning, as it may not fit this situation. Choice (B) successfully conveys the idea of the women’s suffrage movement being one in which many different people worked together over a long period of time.

18. B

Difficulty: Hard

Category: Detail

Getting to the Answer: Be careful to assess not only what topics are mentioned but also how Clinton discusses them. Choice (B) is supported by the passage, which claims in lines 6—8: “Women must enjoy the right to participate fully in the social and political lives of their countries if we want freedom and democracy to thrive and endure.”

19. D

Difficulty: Medium

Category: Detail

Getting to the Answer: Notice how the stem of the question doesn’t ask you to find evidence for an argument; it instead gives you the evidence (the example of V-J Day) and then asks you to figure out what argument this evidence supports. Choice (D) is correct. Clinton mentions V-J Day as an example of something that resulted from cooperation between men and women.

20. C

Difficulty: Medium

Category: Function

Getting to the Answer: Notice how the question is asking you to figure out how the paragraph functions in relation to other parts of the speech. Clinton goes into specific detail in this paragraph to provide examples of freedom. She very specifically states what she means by freedom and accuses some of failing to respect others’ freedom. Therefore, (C) is the correct answer.

21. Suggested passage map notes:

Passage 1

• ¶1: history of tea, Europe and China
• ¶2: tea not received well in Europe at first
• ¶3: China controlled tea production
• ¶4: Europe wanted to produce tea
• ¶5: finally had tea growing success in India

Passage 2

• ¶1: history of tea time in Europe
• ¶2: tea in France served with savory
• ¶3: tea in Germany served with sweet
• ¶4: tea in Russia sign of class
• ¶5: tea in GB
21. A

Difficulty: Medium

Category: Inference

Getting to the Answer: Be careful to choose an answer that is clearly supported by the information in the passage. The passage states that the climate was not right for growing tea “even in the equatorial colonies” (line 28). Choice (A) is the correct answer. Clearly, European tea-drinking nations tried to grow tea in their equatorial colonies; that’s how they learned that the climate there wasn’t right.

23. C

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: The correct answer will be the reason you were able to make the inference in the previous question. Choice (C) works logically. Europeans knew that tea would not grow well in their colonies; this leads to the conclusion that they tried.

24. B

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: You should be able to replace the original word with the correct answer in the sentence. The passage states that in order to “circumvent” the monopoly, European growers tried growing their own tea. It makes sense that Europeans’ attempt at growing their own tea was a way to “get around” the Chinese monopoly. Therefore, (B) is the best choice.

25. C

Difficulty: Hard

Category: Inference

Getting to the Answer: Keep in mind that the graphic focuses on tea consumption, not tea production. The last paragraph of Passage 1 describes Britain’s great success growing tea in India, which resulted in great increases in the amount of tea arriving in London. Therefore, (C) sis a reasonable conclusion that may be drawn by synthesizing information in Passage 1 and the graphic.

26. A

Difficulty: Hard

Category: Inference

Getting to the Answer: Be careful to deduce only information that can reasonably be inferred from the passage. It can logically be inferred that hosting guests in Russia generally involves tea. Passage 2 emphasizes that Russian hosts are judged based on the strength of their tea, and that Russians have elaborate tea-making equipment. Choice (A) is the correct answer.

27. C

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Identify the country associated with the correct answer to the previous question and see what evidence fits. The passage states that Russian tea ceremonies are highly formal and that hosts are judged on their tea making. Choice (C) is the correct answer. The referenced lines support the conclusions about Russia.

28. D

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Look for other words in this sentence that offer clues to the word’s meaning. A noble, or high-ranking, class is likely to have associations with formalism, so (D) is the correct answer.

29. B

Difficulty: Easy

Category: Inference

Getting to the Answer: Make sure to compare only the two countries being asked about. Choice (B) is correct. The passage notes that cookies and cakes are served with tea in Germany, while foods served with tea in France are “savory” and include puff pastry with cheese.

30. A

Difficulty: Easy

Category: Inference

Getting to the Answer: Look for true statements about Passage 1. Then, do the same for Passage 2. Choice (A) is correct. Passage 1 focuses on an earlier period in European history, while Passage 2 compares different cultures within Europe.

31. D

Difficulty: Medium

Category: Inference

Getting to the Answer: For this question, you’re looking for a statement that is reflected in both passages. Choice (D) is the only choice supported by both passages.

32. Suggested passage map notes:
• ¶1: Stromer discovered dinosaur fossils in Egypt, new genus, fossils destroyed in WWII, notes and sketches survived
• ¶2: Ibrahim rediscovered similar fossils, able to make partial skeleton
• ¶3: description of Spinosaurus
• ¶4: Spino unique—lived on land, hunted in water
• ¶5: Ibrahim used digital model and Stromer sketches to create replica
33. A

Difficulty: Easy

Category: Global

Getting to the Answer: Look for the answer choice that describes an important idea that is supported throughout the text rather than a specific detail. The passage is mostly about how the mystery of the Spinosaurus fossils was decoded. Choice (A) is the best summary of the central idea of the passage.

34. D

Difficulty: Medium

Category: Inference

Getting to the Answer: Think about the overall message of the passage and consider why the author would choose to write about this topic. The author’s tone, or attitude, toward the topic of the passage demonstrates the point of view that the study of fossils and ancient life has value. Choice (D) is the correct answer. The evidence in the passage supports the idea that the author thinks the study of fossils and ancient life is important.

35. B

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Some answer choices may seem important. However, if they don’t support your answer to the previous question, they aren’t what you should choose. Choice (B) is correct. The author’s use of the word “significant” in this quote shows that he or she thinks the study of fossils and ancient life is important.

36. D

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Though more than one answer choice might seem acceptable, one comes closest to meaning the same as the phrase in question. Earlier in the paragraph, the author explains that two different bones gathered at different times both had a red line coursing through them. This means that the bones were from the same animal. Choice (D) fits best. “Against all odds” most nearly means “despite low probability.”

37. C

Difficulty: Medium

Category: Function

Getting to the Answer: Be careful to avoid answers that don’t make sense in the context of the paragraph. These phrases help the author describe the animal in a generally positive way. Choice (C) is the correct answer.

38. B

Difficulty: Hard

Category: Inference

Getting to the Answer: Be careful of answers that make sense but are not implied by the information presented in the passage. Choice (B) is correct. The passage does not explicitly state how Ibrahim became familiar with Stromer’s work, but it is implied that he was familiar with Stromer’s work when he found the fossils with the red lines and used Stromer's sketches to aid with the modern digital models as mentioned in the last paragraph.

39. D

Difficulty: Hard

Category: Command of Evidence

Getting to the Answer: Eliminate any answer choices that have nothing to do with your answer to the previous question. Choice (D) is correct. It directly supports the inference that Ibrahim was familiar with Stromer’s work, showing that he used Stromer’s sketches to aid in creating his life-size replica of the Spinosaurus.

40. C

Difficulty: Easy

Category: Vocab-in-Context

Getting to the Answer: Ibrahim and his fellow researchers didn’t know how the bones went together. They were making an educated guess with the help of technology and Stromer’s sketches. Choice (C) is correct. “Hypothetical” in this sentence means “possible.”

41. C

Difficulty: Easy

Category: Inference

Getting to the Answer: Think about the order in which Stromer and Ibrahim’s work with the fossils occurred. Choice (C) is correct. Ibrahim used Stromer’s sketches to create his models of the Spinosaurus. He built on Stromer’s work to complete his own.

42. A

Difficulty: Hard

Category: Inference

Getting to the Answer: Think about the process described in each answer choice and compare it to how Ibrahim went about building his replica of the Spinosaurus. Choice (A) is the correct choice. An architect creating a model of a building would use tools and methods similar to those used by Ibrahim, such as drawings and digital technologies.

43. Suggested passage map notes:
• ¶1: people willing to try anything to be healthy
• ¶2: laughter important part of health
• ¶3: what happens to body when you laugh
• ¶4: humor helps many medical conditions, laugh more = better health
• ¶5: benefits of laughter
• ¶6: various methods to provoke laughter, best achieved in person, not through watching shows
• ¶7: laughter decreases with age
44. B

Difficulty: Easy

Category: Inference

Getting to the Answer: When a question asks you about the point of view of an author, look for words and phrases in the passage that hint at the author’s feelings or attitude toward the topic. Choice (B) is the correct answer because the author speaks quite positively of the studies throughout the passage.

45. B

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Reread each quote in the context of the passage. Consider which one is the best evidence of the author’s point of view toward laughter research. The word “finally” in line 14 helps demonstrate that the author finds laughter research worthwhile. Choice (B) is the best answer.

46. A

Difficulty: Medium

Category: Inference

Getting to the Answer: Think about the connection the passage makes between laughter and the ability to accomplish challenging tasks. Choice (A) is correct. The passage notes that endorphin production is associated with “mental energy and positivity” (lines 27—28).

47. D

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Notice that all of the answer choices are related to the word “reputable,” but the correct answer will reflect the specific context in which the word is used. “Reputable” in this case indicates that the studies are official and are based on empirical data (data based on observation and experiment). This makes (D), “credible,” the correct choice.

48. B

Difficulty: Hard

Category: Inference

Getting to the Answer: Eliminate any answer choices that are not suggested in the passage. Choice (B) is correct because early results of studies into laughter and health all seem to strengthen the relationship between the two.

49. C

Difficulty: Medium

Category: Command of Evidence

Getting to the Answer: Avoid answer choices like (D) that may not support a general conclusion you could take from the passage. Choice (C) is the correct answer. The author expects future research will yield stronger evidence in support of laughter’s health benefits.

50. B

Difficulty: Hard

Category: Function

Getting to the Answer: Look at the verbs provided in each of the answer choices. Decide whether the author wanted to “reach,” “support,” “justify,” or “show” by discussing the function of endorphins. After asserting that laughter produces endorphins, the author explains their function in order to help the reader understand why a positive mental state may result. Choice (B) is the correct answer.

51. D

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Look carefully at the paragraph’s context to help you decide on the correct answer choice. The phrase “Laughter is the best medicine” (lines 15—16) is an example of an adage, or proverb. Therefore, (D) is correct.

52. D

Difficulty: Hard

Category: Inference

Getting to the Answer: Decide whether the phrase “uplifting community” is a reference to a person alone or a group of people. Choice (D) is correct. The graph shows that shared humor with others most significantly increased pain tolerance in individuals.

WRITING AND LANGUAGE TEST

1. B

Difficulty: Medium

Category: Sentence Structure: The Basics

Getting to the Answer: Read the sentence and determine whether it is grammatically complete. To form a grammatically complete sentence, you must have an independent clause prior to a colon. As written, the text that comes before the colon is not grammatically complete because it lacks an independent clause with a subject and predicate. Choice (B) correctly adds a verb to the clause before the comma. It also correctly uses the past tense to match with the tense of “hadn’t” in the first sentence of the passage.

2. B

Difficulty: Medium

Category: Development: Precision

Getting to the Answer: Read the sentences surrounding the word to look for context clues. Watch out for near synonyms that are not quite correct. The word “issues” is not precise and does a poor job of conveying the meaning of the sentence. A better word, such as (B), “adversity,” more precisely conveys hardship, difficulties, or painful situations.

3. C

Difficulty: Medium

Category: Sentence Structure: The Basics

Getting to the Answer: Determine whether a clause is independent or dependent to decide between a comma and a semicolon. The clause is dependent, as it contains only a noun (“an idea”) and a relative clause to modify it. A semicolon is used to separate two independent clauses, so it cannot be used here. A comma is the appropriate punctuation mark to separate the dependent clause from the independent clause in the sentence. Choice (C) is the correct answer.

4. A

Difficulty: Medium

Category: Sentence Structure: Commas, Dashes, and Colons

Getting to the Answer: Figure out the role of the underlined phrase in the sentence to find the correct punctuation. “Like lift and drag on wings” is a parenthetical element provided as an example. The sentence is correctly punctuated as written because it uses dashes to set off the parenthetical element. The answer is (A).

5. B

Difficulty: Hard

Category: Development: Introductions and Conclusions

Getting to the Answer: Read the paragraph and summarize the main idea to predict an answer. Then, look for an answer that matches your prediction. Choice (B) correctly establishes that Kranz stood out as a leader in a time of crisis.

6. A

Difficulty: Easy

Category: Agreement: Verbs

Getting to the Answer: Read the paragraph to establish the correct verb tense for the sentence. Other verbs in the paragraph, such as “were” and “fueled,” are past tense and indicate that another past tense verb is needed for this sentence. Choice (A) is correct because it uses the past tense “was” and logically transitions into the explanation about Kranz’s vest making him easy to spot.

7. A

Difficulty: Hard

Category: Development: Introductions and Conclusions

Getting to the Answer: Quickly summarize the main idea of the paragraph. Eliminate choices that may be accurate but do not support this primary focus. Choice (A) clearly supports the main focus of the paragraph by drawing attention to Kranz’s role as a leader in Mission Control.

8. C

Difficulty: Easy

Category: Agreement: Idioms

Getting to the Answer: Be careful with homophones. Figure out the part of speech and what the target word refers to if it is a pronoun. “Their” is a possessive pronoun indicating ownership. “There” is a pronoun that replaces a place name. “They’re” is a contraction that is short for “they are.” Choice (C), “There,” is the correct choice.

9. A

Difficulty: Hard

Category: Development: Precision

Getting to the Answer: When faced with unfamiliar words, eliminate clearly incorrect answers first. The paragraph indicates that Kranz did not intend for the vest to be stylish. Kranz wore the vest as a military type of symbol, but the correct answer will need to be in contrast to that idea. Choice (A) is the correct answer. The word “sartorial” means “having to do with clothing.”

10. D

Difficulty: Medium

Category: Organization: Transitions

Getting to the Answer: Think about the commonly confused pair between/among. Consider which preposition is usually used to reference two distinct objects. Choice (D) appropriately selects the word “between” because the objects “meetings” and “calculations” are two distinct items. “Among” is used for more than two distinct items.

11. C

Difficulty: Medium

Category: Agreement: Pronouns

Getting to the Answer: Read the target sentence and the sentence before it. Figure out whom or what the pronoun refers to and make sure it matches the antecedent in number. The plural antecedent is found in the previous sentence (“Kranz and the NASA staff”) and is clearly plural. Choice (C) correctly uses a plural pronoun to refer to a plural antecedent.

12. D

Difficulty: Medium

Category: Development: Precision

Getting to the Answer: Read carefully to identify the context of the underlined word. Then, choose the word that best fits the content of the sentence. You’re looking for a word that suggests that the organization has developed over time, as is stated in the last part of the sentence. “Built,” (D), best fits the context of the sentence.

13. B

Difficulty: Medium

Category: Sentence Structure: Commas, Dashes, and Colons

Getting to the Answer: Read the entire sentence to get a better sense for which punctuation would be correct. A colon will introduce an explanation of the “key feature,” allowing the rest of the sentence to elaborate on the preceding clause. Choice (B) is correct. In this case, the colon prompts the reader to see that the part of the sentence after the colon defines the phrase “key feature.”

14. D

Difficulty: Medium

Category: Organization: Sentence Placement

Getting to the Answer: Watch out for any choices that would make the sentence seem out of place. Choice (D) is correct. Sentence 3 offers a transition to a specific discussion of those risks in the next paragraph.

15. B

Difficulty: Medium

Category: Organization: Conciseness

Getting to the Answer: Avoid choices that are redundant, or use more words than necessary to communicate an idea. All of the choices communicate the same idea, but one does so with a greater economy of language. Choice (B) uses a minimal number of well-chosen words to revise the text.

16. C

Difficulty: Hard

Category: Development: Introductions and Conclusions

Getting to the Answer: Watch out for answer choices that correctly identify supporting points but do not explain the main claim. The paragraph contains evidence, including decreased taxable wealth and decreased control over interest rates, to support the main claim. Choice (C) is correct. It expresses the main claim of the paragraph and is supported by the evidence.

17. B

Difficulty: Medium

Category: Sentence Structure: The Basics

Getting to the Answer: Read the text carefully. Notice that the existing structure creates a run-on sentence. Then, consider which answer choice will create two complete sentences. Choice (B) revises the run-on sentence to create two grammatically complete sentences.

18. C

Difficulty: Medium

Category: Development: Introductions and Conclusions

Getting to the Answer: Find the main claim in the paragraph and then come back to the question. The statement found in (C) best supports the paragraph statements that maintaining the current status may not be an option and moving to the Eurozone may be in the best interest of the UK.

19. A

Difficulty: Easy

Category: Development: Precision

Getting to the Answer: Watch out for choices that imply little relationship between the EU and the UK. “Intertwined” most accurately reflects the content of the text, because it implies a complex economic relationship between the UK and the Eurozone. Therefore, (A) is correct. No change is necessary.

20. C

Difficulty: Hard

Category: Development: Relevance

Getting to the Answer: Find the central idea of the paragraph and then come back to the question. The central idea in the paragraph is that economic downturns in the Eurozone also affect the UK. Choice (C) is correct.

21. D

Difficulty: Easy

Category: Organization: Transitions

Getting to the Answer: Decide which transition word makes the most sense in the context of the sentence by reading each choice in the sentence. The correct choice should connect the two sentences as the text transitions from economic concerns to those of “security, power, and protection.” The word “however” is the best transition because it provides a logical contrast between the ideas in the passage. Choice (D) is the correct answer.

22. B

Difficulty: Medium

Category: Sentence Structure: Commas, Dashes, and Colons

Getting to the Answer: Consider which punctuation will correctly set off the parenthetical information in this sentence. Dashes are often used to offset parenthetical sentence elements. Choice (B) is correct.

23. D

Difficulty: Easy

Category: Organization: Precision

Getting to the Answer: Review each answer choice and decide which makes the most sense in terms of what the first sentence says. Choice (D) is the correct answer. “These days” contrasts with the next sentence’s use of “this wasn’t always true.”

24. C

Difficulty: Medium

Category: Agreement: Verbs

Getting to the Answer: Make sure that verbs agree with the subject. Check back and figure out what the subject is and then see if it agrees. The word “cherries” requires a plural verb. Choice (C) is the correct answer.

25. B

Difficulty: Medium

Category: Agreement: Verbs

Getting to the Answer: Read the complete sentence carefully whenever you see a shift in tense or verb form. Decide whether this change is logically correct in the sentence. The verbs in a sentence need to be in parallel form. Choice (B) is in parallel form with the first verb “reached,” so it is the correct answer.

26. D

Difficulty: Medium

Category: Development: Precision

Getting to the Answer: Beware of some answer choices that may have similar meanings but do not fit into the context of this sentence. The word “boasted” is the best fit for the context of the sentence, so (D) is the correct answer.

27. D

Difficulty: Medium

Category: Sentence Structure: The Basics

Getting to the Answer: Pay close attention to commas to ensure that they do not create run-on sentences. Notice that this sentence contains two complete thoughts. Choice (D) is the correct answer because it combines the two complete thoughts into one sentence in the best way.

28. A

Difficulty: Hard

Category: Development: Introductions and Conclusions

Getting to the Answer: To find the best conclusion, look for the choice that summarizes the main points of the paragraph and best completes the paragraph. The paragraph begins by talking about the lack of record of coffee as cargo on the Mayflower and then introduces when it was first referenced. Choice (A) does the best job of retelling what the paragraph is about, therefore providing an effective conclusion.

29. B

Difficulty: Easy

Category: Sentence Structure: Commas, Dashes, and Colons

Getting to the Answer: Study the words in the series and see where commas might need to be placed or eliminated. Choice (B) is the correct answer.

30. C

Difficulty: Medium

Category: Development: Precision

Getting to the Answer: Replace the word with the other answer choices. See which word works best in the context of the sentence. One answer choice indicates the correct relationship between coffeehouses and counterculture, and that is (C). “Associated” works best within the context of the sentence.

31. C

Difficulty: Medium

Category: Development: Introductions and Conclusions

Getting to the Answer: To find the main topic of a paragraph, identify important details and summarize them in a sentence or two. Then, find the answer choice that is the closest to your summary. Choice (C) is the correct answer. The sentence best explains the increasing popularity of coffee in American life, the main topic of the paragraph.

32. D

Difficulty: Medium

Category: Sentence Structure: Commas, Dashes, and Colons

Getting to the Answer: Determine the relationship between the two parts of this sentence, and then consider the purpose of the various forms of punctuation. A colon indicates that the rest of the sentence will be a list or an explanation. Choice (D) is the correct answer as it shows the correct relationship between both parts of the sentence.

33. D

Difficulty: Hard

Category: Agreement: Modifiers

Getting to the Answer: Read the complete sentence carefully and look for sections that do not seem to follow logically. The modifiers need to be in the proper order so the sentence’s meaning is clear. Choice (D) is correct.

34. C

Difficulty: Medium

Category: Agreement: Pronouns

Getting to the Answer: Recall that a pronoun must agree with its antecedent, or the word to which it refers. Begin by identifying the antecedent of the pronoun. Then, check each choice against the antecedent to find the best match. The antecedent for the pronoun “their” is “this phenomenon,” which appears in the main clause. The antecedent and its pronoun do not currently agree as “this phenomenon” is singular and “their” is plural. Although the “s” in “Lights” implies many lights, it is still considered a singular phenomenon and so requires a singular pronoun. Choice (C) is the correct answer.

35. D

Difficulty: Medium

Category: Agreement: Idioms

Getting to the Answer: Read each answer choice carefully to determine the correct preposition. Choice (D) is the correct answer because it correctly uses the preposition “in.”

36. C

Difficulty: Medium

Category: Development: Introductions and Conclusions

Getting to the Answer: Choice (C) is the correct answer because it provides additional information regarding how people are able to view auroras.

37. B

Difficulty: Hard

Category: Agreement: Verbs

Getting to the Answer: When choosing the correct verb, note how it alters the relationship between the subject, the “Sun,” and the stated action, in this case “storm activity.” Choice (B) is correct. The verb “experiences” is the only one that states a direct action upon the subject, the Sun, rather than the Sun “observing” an action occurring externally, as suggested by the other verbs.

38. B

Difficulty: Easy

Category: Agreement: Modifiers

Getting to the Answer: The placement of the adjective has a great effect upon the intention of the noun. Read the sentence carefully to determine where the adjective makes the most sense. By placing the adjective before the nouns, (B) ensures that only those scientists and amateurs interested in the topic at hand use the specific tools mentioned in this passage.

39. C

Difficulty: Hard

Category: Organization: Conciseness

Getting to the Answer: Generalized statements with inexact definitions that border on opinion have no place in a scientific essay. The tone and style must exhibit a reliance on verifiable statements. Because “readily available” cannot be quantified and implies the author’s opinion, using the word “specific” in (C) creates a more exact statement that precedes the information on the precise tools used.

40. A

Difficulty: Medium

Category: Development: Relevance

Getting to the Answer: Reread the paragraph to understand the author’s claims. Which answer choice provides a fact that would best support these claims? Make sure the answer choice does not digress from the progression of ideas. The speed of the solar flare is referenced as being three times the speed of normal solar winds, but neither exact speed is given. To make a stronger case for the author’s statements, both speeds should be stated. Therefore, (A) is the correct answer.

41. B

Difficulty: Medium

Category: Agreement: Verbs

Getting to the Answer: Read closely to find the subject of the verb. Sometimes, the closest noun is not the subject. The subject of the sentence is “strength and direction,” not “energy.” Choice (B) is the correct answer because it matches the subject in number and maintains a consistent tense with the rest of the passage.

42. B

Difficulty: Hard

Category: Organization: Conciseness

Getting to the Answer: Eliminate extraneous and redundant information (“the public”) and needless prepositions. Then, reorder the verb and nouns to achieve the most efficient language possible. Making adjustments to the passage language as shown in (B) results in the most concise phrasing.

43. A

Difficulty: Hard

Category: Organization: Transitions

Getting to the Answer: Consider the meanings of each introductory word carefully. Use the context clues in the rest of the sentence to choose the correct word. The context clues in the rest of the sentence reveal that the Northern Lights can create communication and weather problems and yet are still beautiful. Keeping the word “While” makes the most sense in this context, so (A) is the correct answer.

44. D

Difficulty: Hard

Category: Graphs

Getting to the Answer: Reread paragraph 4 for information that will help you understand how to read the graphic. Use that information to calculate the precise start and end time for the solar flare as indicated in the graphic. The passage states that a solar flare is represented by any Kp-Index of 5 or higher. While there is one three-hour period where the Kp-Index reached 6, there is a consistent period where the chart shows readings of level 5 or higher. Choice (D) is the correct answer. This choice gives the complete time period showing a reading of level 5 or higher, according to the chart.

MATH TEST—NO-CALCULATOR

1. B

Difficulty: Easy

Category: Heart of Algebra / Linear Equations

Getting to the Answer: The average rate of change for a linear function is the same as the slope of the line. Find the slope of the line by either using the slope formula or by counting the rise and the run from one point to the next. If you start at (0, —3), the line rises 5 units and runs 8 units to get to (8, 2), so the slope, or average rate of change, is .

2. D

Difficulty: Easy

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: A root of an equation is an x-value that corresponds to a y-value of 0. The x-intercepts of the graph, and therefore the roots of the equation, are x = —1 and x = 5. When x = —1, the value of x + 1 is 0, so one of the factors is x + 1. When x = 5, the value of x — 5 is 0, so the other factor is x — 5. The equation in (D) is the only one that contains these factors and is therefore correct.

3. C

Difficulty: Easy

Category: Passport to Advanced Math / Exponents

Getting to the Answer: Substitute the values given in the question into the formula. Then, simplify using the rules of exponents. Remember, when raising a power to a power, you multiply the exponents:

Choice (C) is correct.

4. B

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: Choose the best strategy to answer the question. You could start by cross-multiplying to get rid of the denominators, but simplifying the numerators first will make the calculations easier:

Choice (B) is correct.

5. D

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Getting to the Answer: Whenever a quantity repeatedly increases or decreases by the same percentage (or fraction) over time, an exponential model can be used to represent the situation. Choice (B) is not an exponential equation, so you can eliminate it right away. The amount of garbage is decreasing, so the scenario represents exponential decay and you can use the form y = a × (1 — r)t, where a is the initial amount, r is the rate of decay, and t is time in years. The initial amount is 1,800, the rate is 3%, or 0.03, and t is an unknown quantity, so the correct equation is y = 1,800 × (1 — 0.03)t, which is equivalent to the equation y = 1,800 × 0.97t. (D) is correct.

6. C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: The slope-intercept form of a line is y = mx + b. In this question, the graph passes through the origin, so b is 0. Because b is 0, the equation of this line in slope-intercept form is y = mx, which can be rewritten as . Count the rise and the run from the origin, (0, 0), to the next point, (3, 1), to get a slope of . This matches (C).

7. D

Difficulty: Medium

Category: Passport to Advanced Math / Polynomials

Getting to the Answer: When multiplying polynomials, carefully multiply each term in the first factor by each term in the second factor. This question doesn’t ask for the entire product, so check to make sure you answered the correct question (the coefficient of x). After performing the initial multiplication, look for the x terms and add their coefficients. To save time, you do not need to simplify the other terms in the expression:

The coefficient of x is 35 + 3 = 38, which is (D).

8. C

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Getting to the Answer: A graph is decreasing when the slope is negative; it is increasing when the slope is positive. Eliminate (A) because there are some segments on the graph that have a positive slope. Eliminate (B) because the slope is negative, not positive, between 2009 and 2010. Choice (C) is correct because the slope is negative for each segment between 2004 and 2007 and also between 2009 and 2011.

9. A

Difficulty: Medium

Category: Heart of Algebra / Inequalities

Getting to the Answer: Don’t answer this question too quickly. The shading is below the line, but that does not necessarily mean that the symbol in the equation will be the less than symbol (<). Start by writing the equation of the dashed line shown in the graph in slope-intercept form. Then, use the shading to determine the correct inequality symbol. The slope of the line shown in the graph is and the y-intercept is —3, so the equation of the dashed line is . The graph is shaded below the boundary line, so use the < symbol. When written in slope-intercept form, the inequality is . The inequalities in the answer choices are given in standard form (Ax + By = C), so rewrite your answer in this form. Don’t forget to reverse the inequality symbol if you multiply or divide by a negative number:

Choice (A) is correct.

10. C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: When you’re given only one equation but two variables, chances are that you can’t actually solve the equation (unless one variable happens to cancel out), but rather that you are going to need to manipulate it to look like the desired expression (which in this question is This type of question can’t be planned out step-by-step—instead, start with basic algebraic manipulations and see where they take you. First, distribute the on the left side of the equation to get 2a + 5b = b. There are two terms that have a b, so subtract 5b from both sides to get 2a = —4b. You’re hoping for plain b in the numerator, so divide both sides by —4 to get . Finally, divide both sides by a to move the a into a denominator position under b. The result is , which means the ratio is , or , making (C) correct.

11. D

Difficulty: Hard

Category: Heart of Algebra / Systems of Linear Equations

Getting to the Answer: Graphically, a system of linear equations that has no solution indicates two parallel lines, or in other words, two lines that have the same slope. So, write each of the equations in slope-intercept form (y = mx + b) and set their slopes (m) equal to each other to solve for a. Before finding the slopes, multiply the top equation by 3 to make it easier to manipulate:

The slope of the first line is and the slope of the second line is . Now, set the slopes equal to each other and solve:

Choice (D) is correct.

12. A

Difficulty: Hard

Category: Heart of Algebra / Inequalities

Getting to the Answer: Pay careful attention to units, particularly when a question involves rates. The taxi charges $3.00 for the first mile, which is a flat fee, so write 3. The additional charge is $0.25 per mile, or 0.25 × 8 = $2.00 per mile. The number of miles after the first mile is , so the cost of the trip, not including the first mile is . This means the cost of the whole trip is . The clue “no more than $20” means that much or less, so use the symbol ≤. The inequality is , which simplifies to 2.5 + 2m ≤ 20, (A).

13. A

Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: The quadratic equation is given in standard form, so use the method of completing the square to rewrite the equation in vertex form. Then, read the value of k to find the maximum height of the projectile:

The vertex is (2, 72), so the maximum height is 72 feet, (A).

14. 144

Difficulty: Easy

Category: Heart of Algebra / Linear Equations

Getting to the Answer: There is only one equation given and it has two variables. This means that you don’t have enough information to solve for either variable. Instead, look for the relationship between the left side of the equation and the other expression that you are trying to find. Start by clearing the fractions by multiplying both sides of the original equation by 12. This yields the expression that you are looking for, 9x + 10y, so no further work is required—just read the value on the right-hand side of the equation:

15. 150

Difficulty: Medium

Category: Additional Topics in Math / Geometry

Getting to the Answer: There are 360 degrees in a circle. You need to figure out how many degrees each minute on the face of a clock represents. There are 60 minutes on the face of an analogue clock. This means that each minute represents 360 ÷ 60 = 6 degrees. Between 3:20 and 3:45, 25 minutes go by, so the minute hand rotates 25 × 6 = 150 degrees.

16. 8

Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Getting to the Answer: Read the question carefully to determine what part of the expression you need to simplify and what part you don’t. Sometimes, you can work a simpler question and still arrive at the correct answer. The question only asks for the exponent on x, so you do not have to simplify the coefficients. Rewrite the expression without the coefficients and simplify using the rules of exponents:

The exponent on x is 8.

17. 3/25 or .12

Difficulty: Hard

Category: Passport to Advanced Math / Functions

Getting to the Answer: When a question involving a function provides one or more ordered pairs, substitute them into the function to see what information you can glean. Start with x = 0 because doing so often results in the elimination of a variable:

Now you know the value of a, so the equation looks like f(x) = 3 • b^x. Substitute the second pair of values into the new equation:

The exponential function is f(x) = 3 • 5x. The final step is to find the value being asked for, f(—2). Substitute —2 for x and simplify:

Grid this in as 3/25 or .12.

MATH TEST—CALCULATOR

1. B

Difficulty: Easy

Category: Heart of Algebra / Linear Equations

Getting to the Answer: The total cost consists of a flat installation fee and a price per square foot. The installation fee is a one-time fee that does not depend on the number of feet ordered and therefore should not be multiplied by f. This means that 199 is the installation fee. The other expression in the equation, 3.29f, represents the cost per square foot (the unit price) times the number of feet, f. Hence, 3.29 must represent the cost of one square foot of carpet, (B).

2. B

Difficulty: Easy

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: Quickly read each answer choice. Cross out false statements as you go. Stop when you arrive at a true statement. There is no long “tail” of data on either side, so the shape is not skewed and you can eliminate (A). The shape of the data is symmetric because the data is fairly evenly spread out, with about half of the ages above and half below the median. When the shape of a data set is symmetric, the mean is approximately equal to the median so (B) is correct. Don’t let (D) fool you—the median is 55, not the mean.

3. A

Difficulty: Easy

Category: Heart of Algebra / Linear Equations

Getting to the Answer: Think about the best strategy to answer the question. If you distribute the , it creates messy numbers. Instead, clear the fraction by multiplying both sides of the equation by 3. Then, use inverse operations to solve for x:

Choice (A) is correct.

4. A

Difficulty: Easy

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: The minimum value of a quadratic function is equal to the y-value of the vertex of its graph, so vertex form, y = a(x — h)² + k, reveals the minimum without doing any additional work. Choice (A) is the only equation written in this form and therefore must be correct. The minimum value of this function is .

5. C

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Start with the smallest possible lot size, 3,000 square feet. The next lot must be at least 30% larger, so multiply by 1.3 to get 3,900 square feet. Then, round up to the next thousand (which is not necessarily the nearest thousand) to meet the tax assessment requirement. You must always round up because rounding down would make the subsequent lot size less than 30% larger than the one before it. Continue this process until you reach the maximum square footage allowed, 15,000 square feet:

3,000 × 1.3 = 3,900 → 4,000

4,000 × 1.3 = 5,200 → 6,000

6,000 × 1.3 = 7,800 → 8,000

8,000 × 1.3 = 10,400 → 11,000

11,000 × 1.3 = 14,300 → 15,000

Choice (C) is correct.

6. D

Difficulty: Medium

Category: Problem Solving and Data Analysis / Functions

Getting to the Answer: Determine whether the change in the amount of pollution is a common difference (linear function) or a common ratio (exponential function), or if it changes direction (quadratic or polynomial function). Each year, the amount of pollution should be 100 — 8 = 92% of the year before. You can write 92% as , which represents a common ratio from one year to the next. This means that the best model is an exponential function, (D), of the form y = a • (0.92)x.

7. A

Difficulty: Medium

Category: Passport to Advanced Math / Radicals

Getting to the Answer: Don’t spend too much time reading the scientific explanation of the equation. Solve for r using inverse operations. First, square both sides of the equation to remove the radical. Then, multiply both sides by r to get the r out of the denominator. Finally, divide both sides by v²:

This matches (A).

8. D

Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Getting to the Answer: One equation should represent the total number of rentals, while the other equation represents the cost of the rentals. The number of DVDs plus the number of Blu-rays equals the total number of rentals, 209. Therefore, one equation is d + b = 209. This means you can eliminate choices (B) and (C). Now, write the cost equation: cost per DVD times number of DVDs (2d) plus cost per Blu-ray times number of Blu-rays (3.5b) equals the total amount collected (562). The cost equation is 2d + 3.5b = 562. Don’t let (A) fool you. The question says nothing about the cost per hour so there is no reason to divide the cost by 4. Choice (D) is correct.

9. B

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Break the question into short steps. Step 1: Find the number of female senators. Step 2: Use that number to find the number of female Republican senators. Step 3: Find the total number of Republican senators.

Each of the 50 states gets 2 voting members in the Senate, so there are 50 × 2 = 100 senators. The ratio of males to females in the 113th Congress was 4:1, so 4 parts male plus 1 part female equals a total of 100 senators. Write this as 4x + x = 100, where x represents one part and therefore the number of females. Next, simplify and solve the equation to find that x = 20 female senators. To find the number of female senators that were Republican, multiply 20% (or 0.20) times 20 to get 4. Finally, add to get 45 male plus 4 female = 49 Republican senators in the 113th Congress, (B).

10. C

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Find the percent increase by dividing the amount of change by the original amount. Then, apply the same percent increase to the amount for 2012. The amount of increase is 29,400 — 18,750 = 10,650, so the percent increase is 10,650 ÷ 18,750 = 0.568 = 56.8% over 8 years. If the total percent increase over the next 8 years is the same, the average student who borrowed money will have loans totaling 29,400 × 1.568 = 46,099.20, or about $46,100. Choice (C) is correct.

11. D

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: Write the expression in words first: points per large basket (3) times number of beanbags in large basket (b), plus points per small basket (7) times number of beanbags in small basket. If there are 10 beanbags total and b go into the larger basket, the rest, or 10 — b, must go into the smaller basket. Now, translate the words to numbers, variables, and operations: 3b + 7(10 — b). This is not one of the answer choices, so simplify the expression by distributing the 7 and combining like terms: 3b + 7(10 — b) = 3b + 70 — 7b = 70 — 4b. This matches (D).

12. D

Difficulty: Easy

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: To calculate the percentage of the voters in each district who had no opinion on fracking, divide the number of voters in that district who had no opinion by the total number of voters in that district. Choice (D) is correct because 3,205 ÷ 63,539 ≈ 0.05 = 5%, which is a lower percentage than in the other three districts that were polled (District A = 8%; District B = 7.6%; District C = 6%).

13. A

Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: Scan the answer choices quickly to narrow down the amount of information in the table that you need to analyze. Each choice makes a statement about people from District C who support a ban on fracking that can be expected to vote in the next election. To extrapolate from the follow-up survey sample, multiply the fraction of people from the follow-up survey who plan to vote in the upcoming election by the number of people in District C who support a ban on fracking (43,228) to get 18,847.408, or approximately 19,000 people. Choice (A) is correct.

14. B

Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Getting to the Answer: Solve the system of equations using substitution. Then, check that you answered the right question (find the sum of x and y). First, solve the second equation for x to get x = 3y — 11, then substitute this expression into the first equation to find y:

Now, substitute the result into x = 3y — 11 and simplify to find x:

The question asks for the sum, so add x and y to get , which is (B).

15. C

Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: The keyword in the answer choices is “consistently,” which relates to how spread out a player’s scores are. Standard deviation, not mean, is a measure of spread so you can eliminate choice (A) right away. A lower standard deviation indicates scores that are less spread out and therefore more consistent. Likewise, a higher standard deviation indicates scores that are more spread out and therefore less consistent. Notice the opposite nature of this relationship: lower standard deviation = more consistent; higher standard deviation = less consistent. Choice (C) is correct because the standard deviation of Mae’s scores is the lowest, which means she bowled the most consistently.

16. B

Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: Notice the structure of the equation. The expression on the left side of the equation is the square of a quantity, so start by taking the square root of both sides. After taking the square roots, solve the resulting equations. Remember, 4² = 16 and (—4)² = 16, so there will be two equations to solve:

Choice (B) is correct.

17. C

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Pay careful attention to the units. You need to convert all of the dimensions to inches, and then set up and solve a proportion. The real statue’s height is 305 × 12 = 3,660 + 6 = 3,666 inches; the length of the nose on the real statue is 4 × 12 = 48 + 6 = 54 inches; the height of the model statue is 26 inches; the length of the nose on the model is unknown. Now set up and solve your equation:

Choice (C) is correct.

18. B

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Getting to the Answer: When evaluating a function, substitute the value inside the parentheses for x in the equation. Evaluate the function at x = 6 and at x = 2, and then subtract the second output from the first. Note that this is not the same as first subtracting 6 — 2 and then evaluating the function at x = 4:

f(6) = 3(6) + 5 = 18 + 5 = 23

f(2) = 3(2) + 5 = 6 + 5 = 11

f(6) — f(2) = 23 — 11 = 12

Choice (B) is correct.

19. A

Difficulty: Medium

Category: Problem Solving and Data Analysis / Scatterplots

Getting to the Answer: Examine the graph, paying careful attention to units and labels. Here, the years increase by 2 for each grid line and the number of owls by 25. The average change per year is the same as the slope of the line of best fit. Find the slope of the line of best fit using the slope formula, , and any two points that lie on (or very close to) the line. Using the two endpoints of the data, (1994, 1,200) and (2014, 700), the average change per year is , which is (A). Pay careful attention to the sign of the answer—the number of owls is decreasing, so the rate of change is negative.

20. D

Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Getting to the Answer: The solution to a system of equations is the point(s) where their graphs intersect. You could solve this question algebraically, one system at a time, but this is not time efficient. Instead, graph each pair of equations in your graphing calculator and look for the graphs that intersect at x = — 4 and x = 2. The graphs of the equations in (A) and (B) don’t intersect at all, so you can eliminate them right away. The graphs in (C) intersect, but both points of intersection have a positive x-coordinate. This means (D) must be correct. The graph looks like this:

21. C

Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: Read the question, identifying parts of the graphic you need—the question asks about litters of 7 or more pups, so you’ll only use the heights of the bars for 7, 8, and 9 pups. Start by finding the percent of the mice in the study that had a litter of 7 or more pups. Of the 200 mice in the sample, 25 + 14 + 5 = 44 had a litter of 7 or more pups. This is of the mice in the study. Given the same general conditions (such as living in the same geographic region), you would expect approximately the same results, so multiply the number of female mice in the whole population by the percent you found: 35,000 × 0.22 = 7,700. Choice (C) is correct.

22. C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: You’ll need to interpret the information given in the question to write two ordered pairs. Then you can use the ordered pairs to find the slope and the y-intercept of the linear model. In an ordered pair, the independent variable is always written first. Here, the heart rate depends on the amount of exercise, so the ordered pairs should be written in the form (time, heart rate). They are (8, 90) and (20, 117). Use these points in the slope formula, , to find that Then, substitute the slope (2.25) and either of the points into slope-intercept form and simplify to find the y-intercept:

Finally, write the equation using the slope and the y-intercept that you found to get r = 2.25t + 72. Note that the only choice with a slope of 2.25 is (C), so you could have eliminated the other three choices before finding the y-intercept and saved yourself a bit of time.

23. C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Getting to the Answer: Pay careful attention to what the question tells you about the variables. The x-value is the number of payments already made and the y-value is the amount of debt remaining (not how much has been paid). If a solution is (21, 560), the x-value is 21, which means Chantal has made 21 payments already. The y-value is 560, which means $560 is the amount of debt left to be paid, making (C) correct.

24. D

Difficulty: Hard

Category: Problem Solving and Data Analysis / Scatterplots

Getting to the Answer: A line that “represents the trend of the data” is another way of saying line of best fit. The trend of the data is clearly linear because the path of the dots does not turn around or curve, so draw a line of best fit on the graph. Remember, about half of the points should be above the line and half below.

If you draw your line of best fit all the way to the y-axis, you’ll save yourself a step by simply looking at the scatterplot to find the y-intercept. For this graph, it’s about 35. This means you can eliminate choices (B) and (C). Next, find the approximate slope using two points that lie on (or very close to) the line. You can use the y-intercept, (0, 35), as one of them to save time and estimate the second, such as (72, 4). Use the slope formula to find the slope:

The equation that has the closest slope and y-intercept is (D). (Note that if you choose different points, your line may have a slightly different slope or y-intercept, but the answer choices will be far enough apart that you should be able to determine which is the best fit to the data.)

25. B

Difficulty: Hard

Category: Passport to Advanced Math / Functions

Getting to the Answer: Transformations that are grouped with the x in a function shift the graph horizontally and, therefore, affect the x-coordinates of points on the graph. Transformations that are not grouped with the x shift the graph vertically and, therefore, affect the y-coordinates of points on the graph. Remember, horizontal shifts are always backward of what they look like. Start with (x + 3). This shifts the graph left 3, so subtract 3 from the x-coordinate of the given point: (5, 1) → (5 — 3, 1) = (2, 1). Next, apply the negative in front of f, which is not grouped with the x, so it makes the y-coordinate negative: (2, 1) → (2, —1). Finally, — 2 is not grouped with x, so subtract 2 from the y-coordinate: (2, —1 — 2) → (2, —3), which is (B).

26. C

Difficulty: Hard

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Draw a chart or diagram detailing the various price reductions for each 30 days.

You can stop here because the refrigerator was sold on April 2, which is not 30 days after March 15. The final selling price was $911.25, (C).

27. A

Difficulty: Hard

Category: Additional Topics in Math / Geometry

Getting to the Answer: Organize information as you read the question. Here, you’ll definitely want to draw and label a sketch.

The lower level, the vertical distance between levels, and the diagonal elevator track form a 30-60-90 triangle, where the elevator track is the hypotenuse. The vertical distance is opposite the 30° angle so it is the shortest leg. The rules for 30-60-90 triangles state that the shortest leg is half the length of the hypotenuse, so the vertical distance between levels is approximately 170 ÷ 2 = 85 feet, (A).

28. 1/6 or .166 or .167

Difficulty: Easy

Category: Problem Solving and Data Analysis / Statistics and Probability

Getting to the Answer: This question requires concentration, but no complicated calculations. First, you need to identify the rows that contain information about the seating on the 777s, which are the bottom two rows. To find the probability that the seat is a Business Class seat, find the total number of seats in that category (in only the bottom two rows), and divide by the total number of seats on the planes (in only the bottom two rows):

Grid in your answer as 1/6 or .166 or .167.

29. 440

Difficulty: Medium

Category: Heart of Algebra / Systems of Linear Equations

Getting to the Answer: Translate from English into math to write a system of equations with t = the cost of the tankless heater in dollars, and c = the cost of the conventional heater in dollars. First, a tankless heater (t) costs $160 more (+160) than twice as much (2c) as the conventional one, or t = 2c + 160. Together, a tankless heater (t) and a conventional heater (c) cost $1,000, or t + c = 1,000. The system is:

The top equation is already solved for t, so substitute 2c + 160 into the second equation for t and solve for c:

Be careful—that’s not the answer! The conventional hot water heater costs $280, so the tankless heater costs 2(280) + 160 = $720. This means the tankless heater costs $720 — $280 = $440 more than the conventional heater.

30. 252

Difficulty: Medium

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Break the question into steps. First, find how long it took Daniel to spray one lawn, and then use that amount to find how long it took him to spray all the lawns. According to the figure, he started the first house at 9:00 and the sixth house at 10:00, so it took him 1 hour, or 60 minutes, to spray 5 houses. This gives a unit rate of 60 ÷ 5 = 12 minutes per house. Count the houses in the figure—there are 21. Multiply the unit rate by the number of houses to get 12 × 21 = 252 minutes to spray all the lawns.

31. 4

Difficulty: Hard

Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages

Getting to the Answer: This part of the question contains several steps. Think about the units given in the question and what you need to convert so that you can get to the answer. The total acreage of all the lawns in the neighborhood is 21 × 0.2 = 4.2 acres. This is equivalent to 4.2 × 43,560 = 182,952 square feet. Each gallon of spray covers 2,500 square feet, so divide to find that Daniel needs 182,952 ÷ 2,500 = 73.1808 gallons to spray all the lawns. The spray rig holds 20 gallons, so Daniel will need to fill it 4 times. After he fills it the fourth time and finishes all the lawns, there will be some spray left over.